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Mould response and its impact on billet quality Gurton, Randal M. 1997

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M O U L D R E S P O N S E A N D ITS I M P A C T O N BILLET QUALITY by RANDAL M . GURTON B.A.Sc. (Mechanical Engineering), University of British Columbia, 1987 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E REQUIREMENTS FOR T H E D E G R E E OF DOCTOR OF PHILOSOPHY in T H E F A C U L T Y OF G R A D U A T E STUDIES Department of Metals and Materials Engineering  We accept this thesis as conforming to^thg^equired standard  T H E U N I V E R S I T Y O F BRITISH C O L U M B I A January 1997 © Randal M . Gurton, 1997  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or  by  his  or  her  representatives.  It  is  understood  that  copying  or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  j  h  ^  T  ^  C  t  The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  APZ-H— /4> \^Y\-]  R  A  T  g  ^AiX  £jsl&<KSegguNtr ,  Abstract  In the past three decades, continuous casting has emerged as a dominant steel production technology. Global competition and customer expectations are driving the mini-mills to improve billet quality and increase productivity. At the core of billet casting technology is the water-cooled, oscillating copper mould. Mould interaction with the billet, both thermal and mechanical, governs billet quality and productivity. The heat extraction capability of the billet mould has been well addressed in the literature, but the mechanical response of the mould, also fundamental to the process, remains less studied. Quality issues relating to the casting operation include cracks, shape defects and breakouts. Excessive mould-billet friction can certainly contribute to these defects, in addition to restricting caster productivity. Further, wobbly mould oscillation is believed to contribute to cracks and off-squareness.  It is  remarkable to note that even though controlling friction is a necessity to the continuous casting process, few attempts have been made to monitor it. The main objectives of this study were: to quantify the mechanical response of the mould with force and kinematic sensors; to evaluate mould-billet binding using mathematical models; and to provide practical recommendations for on-line ii  monitoring. A series of five industrial plant trials were conducted using instrumented moulds at two Canadian mini-mills. In addition to logging mould temperature, casting speed and metal level, new sensors were installed and tested to measure mould oscillation and mould-strand friction. Billet samples were obtained and process variables and upsets were recorded for correlation with the logged data. Near the end of this work, a prototype on-line system was tested to record mould oscillation parameters and machine forces. This study has lead to a quantitative understanding of mould response through measurements of mould oscillation and friction on industrial casting machines. Oscillation monitoring is imperative for billet producers, since the machines were found to deviate from their design specifications. A highlight of this research was the quantification of mould-billet friction forces. Fundamental lubrication behaviour was elucidated with a force sensor, which is an excellent tool for evaluating lubrication and mould oscillation. Further, the force response varied as a function of process variables and upsets. Mathematical modelling of mould-billet binding has shown that the force signal responds mainly to lubrication effectiveness, and not the degree of binding. In the presence of a lubrication upset, however, high friction forces can be measured. When casting with oil lubrication, the friction response appeared to increase with increasing heat extraction, indicating that lubrication, heat transfer and friction are intimately linked. Modelling of binding has also lead to some recommendations for improvement in mould taper design.  111  Contents  Abstract  ii  List of Tables  xi  List of Figures  xiv  List of Symbols  xxvi  Acknowledgements  xxxi  Chapter 1  Introduction  1  Chapter 2  Literature Review  7  2.1  Description of the Mould Assembly  7  2.2  Heat Transfer in the Mould  9  2.2.1  Carbon Content  11  2.2.2  Influence of Process Variables on Heat Transfer  . . . .  13  2.3  Thermomechanical Behaviour of the Mould  16  2.4  Mould Taper  17  2.5  Process Control  19 iv  2.5.1  Metal Level and Casting Speed  19  2.5.2  Tundish Stream  20  2.6  Mould Oscillation  21  2.7  Lubrication  23  2.7.1  Oil  23  2.7.2  Mould Fluxes  24  2.8  2.9  Billet Quality  26  2.8.1  Crack Formation  26  2.8.2  Oscillation Marks  28  2.8.3  Rhomboidity  29  2.8.4  Shell Bulging and Off-Corner Internal Cracks  31  2.8.5  Laps and Bleeds  31  2.8.6  Transverse Cracks  32  2.8.7  Transverse Depressions  33  Friction Monitoring  38  2.9.1  Strain Gauge Force Sensors  38  2.9.2  Load Cells  39  2.9.3  Accelerometer Based Systems  40  2.10 Quantifying Friction  42  2.11 Influence of Process Variables on Friction  43  2.11.1 Lubrication  43  2.11.2 Casting Speed . . .  43  2.11.3 Breakouts  45  v  2.11.4 Steel Grade  45  Chapter 3  Scope and Objectives  49  Chapter 4  Experimental: Industrial Plant Trials  52  4.1  New Aspects of Industrial Plant Trials  52  4.2  Sensors  54  4.3  4.4  4.2.1  Linear Variable Differential Transformers  56  4.2.2  Accelerometer  57  4.2.3  Oscillator Motor Current  59  4.2.4  Force Sensors  59  4.2.5  Process Control Signals  64  4.2.6  Mould Temperature  64  4.2.7  Sensor Calibration  65  Data Acquisition System  68  4.3.1  Personal Computer  68  4.3.2  Analog-to-Digital Converter  68  4.3.3  Multiplexer  69  4.3.4  Software  70  4.3.5  Parallel Data Acquisition Systems  71  4.3.6  Data Acquisition Issues  72  Plant Trials  76  4.4.1  Casting Conditions . .  76  4.4.2  Billet Samples  .  vi  79  Chapter 5 Industrial Plant Trial Results 5.1  5.2  82  Base Sensor Response  82  5.1.1  Kinematic Sensors  82  5.1.2  Force Sensors  85  5.1.3  Cold Work - Machine Not Casting  88  5.1.4  Oscillator Motor Current  88  Oscillator Characteristics  93  5.2.1  Oscillator Stroke  94  5.2.2  Stroke and Machine Loading  98  5.2.3  Negative-Strip Time and Mould Lead  98  5.2.4  Stroke and Oscillation Frequency  102  5.2.5  Casting Speed Oscillation  104  5.2.6  Horizontal Movement  105  5.3  Process Control  108  5.4  Billet Samples  115  5.4.1  Surface Roughness  115  5.4.2  Shape Defects and Cracks  .  118  Chapter 6 Force Response and Process Upsets 6.1  130  Mould-Strand Friction  130  6.1.1  Friction Response of Oil and Powder Lubrication  6.1.2  Quantifying Force Response  134  6.1.3  Friction Coefficient Calculation  140  vii  . . .  130  6.1.4 6.2 6.3 6.4 6.5  Accelerometer and Force Signals  Transverse Depressions  142 146  Force Response and Steel Grade Friction and Process Control  155 158  Force Upsets  162  6.5.1  Friction and Mould Stroke  162  6.5.2  Nozzle Plugging  162  6.5.3  Breakout  165  6.5.4  Sticking and Jerking  165  Chapter 7  Mathematical Modelling of Thermomechanical Mould  Behaviour  170  7.1  Mathematical Modelling of Mould Heat Transfer  170  7.2  Mould Distortion  176  Chapter 8  Mathematical Modelling of Billet Shrinkage  178  8.1  A B A Q U S Finite-Element Modelling Software  178  8.2  Model Geometry  179  8.3  Heat Transfer Model  181  8.4  Stress Model  186  8.5  Model Verification  189  8.5.1  Heat Transfer  189  8.5.2  Viscoplasticity  193  8.6  .  Preliminary Model Results  194  vm  8.6.1  Shell Shrinkage Near the Meniscus  194  8.6.2  Billet Face  194  8.6.3  Comparison with Chandra's Work  195  Chapter 9  Evaluation of Mould-Billet Binding and Lubrication 198  9.1  Mould Heat Flux  202  9.2  Impact of Material Properties on Billet Shrinkage  208  9.3  Binding Interpretation by Mould-Billet Dimensions  212  9.4  Design of Mould Taper  221  9.5  Binding and Friction Measurements  225  9.6  Friction, Heat Transfer and Steel Grade  226  9.7  Lubrication and Force Upsets  232  9.7.1  Oil Lubrication Friction Upset  233  9.7.2  Mould Flux Friction Upset  241  9.8  The Next Step  248  Chapter 10 Summary and Conclusions  250  10.1 Key Findings  250  10.2 Summary  252  10.3 Concluding Remarks  261  Chapter 11 New Knowledge and Recommendations  267  11.1 New Knowledge  267  11.2 Recommendations  270  IX  11.3 A Primer for Billet Producers  273  11.4 Simple Tools for On-Line Monitoring  275  11.4.1 Sensors  275  11.4.2 Features  276  11.4.3 Display  276  Bibliography  279  Appendix A  Strain Gauge Force Calculation  290  Appendix B  Mould Thermocouple Layout  292  Appendix C  Calibration Data  295  Appendix D  Plant Trial Sensor Schematics  298  Appendix E  Chemical Compositions of Heats Monitored  304  Appendix F  Contour Plots of Surface Defects  307  Appendix G Thermomechanical Tests of Boron Steels  x  315  List of Tables  4.1  Summary of sensor use  54  4.2  Polynomial coefficients for Type T thermocouple voltage-totemperature conversion  67  4.3  Casting machine details at Company A  77  4.4  Casting machine details at Company D  78  5.1  Summary of oscillator stroke measurements  94  5.2  Depths of sample billet shape defects  128  6.1  Example friction coefficient calculations  141  6.2  Inferring stream quality and metal level stability from thermocouple data  6.3  153  Summary of load cell friction measurements from trial D I . O i l lubrication, constant oscillation frequency.  . .  156  6.4  Summary of oil-cast friction measurements from trial D2. . . .  157  6.5  Summary of powder-cast friction measurements from trial D2.  157  6.6  Summary of friction measurements from trial D3  159  xi  6.7  Friction and casting speed response for four powder-cast heats of 0.32 pet. C + B . Trial D2, 203 mm mould  161  8.1  Thermal properties for 0.14 pet. carbon steel  185  8.2  Thermal properties for 0.32 pet. carbon steel  185  8.3  Thermal properties for 0.80 pet. carbon steel  185  8.4  Comparison of shell thickness at mould exit between SamarasekeraChandra model and A B A Q U S model. Heat fluxes taken from trial D2  193  9.1  Heats investigated for mould-shell binding  200  9.2  One-half billet face shrinkage for elastic and viscoplastic cases.  209  9.3  Regions of mould-shell binding  220  9.4  Overall billet shrinkage taper  222  9.5  Binding by mould-billet dimensions and average friction measurements  227  9.6  Heat extraction and friction measurements  228  9.7  Friction response for four powder-cast heats of 0.32 pet. C + B . Trial D2, 203 mm mould  241  11.1 Suggested methods for displaying process parameters on an on-  B.l  line system  278  Mould thermocouple depths used in plant trials D I and D2. .  294  xii  C.l  Sensor calibration data for plant trial D I . Signals logged in millivolts  C.2  295  Sensor calibration data for horizontal mould movement test during plant trial D I . A l l LVDTs were short stroke  296  C.3  Sensor calibration data for plant trial A l . Signals logged in volts.296  C.4  Sensor calibration data for plant trial D2. Signals logged in millivolts  C.5  296  Sensor calibration data for plant trial D3, force sensor test. Signals logged in volts  C.6  297  Sensor calibration data for plant trial A2, force sensor test. Signals logged in volts  E.l  297  Chemical composition, in weight percent, of heats monitored at plant trial A l  E.2  305  Chemical composition, in weight percent, of heats monitored at plant trial D I  E.3  G.l  305  Chemical composition, in weight percent, of heats monitored at plant trial D2  306  Thermomechanical tests  315  xiii  List of Figures  2.1  Schematic of a typical billet mould assembly  8  2.2  M o u l d heat flux as a function of carbon content  2.3  E x a m p l e heat flux profile for oil and m o u l d flux lubrication.  2.4  M o u l d heat flux profile changing w i t h casting speed  2.5  M o u l d heat flux profiles for single and parabolic m o u l d taper  12 .  16  designs 2.6  14  19  Shell uniformity for open stream and submerged entry nozzle casting  21  2.7  Schematic of m o u l d flux i n the m o u l d  25  2.8  M o u l d flux consumption as a function of m o u l d oscillation parameters  2.9  26  Schematic showing a billet w i t h varying shell thickness distorting further into an off-square shape i n the spray cooling zone.  2.10 Shell bulging and the formation of off-corner internal cracks.  30 .  32  2.11 Transverse depression formation by binding - Mechanism 1. . .  34  2.12 Transverse depression formation from o i l vapour - Mechanism 2.  34  xiv  2.13 Transverse depression formation caused by a metal level fluctuation and shell distortion - Mechanism 4  36  2.14 Typical load cell response as reported by Brendzy et al  40  2.15 Mould friction response using powder lubrication  44  2.16 Mould friction response as a function of carbon content on a laboratory caster  46  2.17 Output from accelerometer based "friction" signal  47  4.1  Schematic of sensor locations in the casting machine  55  4.2  Schematic of L V D T sensor  56  4.3  P C B 326A13 accelerometer  58  4.4  Schematic of full strain gauge bridge  61  4.5  Kistler piezoelectric strain sensor  63  4.6  Schematic of ground looping caused by grounding in two locations. 73  4.7  Typical voltage divider used to reduce input voltage to a level suitable for data acquisition  76  5.1  Typical L V D T and accelerometer signals. Trial D3  83  5.2  Mould acceleration as measured by an accelerometer and calculated from a displacement signal. Trial D3  84  5.3  Load cell and strain gauge force sensor signals. Trial D2. . . .  86  5.4  Typical oscillator force and mould displacement responses. Trial D3. 87  5.5  Data used to calibrate the piezoelectric strain sensor with a strain gauge. Trial A2  89  xv  5.6  Strain gauge and piezoelectric strain sensors during casting operations  5.7  90  Force and displacement signals 180° out of phase during a cold oscillator test  5.8  91  Force and acceleration signals i n phase during a cold test. T h e force sensor was responding to inertial forces.  5.9  -.  92  Comparison of force and D C electric motor current - Machine C . 93  5.10 M o u l d displacement and load cell response - Machine A .  . . .  95  5.11 M o u l d displacement and casting speed during the beginning of a heat - Machine B . Note that increasing casting speed increased the oscillation frequency  96  5.12 Non-sinusoidal displacement profile and casting speed variation - Machine B  97  5.13 Illustration of negative-strip time using real data from M a chine C . T r i a l D 2  99  5.14 M o u l d velocity and load cell force - Machine A . T r i a l D I . . . .  100  5.15 M o u l d velocity, casting speed and force corresponding to a period of zero negative-strip time. T r i a l D 3 , 0.70 pet. C , 171 m m mould, o i l lubrication  101  5.16 Negative-strip time for an 8 m m sinusoidal oscillator  103  5.17 Horizontal m o u l d movement 50 m m from m o u l d top - M a chine A unloaded  106  5.18 M o u l d trajectory - Machine A unloaded  xvi  107  5.19 Transient response of metal level and casting speed typical of the machines tested. T r i a l D 2 , 203 m m mould, oil lubrication.  109  5.20 Steel flow rate calculated from metal level and casting speed signals. (1 1 = 0.001 m )  110  3  5.21 Stable metal level and increasing casting speed indicates i n creasing steel flow rate - Machine B  112  5.22 "Rough" casting speed and metal level signals commonly seen when casting w i t h oil lubrication. T r i a l D 3 , 0.80 pet. C , 194 m m mould  113  5.23 T y p i c a l smooth casting speed and metal level signals when casting w i t h m o u l d fluxes. Trial D 3 , 0.30 pet. C + B , 194 m m m o u l d . 114 5.24 Rough surface of a peritectic steel billet. T r i a l D I , 0.12 pet. C , 203 m m m o u l d , oil lubrication  116  5.25 Smooth surface of a hyper-peritectic steel billet. T r i a l D I , 0.32 pet. C , 203 m m m o u l d , oil lubrication  117  5.26 Macro-etched section of a multiple defect billet. T r i a l D I , 0.3 pet. C + B , 171 m m mould, o i l lubrication 5.27 Large transverse depression.  118  T r i a l D 2 , 0.32 pet. C + B , east  face, 203 m m mould, o i l lubrication  119  5.28 Large transverse depression. Trial D 2 , 0.32 pet. C + B , south face, 203 m m m o u l d , oil lubrication  119  5.29 Surface crack on a deep transverse depression. T r i a l D 2 , 0.32 pet. C + B , east face, 203 m m mould, o i l lubrication  xvii  120  5.30 Subsurface cracks under a deep transverse depression. Trial D 2 , 0.32 pet. C + B , south face, 203 mm mould, oil lubrication.  .  121  5.31 Transverse depression showing both subsurface and surface cracks. Trial D 2 , 0.32 pet. C + B , 203 mm mould, oil lubrication. . .  122  5.32 Transverse depressions on a powder cast billet. Trial D 2 , 0.14 pet. C, 203 mm mould  123  5.33 Macroetch of transverse depression on a powder cast billet. Trial D 2 , 0.14 pet. C, 203 mm mould  124  5.34 Typical longitudinal midface depressions on powder cast billets. Trial D 2 , 0.14 pet. C, 203 mm mould  126  5.35 Longitudinal midface depression with corresponding surface crack. Trial D 2 , 0.14 pet. C, 203 mm mould, powder lubrication.  . .  127  5.36 Photograph illustrating the depth of longitudinal midface depressions when powder casting. Trial D 2 , 0.14 pet. C, 203 mm mould 6.1  127  Typical mould velocity and force signals when casting with oil lubrication. Trial D3, 0.70 pet. C, 171 mm mould  6.2  132  Typical mould velocity and force signals when casting with mould powder lubrication. Trial D 3 , 194 mm mould, 0.30 pet. C + B  6.3  133  Force vs. displacement example for oil lubrication. Trial D 2 , 203 mm mould, 0.3 pet. C + B  xviii  135  6.4  Force vs. displacement example for powder lubrication.  Trial  D 2 , 203 m m mould, 0.3 pet. C + B 6.5  136  Machine C oscillator force response under no-load condition. Trials D2 and D3  6.6  138  Machine B oscillator force response under no-load condition using strain gauge and piezoelectric strain sensors. T r i a l A 2 .  6.7  F F T of accelerometer signals corresponding friction.  . .  to high and low  T r i a l D 3 , 0.30 pet. C + B , o i l lubrication, 171 m m  mould 6.8  143  F F T of accelerometer signals corresponding friction.  to high and low  T r i a l D 3 , 0.30 pet. C + B , oil lubrication, 171 m m  mould 6.9  139  144  Smooth mould temperature response.  Trial D I , 0.8 pet. C ,  203 m m mould, o i l lubrication  147  6.10 M o u l d temperature response showing the formation of a transverse depression at the meniscus and its propagation down the mould. T r i a l D I , 0.32 pet. C , 203 m m mould, o i l lubrication. .  148  6.11 M o u l d temperature response illustrating a rough metal level and transverse depressions. Trial D I , 0.32 pet. C + B , 203 m m mould, oil lubrication  149  6.12 Force sensor and mould temperature response during the formation of transverse depressions. T r i a l D I , 0.32 pet. C , 203 m m mould, o i l lubrication  150  xix  6.13 Force sensor and mould temperature response during the formation of transverse depressions. Trial D I , 0.32 pet. C + B , 203 mm mould, oil lubrication  151  6.14 Mould-strand friction change as a function of casting speed. Trial D3, 0.30 pet. C + B , 194 mm mould, powder lubrication.  160  6.15 Oscillator stroke varying as a function of mould-strand friction. Trial D3  163  6.16 Friction response during a nozzle plugging upset.  Trial A2,  0.90 pet. C, 152 mm mould, oil lubrication  164  6.17 Friction response during a strand breakout. Trial A2, 0.90 pet. C, 152 mm mould, oil lubrication  166  6.18 Force sensor response during a period of meniscus sticking. Trial A l , 0.71 pet. C, 203 mm mould, oil lubrication  167  6.19 Force sensor response during a period of strand jerking. Trial A l , 0.90 pet. C, 203 mm mould, oil lubrication.  .  168  7.1  Schematic of longitudinal mould heat transfer model  171  7.2  Example forced convection boiling curves for subcooled water.  174  7.3  Mesh geometry used to model mould distortion  176  8.1  Mesh geometry used in the one-eighth section, thermal-stress shrinkage model  180  xx  8.2  Billet isotherms using constant heat transfer coefficient across the billet face. Cooling time 19 seconds, temperature in degrees K  .  8.3  Mesh geometry used in billet shrinkage stress model  8.4  Mean coefficients of thermal expansion as a function of carbon content and temperature  8.5  187  190  Comparison of the analytical solution to heat conduction with phase change and the A B A Q U S numerical solution.  8.6  183  192  Billet mesh at the bottom of the mould illustrating different face displacement from midface to corner - displacement magnification 4  8.7  195  Example of differing shrinkage profiles between the Chandra and A B A Q U S models  9.1  197  Outline of procedure used to interpret mould-billet binding and lubrication  9.2  201  Mould heat flux and shell thickness. Heat 277, powder lubrication, 0.14 pet. C, trial D2  9.3  203  Mould heat flux and shell thickness. Heat 298, oil lubrication, 0.14 pet. C, trial D2  9.4  204  Mould heat flux and shell thickness. Heat 312, powder lubrication, 0.32 pet. C + B , trial D2  xxi  205  9.5  Mould heat flux and shell thickness. Heat 333, oil lubrication, 0.32 pet. C + B , trial D2  9.6  206  Mould heat flux and shell thickness. Heat 351, oil lubrication, 0.80 pet. C, trial D2  9.7  207  Comparison of shrinkage calculations between elastic and plastic material properties. Trial D2, heat 277  9.8  Sensitivity test of the viscoplastic relationship to billet shrinkage. Trial D2, heat 333  9.9  209  211  Cold mould and distorted mould dimensions. Heat 277, powder lubrication, 0.14 pet. C, trial D2  213  9.10 Mould and billet dimensions from mathematical models. Heat 277, powder lubrication, 0.14 pet. C, trial D2  214  9.11 Mould and billet dimensions from mathematical models. Heat 298, oil lubrication, 0.14 pet. C, trial D2  215  9.12 Mould and billet dimensions from mathematical models. Heat 312, powder lubrication, 0.32 pet. C + B , trial D2  216  9.13 Mould and billet dimensions from mathematical models. Heat 333, oil lubrication, 0.32 pet. C + B , trial D2  217  9.14 Mould and billet dimensions from mathematical models. Heat 351, oil lubrication, 0.80 pet. C, trial D2  218  9.15 Mould and billet taper calculated from mathematical models. Heat 277, powder lubrication, 0.14 pet. C, trial D2  xxii  223  9.16 M o u l d and billet taper calculated from mathematical models. Heat 298, o i l lubrication, 0.14 pet. C , trial D2  224  9.17 Force response and casting speed during a period of low friction. Heat 333, o i l lubrication, 0.32 pet. C + B , trial D2  233  9.18 Force response and casting speed during a period of high friction. Heat 333, oil lubrication, 0.32 pet. C + B , t r i a l D 2 . . . .  234  9.19 Casting speed and metal level were stable during friction upset. Heat 333, o i l lubrication, 0.32 pet. C + B , trial D2  236  9.20 M o u l d temperature profiles during periods of low and high friction. Heat 333, oil lubrication, 0.32 pet. C + B , t r i a l D 2 . . . .  237  9.21 Mould-billet heat flux profiles during periods of low and high friction. Heat 333, oil lubrication, 0.32 pet. C + B , trial D 2 .  .  238  9.22 Standard deviation of mould temperatures corresponding to the periods of low and high friction. Heat 333, o i l lubrication, 0.32 pet. C + B , trial D2  240  9.23 Temperature of the billet midface and corner. Heat 312, powder lubrication, 0.32 pet. C + B , trial D2  242  9.24 Temperature of the billet midface and corner. Heat 313, powder lubrication, 0.32 pet. C + B , t r i a l D2  243  9.25 Rough force sensor response during high friction believed to be caused by sticking. Heat 313, powder lubrication, 0.32 pet. C + B , t r i a l D2  245  xxm  B.l  Layout of m o u l d thermocouples on the east face; used for plant trials D I and D 2  293  D.l  Electrical schematic for plant trial D I  299  D.2  Electrical schematic for plant trial A l  300  D.3  Electrical schematic for plant trial D 2  301  D.4  Electrical schematic for on-line force sensor test D3  302  D.5  Electrical schematic for on-line force sensor test A 2  303  F.l  Longitudinal midface depression believed to be caused by excessive m o u l d taper. Sample 1, trial D I , 0.3 pet. C + B , 203 m m mould, o i l lubrication, north face  F.2  .  308  Longitudinal midface depression believed to be caused by excessive m o u l d taper. Sample 2, trial D 2 , 0.14 pet. C , 203 m m mould, powder lubrication, north face  F.3  Transverse depression, sample 1. T r i a l D 2 , 0.14 pet. C , 203 m m mould, powder lubrication, east face  F.4  Transverse depression, sample 3.  Transverse depression, sample 4.  312  T r i a l D I , 0.3 pet. C + B ,  203 m m mould, o i l lubrication, west face  xxiv  311  T r i a l D 2 , 0.3 pet. C +' B ,  203 m m m o u l d , oil lubrication, east face F.6  310  Transverse depression, sample 2. T r i a l D 2 , 0.14 pet. C , 203 m m mould, powder lubrication, south face  F.5  309  313  F. 7 Transverse depression, sample 5. Trial D 2 , 0.3 pet. C + B , 203 mm mould, oil lubrication, south face  314  G. l Thermomechanical tests of 0.32 pet. C and 0.32 pet. C + B as-cast samples at a strain rate of 1 0  - 2  s  _1  at 1200° C  316  G.2 Thermomechanical tests of 0.32 pet. C and 0.32 pet. C + B as-cast samples at a strain rate of 1 0  xxv  - 2  s  _1  at 1300°C  316  List of Symbols  Ab  cross-sectional area of billet (m )  A  area of steel contact in the mould (m )  2  2  m  aj  c  lattice parameter of delta iron at temperature T and carbon content C (A)  a  T c  lattice parameter of gamma iron at temperature T and carbon content C (A) constant (function of carbon content)  c  specific heat of fluid (J k g Cpi  K  - 1  specific heat of liquid (J k g  specific heat of mould (J k g specific heat of water (J k g  K  - 1  - 1  - 1  K  specifid heat of solid (J k g  c  the coefficient of sliding friction  K  hydraulic diameter (m)  (lyj  width of water channel gap (m)  E  elastic modulus (Pa)  Fcold  cold machine force range (N)  _ 1  XXVI  )  _ 1  _ 1  D  H  _ 1  K  Cp,s  - 1  )  _ 1  )  )  )  Fiiquid  liquid friction or shear stress ( N m  F oi%d  solid friction (N)  S  2  )  Frange  casting force range (N) /  oscillation frequency (Hz)  GF  gauge factor for strain gauge  g  gravitational acceleration (m s ) - 2  Hf  latent heat of vaporization (J k g )  AH  latent heat of solidification (J k g )  h  radiant heat transfer coefficient at hot face above  - 1  g  a  - 1  meniscus ( W m  - 2  K  _ 1  )  hb  heat transfer coefficient on billet face ( W m  hf  forced convection heat transfer coefficient ( W m ~ K  h  height of liquid steel i n the mould (m)  K" ) 1  2  c  m  h  w  heat transfer coefficient at the m o u l d / c o o l i n g water interface ( W m  - 2  K  _ 1  )  kj  thermal conductivity of fluid ( W m  ki  thermal conductivity of liquid ( W m  k  thermal conductivity of mould ( W m  k  thermal conductivity of steel ( W m  m  s  - 2  normal force (N) n  constant (function of temperature)  p  water pressure (kPa)  xxvn  K  - 1  K  _ 1  _ 1  _ 1  _ 1  K  )  - 1  K _ 1  )  - 1  )  )  _ 1  )  Q  constant. (K)  Q  mould flux consumption (kg m )  qb  boiling heat flux (W m )  q/c  forced convection heat flux (W m )  qi  heat flux at point of incipient boiling (W m )  q  heat flux from steel to mould (W m )  q  heat flux transition between forced convection and nucleate  - 2  - 2  - 2  - 2  n  - 2  s  tr  boiling (W m ) - 2  S  mould stroke (mm)  s  constant  As  mould lead (mm)  T  temperature (K)  To  initial mould temperature (K)  T  ambient temperature (K)  Ti  initial temperature (K)  T  melting point temperature (K)  a  mp  T  temperature of solid (K)  To  temperature of solid at surface (K)  T  saturation temperature of water (K)  Th  temperature of superheated steel (K)  T  water temperature (K)  t  time (s)  s  s  sat  s  w  xxvin  negative strip time (s) volume flow rate ( m  V  v v  s )  3  _1  velocity of fluid (m s ) -1  f  input excitation voltage (V)  in  Vout  bridge output voltage (V)  V  voltage ratio ^ ° A  r  v  u t  velocity of water (m s ) _1  w  specific volume of delta unit cell (cm g ) 3  _1  v.  specific volume of gamma unit cell (cm g )  v  relative velocity between mould and shell (m s )  3  _1  _1  r  casting speed (mm s ) _1  w  carbon content of gamma phase (weight pet. )  x  carbon content of delta phase (atomic pet. )  X  thickness of liquid film (m)  x,y,z  spacial coordinates  c  c  U, V,  w  nodal displacements metal level (m) mean coefficient of thermal expansion ( K )  a  a  _ 1  thermal diffusivity of solid (m s ) 2  s  viscosity (Pa s) viscosity of fluid (Pa s) Mi  viscosity of liquid (Pa s)  xxix  _1  /i  viscosity (Pa s)  v  Poisson's ratio  p/  density of fluid (kg m )  pi  density of liquid (kg m )  p  density of mould (kg m~ )  p  density of steel in the mould (kg m )  p  density of saturated liquid (kg m )  p  density of water (kg m~ )  e  strain  m  s  v  w  - 3  - 3  3  - 3  - 3  3  Sth thermal strain £  plastic strain rate ( s ) _1  p  a  mises stress (MPa)  a  surface tension at liquid/vapour interface (N m ) - 1  xxx  Acknowledgements  I would like to express my sincere gratitude to my supervising professors Dr. Keith Brimacombe and Dr. Indira Samarasekera for allowing me the opportunity to work with them and for teaching me the nature of academia and research. Sincere thanks also to Dr. John Meech, who has given me great insight into industrial applications of A l and applied science. I also wish to thank the aforementioned individuals for facilitating the "Intelligent Mould" research project. Working on the project gave me the immense satisfaction of contributing to industry and fulfilling the requirements of a graduate degree. I am grateful to the staff and students of the research group: Neil Walker, Vladimir Rakocevic, Sunil Kumar, Bill Kielhorn, Carlos Pineiro, and summer students Kevin Wilder and Rob Zuber. I also wish to thank the financial contributors of this research: Accumould, Alta Steel, Comdale Technologies, Hatch Associates, Manitoba Rolling Mills, the Natural Sciences and Engineering Research Council of Canada, and the University of British Columbia. My graduate students years at U B C have been awesome; most noteworthy is my recent affinity for martinis. I have enjoyed meeting many international friends in the Department, and I have certainly learned much about xxxi  the world here. To my finite-element colleagues - its all in the boundary conditions. A warm thanks also to Starbucks Coffee, the official caffeine of this thesis.  xxxn  Chapter 1  Introduction  Continuous casting has experienced enormous growth in the past three decades. In the 1960's, virtually all steel was produced by the conventional ingot casting method. In 1995, continuous casting represented 75% of global steel production, and 96% of Canada's steel production [1]. As steel producers began implementing continuous casting, they were faced with the challenges of commissioning a new technology. In 1980, a survey of billet producers indicated that casting practices varied markedly between companies [2]. Although the basic technology of the casting machine was consistent between producers, the operating practices were not. Operating experience and research knowledge gradually filtered through the industry and a follow-up survey in 1994 indicated that operating practices, such as mould oscillation and cooling water parameters, had improved [3]. However, fundamental design parameters such as mould taper still varied significantly between companies. Global competition and customer expectations are driving the mini-  1  mills to improve billet quality and increase productivity. Quality issues relating to the casting operation include cracks, shape defects and breakouts. Cracks form because of thermal and/or mechanical stresses, acting internally or on the billet surface. Surface and shape defects reduce heat transfer in the mould and provide sites for shell breakouts. Further, cracking is often associated with the formation of shape defects. Poor billet quality results in reconditioning of the billets or rejection of the billets and/or rolled product. Surface cracks oxidize and create defects in the rolled product. Billets with surface cracks are subject to costly conditioning, such as scarfing, shot blasting and manual grinding to remove the cracks. Subsurface cracks may be a problem, but studies have shown that hot reductions greater than 6:1 effectively close midway cracks [4]. Surface defects like transverse depressions, in addition to being common sites for cracks, may fold during hot rolling operations and create a seam in the product. Breakouts are catastrophic shell ruptures that spill liquid steel. They are very dangerous, costly and result in excessive machine down-time. The mould is the focal point of the casting process.  The impact of  the thermal and mechanical response of the mould on billet quality cannot be over-emphasized. The heat extraction capability of billet moulds has been well addressed by Brimacombe, Samarasekera and co-workers, e.g. [5, 6, 7], but the mechanical mould response has not been studied in the same detail. Moulds are tapered inwards to compensate for billet shrinkage since the air gap between the mould and shell significantly reduces heat transfer. Unfortunately, the large range of billet tapers currently employed in industry [3] indicates  2  that m o u l d design is not yet fully understood.  Further, the m o u l d distorts  when heated [8], and the amount of distortion can be impacted by operating practice. A n inadequately tapered m o u l d results i n low heat extraction and a t h i n shell at the m o u l d exit, and contributes to defects like shell bulging and off-corner internal cracks.  Excessively tapered moulds cause increased  m o u l d wear and increased mechanical forces on the shell, which may lead to transverse depressions and cracks. In extreme cases, the billet may j a m i n the mould. In addition to heat extraction, m o u l d oscillation and lubrication are fundamental to continuous casting. Mould-shell friction must be m i n i m i z e d to eliminate shell sticking, tearing and cracking. T h e oscillating m o u l d was employed i n early research on continuous casting because it reduced friction and sticking, and allowed for longer casting runs than a stationary m o u l d . M o u l d oscillation parameters such as stroke and negative-strip time have been empirically determined to minimize sticking and oscillation mark depth. T h e issue of casting machine maintenance has recently been raised i n the literature, e.g. [3, 9]; poor machine alignment is believed to contribute to cracking and off-squareness  [3]. A t present, the industry lacks machine tolerances for  wobbly oscillation. Producers have claimed to eliminate a cracking problem by servicing or replacing a machine, without knowing the cause of the problem. Further, machine displacements are often measured statically w i t h a dial gauge, rather than at operating speed and under casting conditions. It is remarkable to note that even though controlling friction is a ne-  3  cessity to the continuous casting process, few attempts have been made to monitor it [10]. The work of Brendzy et al. [11] is possibly the only published work measuring friction on an industrial billet machine. Although this work has provided significant insight into mould-strand interaction, the forces measured were only qualitative, owing to the installation of the force sensors. Most attempts to measure mould-strand friction cited in the literature were conducted on experimental slab casting machines, with the most common objective to evaluate mould flux lubricants. High friction is expected under conditions of poor lubrication, excessively tapered or distorted moulds and sub-optimal mould oscillation parameters. In addition to forming transverse cracks, high friction is also believed to accompany the formation of transverse depression defects [11]. Recently, the influence of the meniscus and process transients on billet quality has been recognized [12, 13]. Particularly problematic is the practice of open stream pouring with oil lubrication [12], commonly used with billet casters. Rough streams and/or a turbulent meniscus create variations in shell growth and mould lubrication which impact billet quality. Metal level changes have been linked to the formation of transverse depressions [14, 15]. The use of submerged entry nozzles when casting with mould fluxes can improve metal level stability, but this practice is more costly than oil casting. Since most billet casters operate without liquid steel flow rate control, metal level and casting speed are prone to being transient, owing to changes in the steel flow rate from the tundish. Thus the nature of the casting speed control system, in 4  the absence of flow control, may contribute to billet defects. As knowledge of the transient behaviour of the process unfolds, the need for on-line analyses of process information to improve billet quality becomes apparent. The concept of an "Intelligent Mould" on-line system has been presented by Brimacombe [16]. This system would use the rule-based reasoning of an expert system to interpret real-time sensor signals in its knowledge base of process information. The power of such a system lies in its ability to interpret information from multiple sources to diagnose process upsets. This research was undertaken to study the mechanical response of the mould in the continuous billet casting process. Mould oscillation and mouldbillet friction were measured in five industrial plant trials at two Canadian mini-mills. The measurement of friction and its subsequent analysis were new aspects of this research. Sensor signals were analyzed with two objectives in mind: firstly, to elucidate process behaviour and improve the understanding of industrial casting machines and secondly, to develop simple tools for an on-line monitoring system to report on process quality. The U B C casting group is well experienced in obtaining mould temperature profiles, which were also used in this work. Existing mathematical models were utilized and new models were developed to investigate mould-billet binding and mould taper. This study has lead to a quantitative understanding of mould response through measurements of mould oscillation and friction on industrial casting machines. Oscillation monitoring is imperative for billet producers, since most machines were found to deviate from their design specifications. Fundamen5  tal lubrication behaviour was elucidated w i t h a friction sensor, which is an excellent tool for evaluating lubrication and mould oscillation. M a t h e m a t i c a l modelling of mould-billet binding has lead to further understanding of the response of the force sensor as well as some recommendations for improvement i n m o u l d taper design.  6  Chapter 2  Literature Review  Mould response significantly impacts the quality of continuously cast steel billets. Although a reasonable field of work exists involving thermomechanical mould behaviour and billet quality, very little work has been published on mould-billet friction. This chapter presents a review of knowledge available in the literature pertinent to this project. Where little information was available in the field of billet casting, scoping knowledge was obtained from the slab casting literature.  2.1  D e s c r i p t i o n of the M o u l d A s s e m b l y Continuous billet casting moulds are typically square copper tubes, ap-  proximately 0.8 m in length. Internal mould dimensions range from 114 to 254 mm, with the mould wall thickness varying from 9.5 to 19 mm. Figure 2.1 illustrates the mould assembly [17]. The mould is installed in a steel jacket which supports the mould and contains the cooling water. The mould is se-  7  1 2 3 4 5 6 7  Mould Steel jacket Housing Support plate Lubricator plate Cover plate Water channel  Figure 2.1: Schematic of a typical billet mould assembly.  8  cured by plates that fit into slots cut in the outer surface of the tube, near the mould top. On top of the mould, plates secure the assembly, seal the cooling water channel and serve as part of the oil distribution system. Inside the steel jacket, water baffles are typically placed within 4 mm of the mould to facilitate a high cooling water velocity [18]. Cooling water enters between the mould and water baffle at the bottom of the mould. At the top of the assembly, the water is routed to the back of the water baffle, before it exits to the cooling water system. The mould assembly can be installed quickly on the oscillator table, to minimize down-time between mould changes. Billet moulds are typically used for several hundred heats; an average heat lasts for 45 to 90 minutes. The moulds are then replaced because of mould wear, distortion or damage. Poor lubrication or mould taper design causes mould wear, usually at the bottom of the mould where the steel shell gouges the mould. Moulds also permanently distort with use, indicating that the thermal stresses in the mould sometimes exceed the elastic limit of the copper. Studies have shown that the mould taper slowly changes with mould use [19].  2.2  H e a t Transfer i n the M o u l d  Heat is extracted, from the liquid steel to the mould cooling water, through the following path [5]: • Convection in the liquid steel  9  • C o n d u c t i o n through the solid steel shell • C o n d u c t i o n and radiation through the mould-shell gap • C o n d u c t i o n through the copper mould • Convection to the cooling water  A s the billet solidifies and the shell grows, heat transfer varies across the m o u l d face, both vertically and horizontally. T h e mould-shell gap is the largest thermal resistance to heat transfer, particularly near the meniscus. Lower i n the mould, the thermal resistance of the solid steel shell may provide a comparable thermal resistance [5]. Thus heat extraction lower i n the m o u l d reduces because of the increased total thermal resistance. T h e corners solidify more quickly because of two-dimensional cooling from two faces of the m o u l d . T h e corners then shrink away from the mould wall more quickly than the midface, contributing further to non-uniform heat transfer.  Based on the  examination of solidification bands, the influence of non-uniform corner cooling extends about 20 m m from the mould corner [20]. M a t h e m a t i c a l models have been successfully used to quantify heat transfer between the billet and the mould. M o u l d heat transfer coefficients have been estimated based on changes i n mould water cooling temperature; subsequently, the heat transfer coefficients were defined based on dwell time i n the m o u l d [21]. In later studies, thermocouples were installed i n industrial moulds to obtain in-situ mould temperature [22]. A x i a l heat flux profiles were  10  then calculated from the thermocouple data, using finite-difference models. Once mould heat transfer was quantified, the corresponding heat flux could be applied to a billet solidification model. Finite difference models were again appropriate for estimating the temperature distribution in the shell and shell thickness as a function of position in the mould [21].  2.2.1  C a r b o n Content  Singh and Blazek demonstrated a heat transfer dependence on carbon content, as shown in Figure 2.2, using a laboratory continuous caster [23]. Overall heat transfer was a minimum for 0.1 pet. carbon steels and was relatively constant for grades above 0.3 pet. carbon. The surface of billets containing approximately 0.1 pet. carbon are rough, characterized by wrinkles and indentations. The low heat flux associated with casting these steels was attributed to this rough surface. Grill and Brimacombe [24] studied heat transfer on operating continuous casting machines. The minimum heat transfer at 0.1 pet. carbon was confirmed on the industrial machines. A small decrease in. heat extraction was also seen with high carbon steels (0.85 pet. carbon) compared with medium carbon grades.  Grill and Brimacombe correlated the 0.1 pet. carbon heat  transfer minimum with the lower limit of the peritectic phase change, where the S to 7 solid state shrinkage is the greatest. The 5 to 7 phase change is associated with a linear shrinkage of 0.38 pet. [24]. The peritectic phase transformation has the greatest effect on grades in the range of 0.08 - 0.14 pet.  11  eooi  1  1  1  1  1  1  1  r  I 023  1 0.50  I 0.75  I 1.00  I 1.25  1 1.50  1 1.75  1— 2.00  "~ 560 L  I OOO  CARBON, wtight ptrctat  Figure 2.2: M o u l d heat flux as a function of carbon content. carbon [18], where the billet surface is the roughest. T h e wrinkled surface is likely associated w i t h a phase change instability of shrinking, gap formation and reheating. G r i l l and B r i m a c o m b e [24] presented the following mechanism: 1. T h e solidifying shell, i n contact w i t h the mould, cools quickly and transforms from the 8 to 7 phase. 2. T h e outer surface shrinks more than the inner surface, which is still 7 phase, causing inward bending of the shell. 3. T h e surface i n the gap reheats because of reduced heat transfer across the gap, shell strength reduces locally, and ferrostatic pressure deforms the shell back towards the mould wall. T h e resulting surface is wrinkled, 12  and retains its shape as the shell cools and strengthens. 4. The mechanism repeats continuously.  2.2.2  Influence of Process Variables on Heat Transfer  Mould Taper As the steel billet cools and shrinks, an air gap forms between the mould and shell. As previously mentioned, the air gap usually represents the largest barrier to heat extraction. Moulds are therefore tapered to minimize the gap and improve heat transfer [20]. In early research on continuous billet casting, Aketa and Ushijima showed an increased heat extraction with increased mould taper [25]. Excessive taper, in this case 2.6 pet. m in the mould. Moderate tapers near 0.9 pet. m  - 1  _ 1  , caused the billet to bind  have increased heat transfer  by 8 - 15 pet. [26]. Evteev reported that mould taper increased heat transfer significantly across the midface, but only had a slight effect on heat transfer near the corners [27]. Mould taper design will be discussed in more detail in Section 2.4.  Lubricant Type Generally, heat transfer is believed to be lower when casting with mould fluxes than oil because of the additional thermal resistance of the flux film. Using an experimental stationary caster, Singh and Blazek obtained heat flux profiles for both oil and powder lubrication [28]. When casting a 0.40 pet. carbon  13  —  IMMERSED TUBE AND NO FLUX IMMERSED TUBE AND FLUX 0.10% CARBON CASTING SPEED » 50 ipm  1000 LU  < a eooh(C ui u. CO z < 600rOi  < ui x a -i o  400  Z00\— 4  6 8 10 12 14 DISTANCE FROM TOP OF MOLD, inches  16  IS  Figure 2.3: E x a m p l e heat flux profile for o i l and m o u l d flux lubrication. steel, the o i l lubricated billet clearly exhibited higher heat transfer.  When  casting a peritectic steel (0.10 pet. carbon), Singh and Blazek reported higher heat transfer near the meniscus and lower heat transfer i n the lower region of the m o u l d w i t h fluxes [28], as shown i n Figure 2.3. The local gaps i n the rough surface of peritectic steels were filled w i t h m o u l d flux, which facilitated improved heat transfer near the meniscus. K l i p o v et al. measured heat flux profiles on a 180 x 500 m m slab caster when casting chromium-nickel steels [29]. In this case, the heat flux near the meniscus was lower with the mould flux, but higher i n the lower portion of 14  the mould. The differences in results between the researchers is likely due to process parameters such as taper and grade, in addition to the lubrication. When casting with oil lubrication, many gases exist in mould-shell gap in addition to nitrogen and oxygen, including shrouding gases and components of combustion. The composition of this atmosphere is believed to impact heat transfer through the mould-shell gap. The pyrolysis of oil at the meniscus creates hydrogen [19], which has a thermal conductivity seven times greater than air [30]. Chandra et al. calculated heat flux profiles when casting with oil flow rates of 20, 30 and 40 ml m i n  - 1  [6]. The difference in heat transfer  between the tests were small, and not enough to affect the shell thickness at the mould exit.  C a s t i n g Speed Early research on continuous casting indicated increasing heat transfer into the mould with increasing casting speed [31]. This was confirmed in later studies [28, 32], where the axial heat flux profile of the mould simply increased with increasing casting speed, as shown in Figure 2.4 [33]. Singh and Blazek [28], noted that the increase of heat flux with speed was much less for a peritectic steel (0.10 pet. carbon) than a medium carbon (0.40 pet. carbon) grade. Although the heat flux increases with speed, the specific heat extraction (J k g ) decreases, based on the work of Singh and Blazek [28]. - 1  15  Distance from the mould top edge in mm Figure 2.4: M o u l d heat flux profile changing w i t h casting speed. 2.3  T h e r m o m e c h a n i c a l B e h a v i o u r of the  Mould  T h e temperature distribution of billet moulds was originally investigated by Samarasekera and Brimacombe [34] using a two-dimensional axial model. Heat flux was applied to the model hot face using a relationship developed by Savage and P r i c h a r d [31]; a heat transfer coefficient, based on cooling water parameters, was applied to the cold face. A n important conclusion of this work was the sensitivity of heat extraction to the cooling water properties, particularly the cooling water velocity. T h e calculated cold face temperature of billet moulds was found to be approximately 140° C [34]. If the m o u l d operated m u c h hotter than this, boiling might commence, reducing heat transfer.  16  In a later study,  Samarasekera et al. [22], used thermocouples embedded i n the m o u l d wall to obtain operating temperature profiles of industrial billet moulds. T h e m o u l d heat transfer model was then used to estimate the heat flux profile. Under casting conditions, the mould distorts because of differential therm a l expansion. M o u l d distortion was investigated by Samarasekera et al. using a three-dimensional, elastic-plastic, finite element model [17]. T h e m o u l d was found to bulge outwards w i t h a m a x i m u m deflection of 0.1 - 0.3 m m , about 90 m m below the meniscus. This behaviour significantly impacts the m o u l d taper. Near the meniscus, the mould taper may invert, forming a "negative taper". In contrast, slab casting moulds are typically made w i t h copper plates reinforced w i t h steel backing plates, which are more rigid and likely less prone to acute m o u l d distortion. One can infer from this work that the cooling water system must be of high quality. M o u l d oxidation and scaling would be very detrimental to heat extraction, and may contribute to permanent m o u l d distortion.  2.4  M o u l d Taper  In the first published study of billet mould taper, Dippenaar et al. [20] evaluated m o u l d tapers by estimating billet shrinkage. The two-dimensional transverse heat transfer model originally presented by Brimacombe [21] was used to calculate the temperature field i n the solidifying billet. For a given axial position i n the m o u l d , the billet dimension was assumed to the the average length of the rows of solidified nodes i n the model. It was assumed that only austenite 17  was present, and the thermal expansion coefficient was constant at 2.3 x l O K  _ 1  - 6  . T h e researchers concluded that large gaps formed i n the low m o u l d re-  gion of single-tapered moulds [20]. Double- and multiple-tapered moulds were believed to be better m o u l d designs for heat extraction. In later work, Chandra et al. [6] modified the model to include a thermal expansion coefficient which was a function of temperature and carbon content. Figure 2.5 shows heat flux profiles for a parabolic and a single-tapered m o u l d [6].  T h e parabolic m o u l d led to uniform heat extraction along the m o u l d  length, while the single-tapered m o u l d had significantly higher heat extraction near the meniscus.  T h i s was surprising, since the parabolic m o u l d had a  steeper taper i n the upper portion of the m o u l d . T h e authors postulated that the distorted single-tapered m o u l d mechanically interacted more strongly than the parabolic m o u l d on the shell near the meniscus. T h e work of Chandra et al. [6] was particularly important when calculating the shrinkage of peritectic steels. A l t h o u g h peritectic steels experience a large shrinkage due to the S to 7 phase transformation, the low heat flux caused by the rough surface is detrimental to shell growth and further billet shrinkage.  T h e result is that low carbon grades contract less while i n the  m o u l d and require a shallower taper. If cast through a m o u l d designed for higher carbon steels, a low carbon grade may b i n d i n the m o u l d , contributing to billet defects [5, 6]. T h e r m a l stress analysis of the solidifying shell has been conducted for slab casting. T w o dimensional transverse models have been used to evaluate  18  55005000PARABOLIC TAPER  4500-  C = 0.42% 1  g 4000-1  SINGLE TAPER,0.6% m-1  •*„3500-{ X  C = 0.32%  < g 2500^ 20001500100O  100  200  500 300 400 600 DISTANCE FROM MENSICUS, mm  700  8(X)  Figure 2.5: Mould heat flux profiles for single and parabolic mould taper designs. the sensitivity of process parameters such as casting speed and mould taper [35, 36, 37].  2.5 2.5.1  Process Control Metal Level and Casting Speed  Metal level is commonly detected by a radioactive metal level sensor. A 7 ray radioactive source and receiver are set across the mould assembly. When the metal level is low, the received signal level is high; when the metal level is high, the signal obtained by the receiver is attenuated. Within a certain range, the received signal is a linear function of metal level. Radioactive sensors are reported to be accurate to ± 5 mm [38]. In slab casting, other sensors types 19  such as the eddy current probe and electromagnetic cassette are commonly used [38]. Casting speed is typically regulated by the plant control system, based on a metal level set point. As the metal level rises, the casting speed increases to restore the metal level and vice-versa. On billet machines, liquid steel flow rate is not controlled, and is governed by the size of the metering nozzle installed in the tundish bed.  2.5.2  Tundish Stream  Off-centre or ropey streams create turbulence at the meniscus, and contribute to non-uniform shell growth and variable lubrication. Stream quality can 1  be influenced by nozzle blockages, nozzle wear and fluid flow in the tundish. Rough tundish streams also entrain gas which rises to the surface in the mould, contributing further to an unstable meniscus [39, 40, 41]. Tundish design also contributes to stream quality, since turbulent flow in the tundish will initiate a turbulent stream. Tundishs may be modified with dams and weirs in order to reduce stagnant zones or turbulence near a metering nozzle [42]. The length of the open stream (i.e. distance between the nozzle and meniscus) also impacts the meniscus stability since the magnitude of stream disturbances increase with time [39]. Stream erosion of the solidifying shell is a natural concern. Of particular concern is centring of the nozzle [43, 44, 12]. Poor alignment of the stream can cause non-uniform shell growth [44] and cracking in low carbon grades 20  300 450  eoo  H, mm 1 - open stream pouring 2 - submerged entry nozzle  Figure 2.6: Shell uniformity for open stream and submerged entry nozzle casting. [43]. Figure 2.6 presents experimental data of shell non-uniformity for both oil casting with an open stream and powder casting with submerged entry nozzles [44]. The powder cast billets clearly had more uniform shell growth.  2.6  Mould Oscillation  Oscillators are simple machines which reciprocate the billet mould to help prevent the steel from sticking to the mould wall. The mould is usually oscillated in a sinusoidal mode, with typical stroke and oscillation frequency parameters being 10 mm and 2 Hz respectively. A machine may be actuated hydraulically, or by an electric motor driving an eccentric cam. Negative-strip time has been well established as an operating parameter fundamental to continuous casting. Negative-strip time is defined as the  21  time period during which the m o u l d moves downward faster than the strand withdrawal rate.  A s s u m i n g a sinusoidal velocity profile, negative-strip t i m e  can be calculated according to E q u a t i o n 2.1 [3].  arccos(^ ) 7  (2.1)  M o u l d lead, defined as the distance the m o u l d moves past the shell during negative strip, can be calculated using E q u a t i o n 2.2 [3].  As = S s i n ( 7 r / t j v ) — v tj^ s  (2.2)  For billet casters, the recommended m o u l d lead and negative-strip t i m e values are 3 - 4 m m and 0.12 - 0.15 seconds respectively [3]. Casting machines w i t h negative-strip times below 0.1 seconds and m o u l d leads below 2 - 3 m m are susceptible to mould-shell sticking, particularly if the meniscus is [3].  fluctuating  M o u l d leads greater than 5 m m may contribute to deeper, non-uniform  oscillation marks [3]. Casting machine maintenance is currently an active topic among steel producers. Several commercial m o u l d oscillation monitoring systems have been noted i n the literature [9, 45, 46]. T y p i c a l output from these systems includes oscillation frequency, horizontal and vertical m o u l d movement, and casting parameters such as negative-strip time. T h e M O Tektor system [46] was used to detect bearing, guide system and eccentric cam defects based on non-uniform oscillation curves. B r i t i s h Steel developed an on-line m o u l d oscillation m o n i toring system for slab casters using displacement sensors [47]. T h e system was 22  implemented to provide early warning of oscillation problems. The Kiss Technologies system uses accelerometers to measure m o u l d movement [9]. Through signal processing, velocity and displacement are calculated from the acceleration signal. The stroke measurement was validated using L V D T (linear variable differential transformer) displacement sensors and was shown to be accurate only w i t h i n 5 pet.  2.7  Lubrication  In addition to m o u l d oscillation, lubrication is fundamental to continuous casting. A lubricant is required to prevent the solidifying shell from sticking to the m o u l d wall. O i l and mould fluxes are used as lubricants, w i t h o i l being the most common among billet producers.  2.7.1  Oil  O i l is pumped from a reservoir to a distribution system at the top of the m o u l d , where it weeps down the mould faces.  Some oil lubrication systems  were found to be of poor design, since the o i l distribution was non-uniform [48]. The oscillating m o u l d likely improves oil infiltration between the m o u l d and shell during negative-strip time [10]. O i l is usually selected based on cost, how cleanly it burns and local plant experience.  Certainly, much of the o i l  vaporizes or pyrolyzes at the meniscus due to interaction w i t h the hot m o u l d and solidifying steel [12, 11, 49]. The remaining o i l components, likely heavier hydrocarbons, lubricate the mould-billet interface below the meniscus. 23  Oil  properties pertinent to lubricant selection include viscosity, flash point and boiling temperature [11, 49]. O i l which is too viscous may not flow down the m o u l d wall uniformly. Oils w i t h low flash points and/or boiling temperatures are less likely to survive the meniscus environment and provide any effective lubrication.  2.7.2  Mould Fluxes  M o u l d powders are synthetic slags used for lubrication i n continuous casting machines. Powder flux is continuously added on top of the meniscus where it forms a slag layer. The slag forms several sublayers, ranging from unreacted powder to liquid flux as shown i n Figure 2.7 [10]. A solid slag r i m forms on and oscillates w i t h the copper mould. The liquid flux layer is consumed as the strand is withdrawn, and provides lubrication between the shell and m o u l d . In addition to lubrication, mould fluxes are also used to [50]:  • Control heat transfer • T h e r m a l l y insulate the meniscus • Protect the liquid steel from oxidizing • Absorb inclusions from the liquid steel M o u l d flux behavior is complex and depends on the chemical composition of the flux, the in-situ temperature distribution and m o u l d oscillation parameters. Figure 2.8 illustrates how mould flux consumption increases w i t h  24  Slag nose Mould-  Powder layer  Glassy stag layer  Sintered layer Liquid layer  Crystalline slag layer Liquid slag layer  Liquid steel Solidified steel shell  Motion of layers  Figure 2.7: Schematic of mould flux i n the mould.  25  250x950-1,800 mm; LG/AK; LL@1,300°C = .2 Pa.s o 70 cpm • 100 cpm (h = 8 mm)  o  .8  1.2  1  1.4  1.6  Casting Speed (m/min)  Figure 2.8: M o u l d flux consumption as a function of m o u l d oscillation parameters. a decrease i n casting speed or oscillation frequency [50]. Consumption also increases w i t h lower flux viscosities since a low viscosity flux can infiltrate the region between the m o u l d and shell more easily [50]. Powder lubrication usually has lower heat flux near the meniscus than oil and can provide smoother shell growth for depression prone grades, but also aggravates sticker breakouts i f the flux properties are poor [10].  2.8 2.8.1  Billet Quality Crack Formation  A crack w i l l form when a tensile force generates a strain which exceeds the strain-to-fracture of the steel [51]. T h e crack w i l l form perpendicular to the  26  tensile force. V i r t u a l l y all surface cracks form i n the m o u l d [51, 52].  Star  cracks are an exception to this guideline, and usually form i n the spray zone as a result of copper pick-up i n the m o u l d [52]. Transverse surface cracks may form due to unbending [52], but are likely initiated i n the m o u l d . Internal cracks may form i n or below the mould. In the m o u l d , axial stresses are imposed on the shell from mould-strand interaction; the shell is i n tension during the upstroke and compression during the downstroke. Below the m o u l d bending stresses are generated i n the straightener [52]. T h e r m a l stresses i n the m o u l d are generally tensile at the surface and compressive at the solidification front [52]. T h e r m a l stresses are complex however, and depend on heat transfer and steel grade.  Reheating  at the m o u l d exit may cause tensile stress at the solidification front, forming midway cracks [52]. If the shell bulges due to ferrostatic pressure, a transverse tensile force is created [53]. In billet casting, virtually all cracks form i n the zone of low ductility [51], w i t h i n about 70° C of the solidus temperature [54]. This mechanism, also called "hot tearing", is caused by solute rich liquid between dendrites.  The  effect is worsened w i t h increasing concentrations of sulphur and phosphorus. Since these cracks form near the solidus temperature, the depth of a subsurface crack is a reasonable estimate of the shell thickness when the crack formed [51].  27  2.8.2  Oscillation Marks  Oscillation marks are fine transverse shell depressions which form due to shell interaction w i t h the oscillating mould. Oscillation marks are typically a fraction of a millimeter wide and deep, extending around the billet perpendicular to the casting direction. • T h e marks are clearly related to m o u l d oscillation, since their spacing is equal to casting speed divided by oscillation frequency. E x a c t mechanisms for oscillation mark formation vary depending on the study, but they most likely form during negative-strip time [11]. Non-uniform oscillation marks may contribute to the formation of other defects such as rhomboidity and off-corner internal cracks [55]. Transverse cracks often form at the base of deep oscillation marks. T h e following operating practice should be adopted to promote the formation of uniform oscillation marks [55]:  • Low negative-strip time • Reduce superheat • H i g h meniscus taper • Four-sided m o u l d constraint • H i g h cooling water velocity  Oscillation marks tend to be deeper when casting w i t h m o u l d fluxes. M o u l d oscillation parameters, flux viscosity and consumption a l l tend to i m pact the size of oscillation marks [50]. T h e oscillating m o u l d creates a transient  28  pressure regime i n the liquid flux, which contributes to the formation of oscillation marks [56].  2.8.3  Rhomboidity  Rhomboidity, or off-squareness, is usually quantified by the difference i n the billet diagonals. R h o m b o i d i t y exceeding approximately 6 m m may be considered serious. R h o m b o i d i t y has been associated w i t h non-uniform heat transfer i n the m o u l d , commencing at the meniscus. Once the off-squareness has been initiated i n the m o u l d , it can be exacerbated by non-uniform spray-cooling. Poor mould-strand alignment and wobbly oscillation were believed to contribute to the non-uniform heat extraction [57]. Samarasekera and B r i m a combe proposed that rhomboidity could be initiated by dimensional instability of the m o u l d tube [57], caused by intermittent boiling on the m o u l d cold face and/or non-uniform m o u l d constraints. Further, the higher heat flux associated w i t h m e d i u m and high carbon steels indicates that boiling, and rhomboidity, would be more severe i n these grades. Subsurface cracks may be observed adjacent to the obtuse corners of the billet [57]. These cracks usually form 2 - 4 m m below the surface, where the shell is locally i n tension as shown i n Figure 2.9. In a later study by B o m m a r a j u et al., deeper oscillation marks were often found on the obtuse corners of off-square billets [58]. Since deep oscillation marks reduce heat transfer, the shell would be thinner at these corners. W h e n the shell emerged from the mould, the billet may cool and shrink  29  u  j—  v  Upper sprays  n  Off-square billet containing off-corner internal cracks  Figure 2.9: Schematic showing a billet w i t h varying shell thickness distorting further into an off-square shape i n the spray cooling zone.  30  non-uniformly, creating off-squareness i n the spray zone. K u m a r reported that rhomboidity was worse i n the m e d i u m carbon grades (0.14 to 0.45 pet. carbon) [13]. T h i s was attributed to the fact that the combination of heat extraction and freezing range of the steel lead to thicker near-meniscus shells i n these grades. K u m a r also noted that rhomboidity could be initiated by metal level fluctuations, which contribute to non-uniform heat transfer [13].  2.8.4  Shell Bulging and Off-Corner Internal Cracks  Inadequate m o u l d taper (i.e. shallow single-tapered moulds) gives rise to excessive mould-shell gaps i n the lower portion of the m o u l d [20]. Ferrostatic pressure may cause the shell to bulge slightly i n these cases, u n t i l the shell midface impinges on the mould. T h e hinging action about the corner creates a tensile strain at the solidification front forming the off-corner internal crack [58], as illustrated i n Figure 2.10 [51]. T h i s effect is more likely to occur i f shell thickness has been reduced i n the off-corner region due to deep oscillation marks which have reduced heat transfer. Cracks which are w i t h i n 8 m m of the surface likely formed i n the mould; cracks deeper than 8 m m may have formed due to bulging below the m o u l d [51].  2.8.5  Laps and Bleeds  Laps and bleeds are surface defects which form very near the meniscus, and tend to be most common on high carbon billets. A lap is characterized by a meniscus shell hook and subsequent overflow. A bleed is a shell tear where l i q -  31  - Deep oscillation marks Shell bulging —i  t  Figure 2.10: Shell bulging and the formation of off-corner internal cracks. u i d steel has filled i n the ruptured shell. K u m a r et al. report that these defects are initiated by metal level fluctuations coupled w i t h poor lubrication [12]. A "hot m o u l d " practice (i.e. when the hot face temperature of the m o u l d i n near the boiling temperature of the oil) is believed to exacerbate the problem.  2.8.6  Transverse Cracks  Transverse cracks can form during straightening if the billet surface temperature is between 700 and 900° C , a region of low ductility [52]. However, casting speeds are often too high i n billet casting for this to occur [18], thus transverse cracks are believed to form i n the m o u l d .  Mechanical forces due to bind-  ing, sticking or poor lubrication are believed to initiate transverse cracks [51]. Knights et al. [43] reported transverse crack severity was sensitive to stream alignment i n the mould. Transverse cracking tends to be worse on steel grades  32  w i t h less that 0.25 pet. carbon.  2.8.7  Transverse Depressions  Mould-Billet Binding - Mechanism 1 If the shell sticks or binds i n the mould, axial withdrawal forces place the shell i n tension. T h e shell may plastically deform and neck like a tensile test specimen as shown i n Figure 2.11 [5]. A s the surface of the shell deforms, the strain may form a transverse crack at the solidification front i n the zone of low ductility. Assuming that the crack does not propagate into the ductile portion of the shell, the depth of the crack from the surface is indicative of the shell thickness when the depression formed [5].  Depressions in Oil Lubricated Billets - Mechanism 2 Samarasekera et al. detected depressions near the meniscus using thermocouples embedded i n the m o u l d wall [14]. T h e thermocouples responded w i t h a local drop i n temperature as the depression moved down the m o u l d due to reduced heat transfer as a function of the increased mould-shell gap. In nearly all cases, the depression detection was preceded by a metal level rise noted by a thermocouple above the meniscus. Depressions were clearly forming at or very near the meniscus based on thermocouple response. D a t a obtained i n a previous U B C study [11] indicated that there may be a relationship between oil flow rate and depression shape or formation. T h e lubricating o i l was postulated to influence depression formation i n conjunction  33  Binding (High Friction)  Zone of i High Ductility  Necking of Ductile Shell to Form Depression  Liquid Steel  Crack Zone of Low Ductility  Withdrawal Force Figure 2.11: Transverse depression formation by binding - Mechanism 1.  Metal Level Stable  Metal Level Rises  Trapped Oil Vapourizes and Pushes on Solidifying Shell  Depression Enlarged by Friction and Mechanical Forces Lower in the Mould  Figure 2.12: Transverse depression formation from o i l vapour - Mechanism 2. 34  with a rise in metal level. O i l may become trapped between the steel skin and the mould given an excessive oil flow rate, downward mould movement during negative-strip time and a rising metal level. The authors argued that vaporizing oil may apply enough pressure to the steel skin at the meniscus to form a depression, shown schematically in Figure 2.12. Early research of slab casting with oil lubrication noted depression formation with variations of casting speed and metal level [59]. Cracks were observed 8 mm below the billet surface in the Samarasekera et al. study [14]. Although the depression was formed near the meniscus, the crack was formed lower in the mould below a point of binding. Tensile strains would be greatest at depression sites because the depression would be hot and thin relative to the adjacent shell. Observations by Lorento [14] indicate a critical casting speed, for a given billet size, above which depressions do not form.  Depressions in Powder Cast Blooms - Mechanism 3 Jenkins et al. [15] studied transverse depressions in 0.06 pet. carbon blooms with a thermocouple instrumented mould. Depressions were observed on all faces of the blooms and ranged from 1 - 4 mm in depth. Depressions were accompanied with longitudinal scrape marks, referred to as "glaciation marks", over a 10 to 20 cm region. Cross-section samples of the depressions indicated solidification bands close to the surface under depressions; indicating a thinner shell as a result of reduced heat transfer. Consistent with the Samarasekera 35  ransverse direction  meniscus  1.5s during level drop  1.2 S level drop  1.8s level rise  mold heat loss  Shell Cooling  B  Resolidification  C  Figure 2.13: Transverse depression formation caused by a metal level fluctuation and shell distortion - Mechanism 4. et al. study [14], the formation of a depression was preceded by a rise i n metal level. T h e depressions were determined to be slag filled rather than air filled, based on heat flux calculations. These depressions were postulated to form by capturing the slag r i m as the metal level increased. If the metal level rose too quickly for the slag r i m to melt, a depression would be formed as the shell solidified around the slag r i m . T h e glaciation marks were theorized to form near the meniscus as lubrication by the slag was interrupted when the r i m was captured i n the depression. B l o o m quality increased when a new metal level control system was installed at the subject facility.  Thermal Distortion - Mechanism 4 Thomas and Zhu modelled the impact of metal level  fluctuations  on  the solidifying shell [60]. A two-dimensional, axial, thermal-stress model was  36  used for the investigation. The metal level was simulated to drop 30 m m for 0.6 seconds, then was restored to a level 20 m m higher. the exposed shell was assumed to air cool.  D u r i n g the drop,  Figure 2.13 illustrates the shell  distortion during the simulated metal level fluctuation. After the metal level drop, the shell had distorted inwards 0.45 m m . T h i s was attributed to the inner face of the shell cooling i n air and bending inwards, toward the centre of the billet. After the metal level rise, the shell had distorted inwards to 1.65 m m . T h e further distortion was caused by the liquid reheating the existing shell, causing expansion, plus the contraction of the newly solidified layers on the liquid side.  Other In slab casting, a depression mechanism called the "plastic hinge effect" has been proposed [59, 61]. T h e depression is postulated to form by a local overcooling of the strand.  Sensitivity of Steel Grade on Depression Formation Transverse depressions tend to form on low carbon [11, 6] and boron-alloyed steels [14]. In the binding mechanism, low carbon grades exhibit lower heat transfer and were believed to b i n d i n the m o u l d because of reduced shrinkage. For mechanisms which form depressions near the meniscus, the high temperature mechanical properties of these grades may be an influencing factor [14, 60]. It is well known that low carbon steels have a short freezing range [62], and  37  form a thicker solid shell near the meniscus than high carbon steels.  Fur-  ther, m i n i m u m segregation of sulphur and phosphorus near 0.10 pet. carbon effectively increases the high temperature strength of these steels [63]. Thus, regardless of the mechanism, low carbon steels are more likely to form and retain the shape of a depression. T h e high temperature behaviour of the boron steels has yet to be fully quantified. It has been argued that the stability of TiN  1  at steelmaking temperatures may increase the high temperature strength  of these steels [14].  2.9  Friction Monitoring  Mould-strand friction has been monitored to evaluate lubrication and detect break-outs i n slab casters. Most research has been conducted on experimental slab casting machines, and very little work has been reported on industrial billet casting machines.  2.9.1  Strain Gauge Force Sensors  In early research on continuous casting, strain gauge bearings were used to measure withdrawal forces caused by different m o u l d materials [64]. T h e i m pact of oscillator condition on withdrawal force was an important conclusion of this work. Exact alignment of the m o u l d and strand was required to m i n i m i z e withdrawal forces. In addition, m o u l d oscillation was required to be robust, 1  Titanium is commonly alloyed with boron to prevent boron from being consumed as  BN.  38  and not a function of the oscillator mechanism. A strain gauge was used on an experimental casting machine to study lubrication between the mould and shell [65]. T h e strain gauge was installed on a p u l l rod used to withdraw the shell. In this study, the friction force was found to increase w i t h reduced mould flux thickness. Strain gauges have been installed on the drive arm of a slab caster [66]. T h e signal was processed into a constant force plus an oscillating force. T h e oscillating force was noted to increase by 10 pet. during sticker breakouts. A surprising result of this study was that the force response d i d not change w i t h casting powder or the w i d t h of the slab.  2.9.2  Load Cells  T h e use of load cells to measure mould-strand friction i n billet machines has been described by Brendzy et al. i n previous work at U B C [11]. Compressive load buttons were installed between the removable mould jacket flange and the oscillator table. Figure 2.14 illustrates a typical load cell response. T h e load was characterized during the upstroke by a compressive m a x i m u m plateau w i t h numerous small peaks.  T h e downstroke load decreased smoothly and  increased, centred about negative-strip time. T h e friction-position relationship was also reported by Saucedo and Blazek, from research on a pilot caster [67]. Brendzy et al. reported higher load cell forces when casting grades w i t h transverse depressions and transverse crack defects.  Transverse depressions  were noted on most of the hypo-peritectic (0.035 - 0.05 pet. carbon) and some  39  Upstroke Downstroke  I  1  O  0.5  1  1  1.0 1.5 Time, s  1  2.0  1  2.5  Figure 2.14: T y p i c a l load cell response as reported by Brendzy et al.. of the peritectic (0.10 pet. carbon) billets. T h e depressions were believed to be caused by mould-billet binding. Load cells have also been installed i n slab casting machines [68, 69, 70, 71, 72, 73]. In most cases, the research was directed at elucidating the behaviour of m o u l d fluxes.  2.9.3  Accelerometer Based Systems  T h e use of an accelerometer to measure m o u l d friction was proposed w i t h the M L Tektor (mould lubrication detector) system [46, 74, 75, 76, 77] for use w i t h slab and bloom casters.  T h e accelerometer was mounted on the  m o u l d assembly and connected to an electronic processing unit which was not  40  described.  T h e processed signal output was reported to be directly related  to mould-strand friction and was reported as "percent friction", although a quantitative description of the signal was not given [46]. T h e M L Tektor signal was reported to vary w i t h casting conditions and was presented as a tool for o p t i m i z i n g casting parameters [46, 75]. T h e M L Tektor signal was claimed to increase during the formation of transverse cracks [46]. Longitudinal cracks i n peritectic steels were also claimed to form i n excessively high and excessively low friction signal environments [46], although a mechanism for their formation was not given. A n accelerometer was used to measure friction on a billet casting m a chine by van der Stel et al. [49]. Friction, i n the form of a slip-stick mechanism, was reported to be seen as amplitude peaks i n the signal. T h e function of accelerometer based friction monitoring systems remains vague i n the literature. E m l i n g describes the function of the M L Tektor as follows [78]:  T h e mechanical vibrations transmitted through the m o u l d are converted to discrete electrical pulses by the accelerometer.  These  electrical signals are, i n turn, assimilated by a computerized data acquisition facility. T h e signal generated is directly related to friction and, after some data processing, yields a relative friction factor.  Wolf notes that these signals are derived from resonance effects [10].  41  T h e author is not aware of any correlations between force sensor response and accelerometer signals. Accelerometers are effective vibration sensors, and these systems likely infer a "friction" signal from machine vibration.  2.10  Quantifying Friction  In a Bethlehem study [69], load cells were used to evaluate m o u l d powders for increased casting speed. In this study, solid and liquid lubrication regimes were used to describe mould-strand friction. T h e liquid friction force was quantified by E q u a t i o n 2.3 [69].  Fliquid  =  (2-3)  Equation 2.3 assumes a constant velocity gradient through the film and uniform viscosity. Thus for a liquid friction mode, the m a x i m u m friction occurs at the point of m a x i m u m velocity. Solid friction was described by the simple relationship of E q u a t i o n 2.4 [69].  F  a o l i d  = cN  (2.4)  Solid friction is independent of the magnitude of relative velocity, but simply depends on the direction of relative velocity.  Solid friction simply  results i n a square wave force response. T h e friction response of m o u l d fluxes was often a combination of solid and liquid friction [69]. T h e Bethlehem study defined the friction force as the difference between  42  the m a x i m u m and m i n i m u m forces over a 10 second period; thus eliminating the force of the m o u l d weight [69]. In another study using an experimental casting machine, the friction force was determined by subtracting the m o u l d inertial force from the measured force [72]. In later research at Bethlehem, the work per oscillation cycle was calculated, then divided by the m o u l d stroke to determine a "work-averaged" force [68]. In this study, the cold force was subtracted from the casting force to obtain the net friction force.  2.11 2.11.1  Influence of Process Variables on Friction Lubrication  In a study of oil lubrication, Brendzy et al. [11] noted slightly higher loads when casting w i t h excessively low oil flow rates. A t o i l flow rates above 34 m l m i n , - 1  little difference was noted i n lubrication effectiveness. Friction measurements have shown that oil lubrication leads to higher and more variant friction forces than m o u l d fluxes [49, 79], thus m o u l d powder is preferred to o i l lubrication i n reducing friction [10].  2.11.2  Casting Speed  O h m i y a et al. reported a relationship between m o u l d friction and casting speed i n an excellent study of m o u l d fluxes, as illustrated i n Figure 2.15 [70]. For a given m o u l d powder, it appeared that a friction m i n i m u m existed at an intermediate casting speed.  43  250  T  1  1  r  Figure 2.15: M o u l d friction response using powder lubrication.  44  2.11.3  Breakouts  A breakout is a catastrophic shell rupture that allows liquid steel to escape uncontrolled. In slab casting, sticker breakouts can be initiated by a disturbance i n m o u l d flux lubrication. T h e steel sticks, or welds, to the m o u l d wall near the meniscus. M o u l d oscillation then tears the shell, and liquid steel fills the gap. In subsequent oscillation cycles, the shell is repeatedly torn and does not fully heal. T h e sticker moves down the mould, and causes a breakout at the m o u l d exit. Sticker breakouts have been detected as hot spots i n thermocouple response; propagating down the mould at approximately one half of the casting speed [80]. Sticker breakouts can also cause increased friction [66, 67, 75], and the detection of sticker breakouts has been a key objective i n the use of force sensors i n experimental slab casters. Sticker breakouts may be more reliably detected by thermocouples however [10].  2.11.4  Steel G r a d e  Singh and Blazek measured withdrawal forces on a bench-scale stationary caster [23]. Figure 2.16 illustrates the friction forces as a function of carbon content. T h e researchers concluded that high carbon steels (i.e. greater than 0.40 pet. carbon) exhibited low friction because of the smooth billet surfaces. Using a pilot oscillating caster, Saucedo and Blazek reported similar friction when casting carbon steels i n the range 0.05 to 0.50 pet. carbon [67]. In the same study, higher friction was reported when casting free-machining steels. 2  2  A l l o y e d with Pb, B i , or Te.  45  ~i  1  1  1  1  1  r-  • 0.»  ' 10  i  -i  1  1  i  1  i 1.7  l.«  i  (A T3 O Q.  T3  3 O  «0 SUIFU* HEAT  o  SULFUR HEAT  °  V  ao  Ol. I 00 0.1  I I 0.Z O.S  I 0.4  I  I  0.8  0.6  I ' 0.7 0.»  ' I.I  i 1.2  i  i  •  i  I.S  1.4  1.5  1.8  i  1.9 2.0  Carbon Content (weight percent)  Figure 2.16: M o u l d friction response as a function of carbon content on a laboratory caster.  46  Figure 2.17: Output from accelerometer based "friction" signal. Using an accelerometer on a billet machine, van der Stel et al. reported a friction index for 0.10, 0.50 and 0.70 pet. carbon grades [49], as shown i n Figure 2.17. T h e 0.10 pet. carbon steel was shown to have the highest friction index.  This was attributed to reduced shrinkage of low carbon grades and  higher normal forces i n the mould, although heat extraction data was not presented.  T h e opposite effect was noted using an accelerometer when slab  casting w i t h powder lubrication [46] . A peritectic steel (0.13 pet. carbon) yielded a friction signal of 25 pet., while a 0.40 pet. carbon steel produced a signal level of 75 pet.  In this case, the low friction signal was attributed to  the high shrinkage associated w i t h the 5 to 7 phase transformation. T h e effect of carbon content, and other process variables, remains i n -  47  complete and somewhat inconsistent i n the literature. T h i s is likely due to various sources of a "friction" signal and the different machines used: experimental casters, billet and slab machines.  48  Chapter 3  Scope and Objectives  M o u l d behaviour profoundly impacts billet quality and productivity, as was evident i n the literature review. The m o u l d interacts w i t h the billet thermally and mechanically, and both are fundamental to process operation. Excellent material is available i n the literature w i t h respect to mould heat extraction, but very little information exists regarding mould-billet friction. M o u l d oscillation and lubrication facilitate casting by reducing friction so the shell w i l l not crack, tear or stick. It is therefore surprising to note that few attempts have been made to monitor friction, and likely only one published work exists on measuring billet machine forces. Friction is certainly impacted by key machine design parameters: m o u l d oscillation and m o u l d taper. The billet producer must ascertain what parameters are desired, and this has been determined empirically though local experience, and machine/mould suppliers.  Once design parameters have been  chosen, does the producer ensure that machine specifications are maintained  49  i n casting operations?  Unfortunately, the answer to this question is usually  "no". T h i s may be due to the history of billet casting, where low-cost, lowquality products like reinforcing bar were produced.  Also, mini-mills often  lack the resources and tools to perform such checks. B u t w i t h the industry shift to higher quality billet steels and near-net-shape casting, these issues must be addressed. Further, there is widespread interest i n industry to move towards higher speed casting for increased productivity. T h i s requires tighter tolerances i n a l l aspects of process quality, as well as the monitoring of process upsets which contribute to poor billet quality. In a single statement, this research investigates the m o u l d response i n the context of process variables and upsets.  T h e following sub-tasks  were  designed to meet this objective.  1. Conduct industrial plant trials to measure m o u l d temperature, m o u l d oscillation, mould-billet friction, casting speed and metal level. Record process and billet quality. 2. Measure m o u l d oscillation using displacement and acceleration sensors. Is the machine operating at design specifications? 3. Test new sensor types to measure machine forces. 4. Evaluate mould-billet friction quantitatively. 5. Develop techniques for measuring m o u l d friction and oscillation using an on-line system. 50  6. Investigate friction when high forces are expected, such as during the formation of transverse depressions and when mould-billet binding is occurring. 7. Investigate friction as a function of process variables: casting speed, lubricant and steel grade. 8. Develop a thermal-stress billet shrinkage model. 9. Use the billet shrinkage model to interpret mould-billet binding with the force sensor and to evaluate mould taper design.  51  Chapter 4  Experimental: Industrial Plant Trials  F i v e industrial plant trials were conducted at two Canadian mini-mills, designated as Companies A and D . T w o m a i n experimental trials were conducted at Company D , and one at Company A . A s the knowledge of this work unfolded, two subsequent force sensor tests were conducted, one at each facility. T h i s chapter discusses the instrumentation of the casting machines and casting conditions of the plant trials.  4.1  N e w A s p e c t s of I n d u s t r i a l P l a n t Trials  Industrial plant trials have been conducted by the U B C continuous casting group i n the past. T h e use of m o u l d thermocouples has been well established i n the work of B o m m a r a j u [22], Chandra [81] and K u m a r [13]. T h e research of Brendzy [82] is likely the only published work measuring mould-strand friction on industrial billet machines.  A l t h o u g h Brendzy's work has provided  significant insight into the process, the forces measured were only qualitative,  52  owing to the installation of the load cells. This work endeavours to study the mechanical response of the billet machine quantitatively.  New sensors were  tested, and a separate data acquisition system was used to meet this objective. Highlights of this new work conducted as part of these plant trials are listed below. 1. D a t a s a m p l i n g .  D a t a was sampled at a higher sampling frequency  than i n the past. This was necessary to more fully quantify the machine response and to identify electrical line noise. 2. S i g n a l i s o l a t i o n . Ground-isolated sensors were used to m i n i m i z e electrical problems such as ground looping. 3. D a t a a c q u i s i t i o n . A separate data acquisition system was developed and used independently of the thermocouple data acquisition system. T h i s was required for high frequency data sampling and signal isolation. 4. A c c e l e r o m e t e r . A n accelerometer was tested for the following reasons: • A s a kinematic sensor to verify the L V D T response. • A s a candidate kinematic sensor to measure m o u l d movement online. • To investigate the accelerometer "friction" signal noted by a slab casting vendor. 5. O s c i l l a t o r m o t o r c u r r e n t .  T h e drive motor current was tested as a  possible indicator of mould-strand friction.  53  Table 4.1: Summary of sensor use.  Plant T r i a l Machine ID LVDT Accelerometer Load cells Strain gauge Piezoelectric strain sensor Oscillator motor current Casting speed M e t a l level M o u l d thermocouples (full length) M o u l d thermocouples (partial)  DI A  Al B  D2 C  D3 C  A2 B  X  X  X  X  X  x x  X  X  X  X  X  X X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  6. S t r a i n g a u g e . Strain gauges were tested as a candidate force sensors. 7. P i e z o e l e c t r i c s t r a i n s e n s o r . Near the end of this research, an experimental strain sensor was tested to measure mould-strand friction.  The strain gauge sensor provided, for the first time, quantitative force measurements on an industrial billet casting machine. A s w i l l be discussed later, the motor current and accelerometer friction signals were abandoned because of the success of the strain gauge.  4.2  Sensors  A summary of sensors employed i n the five plant trials is given i n Table 4.1. Figure 4.1 illustrates the sensor locations i n the casting machine.  54  Metal level  Mould temperature  LVDT Accelerometer  Load cells  Strain gauge Piezoelectric strain sensor Casting speed  Drive arm Motor driven cam  Figure 4.1: Schematic of sensor locations in the casting machine.  55  (Measurement)  0  Primary Coil nsulating Form  Core Displacement  (Measurand) I  Ferromagnetic Core  • •••  2» Secondary Coil  -5 6 "r„f 6  Secondary Coil  Figure 4.2: Schematic of L V D T sensor. 4.2.1  Linear Variable Differential Transformers  A linear variable differential transformer ( L V D T ) was used for measuring m o u l d displacement.  A L V D T is an electromagnetic device which consists  of a cylindrically wound primary coil w i t h a secondary coil wound at the ends of the p r i m a r y coil [83], as illustrated i n Figure 4.2. T h e object of interest moves a steel rod which slides through the centre of the coils. T h e p r i m a r y coil is excited w i t h an A C voltage; an A C voltage of the same frequency is induced i n the secondary coil. T h e output signal of the secondary coil is processed such that the resulting signal is a linear function of displacement [83]. The L V D T , attached to a magnetic base, was anchored to the shop floor near the oscillator. T h e L V D T was placed as close to the m o u l d as possible, near the centre of the oscillator table.  56  T h e A C excitation frequency of the L V D T should be 10 times greater than the highest frequency of interest i n the measured signal [83]. T h e D a tronic 3230 signal conditioners excited the L V D T s at 3000 H z , indicating that the m a x i m u m frequency of interest should be 300 H z .  D a t a was sampled  at frequencies as high as 1000 H z , but no frequency i n the measured signal was near the 300 H z l i m i t . T h i s was later confirmed by a fast Fourier transform analysis. T h e Schlumberger C51 signal conditioner operated at 5000 H z . Schlumberger Sangamo A C R - 1 5 L V D T s were used for the trials.  4.2.2  Accelerometer  Accelerometers are sensors that output a voltage proportional to acceleration. Piezoelectric accelerometers use a piezoelectric crystal as a transducer, which generates a charge when a strain is applied. T h i s effect occurs w i t h asymmetric crystal structures that become charge imbalanced when distorted. In the case of an accelerometer, the strain is caused by the inertial loading of the crystal by its mass or by a fixed mass attached to the crystal. T h e charge generated is then proportional to the acceleration of the crystal [84]. Direction is identified by charge polarity since the crystal generates opposite charges depending tensile or compressive strain. For a constant acceleration or strain, the crystal charge leaks off. T h e piezoelectric device is therefore dynamic, and is not useful for constant acceleration or strain applications.  In the case of most  vibratory systems, constant accelerations are not encountered.  Piezoelectric  accelerometers are usually small, robust and have a wide dynamic range.  57  ELECTRICAL CONNECTOR 0.25 (6.4) 10 FEET (3 METERS) LONG TERMINATING IN PIGTAIL LEADS BLUE: GNO RED: SIG/PWR  8 1.19(a30.2) —] 0.87(822.1 3.47(88.1) PROTECTIVE/THERMAL JACKET MODEL 085A31 (SUPPLIED) A  1.188 (30.17) HEX 01.31 (033.27) ACROSS CORNERS —I 1/^-28 UNF-28 X .23 (5.8) T  /  I  I — 01.00(025.4)  Figure 4.3: P C B 326A13 accelerometer. T h e piezoelectric sensor output requires signal conditioning prior to measurement by a data acquisition system. A charge amplifier is used reduce the charge leak-off rate and provide a signal appropriate for measuring. T h e charge amplifier outputs a voltage proportional to the generated charge, and i n the case of an accelerometer, acceleration. A P C B Piezotronic model 326A13 accelerometer was selected and is illustrated i n Figure 4.3. It was a low frequency, hermetically sealed industrial sensor, w i t h an operating bandwidth of 0.3 - 4000 H z . F u l l scale acceleration output was ± 5 g ( ± 4 9 m s ) ; the sensor was calibrated to 994 m V g - 2  - 1  .  A P C B 482A16 was used to power and process the output signal of the accelerometer. T h e 482A16 powered the accelerometer w i t h a constant current source of 4 m A ; the 482A16 also had selectable output gains of 1, 10 and  58  100. T h e accelerometer was mounted on the mould jacket flange as close to the m o u l d and L V D T as possible. The sensor was attached w i t h a mounting stud, threaded into a 6.35 m m hole which was drilled and tapped i n the m o u l d jacket flange.  4.2.3  Oscillator Motor Current  T h e direct current motor signal was taken from a resistor i n the motor power circuit. A t t r i a l D 2 , the potential across the resistor was 50 m V for the motor's m a x i m u m current of 150 amps. Since the resistor voltage was not relative to ground, an isolation amplifier was required for the signal to be logged by the data acquisition system. A n Analog Devices 289K isolation amplifier was used.  4.2.4  Force Sensors  Load Cells Load cells are commercially available force sensors. Omega L C G - 1 0 K compression load cells were used for the trials. The Omega load cells utilized foil strain gauges as transducers. The load cell output voltage was proportional to the applied force; output was 2 m V per excitation volt. A regulated 10 volt excitation was employed, yielding an output of 20 m V for the full scale load of 45000 N [85]. Load cells were installed at Company D for the first two m a i n experimental trials, D I and D 2 . The load cells were installed between the oscillator table and the m o u l d housing flange, as previously described by B a k s h i et al. 59  [48]. Three load cells were installed i n recessions i n the m o u l d jacket flange. Adjustable spacers centred the cells during installation as the oscillator table bolts were tightened. The cells were installed on the opposite side of the housing to the water inlets and outlets.  Previous experience indicated that the  water O-rings dampened adjacent load cell signals [11]. It has been recognized that the load cells sense only a fraction of the total load. E a c h cell responds to its fraction of the combined bolt and cell loading. Thus the load cell response was significantly desensitized by the mould bolts which have a higher stiffness than the load cells. The objective for this configuration was to obtain a qualitative understanding of mould load.  Strain Gauges T h e function of a strain gauge is based on the principle that the electrical resistance of a material w i l l change when it is mechanically deformed [83]. M e t a l foil is the most common strain gauge material, which is formed into a grid and oriented longitudinally i n the direction that the strain is to be measured [85]. The foil is mounted on an electrically insulating backing material. T h e resistance change of the gauge is linear w i t h strain, thus for a linear-elastic material the force is a also a linear function of strain. The change i n resistance is measured w i t h a simple electrical circuit. Strain gauge output can be increased by mounting four strain gauges i n a "Wheatstone bridge" configuration as shown i n Figure 4.4 [83].  Two  of the gauges measure axial strain, while the other two measure transverse  60  -O Vin  o  Figure 4.4: Schematic of full strain gauge bridge. strain. T h e bridge is said to be "balanced" if the four resistances are equal. As the gauges are strained, the resistance bridge becomes imbalanced and a voltage is created. For axial loading, the bridge strain can be calculated from E q u a t i o n 4.1 [85].  e  -2V  r  (4.1)  T h e strain gauge bridge needed to be installed on a load bearing m e m ber of the machine. T h e drive arm of the oscillator was the selected for the following reasons: • T h e drive a r m actuates the entire machine, and the full machine force would be measured. • T h e a r m is located i n an accessible area to install the sensor.  i.l  • T h e location is not likely to be exposed to a break-out, which would damage the sensor. • T h e a r m is pinned at both ends, and i n a simple state of axial stress. Thus the forces measured should be an accurate measure of machine loading. T h e surface of the drive arms were degreased, and sanded w i t h progressively finer grades of emery cloth. T h e strain gauges were installed using Micro-Measurements M - B o n d 200 adhesive, following the installation guidelines of Micro-Measurements B u l l e t i n B-127-2 [86]. For the m a i n experimental trials, a regulated 10 volt power supply was used to power the bridge. For the force sensor tests, an integral strain gauge power supply-amplifier was used. A Sensor Developments Inc. model 90131 Bridgesensor was installed as close to the bridge as possible, to m i n i m i z e electrical noise. A p p e n d i x A details the strain gauge force calculation.  Piezoelectric Force Sensor A piezoelectric strain sensor was tested as a candidate force sensor late i n this research. T h i s sensor was recently employed measuring a low-frequency oscillating force on a ball m i l l [87, 88]. T h e strain gauge had been verified as a capable sensor for measuring mould-strand interaction, but the installation was time-consuming and tedious.  Since part of this research was directed  towards on-line monitoring, this sensor was tested for industrial use.  62  Figure 4.5: Kistler piezoelectric strain sensor. The new sensor employed a piezoelectric crystal as a transducer, and was developed by Kistler Instrument Corporation. A unique feature of this sensor is that it is installed with a single bolt, and strain is measured relative to two contact pads. To the author's knowledge, Kistler is the only supplier of this sensor type. The principle of operation is similar to that of a piezoelectric accelerometer. As the crystal is strained, the charge generated is converted to a voltage, which is proportional to strain. As mentioned previously, the charge generated by these crystals leaks off, thus this strain sensor is only useful for dynamic, or quasi-static [89], strain measurements. The Kistler 9233B strain sensor, shown in Figure 4.5, and 5038A charge amplifier were tested at trial A2. The 9233B has an operating strain range of ±300 yue, and was installed with a single M6x35-12.9 machine screw. The oscillator arm was degreased and prepared with emery cloth; a hole was drilled and tapped for mounting.  63  4.2.5  Process Control Signals  Casting Speed Casting speed was taken directly from the plant control system as a voltage source. T h e signal originated from the withdrawal roller tachometer, and was typically i n the range of 0 - 10 V .  Metal Level The metal level signal was taken from the system controller. For t r i a l D I , a 1 fi resistor was used i n series w i t h the 4 - 2 0 m A current loop; the associated output voltage was 4 - 2 0 m V . For trial A l , a voltage signal was obtained directly from the controller. T h e second stage of trials used an M - S y s t e m signal isolator (discussed i n Section 4.3.6), which mapped the 4 - 2 0 m A current loop signal to a 1 - 5 V output signal.  4.2.6  Mould Temperature  A x i a l temperature profiles of the m o u l d were required for m o u l d heat transfer calculations. T h e technique for measuring m o u l d wall temperatures had been developed by Brimacombe, Samarasekera and co-workers i n past research [48, 90]. A l t h o u g h the thermocouple instrumentation technique was not an original part of this research, it w i l l be discussed briefly for completeness. B . N . Walker at U B C conducted the thermocouple installation. To install a single thermocouple, threaded holes were prepared through  64  the water baffle and approximately half-way into the copper mould. Singlewire, T y p e T , copper-constantan thermocouples were employed. Constantan thermocouple wire was prepared by forming a bead on the wire w i t h a T I G welder. T h e bead was filed flat, then heat-shrink tubing was applied to the wire to insulate it. T h e bead was inserted through the water baffle into the hole i n the m o u l d and was held i n place w i t h a copper plug.  A plug was  also installed i n the water baffle thread to secure the wire and prevent water cross-flow. T h e constantan wire was then attached to insulated copper wire i n the water channel. Inlet and outlet water temperatures were also measured by installing T y p e T two-wire thermocouples i n the water channel. Groups of wires were bunched together and run through a pipe fitting i n the side of the m o u l d jacket. Rubber plugs and silicone sealant were placed i n the fitting for a water-tight seal, which was retained by a pipe thread collar. Thermocouple wires were then tested for electrical continuity and the assembly was pressure tested w i t h water. The thermocouple layout for plant trials D I and D 2 , and the depths of the thermocouples are detailed i n A p p e n d i x B .  4.2.7  Sensor Calibration  Mechanical Sensors 1.  LVDT. T h e L V D T was calibrated on-site w i t h a block of known dimension.  65  2. A c c e l e r o m e t e r . T h e P C B accelerometer and signal conditioner were calibrated by the supplier. 3. L o a d c e l l s . T h e load cells were calibrated by the supplier. T h e sensor calibration w i t h checked w i t h an Instron machine [91]. 4. S t r a i n g a u g e s . T h e strain gauges were supplier calibrated, by supplying the gauge factor. 5. K i s t l e r s t r a i n s e n s o r . by the manufacturer.  T h e piezoelectric strain sensor was calibrated  T h e associated charge amplifier was  adjustable  and was not supplied calibrated. Since calibration of the charge amplifier required special instrumentation, the strain sensor was calibrated on-site to a strain gauge. 6. M e t a l l e v e l . M e t a l level was calibrated by inserting a billet into the m o u l d at various distances from the m o u l d top. 7. C a s t i n g s p e e d . Casting speed calibration was obtained from the plant technicians. In trial D I , the calibration was checked using a tachometer on the withdrawal roll.  T h e net calibration constants, for converting logged voltages to the appropriate units, are located i n A p p e n d i x C .  66  Table 4.2: P o l y n o m i a l coefficients for T y p e T thermocouple voltage-totemperature conversion.  Coefficient a  0  Ol «2  0-3 CL4  a a a  5 6  7  Value 0.100860910 25727.94369 -767345.8295 78025595.81 -9247486589. 6.97688 E l l -2.66192 E13 3.94078 E14  Mould Temperature Thermocouple voltage was converted to temperature using a p o l y n o m i a l equation. For T y p e T thermocouples, a seventh order polynomial of the form  T = a + ciix + a x ... a-jx 2  0  2  7  (4-2)  yields an accuracy of ± 0 . 5 ° C over the range -160 to 400°C [92]. T h e p o l y n o m i a l coefficients are listed i n Table 4.2. It should be noted that the voltage measured by a m o u l d thermocouple wire was the sum voltage of two copper-constantan junctions; one i n the m o u l d , the other i n the water channel. Since the potential of these junctions opposed each other, the m o u l d thermcouple signal was reduced by the voltage associated w i t h the thermocouple i n the cooling water channel. T h e two-wire thermocouples i n the cooling water were used to compensate for the copperconstantan j u n c t i o n i n the cooler water. Thus to calculate m o u l d temperature, 67  the m o u l d thermocouple voltage was added to the water channel thermocouple voltage plus reference temperature voltage -, then converted to temperature 1  using the calibration equation.  4.3  Data Acquisition System  T h e data acquisition system for the mechanical sensors evolved i n several stages. T h e first three experimental trials, D I , A l and D 2 , tested new sensor types and implemented devices such as isolators and amplifiers for superior data quality. T h e force sensor tests, D3 and A 2 , focussed on on-line monitoring w i t h new devices. T h e electrical schematics for the plant trials D I , A l , D 2 , D 3 , A 2 (ordered chronologically) are illustrated i n Figures D . l to D.5 respectively, located i n A p p e n d i x D .  4.3.1  Personal Computer  A n I B M P C clone was used for data acquisition and storage. T h e P C featured an Intel 80486DX2-66 microprocessor, 16 megabytes of R A M and a Toshiba 870 megabyte hard disk. A 1.2 gigabyte Colorado tape drive was installed for data transfer and back-up.  4.3.2  Analog-to-Digital Converter  A Metrabyte D A S - 8 data acquisition card was installed into the P C - I S A bus slot.  T h e card featured a 12-bit successive approximation analog-to-digital  T h e reference temperature voltage is simply the voltage associated with the ambient temperature, since the calibration equation is referenced at 0°C. 1  68  converter, and was powered by the P C power supply. Conversion times were typically 25 microseconds, 35 microseconds m a x i m u m . T h e theoretical data throughput rate was 30000 H z , but this could not be achieved by the P C . T h e nominal analog input range was ± 5 V . The associated signal resolution for a 12 bit analog-to-digital converter can be calculated using equation 4.3. AV  resolution = ^  _  (4.3)  In this case, the voltage resolution was 2.44 m V ( Q ^ )• 5  4.3.3  4  95  5  Multiplexer  A M e t r a b y t e E X P - 1 6 analog multiplexer and amplifier was employed. T h e board multiplexes 16 analog input channels into 1 analog output channel. T h e channels were selected by software through the D A S - 8 using a 4 bit T T L C M O S compatible address.  T h e E X P - 1 6 connected directly to the D A S - 8  w i t h a standard 37 p i n ribbon cable. The multiplexer was powered by the P C through the D A S - 8 . The board contained an amplifier for applying a common gain to a l l channels. In the plant trials D I and D 2 , a gain of 200 was used allowing an analog input range of ± 2 5 m V . T h e associated signal resolution was 0.012 m V using equation 4.3.  69  4.3.4  Software  Data Acquisition K e i t h l e y Labtech Notebook for Windows data acquisition software was used: The software allowed the user to customize the input channels to be read, the data sampling rate, the output file format and real time graphical display of selected inputs.  D a t a acquisition was such a burden for the P C that the  graphical display was often updated only once per minute.  T h e data was  stored i n binary files rather than A S C I I because this was more efficient for the software. D a t a files sometimes exceeded 100 megabytes. Labtech contained features that allowed input data to be modified or processed i n real time.  These features included algebraic, differential and  integral functions. These features would be ideal for calibrating signals, and for calculating parameters such as negative-strip time on-line. Unfortunately, the P C was not capable of doing this i n real-time, so only raw voltages were logged.  D a t a E x t r a c t i o n and C a l i b r a t i o n Convert [93], a program developed by summer student K . W i l d e r , was used to extract the binary data. The program was also capable of thinning the data, extracting specified columns, and calibrating data w i t h p o l y n o m i a l equations. E x t r a c t i n g and calibrating data often took several hours, so batch jobs were submitted to the P C overnight.  70  Fast F o u r i e r Transforms Fast Fourier transforms ( F F T ) were used to present signals i n a frequency dom a i n format. T h e F F T is a useful tool for identifying frequency  components  i n time-based signals. In particular, logged signals were checked on-site for 60 H z electrical line noise, which would indicate a data acquisition or sensor problem. Labtech Notebook contained a simple F F T function, and the output could be viewed using a P C spreadsheet. F F T program code is readily available, e.g.  4.3.5  [94, 95].  P a r a l l e l D a t a A c q u i s i t i o n Systems  Thermocouple System A parallel data acquisition system was used to sample m o u l d thermocouple signals during the m a i n experimental plant trials. T h i s system was used by other researchers [13, 96, 97] during some of the plant trials. T h e system consisted of a similar P C clone and analog-to-digital converter. T h e multiplexer consisted of 8 cascaded E X P - 1 6 boards called an E X P - E N C device. A power supply powered the multiplexer through a splitter i n the ribbon cable between the D A S - 8 and E X P - E N C . T h e multiplexer was capable of handling 128 input channels.  71  Real-Time System A real time data acquisition system has been under development by V . Rakocevic [98], for use w i t h the Intelligent M o u l d .  The system operates under  Q N X , a unix-like, real-time operating system. The system uses a M e t r a b y t e D A S - 2 0 card for data acquisition. A unique feature of this system is that it calibrates and processes data at the driver level, and therefore is very efficient. C O M D A L E ProcessVision was employed as the user interface to display process parameters. T h e C O M D A L E / C expert system shell was implemented to interpret signals on-line. T h e environment is capable of displaying warnings, alarming, and generating reports of system findings. This system was under development and was tested by Rakocevic during the experimental trial D 2 . T h e prototype was used for this research by the author during the force sensor test D 3 . Since the system interprets and displays data i n real-time, this system was very useful i n identifying upsets on-line. Further, four meniscus thermocouples were installed during this test, allowing thermal and mechanical data to be logged simultaneously.  4.3.6  Data Acquisition Issues  Ground Looping and Electrical Noise G r o u n d looping may be caused by circuits which are grounded i n m u l t i p l e locations. Consider the circuit i n Figure 4.6 [83]. If a potential exists between the two ground points, which is likely i n a high-power industrial environment,  72  Signal-Conditioning Device  Sensor  Loop Broken  Figure 4.6: Schematic of ground looping caused by grounding i n two locations. then a circuit is induced between the ground points and the sensor negative lead. T h e resulting voltage is then superimposed on the sensor signal, leading to an offset or noise. T h e ground loop circuit can be broken using ground isolated sensors. T h i s condition was particularly problematic i n plant trials where a P C and a sensor may be grounded 30 m apart. In the case of the thermocouple data acquisition system, the thermocouples were grounded to the m o u l d and it was not possible to ground isolate the thermocouples. Thus the P C ground  73  and thermocouple ground would likely form a ground loop and reduce data quality. Electrical noise can also be induced i n signal leads from A C power lines. T h i s noise can lead to excessive error on low-level signals such as those from strain gauges [83]. Shielded cables were used for the plant trials i n order to m i n i m i z e the impact of electrical noise. Aliasing is the representation of a high frequency signal by a low frequency signal [94], and is caused by an inadequate sampling frequency.  The  Nyquist sampling theorem states that the sampling frequency must be greater than twice the frequency of the highest frequency component i n a signal [94]. For example, i f 60 H z line noise exists i n a signal, and the sampling frequency was 100 H z , then aliasing would occur. Aliasing has been noted i n past plant t r i a l signals [99]. In this research, signals were sampled at a very high frequency (up to 1000 H z ) , and the frequency components i n the signal were established prior to selecting a sampling frequency.  Common-Mode Voltage A l t h o u g h voltage levels from different devices may be small, their voltage relative to a common ground may be large. T h i s is referred to as commonmode voltage. T h e oscillator motor current signal is an example of a commonmode ground problem. T h e current signal, taken from a resistor i n the motor circuit, was small (50 m V ) , but the signal was several hundred volts relative to ground. If this signal was connected directly to a data acquisition system, it may damage the hardware.  74  A similar problem existed when tapping into 4 - 2 0 m A circuits such as the metal level signal. T h e common-mode voltage w i l l vary depending on where the signal is extracted i n the circuit.  Signal Levels and Isolation A downside of the data acquisition system was that it only allowed for a single gain setting on the E X P - 1 6 multiplexer. For the early trials, signals were acquired at the multiplexer i n the range of ± 2 5 m V , using a gain setting of 200. T h i s signal level was appropriate for logging load cell, strain gauge and metal level signals. Sensor signals w i t h voltages higher than 25 m V (e.g. L V D T , accelerometer) were reduced w i t h voltage dividers, shown schematically i n Figure 4.7. Voltage dividers are simple to build, and were often adapted on-site to optimize signal levels. For the later trials, isolation amplifiers were employed to meet the following objectives: • To reduce data acquisition problems such as ground looping. • To sample signals at a higher voltage level (~5 V ) to reduce the impact of electrical noise. • To allow parallel data acquisition between this system and thermocouple data acquisition system. A n M - S y s t e m Technologies modular isolation amplifier system was used. T h e base unit was capable of containing 1 0 - 2 channel isolation amplifier m o d 75  gain = R2/(Rl+R2)  Rl  6  Vin 9  6  R2  Vout 9  Figure 4.7: Typical voltage divider used to reduce input voltage to a level suitable for data acquisition. ules in a rack mountable frame. Modules were available for different input ranges: a 0 - 100 m V unit for the strain gauge, -10 - 10 V and -5 - 5 V for voltage inputs like L V D T , casting speed and accelerometer, and 4 - 2 0 m A for the metal level. A l l modules output full scale from 1 - 5 V , such that an output of zero volts indicated a system problem. For the later trials, data was logged at the multiplexer in the range ± 5 V .  4.4 4.4.1  P l a n t Trials Casting Conditions  The machine design and casting practices varied between the Companies. Most noteworthy was the difference in mould taper. Company A used a 0.8 pet. m  _ 1  single-tapered mould, while Company D used a steeply tapered ( 4 - 5 pet. m  _ 1  at the meniscus) parabolic mould. Casting machine details are given in Tables 76  Table 4.3: Casting machine details at Company A .  Plant Trial Machine ID  Al B  Machine type M o u l d taper Taper at meniscus (pet. m ) M o u l d size (mm) M o u l d length (mm) M o u l d material M o u l d constraint Water channel gap (mm) Water velocity (m s ) O i l flow rate ( m l m i n ) Stroke (mm) Osc. Frequency (Hz) Casting Speed ( m m s ) Negative-strip time (s) _ 1  straight single 0.8 203 734 DHP 4-sided ~10 30 12.7  _ 1  - 1  - 1  M o u l d Lead (mm)  1.7  k 2.7  ~19 .24 k .17 7.5  k 9.3  A2 B straight single 0.8 152 734 DHP 4-sided ~4 -12 35 12.7 1.7 k 2.7 25 - 30 .21 k .15 @30 m m s" 5.0 k 7.6 @30 m m s  1  _ 1  4.3 and 4.4. W i t h the exception of the instrumented moulds, casting conditions during the plant trials were normal operating practice. The m o u l d design and machine parameters were common operating practice for the individual plants. D a t a were obtained for as many casting conditions as possible, subject  to  plant constraints and production schedules. In fact, the plant trial schedules were very dynamic, owing to the current marketing conditions which changed hourly i n some cases. The m a i n parameters of interest for a given m o u l d were steel grade and the type of lubrication, o i l or mould flux. A p p e n d i x E details 77  Table 4.4: Casting machine details at Company D .  Plant T r i a l Machine ID Machine type M o u l d taper Taper at meniscus (pet. m M o u l d size (mm) M o u l d length (mm) M o u l d material M o u l d constraint Water channel gap (mm) Water velocity (m s ) O i l flow rate (ml m i n ) Stroke (mm) Osc. Frequency (Hz) Casting Speed ( m m s ) Negative-strip time (s) _ 1  - 1  _ 1  M o u l d Lead (mm)  _ 1  )  DI A curved parabolic 5 203 813 DHP 4-sided ~5 -10 50 9 1.9 ~19 .20 4.6  78  D2 C curved parabolic 5 203 813 DHP 4-sided ~5 ~10 50 6 & 9 variable ~19 .17 & .20 @2 H z 2.0 & 4.8 @2 H z  D3 C curved parabolic 4 171 & 194 813 DHP 4-sided ~5 10 - 12 50 6 & 9 variable 20 - 35 .10 & .16 @2 H z , 30 m m s" 0.5 & 2.8 @2 H z , 30 m m s"  1  1  the chemical compositions of the heats monitored in the main plant trials.  4.4.2  B i l l e t Samples  During the main trials, 300 mm billet samples were acquired routinely, typically at a rate of two samples per heat. Samples were also obtained corresponding to process upsets and large defects; these samples were 300 to 1000 mm in length. The billet cooling bay and storage yard were routinely inspected for surface defects, in an attempt to understand what sizes and grades of billets were disposed to forming observed defects. The billet samples were marked with heat number, casting direction and face orientation, then shipped back to U B C for inspection. The preparation and analysis of billet samples have been documented in other sources [81, 90]. Macro-etching was conducted on prepared billet sections to observe internal billet quality. Samples were immersed in a solution of 50 pet. HC1 and 50 pet. water and heated to 85°C for 30 minutes. Samples were then cooled, scrubbed with steel wool in water, dried with ethanol, and finally photographed. Billet quality can be outlined in the following categories: 1. Internal quality. • Internal cracks • Inclusions • Porosity 79  • Microstructure 2. Dimensional quality - rhomboidity. 3. Surface quality • Oscillation marks • Surface roughness • Depressions: longitudinal and transverse • Surface cracks • Bleeds and laps • Pinholes • Slag and zipper marks Depressions and transverse cracks were of particular interest to this research because the formation of these defects has been linked to mould-strand friction. The shape of surface depressions were mapped using a profilometer table normally used for measuring the depth of oscillation marks. A billet sample was placed on the profilometer table, which moved at a regulated speed. A n L V D T was mounted on an arm which was fixed above the sample. The L V D T signal was logged using a Toshiba 286 laptop and Metrabyte DAS-8 and EXP-16 components, described previously. In a single pass, depth data were logged with time, which was converted to axial distance by multiplying time with the speed. The L V D T was moved transversely 10 mm, and the procedure  80  was repeated until the surface defect was completely mapped. This process was conducted to quantify both the orientation and shapes of depressions as repeatable or random in nature.  81  Chapter 5  Industrial Plant Trial Results  Immediate results of the plant trials, including sensor response and billet quality, are presented in this chapter. Mould oscillation and process control observations are also discussed. Mould-strand friction required more detailed analysis, and is presented in Chapter 6.  5.1 5.1.1  Base Sensor Response Kinematic Sensors  Figure 5.1 illustrates typical mould displacement and acceleration responses, as measured by a L V D T and an accelerometer. The displacement trace was reasonably sinusoidal, and the acceleration signal was rough due to jerk in the oscillator mechanism. The displacement and acceleration signals were 180° out of phase, as expected with sinusoidal motion. Figure 5.2 shows the accelerometer signal and acceleration calculated from the L V D T signal . The traces 1  Acceleration was calculated by taking the second derivative of the displacement signal with respect to time. 1  82  Time (s)  Figure 5.1: Typical L V D T and accelerometer signals. Trial D3. overlaid reasonably well, yielding confidence in the sensor response. Also, the magnitudes of the accelerations measured by these independent instruments were consistent.  83  Figure 5.2: M o u l d acceleration as measured by an accelerometer and calculated from a displacement signal. Trial D 3 .  84  5.1.2  Force Sensors  S t r a i n Gauge Strain gauge and load cell force sensors were tested simultaneously during trial D2. Figure 5.3 illustrates that the signals were in phase and had a reasonable match. This was one of the most significant findings of this work. Firstly, force can be measured on the oscillator mechanism, alleviating the difficulties of conventionally installing load cells every time the mould is changed [48]. Secondly, quantitative forces have been measured possibly for the first time on an industrial billet machine.  Force and D i s p l a c e m e n t Response Figure 5.4 illustrates a typical force and displacement trace during casting operations. The character of the force response is similar to that reported by Brendzy et al. [11], with the exception that force is measured with a strain gauge rather than load cell. The force signal leads the displacement signal by approximately 90°. The periodic reduction of force corresponds with the downstroke of the mould, or negative-strip time, which will be discussed in more detail later.  P i e z o e l e c t r i c S t r a i n Sensor As discussed in Section 4.2.4, a Kistler piezoelectric strain sensor was tested late in this research as a candidate force sensor for industrial on-line moni-  85  15000  Figure 5.3: Load cell and strain gauge force sensor signals. T r i a l D 2 .  86  40000  35000 h  CD 30000 o .  o  LL  25000 h  20000  Figure 5.4: Trial D3.  T y p i c a l oscillator force and mould displacement  87  responses.  toring. The piezoelectric sensor was calibrated to the strain gauge using data from a cold oscillation cycle, shown in Figure 5.5. Figure 5.6 shows that the piezoelectric sensor appeared less sensitive to higher frequency signal components such as machine harmonics and the friction peaks seen during positive strip time. However, for tracking the basic force response the Kistler sensor seemed acceptable. The piezoelectric sensor is more sensitive to small strains than a conventional strain gauge, and may be useful for machines with large drive arm sections (and small strains).  5.1.3  Cold Work - Machine Not Casting  During a cold oscillation test, the mould displacement was 180° out of phase with force, as shown in Figure 5.7. Acceleration, shown in Figure 5.8, was in phase with force, indicating that the force sensor was responding to the inertial forces of the machine. The consistency of the kinematic and force sensing provides further confidence that the sensors are providing meaningful and correct information.  5.1.4  Oscillator Motor Current  The current of the DC electric drive motor was measured as a candidate friction indicator in this study. Figure 5.9 shows that the current signal was periodic and in phase with the force sensor. Note that the motor current should increase when the motor load increases, regardless of whether the mould movement is up or down. Although the signal may be useful as a qualitative indicator of  88  Figure 5.5: D a t a used to calibrate the piezoelectric strain sensor w i t h a strain gauge. T r i a l A2.  89  25000  5000 0.0 1  1  1  1  1  1  1  1  1  1  1  0.5  1  1  1.0  1  1  1  1  1  1.5  1  1  1  2.0  Time (s)  Figure 5.6: Strain gauge and piezoelectric strain sensors during casting operations.  90  Figure 5.7: Force and displacement signals 180° out of phase during a cold oscillator test.  91  Figure 5.8: Force and acceleration signals i n phase during a cold test. force sensor was responding to inertial forces.  92  The  Figure 5.9: Comparison of force and D C electric motor current - Machine C. mould-strand interaction, further analysis of the signal was abandoned because of the success of the strain gauge.  5.2  Oscillator Characteristics  Three different oscillation machines were tested during the plant trials; the oscillators were designated as Machines A , B and C in Table 4.1. A l l machines were designed to be operated in a sinusoidal mode. As will be shown, the  93  Table 5.1: Summary of oscillator stroke measurements.  Machine A B C C  Design stroke (mm) 9.0 12.7 6.0 9.0  Operating stroke (mm) 5.5 - 6.5 9.0 - 11.5 4.2 - 5.4 ~ 7  Sinusoidal profile (visual inspection) no no yes yes  oscillation characteristics of these machines varied greatly.  5.2.1  O s c i l l a t o r Stroke  A l l oscillators showed a variance of stroke from their design values, as summarized in Table 5.1. Machine A had a design stroke of 9 mm and was operating near 6 mm as shown in Figure 5.10. Machine B , illustrated in Figure 5.11, operated from 9 - 1 1 mm and had a design stroke of 12.7 mm. Machine C exhibited a high quality sinusoidal oscillation profile while Machines A and B had non-sinusoidal profiles. Figure 5.12 shows the non-sinusoidal profile of Machine B . Machine A had an unloaded stroke of 8 mm; the displacement profile was a smooth waveform but the peaks of the sinusoid were flattened in the centre. This profile was not seen during casting. The difference between load (6 mm) and no-load (8 mm) performance was likely due to either clearances in machine joints or elastic deformation of machine components under load.  94  Time (s)  load cell displacement  Figure 5.10: M o u l d displacement and load cell response - Machine A .  95  -6 10  20  30  Time (s)  40  50  displacement casting speed  Figure 5.11: M o u l d displacement and casting speed during the beginning of a heat - Machine B . Note that increasing casting speed increased the oscillation frequency.  96  Time (s)  Figure 5.12: Non-sinusoidal displacement profile and casting speed variation Machine B .  97  5.2.2  Stroke and M a c h i n e L o a d i n g  The operating stroke of Machine A ranged from 5.5 - 6.5 mm, as shown in Figure 5.10 which presents the displacement and load cell responses.  The  stroke was seen to vary as much as 0.5 mm between periods. The variance of stroke was believed to be a function of loading as the load range was greatest opposite short stroke cycles.  5.2.3  N e g a t i v e - S t r i p T i m e and M o u l d L e a d  Negative-strip time is illustrated schematically in Figure 5.13 using sensor data. Mould velocity was calculated by taking the time derivative of the mould displacement signal. It is evident that the velocity profile was not sinusoidal, due to imperfections in the oscillator mechanism. Of course, an "ideal" oscillator would exhibit perfectly sinusoidal displacement, velocity and acceleration profiles. In this case, the negative-strip time was seen to be approximately 0.15 seconds. Operating negative-strip time can differ from the design value given the observed variance of stroke, and can be further impacted by non-sinusoidal velocity profiles as illustrated in Figure 5.14.  The negative-strip time was  calculated to be 0.20 seconds for Machine A using Equation 2.1. Sensor data indicated the negative-strip time was varying from 0.12 to 0.17 seconds. Thus, the operating negative-strip time was significantly less than expected. The expected mould lead for Machine A (s=9 mm, /=1.9 Hz, v =19 mm s s  was 4.6 mm. Under the operating stroke of 6 mm, the actual mould lead was 98  60  1  < ~  -40 h casting speedvelocity^^  -60 h 0.0  0.5  1.0  1.5  Time (s)  Figure 5.13: Illustration of negative-strip time using real data from M a c h i n e C . Trial D2.  99  8  9  10 Time (s)  11  12 load cell velocity  Figure 5.14: M o u l d velocity and load cell force - Machine A . T r i a l D I .  100  Time (s)  Figure 5.15: Mould velocity, casting speed and force corresponding to a period of zero negative-strip time. Trial D3, 0.70 pet. C, 171 mm mould, oil lubrication. 1.9 mm. For billet casters, the recommended mould lead and negative-strip time values are 3 - 4 mm and 0.12 - 0.15 seconds respectively [3]. Although the operating negative-strip time of Machine A was satisfactory, the operating mould lead was less than desired. During the on-line sensor test at trial D3, the machine was found to be operating with a negative-strip time of nearly zero during one heat. The  101  stroke was set at 6 mm, operating near 4.8 mm, and the oscillation frequency was 1.4 Hz. Figure 5.15 illustrates the mould velocity, casting speed and force. Force was still in phase with velocity, and the load plateau in positive-strip time was apparent. Fortunately, the oil lubrication in this case was adequate to prevent excessive sticking. The billet surface was smooth; the oscillation marks were small and spaced at non-uniform intervals with the spacing likely impacted by metal level fluctuations. This is a clear example of how a "report card" of process parameters, created by an on-line system, would be useful to plant staff. It is likely that operating practices may not be implemented correctly at times given the confusion of changing moulds, lubricants, steel grades, and perhaps casting machines.  5.2.4  Stroke and O s c i l l a t i o n Frequency  Many billet casters operate a control scheme where the oscillation frequency is a function of casting speed. A n unexpected dependence of stroke on oscillation frequency was also observed. The stroke of Machine B (Figure 5.11) increased from 9 to 11.5 mm when the casting speed was increased from 10 to 20 mm s . -1  The oscillator mechanism of Machine B contained springs designed to reduce drive train loading. The increase in stroke was likely due to either inertial forces or spring resonance. Contrary to the performance of Machine B , the stroke of Machine C decreased with increasing casting speed and frequency. The stroke was observed to vary from 5.4 to 4.2 mm over the normal range of casting speeds experienced when casting 203 mm square billets. 102  10  20  30  40  Casting Speed (mm s" ) 1  Figure 5.16: Negative-strip time for an 8 m m sinusoidal oscillator.  103  The practice of varying oscillation frequency with casting speed is common among billet producers. With this technique it is possible to adjust the frequency to maintain a constant negative-strip time. Figure 5.16 presents the negative-strip time relationship for an 8 mm oscillator with changing casting speed and oscillation frequency. Thus, if negative-strip time is to be held constant with mould oscillation frequencies above 2 Hz, the frequency should be reduced with increasing casting speed. In contrast, in many operations, the frequency is changed in direct proportion to the casting speed. Increasing oscillation frequency with casting speed may significantly decrease negative-strip time, depending on how the machine is operating in reference to Figure 5.16.  5.2.5  C a s t i n g Speed O s c i l l a t i o n  Machines A and B exhibited a periodic variation in casting speed as seen in Figure 5.12. This effect was not observed on Machine C. The speed varied between 0.5 and 2 mm s , with the same period of the oscillator but out of _1  phase. The casting speed variation may be due to the upward and downward friction created during positive and negative-strip time respectively. As the friction force acts downwards during the downstroke, the withdrawal drive system may speed up because of the reduced load. This effect may be a function of the withdrawal system. Mould-strand friction may apply enough torque to the withdrawal roll, via the billet, to temporarily speed up or slow down the withdrawal drive system. It is doubtful that this effect impacted billet quality, but it must be recognized that the casting speed varies. Infrequent sampling 104  of the casting speed signal may lead to erroneous results.  5.2.6  Horizontal Movement  Horizontal mould movement was obtained for a no-load case on Machine A . Four short-stroke L V D T displacement sensors were installed on a frame and inserted into the mould in a region of zero taper. The frame was attached to the plant floor. Horizontal movement with the sensors 50 m m from the mould top is illustrated in Figure 5.17. Movement was greatest in the northsouth direction at 0.4 mm. Figure 5.18 illustrates the mould vertical-horizontal mould trajectory for one oscillation cycle; note that the mould was moving diagonally. How the horizontal movement changed under casting load was not known. In a study of caster alignment of four steel companies [100], all machines indicated greater alignment variation than the tolerances set for new machines. The threshold for excessive movement causing potential defects is not known. A suggested practice for slab machines has been to maintain horizontal movement below 0.2 mm [68].  105  Figure 5.17: Horizontal mould movement 50 mm from mould top - Machine A unloaded.  106  4  c  Q) iS Q.  0  ..X)  or  cd o  CD  >  o  D  -0.20  downstroke upstroke _L  _l  I  oo. I  L.  -0.10  0.00  0.10  Horizontal Displacement (mm)  Figure 5.18: M o u l d trajectory - Machine A unloaded.  107  0.20  5.3  Process Control  On the machines tested, the casting speed was regulated by the plant control system based on the metal level set point. As the metal level rose, the casting speed would increase to restore the metal level, and vice versa. Radioactive metal level sensors, used in all plant trials, are reported to be accurate to ± 5 mm [38]. Further error can be introduced if the controller is not tuned correctly. The transient nature of this process is well illustrated in Figure 5.19. Large variations in casting speed and metal level lasted for up to 50 seconds, greater than the dwell time of the steel in the mould. This behaviour was observed on all machines. The steel flow rate was calculated using Equation 5.1, which is simply the bulk flow of steel due to casting speed plus the volume flow rate associated with metal level fluctuations.  V = (v + s  -~-)A  d  b  (5.1)  The casting speed and metal level signals shown in Figure 5.19 were used to calculate steel flow rate, presented in Figure 5.20. Metal level changes impacted the flow rate calculation very little. It is evident from Figure 5.20 that flow rate from the tundish is a transient process variable. Steel flow rate was not controlled, other than by steel head in the tundish and nozzle size, on all machines tested. Steel level in the tundish is usually manually controlled by an operator activating a slide gate valve on  108  Figure 5.19: Transient response of metal level and casting speed typical of the machines tested. T r i a l D 2 , 203 m m mould, oil lubrication.  109  0  50  100  150  200  250  300  Time (s)  Figure 5.20: Steel flow rate calculated from metal level and casting speed signals. (11 = 0.001 m ) 3  110  the ladle. The operator sets the tundish level by monitoring tundish weight given by a load cell or by watching the level. Flow rate can also be affected by nozzle erosion and blockage. Since mould taper is designed for a particular casting speed and grade, flow rate variation will impact billet quality via changes in casting speed. The transient nature of this system could be reduced, and hence billet quality improved, by the addition of flow control to each casting machine. Metal level and casting speed should be set points, controlled by the flow rate. Figure 5.21 illustrates another example of a process control problem in billet casting. The metal level fluctuated about a set point and the casting speed steadily increased, indicating an increase in steel flow rate into the mould. The increasing flow rate was likely caused by an eroding nozzle. Immediately after this data set was logged, a breakout occurred. The casting speed of 20.5 mm s  _1  was not excessively high for casting 203 mm billets, and  the force had not increased prior to the breakout. The increasing steel flow rate was the only potential "breakout warning" seen in logged signals. The process control response also varied depending on the lubricant type: oil or powder.  In powder casting, liquid steel flows into the mould  through a submerged entry nozzle, so the slag layer remains undisturbed. Figures 5.22 and 5.23 illustrate typical responses for oil and powder casting respectively. The oil cast control signals were typically "rougher". Much of this response was due to stream quality, which may cause meniscus turbulence. A rough meniscus will negatively impact billet quality, e.g. [13], and also cause 111  Figure 5.21: Stable metal level and increasing casting speed indicates increasing steel flow rate - Machine B .  112  I  i  i  i  i  100  I  LJ  200  i  i  i  I  300  i  i  i  i  I  125  400  Time (s)  Figure 5.22: "Rough" casting speed and metal level signals commonly seen when casting w i t h o i l lubrication. Trial D 3 , 0.80 pet. C , 194 m m m o u l d .  113  Figure 5.23: Typical smooth casting speed and metal level signals when casting with mould fluxes. Trial D3, 0.30 pet. C + B , 194 mm mould.  114  a noisy metal level signal. Open stream pouring, i.e. oil casting, is also prone to forming small, solidified globules of steel at the nozzle exit. The globules form and release on the nozzle exit, and impact both stream quality and steel flow rate.  5.4  B i l l e t Samples  Shape defects, cracks, and bleeds and laps were common defects in the billets. Defects which have been linked to mould-strand friction (i.e. transverse depressions and cracks) and mould taper were most important to this work. Rhomboidity, and bleeds and laps were the focus of another study [13] and were not investigated in detail.  5.4.1  Surface Roughness The difference in surface roughness between grades has been well es-  tablished in the literature [24]. Peritectic steels tend to have a surface characterized by wrinkles and indentations, which are believed to be caused by the S to 7 phase transformation. Figure 5.24 shows the surface of a typical peritectic steel billet containing 0.12 pet. carbon, taken from trial DI using oil lubrication. Figure 5.25 illustrates the surface of a hyper-peritectic steel billet, in this case 0.32 pet. carbon, also taken from trial D I . As discussed in Section 2.2, the rough surface seen in Figure 5.24 reduces heat transfer in the mould.  115  Figure 5.24: Rough surface of a peritectic steel billet. Trial D I , 0.12 pet. C, 203 mm mould, oil lubrication.  116  Figure 5.25: Smooth surface of a hyper-peritectic steel billet. Trial D I , 0.32 pet. C, 203 mm mould, oil lubrication.  117  Figure 5.26: Macro-etched section of a multiple defect billet. Trial D I , 0.3 pet. C + B , 171 mm mould, oil lubrication. 5.4.2  Shape Defects and C r a c k s Figure 5.26 illustrates a 171 mm billet with serious defects. The billet  was severely off-square, and contained large off-corner internal cracks caused by the billet distorting. Shell bulging was also evident on the left face, which may have formed inside or below the mould where the shell was thin. Midway cracks also formed below the mould when the shell reheated. Transverse depressions were common shape defects, particularly at Company D. The peritectic steels and boron grades were notably prone to forming transverse depressions. However, these defects were seen on all grades from peritectic to high carbon steels.  Figures 5.27 and 5.28 illustrate two large  118  Figure 5.27: Large transverse depression. Trial D2, 0.32 pet. C + B , east face, 203 mm mould, oil lubrication.  o (/>  5'  f-t(• '"  :-. * '  '' ,  ;• • •. " '  Figure 5.28: Large transverse depression. face, 203 mm mould, oil lubrication.  119  -»,...,  .  -  .  -,,  -  . •  V  .  Trial D2, 0.32 pet. C + B , south  Figure 5.29: Surface crack on a deep transverse depression. Trial D2, 0.32 pet. C + B , east face, 203 mm mould, oil lubrication.  120  Figure 5.30: Subsurface cracks under a deep transverse depression. Trial D2, 0.32 pet. C + B , south face, 203 mm mould, oil lubrication.  121  Figure 5.31: Transverse depression showing both subsurface and surface cracks. Trial D 2 , 0.32 pet. C + B , 203 mm mould, oil lubrication.  122  transverse depression  transverse depression  Figure 5.32: Transverse depressions on a powder cast billet. Trial D2, 0.14 pet. C, 203 mm mould. transverse depressions on 203 mm billets. Cracks were often seen with transverse depressions. Figure 5.29 shows a cross-sectional view of the depression shown in Figure 5.27; a surface crack is evident. Subsurface cracks, below a depression, are shown in Figure 5.30, which is a cross-section of the depression in Figure 5.28. Both surface and subsurface cracks are apparent in the cross-section shown in Figure 5.31. The transverse surface cracks are believed to form in the top of the mould, when the shell is thin and weak. Thus depressions with surface cracks most likely formed at the meniscus. Subsurface cracks are believed to form at the solidification front when the depression is lower in the mould. Since the shell is thin at a depression site due to reduced heat transfer, axial forces place the shell in tension and initiate cracks.  123  Figure 5.33: Macroetch of transverse depression on a powder cast billet. Trial D2, 0.14 pet. C , 203 mm mould.  124  A surprising observation from trial D 2 was the formation of transverse depressions i n powder cast billets. Figure 5.32 illustrates typical transverse depressions seen on 0.14 pet. carbon billets. In all cases the depressions were hinged about oscillation marks; the oscillation marks were deep because of the m o u l d flux lubrication. T h e transverse depressions were also more acute than those found on billets cast w i t h oil lubrication.  Since the depressions  were hinged about oscillation marks, they likely formed near the meniscus when the shell was thin.  T h e weak shell adjacent the oscillation mark was  easily deformed to produce the depression shape.  Surface cracks were also  commonly seen w i t h these depressions, as shown i n Figure 5.33. Longitudinal midface depressions were observed on billets from trials D I and D 2 , using both oil and powder lubrication.  O n the o i l cast billets  w i t h this defect, the surface was smoothly concave and the defect was difficult to see without viewing a cross-section. Figure 5.34 shows typical longitudinal midface depressions seen on powder cast, 0.14 pet. carbon billets from t r i a l D 2 . In contrast to the o i l cast longitudinal depressions, the powder cast depressions were very acute as if the shell buckled abruptly. Also apparent i n this photograph is that the depression wandered about the midface. Cracks sometimes accompanied these depressions, as is evident i n Figure 5.35. Thus the longitudinal depressions and cracks most certainly formed near the meniscus when the shell was thin. A s w i l l be discussed later, these defects were believed to be formed by an excessive taper (relative to cooling and shrinkage of the shell) near the meniscus, causing the shell to buckle. Figure 5.36 illustrates  125  Figure 5.34: Typical longitudinal midface depressions on powder cast billets. Trial D2, 0.14 pet. C, 203 mm mould.  126  Figure 5.35: Longitudinal midface depression with corresponding crack. Trial D2, 0.14 pet. C, 203 mm mould, powder lubrication.  surface  Figure 5.36: Photograph illustrating the depth of longitudinal midface depressions when powder casting. Trial D2, 0.14 pet. C, 203 mm mould.  127  Table 5.2: Depths of sample billet shape defects.  Depression T y p e longitudinal longitudinal transverse transverse transverse transverse transverse  Sample 1 2 1 2 3 4 5  Lubricant T y p e oil powder powder powder oil oil oil  D e p t h (mm) 3 7 3 2 5 4 4  the depth and severity of some of these longitudinal depressions. Contour plots of sample shape defects are presented i n A p p e n d i x F . T h e depths of these typical shape defects are summarized i n Table 5.2. These defects create serious barriers to heat transfer considering the fact that m o u l d tapers are designed to a fraction of a millimeter. T h e shell adjacent to a depression is therefore very thin, and leaves the shell susceptible to cracking and breaking out, as well as incurring non-uniform shell growth. In addition to the cracks often associated w i t h these defects, depressions can impact rolled product quality. Depressions which are acute, or contain a steep face, may fold during rolling operations and create a seam i n the product. B i l l e t conditioners must grind depression faces, as well as cracks, to ensure a smooth rolled product. T h e contour plots also indicate a clear geometric orientation of these defects. These depressions are clearly longitudinal or transverse, there are no diagonal or corner depressions. This may appear like an obvious statement,  128  but it implies that credible mechanisms for depression formation must include a geometric component.  129  Chapter 6  Force Response and Process Upsets  The use of a strain gauge force sensor has provided, for the first time, quantitative force measurements on an industrial billet machine. This has facilitated more detailed evaluations of mould friction. This chapter presents an analysis of mould-strand friction and investigates friction response as a function of process variables and upsets.  6.1  6.1.1  Mould-Strand Friction  Friction Response of O i l and Powder L u b r i c a t i o n  The decompression of load cell signals has been shown to occur during the negative strip period [11]. Following this concept further, Figure 6.1 illustrates that load cell and mould velocity signals were in phase when casting billets with oil lubrication. This indicates that mould-strand interaction is a function of mould velocity (recall that force and mould acceleration were in phase during the no-load case) and it dominates the inertial force during casting.  130  The  inertial force depends on stroke, oscillation frequency and m o u l d mass.  The  magnitude of the velocity-dependent force likely depends on process variables such as lubrication and m o u l d taper. Solid and liquid lubrication regimes have been used to describe mouldstrand friction [69]. L i q u i d friction, or hydrodynamic lubrication, is a function of relative velocity as governed by Newton's law of viscous flow [69, 101, 102], and was shown i n E q u a t i o n 2.3.  Equation 2.3 assumes a constant velocity  gradient through the lubricant film and uniform viscosity. Thus for a liquid friction mode, the m a x i m u m friction occurs at the point of m a x i m u m velocity. L i q u i d friction should favor a smooth sinusoidal force response, similar to the mould-strand relative velocity profile. Solid friction was described by the simple relationship of E q u a t i o n 2.4. Solid friction is also called boundary lubrication, which is a lubrication regime governed by the type of metal surfaces and lubricant present [102].  Solid  friction is not a function of relative velocity, or lubricant viscosity, but only depends on the direction of relative velocity: positive or negative. Solid friction is therefore characterized by a square wave force response, w i t h the duration of the square wave longer during positive strip than negative strip. T h e maxi m u m load plateau seen during oil casting (Figure 6.1) is indicative of solid lubrication. However, the smooth change i n force during negative strip, coincident w i t h m o u l d velocity, indicates at least some dependence on relative velocity. Further, the change of m i n i m u m load w i t h casting speed noted i n one study [11] also supports a lubrication condition dependent on velocity.  131  Figure 6.1: T y p i c a l m o u l d velocity and force signals when casting w i t h o i l lubrication. T r i a l D 3 , 0.70 pet. C , 171 m m mould.  132  Figure 6.2: T y p i c a l m o u l d velocity and force signals when casting w i t h m o u l d powder lubrication. T r i a l D 3 , 194 m m mould, 0.30 pet. C + B .  133  A typical force response using m o u l d flux is illustrated i n Figure 6.2. A s is evident, the force response was more sinusoidal and lacked the m a x i m u m load plateau seen when oil casting. T h e sinusoidal force response closely matches the m o u l d velocity profile, supporting a liquid friction mode. It is evident that oil and powder lubrication fundamentally differ. A s billet producers are implementing powder casting practice, a friction sensor would be helpful i n evaluating m o u l d oscillation and lubrication.  6.1.2  Quantifying Force Response  Force response can be evaluated by monitoring the force range ( m a x i m u m m i n i m u m ) or by the work done per cycle [68].  Work per Oscillation Cycle Calculating work expended during an oscillation cycle is determined by i n tegrating force over displacement for one cycle. For completeness, the work done during no-load operation can be subtracted to yield the work expended as m o u l d friction. Figures 6.3 and 6.4 show example force-displacement plots for oil and powder lubricants respectively, when casting boron(Ti)-alloyed steels during t r i a l D 2 . Figure 6.3 (oil cast) has a force range of 25000 N and work per cycle of 68 N m ; Figure 6.4 (powder cast) has a force range of 12000 N and work per cycle of 25 N m . T h e no-load work per cycle was less than 5 N m . T h e character of force signals varied greatly, but general differences existed between o i l and powder casting. Since oil is a less effective lubricant, o i l usually  134  0  1  2  3  4  5  Mould Displacement (mm)  Figure 6.3: Force vs. displacement example for o i l lubrication. 203 m m m o u l d , 0.3 pet. C + B .  Trial D2,  has a larger load range and work per cycle. Also, as the oil-cast force response tends to exhibit a square wave character, the oil-cast force-displacement plot has a larger area, or work done, for a given force range.  For the  diagrams  presented, the oil-cast plot has approximately 2 times the load range and 2.5 times the work per cycle.  135  25000  20000 h  g  15000 -  Q) O  o u.  1  2  3  4  Mould Displacement (mm)  Figure 6.4: Force vs. displacement example for powder lubrication. T r i a l 203 m m m o u l d , 0.3 pet. C + B .  136  5  Force Range Force range is a simpler way to track mould-strand friction on-line, although it is less rigorous than the work calculation. T h e raw force range includes machine forces as well as the mould-strand friction, thus the machine forces should be subtracted from the force range to yield a more accurate measure of mould-strand friction. T h e machine force consists of inertial loading from the mass of the m o u l d assembly, plus machine friction. T h e machine forces were estimated on Machines B and C , by running the machines at various oscillation frequencies under cold conditions.  Mould-strand friction was estimated by  measuring the casting force range, and subtracting the cold machine force at the corresponding oscillation frequency. T h i s calculation was assumed to be valid for the following reasons: • T h e casting force range was significantly less than the cold force range. T h e cold force range was typically 10 - 30 pet. of the casting force on Machine C . Thus small errors i n the cold machine force should not significantly impact the estimate of the mould-strand friction. • W h e n casting, force was i n phase w i t h velocity, indicating that the casting response was indeed governed by mould-strand interaction. • T h e inertial force could be theoretically calculated based on m o u l d acceleration. However, the acceleration signal was often very chaotic and it was simpler to combine and treat the inertial forces and machine friction together as a single machine force. 137  Oscillation Frequency (Hz)  Figure 6.5: Machine C oscillator force response under no-load condition. Trials D 2 and D 3 . Figure 6.5 illustrates the cold oscillator force response of Machine C as a function of oscillation frequency, using data from trials D 2 and D 3 . T h e data were arbitrarily fitted w i t h an exponential curve, to facilitate easy calculation of the machine forces. T h e cold force range was quite low, near 4000 N , at a typical oscillation frequency of 2 H z . A similar test was conducted on Machine B during plant trial A 2 . Figure 6.6 shows the cold machine forces using the strain gauge and piezoelectric strain sensors.  138  Since the piezoelectric sensor  Figure 6.6: Machine B oscillator force response under no-load condition usin strain gauge and piezoelectric strain sensors. T r i a l A 2 .  139  was less responsive to high frequency signal components, the force range was lower for cold and casting conditions, particularly at high frequencies.  The  cold response of machine B was more complex than M a c h i n e C , likely due to the more complicated mechanism of Machine B which contains springs. These data sets were curve fitted with a t h i r d order p o l y n o m i a l . T h e character of both strain signals were similar, again giving confidence i n the sensor response.  6.1.3  F r i c t i o n Coefficient C a l c u l a t i o n  A friction coefficient was calculated assuming the simple solid friction model of E q u a t i o n 2.4. F ud was assumed to be the casting force range ( F so  the cold machine force (F id) co  r a n g e  less  )  divided by 2, to account for friction upwards and  downwards during the oscillation cycle. T h e normal force, N, was assumed to be the average ferrostatic pressure i n the m o u l d m u l t i p l i e d by the mould-shell contact area as shown i n Equation 6.1.  N =  -^A  P  m  (6.1)  C o m b i n i n g Equations 2.4 and 6.1, the friction coefficient, c, can be calculated using E q u a t i o n 6.2.  Frange  F ld co  ^  ^  p gh A s  m  E q u a t i o n 6.2 leads to a conservative estimate of the friction coefficient because it assumes full mould-shell contact. T h e true normal force would likely  140  Table 6.1: E x a m p l e friction coefficient calculations. Heat 312 333  Lubricant powder oil  TP  Frequency •»(N) range (Hz) 11500 25000  1.80 1.67  Fcold Net Force (N)  (N)  3300 2900  8200 22100  Friction (c) 0.38 1.04  be less because of local shrinkage i n the corners and shell strength containing some of the ferrostatic pressure. Thus the true friction coefficient may be higher than calculated.  Table 6.1 illustrates two friction coefficient calcula-  tions using the force signals shown i n Figures 6.3 and 6.4. T h e machine force was derived from Figure 6.5. The calculation assumes a boundary lubrication mode, but hydrodynamic lubrication (dependent on relative velocity) is likely present during powder casting. The m a i n advantage of hydrodynamic lubrication is that it yields lower friction forces than boundary lubrication. Thus if liquid friction was present, the calculated friction coefficient would only be an "effective" solid coefficient and its value would be low. H i g h friction coefficients seen during powder lubrication might indicate that a solid friction mode was operating or sticking/binding was taking place. T h e calculated friction coefficients varied from 0.38 to 1.04, a significant range, but what friction coefficient value is to be expected? F r i c t i o n between clean metal surfaces is rarely seen i n practice due to contamination and the oxidation of metals [102]. Dry, contaminated metal surfaces typically have a friction coefficient between 0.1 and 0.3. Also, grease films are usually present  141  due to handling and forming of metals. T h i n grease films have a strong affinity for metal surfaces and usually cannot be removed completely even w i t h solvents [102]. For copper on steel i n a boundary lubrication condition, the friction coefficient is typically 0.09 to 0.28 [102]. Perfectly clean metal surfaces, rarely seen i n practice, can exhibit very high friction coefficients due to welding of the surfaces.  It is generally accepted that friction coefficients  greater than unity are not possible without adhesion. It has been reported that little lubricating o i l survives the m o u l d environment at the meniscus, particularly when the m o u l d is operating above the boiling temperature of the o i l [13]. Thus calculated friction coefficients near 0.3 or 0.5 seem reasonable.  H i g h friction coefficients (i.e. greater than  1) are believed to be caused by mould-billet binding or sticking. T h e concept of mould-billet binding has been postulated assuming that the m o u l d was too steeply tapered for billet shrinkage  [6]. However, this is the first work to  attempt to quantify binding or sticking using actual friction measurements. If the m o u l d is excessively tapered, it may squeeze the billet and cause an excessively high normal force, resulting i n a high friction coefficient. Mould-billet binding w i l l be discussed i n further i n Chapter 9.  6.1.4  Accelerometer and Force Signals  A s discussed i n Section 2.9.3, claims have been made that accelerometers can produce "friction" signals using suitable signal processing and/or  software.  A l t h o u g h the nature of these calculations has not been reported, they likely  142  E. CD  0.500  T — i — i — | — i — i — i — i — | — i — i — i — i — i — i — i — i — i — |I— i — i — i — i —I | — i — i — i — Ii — | — i — i — iI — i — | — i — i — i — i — | — i — i — i — r  0.400  data set 1 - low friction data set 2 - high friction  1  1  1  1  1  1  1  1  1  1  1  1  3  E  0.300  < c  «  0.200 h  0) +—'  <u E | 0.100 h o o  < 0.000  •  1  10  20  30  •  •'  '  40 50 Frequency (Hz)  '  '  1  • '  60  '  1  '  70  ' • i  ' I  80  90  Figure 6.7: F F T of accelerometer signals corresponding to high and low friction. T r i a l D 3 , 0.30 pet. C + B , oil lubrication, 171 m m m o u l d . originate from frequency measurements since accelerometers are often used for measuring vibration on machinery. W h e n casting 171 m m , oil-lubricated, boron(Ti)-alloyed billets during t r i a l D 3 , a force upset occurred during heat 046. T h e force range increased, between logged data sets, from 17000 to 40000 N . T h e friction coefficient, c, increased significantly from 0.6 to 1.7. Since the machine, steel chemistry and lubricant type had not changed, these data sets seemed appropriate to  143  Figure 6.8: F F T of accelerometer signals corresponding to high and low friction. T r i a l D 3 , 0.30 pet. C + B , oil lubrication, 171 m m mould.  144  investigate the accelerometer response.  Fast Fourier transforms (FFTs) of  the accelerometer signals corresponding to these friction measurements were calculated.  Figure 6.7 shows the amplitude response of the accelerometer  signals versus frequency. As is evident, little frequency information existed in the signals above 25 Hz. Figure 6.8 illustrates the same data as Figure 6.7 with a reduced frequency scale. The F F T plots clearly show the oscillation frequency near 2 Hz, plus higher order harmonics and machine vibrations. It is uncertain if anything regarding friction can be inferred from this information. It appears that the low friction data (set 1) may have slightly higher amplitude peaks from 8 - 13 Hz. Perhaps one would expect higher vibration in the higher friction case. Regardless, there is nothing apparent in this information that is as clear as the force range changing from 17000 to 40000 N . Other accelerometer data sets were investigated, and similarly an obvious correlation was not seen. This is not to imply that the accelerometer claims in the literature are false. The reports of the M L Tektor system seem promising, but that research was conducted on slab casting machines. Since acceleration is a strictly a function of mould movement, any accelerometer based system must be highly dependent on machine response. The objective of this work was to measure friction quantitatively, and strain gauge force sensing has provided this. The accelerometer signal is an implicit measure of friction at best, thus these signals were not investigated further given the success of strain gauge force sensing.  145  6.2  Transverse Depressions  Several mechanisms for the formation of transverse depressions have been published, as discussed i n Section 2.8.7. T h e formation of transverse depressions was investigated using simultaneous load cell, metal level and m o u l d temperature data from trial D I . The midface array of thermocouples on the east face was used for the detection of transverse depressions. T h e sequence inventor ( S E Q I V ) animation tool, developed by John Hogg at U B C [103], was used to view the temperature data i n space-time-temperature.  S E Q I V is a powerful  tool that allows the user to view a depression clearly on an animated surface. It also serves as a filter for "false" depressions which appear as a temperature drop i n meniscus thermocouple signals caused by metal level  fluctuations.  Once a clear, large depression was detected w i t h S E Q I V , pertinent load cell, thermocouple and metal level data were investigated. Figure 6.9 shows an image of stable m o u l d temperature response, i.e. the m o u l d temperature profile was not changing i n time. T h e vertical lines i n the image represent thermocouple locations i n the mould. Figure 6.10 illustrates a transverse depression as a diagonal feature i n the  temperature-space-time  surface. T h e depression clearly formed at the meniscus, then propagated down the m o u l d as a local decrease i n temperature.  Figure 6.11 is an image that  presents two effects: multiple transverse depressions were evident and a rough meniscus was indicated by unstable temperatures i n the meniscus region. Candidate depressions were evaluated i n 3 heats of 0.32 pet. carbon and  146  1-17  Figure 6.10: Mould temperature response showing the formation of a transverse depression at the meniscus and its propagation down the mould. Trial D I , 0.32 pet. C , 203 mm mould, oil lubrication.  148  Figure 6.11: Mould temperature response illustrating a rough metal level and transverse depressions. Trial D I , 0.32 pet. C + B , 203 mm mould, oil lubrication.  149  Figure 6.12: Force sensor and mould temperature response during the formation of transverse depressions. T r i a l D I , 0.32 pet. C , 203 m m m o u l d , o i l lubrication.  150  10000  -i  1  200  r-  9000 8000 7000  150  O  CD  O •a cc o  6000 5000 4000 load max load range thermocouple 1 thermocouple 2  3000 2000  20  40  100  60  Time (s)  Figure 6.13: Force sensor and mould temperature response during the formation of transverse depressions. Trial D I , 0.32 pet. C + B , 203 m m m o u l d , o i l lubrication.  151  0.32 pet. carbon, boron(Ti)-alloyed grades. Figure 6.10 is an excellent example of depression formation. T h e m o u l d temperature response was relatively smooth and the large temperature drop, 50°C, indicated a large depression. Figure 6.12 shows the force sensor response ( m a x i m u m load and load range) and m o u l d temperature of 2 thermocouples near the meniscus during the time period of the S E Q I V image i n Figure 6.10.  Transverse depressions can be  seen at 220 and 240 seconds. A s is evident i n Figure 6.12, there is no clear change i n force response during the formation of these depressions. Figure 6.13 illustrates sensor data under more "chaotic" operating conditions, when the metal level was very rough and many transverse depressions were forming. T h e load range varied significantly, perhaps due i n part to variable lubrication, but again there was no correlation to individual depression events. A n unexpected result of using the S E Q I V tool was the visualization of near meniscus temperature data indicating the metal level stability. Figure 6.9 illustrates a smooth metal level. A rough metal level caused by an off-centre or ropey stream is indicated by a "wavy" surface at the meniscus, apparent i n Figure 6.11. T h e average and standard deviation of the meniscus thermocouple temperature is presented i n Table 6.2 for several oil-cast heats. A smooth metal level (Figure 6.9) w i l l exhibit a standard deviation of the meniscus thermocouple temperature of less than 3 ° C . A rough meniscus (Figure 6.11) w i l l have a standard deviation near 8°C. Thus the metal level stability can be i m plied by the standard deviation of meniscus thermocouple temperature. T h i s simple logic could be easily implemented i n an on-line system and presented  152  Table 6.2: Inferring stream quality and metal level stability from thermocouple data.  Heat  Grade  142 146 147 148.1 148.2 149  0.12 0.32 0.32 0.32 0.32 0.84  pet. pet. pet. pet. pet. pet.  C C C+B C+B C+B C  SEQIV surface smooth very smooth rough rough very rough very smooth  Meniscus Thermocouple (°C) 123 190 169 165 169 193  Standard Deviation (°C) 2.47 2.68 7.15 6.85 8.22 2.96  as a measure of process control quality. It is evident from these examples that the formation of transverse depressions cannot be seen uniquely in force signals. Force sensing may not clearly detect local mould-strand interaction events, particularly when the shell is thin. This is supported by the weak correlation of force sensing with sticker breakouts in slab casting [78]. Metal level variation prior to a depression forming has been noted in the literature [14, 15] and observations in this work has confirmed this. Using the SEQIV tool, a short term metal level rise was seen as an increase in temperature just above the meniscus prior to the formation of many depressions. The rough metal level inferred by the meniscus thermocouple has two main implications. Firstly, more transverse depressions were seen in the presence of the turbulent meniscus, supporting the influence of metal level on depression formation. Secondly, the metal level was more unstable when casting the boron(Ti)-alloyed grades. This was believed to be 153  caused by the steelmaking practice of these grades. T h e boron(Ti) steels were aluminum-killed to achieve very low oxygen levels, which is required to successfully alloy steel w i t h boron(Ti). T h e formation of AI2O3 i n aluminum-killed steels is problematic for continuous casting operations, since AI2O3 plugs metering nozzles [104, 105]. Thus the AI2O3 blockages were believed to contribute to poor stream quality and a rough meniscus. Boron(Ti)-alloyed steels have been reported to be prone to forming depressions because of possible increased strength near the solidus temperature [14]. T h e strength of as-cast samples from trial D I were evaluated on a Gleeble thermomechanical testing machine.  Samples w i t h 0.32 pet. carbon and  0.32 pet. carbon boron(Ti)-alloyed were tested at a strain rate of 1 0  - 2  s  _ 1  1200 and 1300° C [106]. A p p e n d i x G contains the stress-strain curves.  at  The  boron(Ti) steels exhibited a significantly higher flow stress, supporting the theory of Samarasekera et al. [14]. Further metallurgical research must be conducted to ensure that the testing is conducted as close to in-situ conditions as possible. A summary of the knowledge of transverse depression formation is listed below.  1. T h e formation of a transverse depression is often preceded by a metal level rise. 2. Transverse depression formation cannot be seen w i t h a force sensor. 3. Transverse depressions have not been seen to form lower i n the m o u l d 154  i n the m o u l d temperature response. Thus their complete formation by binding is unlikely. However, axial friction forces can crack the t h i n shell of a depression at the solidification front. 4. Transverse depressions exhibit a clear geometry across the billet face. A mechanism such as "local overcooling" is incomplete since it does not include an explanation of the geometry. 5. Depressions i n oil-cast billets are likely caused by thermal distortion [60], or interaction w i t h the lubrication oil [14] during a metal level rise. 6. Depressions i n powder-cast billets may be caused by thermal distortion [60] or consumption of the slag r i m during a metal level rise [15]. T h e author postulates that the shell may buckle at the meniscus due to friction or interaction w i t h the slag r i m . 7. It is unlikely that a "unified" theory of depression formation exists; more than one type of upset may form transverse depressions.  6.3  Force Response and Steel Grade  A l t h o u g h the friction response may be impacted by process upsets, force was generally noted to vary between steel grades. Table 6.3 presents force range values for various steel grades cast w i t h o i l lubrication during t r i a l D I . E a c h value represents an average force range taken from a 300 second data set; thus the force values represent average friction, and not instantaneous values. T h e  155  Table 6.3: Summary of load cell friction measurements from trial D I . O i l lubrication, constant oscillation frequency. Heat  Grade  142.1 142.2 146.1 146.2 147.1 147.2 148.1 148.2 149.1 149.2  0.12 0.12 0.32 0.32 0.32 0.32 0.32 0.32 0.83 0.83  pet. pet. pet. pet. pet. pet. pet. pet. pet. pet.  C C C C C C C C C C  + + + +  B B B B  Mould (mm) 203 203 203 203 203 203 203 203 203 203  Force Range (N) 3200 3300 4200 . 3900 5400 5600 3700 6100 4700 4600  peritectic grades exhibited the lowest forces, followed by the hyper-peritectic steels, and finally the boron(Ti)-alloyed steels showed the highest forces. The oscillation frequency was constant (1.9 Hz) during this trial, so the machine forces should have been constant.  The lower forces measured when casting  peritectic steel is consistent with the results of Singh and Blazek [23], who measured withdrawal forces on a bench-scale caster. The results are not consistent with the research of van der Stel et al. [49], where a "friction index" was measured with an accelerometer based system. In the case of van der Stel et al, the peritectic steels showed the highest accelerometer "friction index". Similar results were obtained with quantitative force measurements at trial D2. Table 6.4 presents friction measurements for the oil-cast heats. The peritectic grades exhibited an average friction coefficient of 0.53 and the hyper-  156  Table 6.4: Summary of oil-cast friction measurements from t r i a l D 2 . Heat  Grade  298.1 298.2 299.1 299.2 300.1 300.2 333.1 333.2 333.3 334.1 334.2 334.3 351.1 351.2 352.1 352.2 353  0.13 pet. 0.13 pet. 0.12 pet. 0.12 pet. 0.13 pet. 0.13 pet. 0.32 pet. 0.32 pet. 0.32'pct. 0.32 pet. 0.32 pet. 0.32 pet. 0.80 pet. 0.80 pet. 0.81 pet. 0.81 pet. 0.80 pet.  C C C C C  c  C+B C+B C+B C+B C+B C+B C  c c c c  Mould (mm)  Raw Force (N)  203 203 203 203 203 203 203 203 203 203 203 203 203 203 203 203 203  12700 14600 14200 13200 14200 16700 12800 12200 23700 27400 24200 18800 15000 18600 16500 17200 16200  Frequency  Friction  (Hz) 1.60 1.80 1.67 1.75 1.43 1.75 1.49 1.50 1.67 1.60 1.56 1.46 1.63 1.60 1.67 1.70 1.54  0.47 0.53 0.53 0.47 0.55 0.63 0.48 0.46 1.00 1.15 1.00 0.77 0.57 0.74 0.63 0.66 0.63  (c)  Table 6.5: Summary of powder-cast friction measurements from t r i a l D 2 . Heat  Grade  265 266 277.1 277.2 278.1 278.2 310 311 312  0.13 0.13 0.14 0.14 0.13 0.13 0.30 0.33 0.30  c c c c c c  pet. pet. pet. pet. pet. pet. pet. C + B pet. C + B pet. C + B  Mould (mm)  Raw Force (N)  Frequency (Hz)  203 203 203 203 203 203 203 203 203  14000 13000 14500 15700 13700 16000 12500 11000 11000  2.27 2.05 2.50 2.50 2.27 2.50 2.00 1.80 1.80  157  Friction (c) 0.41 0.41 0.37 0.43 0.40 0.44 0.40 0.36 0.36  peritectic grades showed a slightly higher friction coefficient of 0.65. A g a i n , the boron(Ti)-alloyed steels exhibited a higher and more varied force response, w i t h an average friction coefficient of 0.81. Heats cast w i t h m o u l d fluxes exhibited a significantly different friction response than the oil-cast heats. Table 6.5 presents the friction response of powder-cast heats from t r i a l D 2 . T h e friction response of powder lubrication can vary significantly depending on powder properties and m o u l d oscillation, but the friction was generally less than that of oil lubrication. Also, the average friction coefficient when powder casting was likely independent of steel grade. T h e average friction coefficient when powder casting was 0.40. T h i s was less than the friction measured when oil casting peritectic steels (c = 0.53) and significantly less than the corresponding oil-cast boron(Ti) steels (c = 0.81). It appears that casting w i t h m o u l d fluxes has a very forgiving effect on the boron(Ti) grades. Table 6.6 details force measurements from trial D 3 . N o peritectic steels were cast during this trial, but once again the oil-cast boron(Ti) grades exhibited high and varied forces. T h e powder-cast grades exhibited higher friction than t r i a l D 2 . T h i s was likely caused by the use of the different m o u l d , and higher casting speeds.  6.4  Friction and Process Control  A s discussed previously, lack of flow rate control i n billet casting leads to casting speed variations. A s the casting speed changes, the m o u l d taper may be '158  Table 6.6: Summary of friction measurements from trial D 3 . Heat  Grade  036 038 039 041 046.1 046.2 046.3 046.4 056 058 073 089 090  0.25 0.45 0.70 0.70 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30  pet. pet. pet. pet. pet. pet. pet. pet. pet. pet. pet. pet. pet.  C C  c c  C+B C+B C+B C+B C+B C+B C+B C+B C+B  Mould (mm)  Lubricant  Force Range(N)  171 171 171 171 171 171 171 171 194 194 194 194 194  oil oil oil oil oil oil oil oil powder powder powder powder powder  14500 16200 18800 18000 17000 40000 27000 40000 21900 22900 19300 16800 18700  159  Frequency  Friction  (Hz) 2.31 2.31 2.27 2.31 2.11 1.90 1.90 1.90 2.31 2.34 2.34 2.34 2.34  (c) 0.43 0.51 0.64 0.59 0.59 1.70 1.15 1.70 0.59 0.71 0.58 0.47 0.55  0  500  1000  1500  2000  2500  Time (s)  Figure 6.14: Mould-strand friction change as a function of casting speed. T r i a l D 3 , 0.30 pet. C + B , 194 m m mould, powder lubrication. inappropriate for the casting conditions, causing binding or excessive gap formation. L u b r i c a t i o n effectiveness also changes w i t h casting speed, particularly w i t h m o u l d fluxes. Trending the force range over long time periods has shown a clear dependency of force on casting speed. Figure 6.14 shows force range and casting speed signals when casting a boron(Ti) grade w i t h m o u l d flux i n a 194 m m mould. For the first 500 seconds, the casting speed was 18.5 m m s  160  _ 1  due to  Table 6.7: Friction and casting speed response for four powder-cast heats of 0.32 pet. C + B . T r i a l D 2 , 203 m m m o u l d . Heat 310 311 312 313.1 313.2 313.3  Force Range (N) 12500 11000 11000 24000 24500 26000  Friction  (c) 0.40 0.36 0.36 1.05 1.05 1.15  Casting Speed (mm s ) 18.4 19.1 18.0 12.5 14.3 13.8 _ 1  a slightly plugged metering nozzle. W h e n the nozzle cleared and speed i n creased, the friction decreased. T h e metal level was stable during this period. T h e m i n i m u m recommended casting speed for this m o u l d was 21 m m s ; at _ 1  this speed, the force range was at its m i n i m u m . A t 500 seconds (Figure 6.14), the effective friction coefficient was 1.2.  W h e n the casting speed increased  from 18.5 to 21 m m s , the friction coefficient dropped to 0.6. It is evident _ 1  that a force sensor is a useful tool for developing process control guidelines for specific m o u l d tapers, grades and lubricants. Table 6.7 shows the force sensor response for four powder-cast heats when casting a 0.32 pet. carbon, boron(Ti)-alloyed steel. T h e friction increased significantly i n heat 313, and the friction coefficient suggests that binding was occurring. Table 6.7 also indicates that the casting speed.had dropped markedly during heat 313. T h e possibility of binding w i t h decreasing casting speed has been reported [5]. A further complication arises when casting w i t h m o u l d powder lubrication; m o u l d powder consumption and friction change 161  w i t h varying oscillation parameters and casting speed. T h i s w i l l be discussed in detail i n Chapter 9. Friction upsets also occur when casting w i t h o i l lubrication, but a correlation w i t h casting speed was not established. Trending of the sensor signals showed no clear relationship between force and casting speed. In oil casting, the varying friction was believed to be caused by a combination of binding and lubrication effectiveness. T h i s w i l l be discussed i n later sections.  6.5 6.5.1  Force Upsets Friction and Mould Stroke  T h e oscillator stroke varied w i t h m o u l d friction, as shown i n Figure 6.15, where these signals were trended for 3000 seconds. T h e correlation was particularly clear at 600 seconds, when the force range dropped from 35000 to 17000 N and the stroke increased from 4.05 to 4.4 m m . T h e difference i n stroke was likely caused by elastic deformation of machine components under load. T h e design stroke for this machine was 6 m m , and the machine oscillated at an average stroke of 4.3 m m . T h e m o u l d lead was approximately 0.7 m m , much less than the recommended value of 3 - 4 m m [3].  6.5.2  Nozzle Plugging  D u r i n g t r i a l A 2 , the metering nozzle began to severely plug when open stream pouring. Figure 6.16 shows the friction and casting speed signals during this  162  4.5  35000  4.4  H4.3  H 4.2  4.1  4.0  15000 500  1500  1000  2000  2500  3000  Time (s)  Figure 6.15: Oscillator stroke varying as a function of mould-strand friction. Trial D3.  163  -1  1  -i  l  1  1  1  r-  -i  1  l  r-  80  1.4 h 1.2  speed friction 60  c  1.0 h  CD H—  CD O  o  c o  600  700  650  750  0 800  Time (s)  Figure 6.16: Friction response during a nozzle plugging upset. 0.90 pet. C , 152 m m mould, o i l lubrication. event.  Trial A 2 ,  W h e n the casting operator was clearing the nozzle w i t h an oxygen  lance, the strand was stopped and restarted, causing high forces.  After the  upset, the friction returned to normal levels quickly. The surface quality of the billet section i n the mould during the upset would likely be poor, w i t h possibly cracks caused by the high forces. upset should have been discarded.  164  T h e billet corresponding to this  6.5.3  Breakout  T w o breakouts were logged during plant trials at Company A . Figure 6.17 illustrates the friction and casting speed response during a breakout when casting through a 152 m m m o u l d using oil lubrication. There was no "breakout warning" issued by the force signal. W h e n the breakout occurred, however, the m o u l d was exposed to high forces as the liquid steel flowed through the m o u l d uncontrolled, likely sticking to the m o u l d wall. T h e stream quality was very poor during this heat, causing a rough meniscus. Globules of steel were forming constantly on the nozzle exit, possibly as a result of poor steelmaking. A breakout also occurred when casting through a 203 m m m o u l d using powder lubrication. A g a i n , no change i n the friction signal preceded the breakout.  6.5.4  S t i c k i n g and J e r k i n g Figure 6.18 illustrates the strain gauge response during a period of ob-  served meniscus sticking when casting w i t h oil lubrication. Meniscus sticking is characterized by the steel welding to the m o u l d wall due to a combination of poor lubrication and a fluctuating metal level. T h e "sticks" are subsequently stripped off by m o u l d oscillation. Despite the sticking and changing casting speed, the force response (c = 0.3) lacked any correlation to these events. It appears than meniscus sticking could not be seen w i t h force sensors. However, the poor lubrication which contributed to the sticking may have resulted i n increased friction. 165  2.0  O.o  L  400  i  i  i  I  420  i  i  i  i  I  i  i  i  i  440  I  i  460  i  i  i  I  480  i  i  "l ~  r l - l -  500  t  - r  -  -rA 520  Time (s)  Figure 6.17: Friction response during a strand breakout. T r i a l A 2 , 0.90 pet. C , 152 m m mould, o i l lubrication.  166  14  Time (s)  Figure 6.18: Force sensor response during a period of meniscus sticking. Trial A l , 0.71 pet. C, 203 mm mould, oil lubrication.  167  Figure 6.19: Force sensor response during a period of strand jerking. T r i a l A l 0.90 pet. C , 203 m m mould, oil lubrication.  168  Figure 6.19 shows the strain gauge response when strand jerking was occurring. A fluctuating force range was evident; the friction coefficient varied between 0.2 and 0.5. It is unknown i f the jerking was caused by binding or poor lubrication, but one would not expect excessive binding w i t h the 0.8 pet. m  _ 1  tapered m o u l d used during trial A l . Strand jerking was observed i n the spray chamber below the mould and the jerking produced a squeak/groan noise, which likely indicated poor lubrication.  169  Chapter 7 Mathematical Modelling of Thermomechanical Mould Behaviour  T h i s chapter discusses existing mathematical models which were used to calculate the mould temperature distribution and mould distortion. Results of these models were used to interpret mould-billet binding, and w i l l be presented i n Chapter 9.  7.1  M a t h e m a t i c a l M o d e l l i n g of M o u l d H e a t Transfer  T h e m o u l d heat transfer model was used for two reasons. F i r s t , to calculate a temperature field i n the mould so mould distortion could be calculated by a stress model. Second, to calculate an axial heat flux profile to apply to a billet solidification model. T h e heat transfer model calculates the mould temperature distribution through a longitudinal, midface section of the m o u l d . Details of the model have been published i n several sources [8, 34, 107, 17]; an overview of the model  170  x«0  x«X„  backing piata mould jackot  cooling watar  Figure 7.1: Schematic of longitudinal mould heat transfer model.  171  w i l l be presented here for completeness. Figure 7.1 illustrates the m o u l d model geometry. T h e model simply takes an input heat flux profile, and calculates the m o u l d temperature distribution based on cooling water parameters. T h e input heat flux profile was modified until the calculated temperature profile matched (within 1°C) the temperature profile measured i n the subject plant trial. T h e following assumptions were made i n the model formulation [34]. • Heat transfer i n the transverse direction was negligible, from symmetry. • Heat transfer to the water baffle was negligible. • T h e cooling water between the the mould and water baffle was i n plug flow. • T h e r m a l properties of the mould were independent of temperature. • Top and b o t t o m surfaces of the mould were adiabatic. • Transient variations of heat flux caused by m o u l d oscillation and metal level fluctuations were neglected. Heat transfer i n the m o u l d is governed by the two-dimensional transient heat conduction equation:  (7.1) A steady-state model was originally employed [34]; the transient model was later developed to investigate thermal cycling caused by various boiling regimes [107]. T h e following m o u l d boundary conditions were assumed. 172  1. Top and b o t t o m mould wall boundaries were assumed to be adiabatic. 0 < x < X, m  z — 0 and z = Z ,  t > 0  m  dT ~ mg; = 0  (7.2)  k  2. M o u l d cold face x = 0, 0 < z < Z ,  t > 0  m  dT  -k ^ m  = h {z, t)[T(0, z, t) - T (z, t)] w  w  (7.3)  3. M o u l d hot face below meniscus x = X,  Zp < z < Zm, t > 0  m  -k —  dT  = q (z)  m  (7.4)  s  4. M o u l d hot face above meniscus x = X,  0 < z < Z , t > 0  M  F  -k ^ m  = K(z, t)[T(X , M  z, t) - T ] a  (7.5)  The i n i t i a l temperature of the mould was assumed to be constant. 0 < x < X, M  0 < Z < Z  M  ,  t = 0  T = T  0  (7.6)  The inlet temperature of the mould water was assumed to be constant. z = Zm, t > 0  T = Ti w  173  (7.7)  Figure 7.2: E x a m p l e forced convection boiling curves for subcooled water. Heat transfer between the mould and cooling water (Equation 7.3) was defined i n three heat transfer regimes: forced convection, transition boiling, and film boiling [81]. The following relationship defines the forced convection heat transfer coefficient,  hj . c  = 0.023\ ' ~ rj J  k,  Pi  I ^ P I  r  JI  J  L  f  k  (7.8)  J  T h e fluid properties correspond to the bulk temperature of the fluid. T h e heat flux by forced convection, qj , was calculated by the heat transfer coefficient c  relationship, qj = hf (T — T ). c  c  w  Equation 7.8 is valid as long as the cold face  of the m o u l d is less than approximately 160° C [34]. This is a valid assumption i n most cases. However, under conditions of pool boiling, the heat flux was  174  obtained from the following empirical relation [34].  C l{T p  — T t) sa  H fg  = a  r  a  <n>  0.5  0.33 L  - pv)  1  (7.9)  h J  A transition region exists between the commencement of boiling and when fully developed pool boiling exists, i.e. when Equation 7.9 is valid. The following relationship was used to calculate the transition boiling heat flux, q , as a tr  function of equations 7.8 and 7.9 [34].  |  [1+-^  Qin' 2- 0.5  (7.10)  The heat flux at the point of incipient boiling is given by the following relationship.  q  in  = 5.281 • 1 0 " V  [1-8(T - T  s o t  (7.1i;  )]™^  Figure 7.2 shows example heat flux values for forced convection boiling developed from the preceding equations [107]. Heat transfer in the cooling water channel was governed by the following relationship, assuming that the water was in plug flow.  Pw Vyj dyj C'pw t  on  -h {z,t)[T(0,z,t)-T {z,t)] w  w  = 0  (7.12)  Equations 7.1 and 7.12 were solved in the finite difference model to obtain the mould and cooling water temperature distributions.  175  Cb)  Figure 7.3: Mesh geometry used to model m o u l d distortion. 7.2  Mould Distortion  M o u l d distortion has been quantified by Samarasekera and B r i m a c o m b e using a three-dimensional elastic-plastic finite element model [8, 17, 107]. T h e model employed a one-eighth billet mould geometry, shown i n Figure 7.3, because of the symmetry of the square mould tube. The temperature distribution of the m o u l d tube from the heat transfer model was used as input to the stress model to calculation the m o u l d distortion.  176  M o u l d distortion depends on the mould geometry, the thermal field of the m o u l d , and the physical mould constraints.  The following boundary  conditions, referring to Figure 7.3, were assumed for the stress model. 1. M o u l d displacement orthogonal to the midface plane of symmetry A B C D , v, was zero. 2. M o u l d displacement orthogonal to the corner diagonal plane of symmetry E F G H was zero. This implies that displacements u and v are equal along this plane. 3. The m o u l d constraint near the top of the mould tube was simulated by fixing displacement u to zero along the plane K L M N . 4. T h e w displacements along the line M N were set to zero to fix the m o u l d in the z direction. A l t h o u g h the model included plasticity, only a small region of the m o u l d near the meniscus was found to exceed the yield stress of the m o u l d material [17].  T h i s finding certainly explains how permanent m o u l d distortion can  occur, but for the purposes of this work a three-dimensional elastic model is sufficient to compute mould distortion.  177  Chapter 8 Mathematical Modelling of Billet Shrinkage  T h i s chapter discusses the mathematical modelling of billet shrinkage using finite-element methods. Results were used i n conjunction w i t h m o u l d distortion calculations to interpret mould-billet binding, which w i l l be discussed i n Chapter 9. Modelling of billet shrinkage is a classic thermal-stress problem. A heat transfer model was used to calculate the temperature field i n the billet using the heat flux calculated from m o u l d temperature measurements.  Billet  shrinkage was then calculated by a stress model using the billet temperature field.  8.1  A B A Q U S Finite-Element Modelling Software  T h e finite-element modelling was conducted using A B A Q U S commercial software [108]. A B A Q U S is a general purpose finite-element package well suited for non-linear stress and heat transfer modelling discussed i n this work. T h e finite-element  mesh (i.e. node locations and element connectivity) was defined  178  using Patran3, a "tool-kit" for building finite-element geometries. T h e A B A Q U S program was run on a Silicon Graphics workstation network because of its computational efficiency and graphical capabilities. T h e program is set-up by creating an input file containing the finite-element geometry, material properties and a time history of boundary conditions. C o m p l e x material properties, such as creep, or boundary conditions, such as heat flux, may be defined i n user-written subroutines as a function of model state. T h e finite-element equations for heat transfer and stress-displacement elements are well established and are available i n many sources, e.g. [109, 86]. T h e equations w i l l not be presented here because they were not an original part of this research, i n custom program code or otherwise. T h e finite-element mesh, material properties and boundary conditions w i l l be described to quantify the problem and the model.  8.2  Model Geometry  A two-dimensional transverse geometry was adopted for this model. T h e approach of following a transverse "slice" of the billet through the m o u l d has been used i n past heat transfer models [21]. T h i s is a reasonable assumption since the axial bulk heat flow by convection is significantly greater than the axial heat flow by conduction [7]. Further, convection i n the liquid pool can be neglected based on the work of Szekely [110]. A l t h o u g h the rate of superheat extraction is significantly affected by liquid flow, the solidus isotherm is relatively insensitive to flow i n the liquid phase because of the large latent heat 179  y 4  YB  Isotherm (heat transfer model)  Corner of billet  Billet mesh  V  Billet surface  XB  x  Centre of billet face  Figure 8.1: M e s h geometry used i n the one-eighth section, shrinkage model.  thermal-stress  evolution. A one-eighth transverse section model was employed because of the symmetry of the geometry, to reduce computational time. Figure 8.1 illustrates the geometry used i n the model. T h e mesh was terminated 20 m m from the billet surface. Since the interior mesh would be above the liquidus temperature at the b o t t o m of the m o u l d , it was neglected for computational efficiency. T h e mesh density included 100 elements across billet half-face, and 20 elements from the billet surface to the mesh termination 20 m m from billet surface. The node spacing was finer near the billet surface, becoming coarser toward the centre of the billet. T h e typical surface element was 1 m m wide (across the face) by 0.3 m m thick. Linear (first order) elements were employed because of the significant  180  non-linearity associated w i t h latent heat i n the heat transfer model. Linear elements are reported to be superior than higher ordered elements i n highly non-linear problems [108].  8.3  Heat Transfer Model  T h e following assumptions were made i n the formulation of the heat transfer model.  1. T h e midface symmetry line was adiabatic. x = 0, 0 < y <Y , b  t>0  dT - k ,  T  x  = ,  .  •  (8.1)  2. T h e corner diagonal line of symmetry was adiabatic. {X  b  -Y )<x<X , b  y = -x  b  + X,  t>0  dT-  dT^  b  3. T h e 20 m m boundary from surface was treated as a liquid isotherm. T h e temperature was chosen to be the liquidus temperature plus a 25° C effective superheat. 0 < x < (X  b  - y ), y = 6  Y ,t>0 b  T =T  sh  (8.3)  4. T h e heat flux obtained from the m o u l d heat transfer model was applied to the billet surface. 181  0<x<X ,y b  =  0,t>0  -k —  =  a  (8.4)  h (t)[T(x,0,t)-T ] b  w  The reduced heat transfer near the corner of the billet (caused by twodimensional cooling and shrinkage) was accounted for using a constant heat transfer coefficient, h , across the billet face [81]. T h e heat transfer b  model was run twice to obtain the final temperature field i n the billet. T h e first model run applied the heat flux, q (t), to the surface to obtain s  the midface temperature, T ( 0 , 0 , t ) , which was used to calculate the effective heat transfer coefficient, hb(t), as a function of time. The second model run applied the heat transfer coefficient, as shown i n E q u a t i o n 8.4. Midface temperature profiles were verified between the runs. This approach only impacted the billet temperature field near the corner, as the billet isotherms paralleled the face for most of the billet w i d t h , as illustrated i n Figure 8.2. 5. The i n i t i a l billet temperature included a 25°C effective superheat. t = 0  T h e r m a l conductivity, specific heat, solidus and liquidus temperatures were available i n the literature as a function of carbon content and temperature [111, 62].  T h e latent heat of solidification (272 k J k g ) was included as - 1  specific heat i n the A B A Q U S input file. The conductivity of the l i q u i d steel  182  NTH  VALUE  2 3 '  1  TIME COMPLETED IN THIS STEP ABAQUS VERSION: S.5-1  1.00  TOTAL ACCUMULATED TIME  DATE: 19-APR-96  19.0  TIME: 18:19:32  STEP 3 6 INCREMENT 1  Figure 8.2: Billet isotherms using constant heat transfer coefficient across the billet face. Cooling time 19 seconds, temperature in degrees K .  183  was doubled to simulate convection i n the liquid pool [111]. Tables 8.1 to 8.3 contain the thermal properties used i n the models.  184  Table 8.1: T h e r m a l properties for 0.14 pet. carbon steel. Temperature (K) 1173 1723 1762 1769 1788 1799  Specific heat (J k g " K " ) 1  Temperature  1  (K) 973 1373 1762 1799 1813  620 700 900 10365 10368 750  Conductivity (W m - K - ) 1  1  30 25 33 27 50  Table 8.2: T h e r m a l properties for 0.32 pet. carbon steel. Temperature (K) 1273 1741 1754 1771 1786  Temperature  Specific heat (J k g " K - ) 620 772 9421 9435 750 1  1  (K) 1073 1373 1741 1786 1813  Conductivity (W m - K " ) 1  1  30 25 33 27 50  Table 8.3: T h e r m a l properties for 0.80 pet. carbon steel. Temperature (K) 1040 1647 1657 1745 1752 1873  Specific heat (J k g " K " ) 1  Temperature  1  (K) 973 1373 1662 1752 1813  608 685 3500 3500 670 750  185  Conductivity (W m " K - ) 30 25 33 27 50 1  1  8.4  Stress M o d e l  T h e stress model employed the same mesh geometry as the heat transfer model to facilitate the implementation of temperature i n the stress model. T h e following assumptions were made i n the formulation of the stress model.  1. T h e m o u l d was treated as a rigid surface 1 pm from the billet surface. Contact interface elements were defined between the m o u l d rigid surface 1  and the billet surface nodes, as illustrated i n Figure 8.3. This feature was required because the shell would bend past the m o u l d wall at the midface during i n i t i a l solidification.  In reality, the shell would be ex-  tremely fragile at this stage, and the reaction forces on the m o u l d wall would be very small. T h e geometry of the process must be preserved however, otherwise the billet would retain its falsely distorted shape as the shell cooled and became stronger.  2. Plane strain elements were employed [112, 35, 36]. 3. Transverse displacement (u), or rotation (</>), about the midface line of 2  symmetry was zero. 4. Displacement normal to the corner diagonal line of symmetry , or rotation (<f> ) was zero. A l o n g this line, the displacements u and v were equal z  and of opposite direction. A contact element is not a conventional element type like a stress-displacement element, it is simply a notation used by A B A Q U S to restrict nodal displacement. 1  186  y. v iiiiiiiiHHm\m\H\\\\\\\\\\\\\\\\\\\\\\\\\^ HllllllllllllltlllHUH\m\\\\\\\\\\\\\\\\\\\\\\V\^^^ •••••iiiiiiiiittiiii\Hiumum\\\\i\\\\\\\\\w^ llllllllllllllllliliiiimi\uu\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\w  IIIIIIIIIIIIII1I1IH111U1UUHUU%\U\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\V^^ iiiiiiiiiiiiiiiiiiiiiniiiMiiHi\\i\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\^^  x, u  Mould (rigid surface)  Interface element  Figure 8.3: M e s h geometry used i n billet shrinkage stress model. 5. Ferrostatic pressure was not included since the objective of this model was to calculate natural shrinkage of the shell.  187  Elastic and viscoplastic equations were obtained from an excellent summary of constitutive relationships applicable to continuous casting [113]. T h e following temperature dependent elastic modulus was employed [113].  E = 968 — 2.33(T - 273) + 1.90 • 1 0 ( T - 273) - 5.18 • 1 0 ~ ( T - 273) - 3  2  7  3  (8.6)  Plasticity was input through the A B A Q U S creep subroutine. The viscoplastic relation used was a power law of the following form [113].  e = C exp(=f-)a  (8.7)  n  p  C = 24233 + 49973(pct. C) + 48757(pct. Cf  MPa"  7 1  s"  1  Q = 49480 K n = 5.331 + 4.116 • 1 0 - T - 2.116 • 1 0 - T 3  6  2  T h e r m a l shrinkage, as a function of temperature and carbon content, was obtained from Chandra [81]. The lattice parameter for delta phase steel was calculated using the following equation.  aL = aJ  +SAO-10- X 3  c=0  C  (8.8)  Where the specific volume of pure delta iron was calculated using  V = 0.1234 + 9.38 • 1 0 ( T - 20) - 6  5  T h e lattice parameter for gamma phase iron was estimated w i t h  188  (8.9)  a^ = a? c  + (0.0317 - 11.65 • 1 0 ~ r - 0.05 • IQ~ T )W 7  c=0  7  2  C  (8.10)  T h e specific volume of pure gamma iron was calculated using  V = 0.1225 + 9 . 4 5 - 1 0 - ( T - 2 0 ) 6  7  (8.11)  W i t h the preceding equations, the lattice parameter can be calculated as a function of temperature and carbon content. In a two phase region, C h a n d r a employed the phase diagram and lever rule to calculate an average lattice parameter [6]. T h e mean coefficient of thermal expansion is calculated relative to a reference length at the solidus temperature for a given carbon content, and was implemented i n A B A Q U S w i t h the following equation [108].  e  th  =  a(T)(T-T  )  sotidus  (8.12)  T y p i c a l mean coefficients of thermal expansion used i n this work are presented i n Figure 8.4. T h e calculated values were consistent w i t h those reported by C h a n d r a [81].  8.5 8.5.1  Model Verification Heat Transfer  T h e A B A Q U S heat transfer model was validated using an analytical solution to the one-dimensional semi-infinite heat conduction problem w i t h latent heat evolution and an isothermal boundary [114]. 189  5E-05 h 0.14% carbon 0.32% carbon 0.80% carbon  4E-05 |  3E-05  •2 2E-05 a)  ° 1E-05f-  fOOO  1100  1200  1300 1400 1500 Temperature (K)  1600  1700  1800  Figure 8.4: M e a n coefficients of thermal expansion as a function of carbon content and temperature.  190  T = T s  s0  +  ^ ^ e r f \  7  ^  ]  I  (8.13)  2(a,t)  A s s u m i n g that the i n i t i a l temperature of the liquid is the solidification temperature (i.e. there is no superheat or temperature gradient i n the liquid), the variable A can be solved for iteratively, using the following equation.  A^erfA = -  ^ / -  C  o  (8.14)  )  T h e analytical and A B A Q U S numerical solutions were consistent. Figure 8.5 shows the temperature response of a node 1 m m from the surface of a mesh w i t h 0.5 m m node spacing. T h e initial temperature of the material was 1500°C, w i t h the isothermal boundary set at 1200° C . T h e material properties were: k = 30 W m "  1  K - \ C  heat = 272 k J k g  - 1  = 700 J k g " K 1  p  _  1  , p = 7400 kg m ~ , and latent 3  . T h e A B A Q U S solution matched the analytical solution  very closely, even though the node was only 2 elements (using linear interpolation) from the surface. T h e A B A Q U S finite-element heat transfer model and the SamarasekeraC h a n d r a finite-difference heat transfer model [8, 81] were run using the same test heat flux profiles. M o d e l results are compared i n Table 8.4, which presents the calculated shell thickness at the mould exit. It is interesting to note that the results become more consistent as the shell thickness increases. T h i s was likely due to the coarse node density i n the finite-difference model. In test heat 3 for example, the shell thickness was only 5 nodes from the model surface at the m o u l d exit. In verifying the finite-difference model, C h a n d r a matched 191  Time (s)  Figure 8.5: Comparison of the analytical solution to heat conduction w i t h phase change and the A B A Q U S numerical solution.  192  Table 8.4: Comparison of shell thickness at m o u l d exit between SamarasekeraC h a n d r a model and A B A Q U S model. Heat fluxes taken from t r i a l D 2 . Test Heat 1 2 3 4  ABAQUS (mm) 12.2 10.6 6.4 14.2  Samarasekera-Chandra (mm) 12.0 9.5 5.0 14.0  the calculated shell thicknesses to the depth of solidification bands  2  i n billet  samples [81].  8.5.2  Viscoplasticity  T h e viscoplastic relationship was implemented i n A B A Q U S using a userwritten subroutine. T h e plastic strain rate was verified using a simple isothermal, one-dimensional problem. E q u a t i o n 8.7 was implemented using C = 50000 MPa"  n  s" , Q = 49480 K , and n = 7 at 1400 K e l v i n . T h e model was loaded 1  at 10 M P a for 10 seconds. T h e plastic strain is found by simply integrating E q u a t i o n 8.7 w i t h time. The theoretical strain of 2.24 T O  - 3  exactly matched  the A B A Q U S model strain. The validation of viscoplasticity i n the A B A Q U S code is also available i n the A B A Q U S verification manual [115]. Solidification bands indicate the location of the solidification front at the mould exit. They are caused by a sudden change in heat transfer. 2  193  8.6 8.6.1  Preliminary Model Results Shell Shrinkage Near the Meniscus  A t what point can the solidifying shell withstand enough stress to commence shrinking? For this macroscopic model, T ud s was used as the reference temso  U  perature for shrinkage to begin. One might argue that the zero-strength temperature or zero-ductility temperature could be used to define shell strength, but the combined shell properties of thickness, temperature distribution and plasticity likely govern when the entire billet shell can commence shrinking. Since some uncertainty exists w i t h respect to material properties near the solidus temperature, these conditions cannot be exactly quantified. In this work, it was assumed that the shell thickness must be 0.5 m m prior to the commencement of shrinkage.  8.6.2  Billet Face  The A B A Q U S results showed that the shell shrinkage was not uniform from the midface to the corners. T h e billet surface typically took a slightly bulged shape, w i t h the corners shrinking away from the mould more than the midface. Figure 8.6 illustrates an example displacement profile of the one-half billet face model, w i t h a displacement magnification of 4. Consistent w i t h this result, the natural bending tendency of an unconstrained solidifying shell has been shown to form a convex shape [112].  T h e shell bends because of thermal  stresses, and the severity of bending w i l l depend on the applied heat flux and  194  + 2 DISPLACEMENT MAGNIFICATION FACTOR =  .3 n  1  TIME COMPLETED IN THIS STEP ABAQUS VERSION: 5.5-1  4.00  18.0  TOTAL ACCUMULATED TIME  DATE: 17-APR-96  40.0  TIME: 21:55:09  STEP 3 9 INCREMENT 9 6  Figure 8.6: Billet mesh at the bottom of the m o u l d illustrating different face displacement from midface to corner - displacement magnification 4. material properties. Thus when casting w i t h insufficient taper, the billet w i l l naturally form a bulged shape. Ferrostatic pressure likely enhances this effect. T h e length of the curve of the billet face was calculated for several cases to check the true shrinkage of the face. T h e face shrinkage was nearly identical to the corner displacement; this can be reasoned since the angle of the face bending is very small.  8.6.3  Comparison with Chandra's Work  Chandra's model assumed that shrinkage was a function of the solid shell temperature distribution [81]. T h e billet dimension output from Chandra's model was the average length of solidified rows of nodes i n the model. T h e intuitive approach to this model was reasonable, but the model lacked complete thermophysical characterization. If the material was plastic, plastic strain may 195  offset thermal strain causing the overall shrinkage to differ from Chandra's estimate.  T h e combined effect of material properties is far from intuitive,  particularly w i t h varying heat flux on the shell surface. Another complication when comparing model results was the differing mesh densities since the C h a n d r a model employed a coarser mesh. A coarser element would require more time to evolve the latent heat and would result i n a delayed solidification of the first row of nodes.  A finer element density  would result i n a more accurate prediction of shell behaviour, particularly w i t h temperature varying material properties. In test model runs using heat flux measurements from plant trials, the C h a n d r a model was found to both underpredict and overpredict the shrinkage of the A B A Q U S model. W i t h the billet dimension i n Chandra's model a function of temperature only, changes i n billet temperature result i n proportional changes i n billet dimension. W i t h the inclusion of plasticity i n the A B A Q U S model, plasticity tended to "soften" the change of billet dimension w i t h temperature.  T h e trend of shrinkage was certainly consistent between  the models, and the change i n billet dimension is governed m a i n l y by thermal contraction rather than deformation caused by thermal stresses. Figure 8.7 shows an example of differing billet shrinkage profiles for the C h a n d r a and A B A Q U S shrinkage models.  196  104.6  1  104.4 h c o £ 104.2 P  Chandra model ABAQUS model  <D  E b  CD  104  8 103.8 103.6 103.4 _i  L _i i i i_ 400 600 Distance from Top of Mould  800  Figure 8.7: E x a m p l e of differing shrinkage profiles between the C h a n d r a and A B A Q U S models.  197  Chapter 9 Evaluation of Mould-Billet Binding and Lubrication  In Chapters 5 and 6, significant knowledge was obtained using sensor measurements to quantify the mould response. M o u l d oscillation was found to differ from design specifications on all three machines tested. Further, the oscillator response was dynamic, and changed as a function of oscillation frequency and machine loading. Process control i n billet casting is inherently transient, owing to changes i n liquid steel flow rate. Measurements of casting speed have shown that the speed may vary by as much as 30 pet., as the flow rate changes w i t h nozzle and tundish conditions. T h e installation of strain sensors on the oscillator drive a r m has facilitated the measurement of mould-billet friction forces, likely for the first time on industrial billet machines. Fundamental l u brication phenomena were elucidated w i t h the force sensor.  O i l lubrication  responds i n a solid friction mode, while m o u l d flux lubrication exhibits liqu i d friction. Friction was investigated i n the context of process variables and  198  upsets. T h e force signal did not respond to small, local events i n the m o u l d , such as a meniscus stick or the formation of a transverse depression. It d i d respond, however, to the average interaction of the billet and m o u l d . Thus the force signal is effective i n evaluating lubrication, and the variables which impact lubrication. Gross process upsets like strand plugging and breakouts show high friction during the upsets, likely because of rapid changes i n metal level and large regions of sticking. Since m o u l d flux lubrication operates i n a liquid friction regime, the variables which impact hydrodynamic lubrication, namely relative velocity and lubricant thickness, impact the measured friction response. Thus m o u l d oscillation, i n addition to stripping "sticks" at the meniscus, impacts friction measurably w i t h m o u l d fluxes. This chapter combines sensor measurements, the knowledge developed i n Chapters 5 and 6, and the results of mathematical modelling to interpret mould-billet binding and lubrication effectiveness. properties on billet shrinkage is also presented.  T h e impact of material  T h e models were employed  using the following logic, also outlined i n Figure 9.1.  1. T h e m o u l d temperature profile was taken from the subject plant t r i a l as a 15 minute average of m o u l d temperature, to obtain a sense of average heat transfer. 2. M o u l d heat flux was calculated using the Samarasekera-Chandra m o u l d heat transfer model detailed i n Section 7.1. 3. T h e m o u l d temperature distribution was obtained using the m o u l d heat  199  Table 9.1: Heats investigated for mould-shell binding. Heat 277 298 312 333 351  Grade 0.14 pet. 0.14 pet. 0.32 pet. 0.32 pet. 0.80 pet.  C C C + B C + B C  Lubricant powder oil powder oil oil  transfer model. 4. M o u l d distortion was calculated by implementing the m o u l d temperature distribution into the Samarasekera mould distortion model, described i n Section 7.2. The cold mould dimensions used i n the model were measured values, not m o u l d design specifications. 5. T h e A B A Q U S billet solidification model was run using the m o u l d heat flux profile to obtain the billet temperature distribution. 6. The A B A Q U S billet shrinkage model was run using the calculated billet temperature distribution. The initial billet dimension was taken to be the dimension of the distorted mould at the meniscus. Several heats from trial D2 were investigated for mould-shell binding. T h i s t r i a l was selected because a fully instrumented m o u l d was used, quantitative forces were obtained, and a range of grades were cast using both o i l and m o u l d flux lubrication. Table 9.1 lists the heats investigated i n detail.  The  heats that were investigated were not unique, and represented typical sensor responses for the given grade and lubricant. 200  Plant Trial 1. Mould temperature profile 2. Friction measurement  Mould Heat Transfer Model 1. Mould heat flux profile 2. Mould temperature field  Mould Distortion Model Distorted mould dimensions  Billet Heat Transfer Model 1. Billet solidification 2. Billet temperature field  Billet Shrinkage Model Billet dimensions  Interpretation 1. Mould-billet binding 2. Design of mould taper 3. Evaluation of lubrication  Figure 9.1: Outline of procedure used to interpret mould-billet binding and lubrication.  201  9.1  M o u l d Heat F l u x  The calculated mould heat flux profiles and shell thicknesses are shown in Figures 9.2 to 9.6. Clear differences in heat transfer were observed between the heats as a function of steel grade and lubricant. With the oil-cast heats, heat 298 (peritectic) yielded lower heat extraction than heats 333 and 351 (hyperperitectic). It is well established that oil-cast peritectic steels exhibit low heat transfer because of the rough surface associated with these grades [23, 24]. When casting peritectic steels, the heat flux near the meniscus of heat 277 (powder-cast) was higher than that of heat 298 (oil-cast). This is consistent with the experimental research of Singh and Blazek [28]. Even more striking is the difference in heat flux between the boron(Ti)-alloyed steels using the different lubricants. Heat 312 (powder-cast) showed significantly less heat extraction than heat 333 (oil-cast). This is consistent with the generally accepted knowledge that heats cast with mould fluxes exhibit lower heat transfer than those cast using oil (for non-peritectic steel grades).  202  4000  "1  -E 12  3500  1  3000  i  1  0  E  &  9  \  w  8  CO CD  •E 7 c  2000  X  1 1  \  2500  CD CD  1 3  \  1500  i  o h-  6  "Q  5  si  J 4 1000  •z  heat flux shell thickness  500 0  200  J I I I I I I _L 300 400 500 600 Distance from Top of Mould (mm)  !  I I I 700  3  -j 2  I1 I  L  800  0  Figure 9.2: M o u l d heat flux and shell thickness. Heat 277, powder lubrication, 0.14 pet. C , t r i a l D 2 .  203  4000  TI3 - 12  3500 h  -i  11  i  10  3000 P  -i 9 ^ 8 •= 7 heat flux shell thickness  -i 6  :  i  5  :  i  4  '  J 3 •E 2  500 h  •= 1 _L_L_1_  200  J  I  I  L.  J  I  300, 400 500 600 Distance from Top of Mould (mm)  Figure 9.3: M o u l d heat flux and shell thickness. 0.14 pet. C , t r i a l D 2 .  204  I  L.  700  800  0  Heat 298, o i l lubrication,  Figure 9.4: M o u l d heat flux and shell thickness. Heat 312, powder lubrication, 0.32 pet. C + B , t r i a l D 2 .  205  14 13 12 11 10 | 9  8  »  8  7  6  i  5  i  4  -{ 3  200  heat flux shell thickness i I i i i i I i i i i L 300 400 500 600 700 Distance from Top of Mould (mm)  Figure 9.5: M o u l d heat flux and shell thickness. 0.32 pet. C + B , trial D 2 .  206  ~z 2 -E 1  800  0  Heat 333, o i l lubrication,  14 13 12 11 10 | 9  8  V 8  7 6 45 i  \3  - heat flux shell thickness _j i i i i i i 400 500 600 Distance from Top of Mould (mm)  J  200  300  I  I  !_  Figure 9.6: M o u l d heat flux and shell thickness. 0.80 pet. C , trial D 2 .  207  i  4  i  700  800  1 0  Heat 351, o i l lubrication,  9.2  I m p a c t of M a t e r i a l P r o p e r t i e s on B i l l e t Shrinkage  In this section, the plastic equation i n the billet shrinkage model was m o d ified to determine its impact on shrinkage.  For a given thermal stress, a  strong shell would exhibit less plastic strain than a weaker shell. A n excessively strong shell, as an extreme case, would behave elastically w i t h no plastic strain. T h e A B A Q U S model was also run assuming elastic properties only, i n order to compare shrinkage w i t h the viscoplastic model. Figure 9.7 illustrates the shrinkage profile of heat 277, assuming elastic and plastic material properties. T h e elastic model predicted lower shrinkage; and the effect of plasticity accumulated as the plastic shell grew and moved down the m o u l d . In five test cases, the shrinkage predicted by the elastic model was less than that of the corresponding viscoplastic model as shown i n Table 9.2. It is evident that a stronger shell (elastic i n this case) would shrink less than a weaker shell, for a given heat flux. Heat 312 exhibited a low heat flux and the corresponding elastic and plastic model runs had similar billet dimensions. Heat 333 had a high overall heat flux and a large difference was observed between the elastic and viscoplastic model displacements. T h e impact of plasticity i n the shrinkage model increases w i t h increasing heat flux. Increased heat extraction i n the m o u l d would cause steeper temperature gradients i n the solid shell and higher thermal stresses. Higher thermal stresses then cause increased plastic strain i n the viscoplastic equation, which contributes to a change i n billet shrinkage relative to the elastic case.  208  Table 9.2: One-half billet face shrinkage for elastic and viscoplastic cases. Test Case 277 298 312 333 351  Grade 0.14 0.14 0.32 0.32 0.80  Lubricant  pet. pet. pet. pet. pet.  C C C + B C+ B C  powder oil powder oil oil  Elastic (mm) 0.74 0.50 0.20 0.68 0.53  Viscoplastic (mm) 0.95 0.58 0.21 1.12 1.01  1 F  Distance from Top of Mould (mm)  Figure 9.7: Comparison of shrinkage calculations between elastic and plastic material properties. Trial D2, heat 277.  209  A hyperbolic sine law of the following form was also tested i n the viscoplastic model [113].  ep = C e x p ( - ^ ) s i n h ( a « , e r )  n  (9.1)  T h e hyperbolic sine law yielded nearly identical shrinkage results to the power law (Equation 8.7); the power law was retained for this work because of its simplicity. T h e carbon content dependent coefficient, C , of the power law equation was varied to determine its impact on shrinkage results. T h e shrinkage of a 0.30 pet. carbon billet was calculated w i t h a value of C that was one half of its correct value, to simulate a stronger, i.e. less plastic, material. T h e stronger material exhibited only marginally less shrinkage, as shown i n Figure 9.8. Several conclusions can be made regarding the calculation of billet shrinkage.  T h e material properties must include plasticity, since plasticity  was shown to increase the calculated billet shrinkage. Further, the impact of plasticity was greater w i t h higher heat extraction. T h e billet shrinkage results were not sensitive to the viscoplastic equation however, but simply the inclusion of plasticity i n the stress model had a marked impact on billet shrinkage.  210  Distance from TOD of Mould (mm)  Figure 9.8: Sensitivity test of the viscoplastic relationship to billet shrinkag T r i a l D 2 , heat 333.  211  9.3  Binding Interpretation by Mould-Billet Dimensions  B i n d i n g may be interpreted by simply comparing the billet and distorted m o u l d dimensions at any axial position. If the billet is larger than the m o u l d , the billet may b i n d or j a m i n the m o u l d w i t h the resulting generation of high axial forces on the billet shell such that cracks may form or a breakout may be initiated. A s shown i n previous work [8, 107], the m o u l d bulges during casting operations due to thermal expansion. Figure 9.9 shows a typical cold m o u l d and distorted m o u l d profile from trial D 2 . T h e taper is most seriously influenced by distortion near the meniscus, where the in-situ taper may be reduced by 1 pet. m  _ 1  . Lower i n the m o u l d , the distortion impacts the taper  less severely. In the billet solidification model, the original billet dimension was taken to be the dimension of the distorted m o u l d when solidification commenced. Figures 9.10 to 9.14 present the calculated m o u l d and billet dimensions for the heats investigated.  212  Figure 9.9: C o l d m o u l d and distorted mould dimensions. Heat 277, powder lubrication, 0.14 pet. C , trial D 2 .  213  200  400  600  800  Distance from Top of Mould (mm)  Figure 9.10: M o u l d and billet dimensions from mathematical models. Heat 277, powder lubrication, 0.14 pet. C , trial D 2 .  214  104.6  If  104.4  E,  c 104.2 o "w c E 104 h CD  cr> co 103.81 CO  X 103.6 h distorted mould billet  103.4 h 200  J  I  I  L.  400  600  _l  I  I  L.  800  Distance from Top of Mould (mm)  Figure 9.11: M o u l d and billet dimensions from mathematical models. Heat 298, o i l lubrication, 0.14 pet. C , trial D 2 .  215  104.6  i  200  i  i  i  i  I  i  i  i  i  I  i  400 600 Distance from Top of Mould (mm)  i  i  i  U  800  Figure 9.12: M o u l d and billet dimensions from mathematical models. Heat 312, powder lubrication, 0.32 pet. C + B , trial D 2 .  216  104.6 _104.4h E E ~ 104.2 h g |  104 h  Q o 103.8 h  5 103.6 h distorted mould billet  103.4 h 103.2  J  200  400  !_  600  J  I  l_  800  Distance from Top of Mould (mm)  Figure 9.13: M o u l d and billet dimensions from mathematical models. Heat 333, o i l lubrication, 0.32 pet. C + B , trial D 2 .  217  104.6 _ 104.4 h E E, c 104.2 1 0 "w  1  1041  CD  co 103.81 CO  X 103.6 distorted mould billet  103.4 200  _i i i i_ _L 400 600 Distance from Top of Mould (mm)  800  Figure 9.14: M o u l d and billet dimensions from mathematical models. Heat 351, o i l lubrication, 0.80 pet. C , trial D 2 .  218  It is evident that binding was occurring i n heats 277, 298 and 312, while the billet was slightly smaller than the mould when casting the hyper-peritectic steels w i t h oil lubrication, heats 333 and 351. Thus the m o u l d was too steeply tapered for the peritectic steels, heats 277 and 298, as well as the powder-cast boron(Ti) steel, heat 312. The mould taper appears reasonable for heats 333 and 351, since the billet dimensions reasonably matched the m o u l d dimensions. In the past, binding may have been interpreted simply as the region where the billet dimension was greater than the mould dimension. Using heat 277 (Figure 9.10) as an example, the billet appears to be binding from 220 to 780 m m along the m o u l d length. Since the billet can never be larger than the m o u l d , the billet shell is plastically deformed to the m o u l d dimension. Below 450 m m , the billet tapers more steeply than the mould, thereby fitting inside the m o u l d . B i n d i n g i n this case is restricted to 220 - 450 m m , rather than v i r t u a l l y the entire mould length. Therefore, i n interpreting binding, it may be appropriate to look at both the tapers and dimensions of the m o u l d and billet. Table 9.3 details the regions of binding for the heats investigated.  Heat  312 exhibited excessive binding, due to low heat extraction. Evidence of excessive mould taper can also be seen i n the billet samples. A s noted i n Section 5.4.2, longitudinal midface depressions were observed on billets from trials D I and D2 (the same mould was used), using both o i l and powder lubrication. A s was shown by the mathematical modelling of binding, the most severe binding (by mismatch of mould and billet taper) occurred i n the top t h i r d of the mould where the mould taper was the steepest. T h e ex-  219  Table 9.3: Regions of mould-shell binding. Heat  Grade  277 298 312 333 351  0.14 0.14 0.32 0.32 0.80  pet. pet. pet. pet. pet.  C C C + B C + B C  Lubricant  Region of binding along m o u l d length (mm)  powder oil powder oil oil  220 - 450 meniscus - 640 meniscus - 720 none none  cessive taper near the meniscus was believed to buckle the t h i n shell, forming these depressions. Longitudinal surface cracks were seen at the base of some of these depressions, confirming that the cracks formed high i n the m o u l d when the shell was t h i n , i n the high temperature zone-of-low-ductility. It is interesting to note that the longitudinal depressions i n peritectic powder-cast billets (e.g. Figures 5.34 and 5.36) were very abrupt, while those i n b o r o n ( T i ) alloyed powder-cast billets and oil-cast billets (e.g. Figure F . l ) were smoothly concave across the billet face. T h e differences between the abrupt and smooth depression types could originate as a function of the lubricant or steel grade. T h e powder-cast peritectic shell likely buckled abruptly because of local weak areas i n the shell caused by the peritectic rough surface.  T h e weak areas  would provide sites prone to acute buckling. Another factor which may have contributed is the lubricant.  Small variations i n m o u l d flux film thickness  would impact heat transfer, possibly leaving some regions thinner and weaker. W h e n comparing the powder-cast peritectic (acute depression) and powdercast boron(Ti) grades (smooth depression), two differences existed i n the cast-  220  ing conditions: metal level and heat extraction. T h e metal level was m u c h higher for the peritectic grades, 155 m m , than the boron(Ti) steels, 225 m m (the metal level was dropped after the defective peritectic billets were cast). T h e meniscus heat transfer was higher w i t h the peritectic steels and mathem a t i c a l modelling of billet solidification showed that the solid shell grew m u c h more quickly. Referring to Figures 9.2 and 9.4, the peritectic shell was 2 m m thick at 210 m m from the m o u l d top while the boron(Ti)-alloyed billet was not 2 m m thick until 330 m m from the m o u l d top. Since the boron(Ti) steel shell was less developed i n the upper region of the m o u l d (because of the low metal level and very low heat flux) it may not have been exposed to the steep taper which acutely buckled the peritectic billet. Interestingly, this observation contrasts the behaviour of the oil-cast boron(Ti) grades, which exhibit a high heat flux and a well developed shell near the meniscus.  9.4  D e s i g n of M o u l d T a p e r  For operations convenience, mini-mills use a single m o u l d taper for a given billet section size. A s previous discussed, the m o u l d taper should be adequate enough to m i n i m i z e the mould-shell gap to improve heat extraction, but not too steep to cause m o u l d wear and excessive axial forces. It is evident from the literature and this research that the heat extraction and billet shrinkage are largely a function of steel grade and lubricant type. Thus it is difficult to design an "all-purpose" m o u l d taper. Ideally, m o u l d taper should be designed to match billet shrinkage. Ta221  Table 9.4: Overall billet shrinkage taper. Heat  Grade  Lubricant  Billet shrinkage (pet. m ) _ 1  277 298 312 333 351  0.14 0.14 0.32 0.32 0.80  pet. pet. pet. pet. pet.  C C C + B C + B C  powder oil powder oil oil  1.56 0.92 0.54 1.77 1.66  ble 9.4 shows the overall billet taper for the heats investigated, calculated from the meniscus to the mould exit. A s is evident, these values vary greatly, by a factor of 3. The m o u l d taper should also match the billet shrinkage profiles, as shown previously i n Figures 9.10 to 9.14. The shrinkage profiles for heats 277, 298 and 312 indicate that the m o u l d taper was too steep for casting these heats. The Company D 200 m m mould taper was parabolic, w i t h a steep 5 pet. m  _ 1  taper near the meniscus; the in-situ taper, w i t h the m o u l d  distorted, was typically 4 pet. m  _ 1  .  Figures 9.15 and 9.16 illustrate the billet and distorted m o u l d tapers for heats 277 and 298 respectively.  It should be noted that the m o u l d ta-  per appears "rough" because the mould distortion model was run using actual m o u l d dimensions. P l o t t i n g the tapers assists i n mould taper design, as well as visualizing when binding occurs (e.g. binding ceases for heat 277 at 450 m m ) . T h e C o m p a n y D mould taper was clearly too aggressive i n the upper portion of the m o u l d . Also, the required taper i n the upper portion of the m o u l d is greater than i n the lower portion, as previously recognized [20]. A reasonable  222  Figure 9.15: M o u l d and billet taper calculated from mathematical models. Heat 277, powder lubrication, 0.14 pet. C , trial D 2 .  223  Figure 9.16: M o u l d and billet taper calculated from mathematical models. Heat 298, o i l lubrication, 0.14 pet. C , trial D 2 .  224  compromise for these peritectic grades would be to use a parabolic taper commencing at approximately 2 pet. m  and reaching 1 pet. m  _ 1  _ 1  at the b o t t o m  of the m o u l d . A double-tapered m o u l d could also be used, w i t h 2 pet. m for the top one-third and 1 pet. m  _ 1  _ 1  for the lower two-thirds of the m o u l d .  As previously mentioned, the taper is reduced near the meniscus due to acute bulging.  T h e cold m o u l d dimensions near the meniscus would be adjusted  slightly using the results of Figure 9.9 to compensate for the loss of effective taper. T h e m o u l d taper practices varied markedly between Companies A and D . C o m p a n y A employed a shallow 0.8 pet. m  _ 1  single-tapered m o u l d , while  C o m p a n y D used a steeply tapered parabolic mould, commencing at 5 pet. m  _ 1  at the meniscus. Results of this work indicate that a more appropriate taper would be intermediate between the two practices. Further, a recent survey of billet casting mini-mills indicated that most employ single tapers, some as low as 0.3 pet. m  _ 1  [3]. M o u l d taper is of extreme importance to billet quality, and  it is apparent from the varying practices i n the mini-mills that improvement is needed i n this area. Double- or multiple-tapered moulds should be used [3]. Results of the billet shrinkage model developed i n this work and the m o u l d distortion model are effective tools for designing m o u l d taper.  9.5  Binding and Friction Measurements  One of the m a i n objectives of the mathematical modelling of billet shrinkage and m o u l d distortion was to relate the degree of binding w i t h friction mea225  surements.  In the past, it was believed that binding would result i n higher  measured forces. For example, the lower overall shrinkage of a low carbon steel would causing binding i n a m o u l d designed for higher carbon steels, possibly causing transverse defects [6]. Table 9.5 shows binding results from mathem a t i c a l modelling and average friction coefficients from force measurements for the heats investigated. A s is evident, binding d i d not cause a friction i n crease using these average measurements. Quite the opposite was observed i n heats 333 and 351, which did not exhibit binding by mould-billet dimensions but were cast w i t h high forces. Thus under steady-state operation, force alone is not a good indicator of binding. T h e missing variable i n the simplified binding-friction assumption is lubrication. If the lubrication is effective, the billet w i l l cast through an excessively tapered m o u l d without being exposed to high axial forces. T h i s is particularly evident i n heat 312, which exhibited excessive binding and very low forces. A s w i l l be discussed later i n a force upset example, the force signal does respond well to lubrication related upsets. Good lubrication is not an excuse for an excessively taper m o u l d because i f a lubrication upset occurs, the billet w i l l be exposed to very high forces.  9.6  Friction, Heat Transfer and Steel Grade  Table 9.6 shows friction and heat extraction values from t r i a l D 2 heats. Heat extraction is simply the integrated heat flux profile, which is the total amount of heat extracted from the billet by the mould. There appeared to be a corre226  Table 9.5: B i n d i n g by mould-billet dimensions and average friction measurements. Heat  Grade  277 298 312 333 351  0.14 0.14 0.32 0.32 0.80  pet. pet. pet. pet. pet.  C C C + B C + B C  Lubricant  Binding  Friction Coefficient  powder oil powder oil oil  yes yes yes no no  0.40 0.50 0.36 0.65 0.66  lation between heat extraction and friction w i t h the oil-cast heats. Heats w i t h high heat extraction yielded higher forces. Peritectic grades, known for their low heat extraction, also exhibited lower casting forces.  One would expect  that lower friction would occur w i t h reduced mould-billet contact. W h a t factors influence mould-billet contact? Increased heat extraction forms a colder shell and causes increased billet shrinkage. Thus from a mould-billet gap perspective, a higher heat extraction might be expected to yield lower friction forces: yet higher forces are seen w i t h higher heat extraction. T h e other factor is the billet surface roughness.  Peritectic billet surfaces are wrinkled, as  shown i n Figure 5.24. It appears that this rough surface facilitates low friction because of the intermittent m o u l d billet contact.  T h e hyper-peritectic  billet surfaces are smooth, and the increased contact of the smooth surface likely results i n both increased heat extraction and friction. It appears from the sensor data that the billet surface condition impacts friction more positively than the mould-shell gap (caused by increased heat extraction) impacts friction negatively. 227  Table 9.6: Heat extraction and friction measurements. Heat 277 298 312 333 334 351  Grade 0.14 0.14 0.32 0.32 0.32 0.80  pet. pet. pet. pet. pet. pet.  Lubricant C C C + B C + B C + B C  powder oil powder oil oil oil  Friction Coefficient  Heat E x t r a c t i o n (MJ m- )  0.40 0.52 0.36 0.65 0.97 0.66  47 38 25 58 64 55  2  T h e results of trial D I also support this finding. Referring to Table 6.3, heat 142 (peritectic) exhibited the lowest load cell forces. T h e peritectic heat also exhibited the lowest heat flux [116]. Heat 142 (peritectic) extracted approximately 32 M J m on average.  - 2  , while the hyper-peritectic heats extracted 48 M J m ~  2  It should be noted that casting speed was not obtained i n this  plant t r i a l and the heat flux calculations assumed a constant casting speed of 19 m m s ; thus these heat extraction values are not exact but should be _1  reasonable estimates. This correlation likely does not exist when using m o u l d fluxes. Friction changes significantly w i t h different oscillation settings and casting speed when using m o u l d fluxes lubrication. Results of this work suggest that heat extraction and friction are linked when using oil lubrication. T h e peritectic steels i n particular, known for their low heat extraction, were also found to exhibit lower mould-billet friction i n two plant trials - a significant finding. To the author's knowledge, no industrial data has been published to confirm this finding. Singh and Blazek measured 228  withdrawal forces on a bench-scale stationary caster [23], as shown i n Figure 2.16.  T h e researchers concluded that carbon steels w i t h greater than 0.40  pet. carbon exhibited low friction because of the smooth billet surfaces. B u t noteworthy i n this figure is the decrease i n friction near 0.10 pet. carbon, indicating that the peritectic grades exhibited lower friction i n this experimental research. Using a pilot oscillating caster, Saucedo and Blazek reported similar friction when casting steels w i t h less than 50 pet. carbon, but the authors recommended further work to determine i f any grade sensitivity to friction existed [67]. In the same experimental study, higher friction was reported when casting highly alloyed steels. It must be stressed that this past work was conducted on experimental casting machines [23, 67], and the results may not be applicable to industrial billet machines. Another factor which may have a small impact on friction is oscillation mark size. Large oscillation marks would slightly reduce heat transfer because of the mould-shell gap associated w i t h the oscillation mark. It is well known that oscillation marks are more pronounced i n low carbon steels, e.g. [22]. Perhaps the reduced contact resulting from large oscillation marks may have a slight effect reducing friction. T h e issue of steel grade and shell strength has a profound impact on billet defects, and how friction should be considered w i t h respect to these defects. A s discussed i n Sections.2.8.7 and 6.2, the formation of transverse depressions is influenced by metal level fluctuations and steel grade. Low carbon steels [11] and boron(Ti)-alloyed steels [14] tend to be sensitive to depression formation; this was confirmed i n this research. Since transverse depressions  229  form near the meniscus the effective shell strength near the meniscus w i l l i m pact how the shell can form and retain the depression shape.  T h e effect of  the narrow freezing range of low carbon steels is known to increase the shell strength near the meniscus [14]. T h e increased shell strength of b o r o n ( T i ) alloyed steels was postulated by Samarasekera et al. [14] and was supported further by the thermomechanical testing detailed i n Section 6.2. In contrast, high carbon steels are known for their wide freezing range and weak, perhaps semi-solid [14], meniscus shells. These steels are more prone to forming bleeds and laps [12, 13]. Mechanisms for bleeds and laps have been presented by K u m a r [13]; these mechanisms involve sticking, and subsequent meniscus overflows or shell tearing. To simplify, some grades are sensitive to depressions because of a strong meniscus shell; others are sensitive to sticking because of a weak meniscus shell. Depression-sensitive steels are prone to forming cracks about the depressions themselves, as seen i n the billet samples i n Section 5.4.2. Transverse surface cracks at the base of depressions (e.g. Figure 5.29) certainly form at the meniscus when the depression formed. Subsurface cracks, below the base of depressions (e.g. Figure 5.30), are believed to be formed by axial withdrawal forces [14]. Thus, high friction w i l l crack, and perhaps widen, a depression lower i n the m o u l d because the shell is t h i n and hot adjacent to a depression. T h e solution to reducing the severity of transverse depressions appears to be i n implementing m o u l d flux lubrication.  This practice has two m a i n  influences. Firstly, the meniscus remains much more stable, owing to the sub-  230  merged entry nozzle, and the metal level fluctuations which initiate depression formation reduce significantly. This effect was clearly seen i n the process control signals of Figure 5.23.  Secondly, the m o u l d flux provides reduced heat  transfer and slower shell growth for the boron(Ti) grades. Transverse depressions and cracks may still form when using mould flux lubrication (e.g. Figure 5.32, but they are generally much less severe. In contrast, the higher carbori steels are known to stick, so friction is clearly an issue i n reducing defects. This occurs because of two reasons: the shell is much weaker and prone to tearing; and because the m o u l d may be hot (because of the high heat flux associated w i t h high carbon grades) w i t h little lubricating o i l present [13]. Thus, a "cold m o u l d " practice should be adopted w i t h stick-sensitive grades so the hot face temperature of the m o u l d is below the boiling temperature of the o i l [13]. A s discussed i n Section 6.5.4, the i n d i v i d u a l meniscus sticks cannot be seen i n the force sensor response, because the force required to strip the stick or tear the shell is small compared to the overall surface friction force. Since poor lubrication facilitates sticking and the formation of bleeds and laps, one would expect higher overall friction in the presence of poor lubrication.  In addition, transverse surface cracks  are believed to form by axial mechanical forces [5]. M o u l d oscillation also influences bleeds and laps [13]; thus mould oscillation and friction monitoring should be employed to minimize friction i n stick-sensitive grades. W h e n slab casting using mould fluxes, Wolf notes that friction control is mandatory for "sticker" grades [10].  231  9.7  Lubrication and Force Upsets  Lubrication plays a significant role i n both heat transfer and m o u l d friction. In general, the use of m o u l d fluxes results i n reduced heat extraction because of the increased thermal resistance associated w i t h the m o u l d flux film. A n exception to this occurs w i t h the peritectic steel grades. Heat 277, powdercast, exhibited slightly higher heat extraction than heat 298, oil-cast, which is consistent w i t h the work of Pinheiro et al. [96]; peritectic grades yielded similar heat extraction between oil and powder lubricated heats. M o u l d powder is also a better lubricant than o i l , and consistently results i n lower m o u l d friction. W i t h the peritectic grades, m o u l d powder (heat 277) had a lower friction coefficient than oil (heat 298). T h e most striking results were noted between the boron(Ti) grades. Heat 312, powder-cast, had a friction coefficient of 0.36 while heat 333, oil-cast, had an average friction coefficient of 0.65. Thus m o u l d powder has a very forgiving effect on the boron(Ti) grades. T h e friction and mathematical modelling results presented so far i n this chapter have dealt w i t h average m o u l d response. In the presence of transient phenomena and/or poor operating practices, the instantaneous m o u l d response can vary markedly. T w o examples w i l l now be presented, illustrating transient changes i n m o u l d response.  232  19  30000  casting speed n I  295  i  i  i  i  i  296  i  i  i  i  i  i  i  i  297  i  i—i—i—i—i—i—i—i—i—i—114  298  299  300  Time (s)  Figure 9.17: Force response and casting speed during a period of low friction. Heat 333, oil lubrication, 0.32 pet. C + B , trial D 2 .  9.7.1  Oil Lubrication Friction Upset  A friction upset occurred when casting heat 333 (boron(Ti)-alloyed w i t h o i l lubrication). Ten minutes after the heat commenced, the force range was stable at 12500 N (c = 0.48) as shown i n Figure 9.17. Twenty minutes later, the force range was 24000 N (c = 1) as shown i n Figure 9.18. Process control was excellent during this heat; casting speed and metal level remained consistent between the data sets. Figure 9.19 illustrates the casting speed and metal level stability during the period of high friction. Figure 9.20 illustrates the m o u l d temperature profiles corresponding  233  Figure 9.18: Force response and casting speed during a period of high friction. Heat 333, o i l lubrication, 0.32 pet. C + B , t r i a l D 2 .  234  to the t i m e periods when the forces were obtained. T h e mould temperature clearly increased during the period of high friction: this is a significant finding in this research. T h e temperature profiles were not instantaneous values, but 5 minute averages of m o u l d temperature that represent the short t e r m steadystate response. T h e temperature profiles had the same shape and location i n the mould, confirming that the metal level was constant.  T h e high friction  therefore could not be correlated to a process control event, since the casting speed was constant also. T h e mould heat transfer model was employed to calculate the heat flux profiles corresponding to the the periods of low and high friction, shown i n Figure 9.21. These heat flux profiles correspond to heat extractions of 49.5 M J m  - 2  for the low friction case and 66.6 M J m  - 2  for  the high friction case. These data support the previously mentioned finding that there was a correlation between friction and heat transfer seen when comparing the response of different steel grades cast w i t h o i l lubrication. B u t what event was responsible for this increase i n heat extraction and friction? A s seen i n this work, process control and steel grade are known variables of heat extraction, but these factors were constant i n this case. V a r y i n g m o u l d flux films are known to impact heat extraction and friction, but such relationships should not exist w i t h o i l lubrication. T h e m o u l d response was investigated further to determine the thermal stability during the periods of low and high friction.  A s noted previously i n Section 6.2, the standard de-  viation of the thermocouple temperature at the meniscus is an indicator of the metal level stability. A fluctuating metal level has been clearly linked to  235  Figure 9.19: Casting speed and metal level were stable during friction upset. Heat 333, oil lubrication, 0.32 pet. C + B , trial D 2 .  236  220  Time (s)  Figure 9.20: M o u l d temperature profiles during periods of low and high friction. Heat 333, o i l lubrication, 0.32 pet. C + B , t r i a l D 2 .  237  low friction high friction  200  300  -I  ! I  400 500 600 700 Distance from Top of Mould (mm)  I  !  I  L-  800  Figure 9.21: Mould-billet heat flux profiles during periods of low and friction. Heat 333, o i l lubrication, 0.32 pet. C + B , trial D 2 .  238  the formation surface defects like transverse depressions [14, 15, 60]; a smooth meniscus facilitates uniform shell growth. Figure 9.22 illustrates the standard deviations of the m o u l d thermocouple temperatures during the periods of low and high friction. A s is evident, the period of low friction exhibited a noisier m o u l d temperature profile.  Particularly notable is the m o u l d thermocouple  signal at 175 m m , near the meniscus, which was very noisy i n the low friction case but relatively stable during the period of high friction. Based on these data, the low friction billets were believed to contain many more shape defects like transverse depressions, which reduce heat transfer. Further, the reduction of average m o u l d temperature for the full m o u l d length implies reduced heat transfer, and this can certainly be caused by the poorer surface quality of the low friction billets. T h e cause of the rough meniscus is the tundish stream. A s discussed i n Section 6.2, the aluminum-killed steelmaking practice used w i t h the boron(Ti) steels routinely causes nozzle plugging and poor stream quality. Stream quality is a chaotic process variable that can change as the nozzle plugs and releases, or as globules of steel form on the nozzle exit and are cleared manually by operators using an oxygen lance. T h i s finding ties i n well w i t h the observation that peritectic steels exhibit lower heat transfer and lower friction because of their rough surface. It appears that shells w i t h surface defects can have the same effect reducing heat transfer. Thus, when casting w i t h o i l lubrication, there is a link between friction and heat transfer. For a given m o u l d and casting speed, it appears that increased surface contact between the m o u l d and billet raises friction as well  239  Figure 9.22: Standard deviation of mould temperatures corresponding to the periods of low and high friction. Heat 333, oil lubrication, 0.32 pet. C + B , trial D2.  240  Table 9.7: Friction response for four powder-cast heats of 0.32 pet. C + B . T r i a l D 2 , 203 m m mould. Heat  310 311 312 313.1 313.2 313.3  Force Range (N) 12500 11000 11000 24000 24500 26000  Friction Coefficient  Casting Speed (mm s ) 18.4 19.1 18.0 12.5 14.3 13.8  Mould Powder  _ 1  0.40 0.36 0.36 1.05 1.05 1.15  A A A A B B  Oscillation Frequency (Hz) 1.87 1.95 1.81 1.28 1.45 1.40  as heat extraction.  9.7.2  Mould Flux Friction Upset  T h e importance of m o u l d oscillation and friction control when casting w i t h m o u l d fluxes is well illustrated i n the following example. A s previously noted i n Section 6.4, a force upset occurred when casting heat 313, a boron(Ti)alloyed steel using powder lubrication. Pertinent data are detailed i n Table 9.7. W h e n the casting speed dropped from 18 to 13 m m s  _ 1  the friction coefficient  increased significantly, from 0.36 to above 1. In evaluating this friction upset, several factors must be considered, including m o u l d flux properties and m o u l d oscillation settings. M a t h e m a t i c a l modelling has shown that there was significant m o u l d billet binding occurring i n heat 312 (and similarly i n heats 310 and 311). T h e reduced casting speed i n heat 313 did result i n some increased heat extraction.  241  Figure 9.23: Temperature of the billet midface and corner. Heat 312, powder lubrication, 0.32 pet. C + B , trial D 2 .  242  1450 r 1400 -  o 1350 CD i_  -  £ 2 1300 CD  1250 E CD I- 1200 CL  CD O CO  1150 r  CO  1100 r  t  m  1050 1000 950 200  -  midface corner 400 600 Distance from Top of Mould (mm)  800  Figure 9.24: Temperature of the billet midface and corner. Heat 313, pow lubrication, 0.32 pet. C + B , t r i a l D 2 .  243  Heat 312 exhibited an average heat extraction of 25.1 M J m 313 the m o u l d extracted 36.4 M J m  - 2  - 2  , while i n heat  . Even with this increase i n heat transfer,  binding was certainly still occurring since heat 351 required 55 M J m  - 2  to avoid  binding. W h y would heats 310 - 312 exhibit low friction and heat 313 exhibit high friction when binding was occurring i n a l l cases? T h e answer likely lies i n lubrication effectiveness. A s shown i n Table 9.7 the m o u l d powder was changed during heat 313, but data logged before and after the change indicate that the powder composition was not responsible for the friction increase. W i t h m o u l d flux lubrication, a stable liquid layer of flux along the m o u l d length is required for effective lubrication and thus the billet surface temperature must be above the break-point temperature  1  of the m o u l d flux [10].  If the flux solidifies  between the m o u l d and billet, the friction w i l l increase i n a solid friction mode. Figures 9.23 and 9.24 present the midface and corner billet temperature profiles for heats 312 (low friction) and 313 (high friction) respectively. M o u l d flux A had a break-point temperature of 1000°C, while flux B had a break-point temperature of 1135°C. Figure 9.23 illustrates that the billet temperature of heat 312 (low friction)was above the break-point temperature of m o u l d flux A . Therefore, one would expect stable liquid flux along the m o u l d length. Figure 9.24 shows that the midface billet temperature of heat 313 (high friction) was well above the break-point temperature of both fluxes. T h e corner billet temperature of heat 313 dropped below the break-point temperature of flux A near the m o u l d exit, and was below the break-point temperature of flux B T h e breakpoint temperature of a mould flux is defined as the temperature at which the viscosity of the flux significantly increases, as the flux becomes semi-solid. 1  244  40000 F  15000h  Figure 9.25: Rough force sensor response during high friction believed to be caused by sticking. Heat 313, powder lubrication, 0.32 pet. C + B , t r i a l D 2 . for approximately two-thirds of the m o u l d length. However, since the midface temperature of the billet extends nearly the full w i d t h of the billet (to w i t h i n 10 - 15 m m of the corners) any solidified flux would have had a very small contact area relative to the amount of liquid flux.  Further, there would be  only a t r i v i a l amount of solidified flux when powder A was used, and high friction forces were measured. Thus, crystallized flux was likely not the cause of the high friction. M o u l d flux consumption is impacted by oscillation parameters and casting speed [50]. M o u l d flux consumption increases w i t h decreasing oscillation  245  frequency and decreasing casting speed.  T h e casting machine i n this case  had oscillation frequency synchronized w i t h casting speed, thus a decrease i n speed had a significant impact on powder consumption (the decreased oscillation frequencies are noted i n Table 9.7). T h e impact of speed and oscillation frequency can be seen i n the following equation, which estimates m o u l d powder consumption [50].  Q = 0.55f- (n(0Mv ) )-°1  2  (9.2)  5  s  For the low friction heats, powder consumption was approximately 0.23 kg m (v  = 18.5 m m s , - 1  s  /  = 1.9 H z , n = 1.3 poise for flux A ) ; for heat 313  the consumption had effectively doubled to 0.44 kg m / = 1.35 H z ) . F l u x consumption near 0.3 kg m and 0.44 kg m  - 2  - 2  - 2  - 2  (v  = 13.5 m m s , _ 1  s  is a common target [10],  does not seem like an excessive consumption. T h e problem  i n this case may involve the melting rate of the powder, and the supply of l i q u i d flux. D u r i n g this trial, the measured thickness of the liquid flux was found to be only between 1 and 3 m m [117].  It is recommended that the  liquid flux layer is greater than the m o u l d stroke [117], to facilitate smooth infiltration of the lubricant between the m o u l d and billet. D u r i n g this plant trial, the m o u l d stroke was approximately 5 m m , and the liquid flux layer was found to be very small. W h e n the casting speed dropped i n heat 313, the flux consumption doubled, and it was likely that the liquid flux supply was insufficient for the consumption demand. T h i s would result i n local starving of flux causing sticking, or the consumption of solid material from the flux layers 246  above the liquid flux. Either condition could result i n unstable flux lubrication and the increased friction observed.  Figure 9.25 shows the force response  during the high friction i n heat 313.  T h e force signal did not exhibit the  smooth response seen Figure 6.2, which is indicative of stable liquid friction. T h e large force range and rough signal trace was believed to be caused by sticking, as a result of the unstable flux lubrication. Thus, when mould-billet binding exists and a lubrication upset occurs, very high friction forces w i l l be measured. In this case, the lubrication upset increased friction nearly threefold. It is evident that a different m o u l d flux should be used, perhaps w i t h a lower melting temperature, to increase the liquid flux layer thickness. It should also be noted that unstable liquid lubrication may occur w i t h m o u l d fluxes i f the viscosity is low or the relative velocity between the m o u l d and billet is low (caused by a short stroke or low oscillation frequency). These conditions may cause increased friction i n a combination hydrodynamic-boundary lubrication regime [10, 101], which is i n essence a transition between solid and liquid l u brication.  It is clear from this example that m o u l d oscillation and friction  monitoring is essential i n selecting lubricants and setting casting parameters to m i n i m i z e friction. T h i s is particularly crucial as mini-mills are now implementing powder casting practice to improve billet quality, and relatively little powder casting experience exists i n the billet industry. Further, as producers are considering high speed casting, friction monitoring becomes more critical as the shell becomes thinner and the relative velocity between the m o u l d and  247  billet increases.  9.8  The Next Step  T h i s research has shown that mathematical modelling (mould heat transfer, m o u l d distortion, billet solidification and billet shrinkage) and sensor measurements (temperature, process control, oscillation and force) are powerful tools for evaluating the fundamental process behaviour of continuous billet casting. W h e n used on-line, sensors may be used to evaluate process quality, and flag when process upsets occur. M a t h e m a t i c a l models are best used i n the design stage, or for diagnosing the causes of process upsets. T h e goal: high quality billets and high speed casting. Before this goal can be reached, known impediments to process quality must be addressed first. Recently, great insight has been shed on the importance of the meniscus on billet defects, e.g. [12, 13, 14, 15, 60]. Thus metal level changes, intermittent lubrication, and meniscus turbulence must be controlled. This may be achieved by a number of process variables, including: improved tundish design, reducing the height of the open stream'pour, careful centring of nozzles, improved steelmaking, or the implementation of m o u l d flux lubrication practice. This work has shown that m o u l d oscillation parameters i n practice differ significantly from those expected. Thus, m o u l d oscillation must be measured, and the casting machine must be maintained for precise, robust oscillation; guidelines exist for machine operation, e.g. [3]. A major influence of billet quality is m o u l d taper. Taper practices vary widely [3], yet guidelines exist for 248  improving m o u l d taper using multiple-tapered moulds [6, 17, 20]. T h e mathematical modelling of billet shrinkage i n this work has assisted i n the designing of m o u l d taper, for improving mould-billet heat extraction and reducing the risk of mould-billet binding. T h e hard recommendations from past work and this research are: quiet meniscus, precise oscillation, multiple-tapered moulds. T h e next step: improvements i n process control, lubrication design and high speed casting. T h e existing, transient casting speed control system is unacceptable, particularly when using m o u l d fluxes. L i q u i d steel flow control must be added, w i t h casting speed and metal level being system set-points. A s a result of this research, the tools of m o u l d oscillation and friction monitoring are now i n place to design lubrication for minimizing friction. Lubricants may be selected, and casting speed targets/ranges set for m i n i m i z i n g friction. W i t h precise oscillation, a correct m o u l d taper, stable process control and m i n i m i z e d friction, billet productivity may be increased.  249  Chapter 10  Summary and Conclusions  T h i s study has lead to a quantitative understanding of m o u l d response through measurements of mould oscillation and friction on industrial casting machines. Fundamental lubrication behaviour was elucidated w i t h a friction sensor, which is an powerful tool for evaluating lubrication and m o u l d oscillation. Mathematical modelling of mould-billet binding has lead to further understanding of the response of the force sensor as well as some recommendations for i m provement i n mould taper design.  10.1  K e y Findings  1. M o u l d oscillation parameters varied significantly from design specifications. 2. Casting speed varied continuously due to lack of liquid steel flow rate control. 3. Mould-billet friction has been quantified. 250  • O i l and m o u l d flux lubricants fundamentally  differ.  • A n effective friction coefficient may be used for on-line monitoring.  4. Mould-billet binding has been mathematically modelled; model results may be used to improve mould taper design. 5. Mould-billet friction  • The force sensor mainly responded to lubrication effectiveness.  Bind-  ing likely can only be detected when lubrication is poor. • T h e force signal responded to gross process upsets (e.g. strand jerking, breakout). • T h e signal did not respond to small, local events i n the m o u l d like a transverse depression forming or a meniscus stick. • O i l lubrication — Lower friction was measured when casting peritectic steels (i.e. billets w i t h rough surfaces). — A reasonable correlation was seen between friction and heat extraction. • M o u l d flux lubrication — Friction is a function of m o u l d oscillation, casting speed and flux properties.  251  10.2  Summary  Sensors 1. L V D T and accelerometer sensors were successfully employed to monitor m o u l d oscillation. T h e L V D T calculated acceleration and accelerometer signals matched, confirming the kinematic response of the sensors and mould. 2. T h e L V D T is an appropriate, readily available, oscillation monitoring sensor.  A n accelerometer would also likely provide appropriate m o u l d  velocity and displacement signals, but a stable integration device (either hardware or software) would be required. 3. Three force sensor types were tested: load cells, strain gauges and a K i s t l e r piezoelectric strain device.  T h e load cells provided a qualita-  tive force response, due to the installation of the load cells under the m o u l d housing flange.  B o t h strain sensor types were installed on the  oscillator drive arm to measure m o u l d friction quantitatively. T h e strain gauge signal matched the character of the load cell response, indicating that installing a force sensor on the drive arm of a billet machine would provide an accurate indication of m o u l d response. T h e piezoelectric strain signal and the strain gauge signal matched reasonably well, but the piezoelectric sensor was designed to be a "quasi-static" device, and d i d not respond to higher frequency components i n the force signal  252  (like oscillator jerking or mould-billet sticking). 4. A conventional strain gauge installed on the machine drive a r m was the most effective force sensor tested. A Kistler piezoelectric strain sensor has the advantage of being simpler to install, but at present requires a higher operating frequency range to provide information comparable to the strain gauge.  asic M a c h i n e Response 1. D u r i n g cold operation, the casting machine force signal was i n phase w i t h m o u l d acceleration, indicating that the force sensor was responding to inertial machine forces. 2. D u r i n g casting operations, the force signal was i n phase w i t h m o u l d velocity, indicating that mould-strand friction is a function of velocity. T h i s also implies that mould-strand friction dominates the inertial force when casting.  3. T h e three industrial billet machines tested operated at strokes less than their respective design strokes (as much as 35 pet. less). 4. Machine C exhibited a sinusoidal oscillation profile. Machines A and B exhibited time-varying non-sinusoidal profiles. 5. Machines B and C were observed to dynamically change stroke w i t h changing oscillation frequency. Machine B increased stroke w i t h increas-  253  ing oscillation frequency; Machine C decreased stroke w i t h increasing oscillation frequency. 6. Machines A and B showed a casting speed oscillation of 0.5 - 2.0 m m s , - 1  at the same frequency as the oscillator. T h i s was believed to be caused by mould-strand friction pushing and pulling the billet against the w i t h drawal rollers. 7. Machines A and C exhibited a reduced stroke w i t h increasing m o u l d strand friction. T h e stroke of Machine C increased by 10 pet. when the friction decreased by 50 pet. 8. Since the machines operated at reduced strokes and i n non-sinusoidal oscillation profiles, the operating negative-strip times and m o u l d lead values differed significantly from.design values.  In one instance,  the  operating negative-strip time was virtually zero.  9. Oscillation frequency is commonly synchronized w i t h casting speed on billet machines. If the scheme is set up i n a hap hazard fashion, it can lead to undesirable changes i n negative-strip times. 10. Horizontal movement was measured on Machine A , and was found to be double the suggested tolerance for slab casting machines. T h e m o u l d also moved i n a diagonal vertical-horizontal trajectory.  254  Process Control 1. Casting speed and metal level signals often changed i n phase, caused by the control system responding to changes i n the steel flow rate. 2. In some instances, casting speed was noted to steadily increase as the steel flow rate increased, uncontrolled. 3. W h e n pouring open stream w i t h oil lubrication, the casting speed and metal level signals were often "rough".  T h i s was caused by the open  stream creating a turbulent meniscus, which may emanate from several conditions: air entrained i n the tundish stream, nozzle condition, and globules of steel forming and releasing on the nozzle exit. In contrast, casting speed and metal level signals were relatively smooth when casting through submerged entry nozzles w i t h m o u l d flux lubrication.  4. T h e "roughness" of the meniscus can be implied by calculating the standard deviation of the meniscus thermocouple signal. A smooth meniscus yields a standard deviation of about 3°C; a rough meniscus about 8°C or greater.  Friction 1. Mould-strand friction is a function of the relative velocity between the m o u l d and billet.  255  2. A n oil-lubricated mould responds i n a solid friction regime, where the force signal is i n the shape of a "square wave".  Solid friction is not  dependent on the magnitude of relative velocity, but only the direction of relative velocity. 3. A m o u l d lubricated w i t h mould flux responds i n a l i q u i d friction regime. T h e friction response is sinusoidal, since l i q u i d friction is a function of relative velocity. 4. F r i c t i o n may be quantified by calculating the work expended per oscillation cycle or by estimating the friction coefficient.  • Work per cycle is calculated by integrating the force over displacement for one oscillation cycle. The cold work  1  per cycle can be  subtracted from the casting work per cycle to yield the work expended as friction. • A friction coefficient can be estimated by dividing the casting force by the normal force due to ferrostatic pressure. The cold machine force range is subtracted from the casting force range to y i e l d a more accurate estimate of the friction coefficient.  B o t h of these methods provide a quantitative sense of friction and can track friction changes. Although only an approximation, a friction coefficient near unity may indicate sticking or mould-billet binding. 1  Cold work refers to the cold mould state without casting.  256  Mathematical Modelling of Mould-Billet Binding 1. E x i s t i n g mathematical models were employed to calculate m o u l d heat flux and m o u l d distortion. 2. A thermal-stress, elastic-viscoplastic billet shrinkage model was developed using A B A Q U S commercial finite-element software.  T h e model  calculated billet shrinkage based on heat flux measurements taken during plant trials. 3. Stronger steels, i.e. less plastic, shrink slightly less than weaker steels. 4. T h e model was not sensitive to the exact viscoplastic equation, but the inclusion of plasticity i n the model had a marked impact on overall billet shrinkage. The effect of plasticity on shrinkage was greater w i t h increasing heat flux because thermal stresses cause plastic strain i n the billet shell. Thus estimates of billet shrinkage based on temperature alone may be inaccurate. 5. Mould-billet binding can be evaluated by comparing the calculated m o u l d and billet dimensions and tapers.  Peritectic steel grades, and hyper-  peritectic steels cast w i t h mould flux were noted to b i n d i n the parabolic m o u l d at Company D . Hyper-peritectic steels cast w i t h o i l lubrication more closely matched the m o u l d taper. 6. M o u l d taper design can be improved by using results of the billet shrinkage model.  The parabolic mould at Company D employed a steep 257  5 pet. m  _ 1  at the meniscus, which was too aggressive. Company A used  a shallow single-tapered mould, which has previously been recognized as inadequate [20]. A n "all-purpose" m o u l d taper should be able to cast the peritectic grades, which are known for exhibiting lower heat transfer and shrinkage. Based on model calculations from the 200 m m m o u l d at Company D , a suitable taper for casting the peritectic steels would be a multiple-tapered m o u l d commencing at approximately 2 pet. m the meniscus, reducing to 1 pet. m  _ 1  _ 1  at  at the bottom of the m o u l d .  Investigation of Friction Response as a Function of Process Variables and Upsets 1. Low carbon and boron(Ti)-alloyed steels are sensitive to transverse depression formation. T h e boron(Ti) steels generally exhibited high friction, yet the formation of transverse depressions could not be seen i n the force signal. T h e formation of transverse depressions has been linked to metal level changes [14, 15, 60], consistent w i t h this research. T h e high friction environment was believed to be caused by the metal level fluctuations, which removed oil lubricant from the m o u l d wall intermittently, causing poor lubrication. The boron(Ti)-alloyed billets contained the highest depression population and these steels were also noted to have the greatest metal level instability. This was believed to be caused by the aluminum-killed steelmaking practice, which contributed to nozzle clogging, poor stream quality and large metal level fluctuations.  258  Fur-  ther, thermomechanical testing of the boron(Ti) steels indicated that they have increased high temperature strength, which may contribute to depression formation at the meniscus [14]. 2. Friction was noted to vary between steel grades when using oil lubrication.  T h e peritectic grades exhibited the lowest forces, followed by  the hyper-peritectic steels, and the boron(Ti)-alloyed grades exhibited the highest friction. A s previously mentioned, the boron(Ti)-steel billets were believed to be poorly lubricated because of the unstable metal level associated w i t h these grades. Peritectic steels are well known for their rough billet surface, and it appears that the rough surface results i n lower m o u l d friction because of the reduced contact area. W h e n using m o u l d flux lubrication, the friction was not noted to vary between grades.  3. A nozzle plugging upset may expose the shell and machine to high friction.  R a p i d changes i n casting speed and the associated intermittent  lubrication may cause sticking i n the mould. 4. D u r i n g two logged breakouts, the force signal did not increase prior to the breakout. D u r i n g the breakout however, very large forces were experienced because of sticking i n the mould. 5. S m a l l amounts of sticking at the meniscus cannot be seen as i n d i v i d u a l events i n the force response.  259  6. Strand jerking can be seen i n the force signal as a  fluctuating  friction  response. 7. T h e friction signal does not correlate w i t h steady-state mould-billet binding calculations, i.e. if modelling results indicated significant binding, a large friction response was not necessarily seen.  Therefore, the force  signal responds mainly to lubrication effectiveness. 8. W h e n casting w i t h oil lubrication, there appeared to be a steady-state correlation between friction and heat extraction. Heats w i t h higher heat extraction yielded higher friction.  The peritectic steels exhibited low  heat extraction and low friction. A relationship using mould flux lubrication was not seen. 9. W h e n casting w i t h o i l lubrication, a transient increase i n friction during a boron(Ti)-alloyed heat was clearly accompanied by an increase i n heat extraction. D u r i n g the period of lower friction, the standard deviations of the m o u l d thermocouple temperatures were much greater than i n the high friction case. T h e meniscus thermocouple was responding to a fluctuating metal level, and the  fluctuations  i n lower m o u l d temperatures  were believed to be caused by a high population of transverse depressions causing intermittent mould-shell gaps. In this case, a defect-ridden billet reduced heat transfer and friction. 10. The friction signal responded well to lubrication upsets.  W h e n cast-  ing w i t h powder lubrication during a period of subnormal casting speed 260  and low oscillation frequency, very high friction was measured (friction coefficient greater than one).  Modelling results indicated that m o u l d -  billet binding was occurring. Under conditions of normal casting speed and m o u l d oscillation parameters (with binding), low friction forces were measured. T h e high friction was believed to be caused by increased flux consumption exceeding the liquid flux supply, causing intermittent l u brication and sticking. 11. W h e n casting w i t h m o u l d flux lubrication, trending logged data over long time periods has shown a clear relationship between friction and casting speed.  A s i n the upset example above, the friction increased  at low casting speeds. This was believed to be caused by either a flux consumption problem (as above) or a transition solid-liquid lubrication regime caused by the low relative velocity. It should be noted that excessively high casting speeds d i d not occur during this research. A clear relationship between casting speed and friction was not observed w i t h oil lubrication.  10.3  Concluding Remarks  New sensors were tested to quantify the kinematic and dynamic response of the m o u l d . T h e use of redundant sensors validated both the sensor responses and machine response.  Simple, inexpensive sensors are available for quantifying  the mechanical response of the mould.  261  T h e kinematic responses of the three machines tested varied from design specifications. Thus the fundamental mould oscillation parameters of stroke, negative-strip time and mould lead differed significantly from those expected. Further, machine response was dynamic, and varied as a function of oscillation frequency and machine loading. Given the importance of m o u l d oscillation i n surface quality, reducing friction, and preventing sticking, the measured machine responses were unacceptable.  Since the design specifications of these  machines were not being met (even on new machines), the issue of casting machine maintenance is likely even less recognized. W o b b l y oscillation is believed to contribute to cracking and off-squareness [3, 38]. Based on the  operating  responses of the machines tested, on-line oscillation monitoring is imperative. Process control of billet casting is inherently transient due to lack of steel flow rate control. Changes i n flow rate due to tundish and nozzle conditions cause the casting speed to vary significantly. The varying casting speed leads to changing shell properties at the mould exit, i n addition to varying lubrication properties when using m o u l d flux lubrication. Casting speed control should be improved, perhaps w i t h the addition of flow control, to improve billet quality. This is particularly important when considering high speed casting, an active topic among billet producers. Meniscus stability is also very important w i t h respect to both billet quality and o i l lubrication effectiveness.  T h e stability  of the meniscus can be quantified by monitoring the m o u l d temperature near the metal level. Casting friction is a function of the relative velocity between the m o u l d  262  and billet. W h e n using o i l lubrication, the force signal responds i n a solid friction mode; when using stable m o u l d flux lubrication, liquid friction is evident. T h e estimation of a friction coefficient on-line is a simple technique for quantifying friction. A l t h o u g h the calculated friction coefficient is only an estimate, since the true normal force not only includes the ferrostatic pressure but also sticking, binding and mould-billet misalignment, it does provide a reference point for the friction magnitude.  Further, one can i m p l y that binding may  be occurring (in the presence of poor lubrication) i f the friction coefficient is near unity. In any technique for quantifying mould-billet friction, the machine forces must be subtracted from the gross force signal. In the cases of the billet machines tested, this was relatively simple since the casting forces significantly dominated the cold machine forces. If the machine forces were large relative to the casting forces, the work per oscillation cycle technique would be the superior method for quantifying friction. T h i s method provides a more exact measure of the work expended as friction and would be less prone to error w i t h large machine forces. M a t h e m a t i c a l models were employed to calculate the m o u l d and billet dimensions to determine if binding was occurring. A thermal-stress, elasticviscoplastic, finite-element model was developed to calculate billet shrinkage using in-situ heat flux measurements.  T h e billet shrinkage was not sensitive  to the viscoplastic model used, but the inclusion of plasticity i n the model had a marked impact on billet shrinkage. Stronger shells, i.e. less plastic, shrunk slightly less than weaker shells. T h e parabolic m o u l d taper at C o m p a n y D ,  263  commencing at 5 pet. m  _ 1  was too aggressive. T h i s was confirmed by binding  calculations and longitudinal midface depressions i n billet samples, caused by the excessive taper buckling the billet face. W h e n designing an "all-purpose" m o u l d taper, one should look at the grades which shrink less, namely the peritectic steels. A s previously mentioned, a suitable taper i n this case would be a multiple-tapered mould, commencing at approximately 2 pet. m meniscus and reducing to 1 pet. m  - 1  _ 1  at the  at the bottom of the m o u l d .  T h e development of quantitative force sensing on industrial billet machines has allowed the process to be studied from a different perspective i n the context of process variables and upsets. T h e friction of stable m o u l d powder lubrication was consistently less than oil lubrication. Interestingly, the force response d i d not clearly vary as a function of mould-billet binding. Perhaps one might expect higher forces w i t h increased mould-billet binding, but the lubrication effectiveness appears to dominate the force signal. In cases when severe binding was occurring the force signal may be low because of stable lubrication. T h i s is not to i m p l y that satisfactory lubrication is an excuse for an excessively tapered m o u l d . In the case of a lubrication upset, excessive forces w i l l be experienced because of the binding. Peritectic steels exhibited less friction than hyper-peritectic steels when casting w i t h oil lubrication. Peritectic steels are well known for their rough billet surface which contributes to low heat transfer; it appears that the rough surface results i n lower m o u l d friction because of the reduced contact area. A l s o , there appears to be a correlation between heat extraction and friction  264  when casting w i t h oil lubrication, based on average heat extraction and friction measurements.  This effect was studied i n further detail w i t h a significant  friction upset during a boron(Ti)-alloyed heat. W h e n the friction increased, there was a clear and significant increase i n mould temperature, confirming a relationship between heat extraction and friction. Process control was stable during this heat, so the effect of casting speed could be neglected. T h e grade and heat extraction sensitivity to friction was not seen when casting w i t h m o u l d fluxes. Fundamentally, the friction signal responds to lubrication effectiveness, and thus is a powerful tool for evaluating lubricants and m o u l d oscillation parameters, particularly with mould fluxes. Casting speed changes resulted i n clear changes i n friction when casting w i t h mould powders, confirming the importance of the relationship between mould oscillation, casting speed and friction. Friction upsets were also seen when casting w i t h o i l lubrication, but a clear relationship w i t h casting speed was not seen. The friction signal represents an average force response to the billet-mould interface.  Local events  to an isolated area of the mould, e.g. meniscus sticking and transverse depression formation, cannot be seen i n the force signal.  If, however, lubrication  was poor i n these conditions, a slightly higher friction signal may be observed. D u r i n g gross process upsets such as strand plugging or breakouts, significantly increased friction may be observed due to rapid speed changes or lubrication problems. The force signal did not change prior to the observed breakouts i n this research, and thus the friction signal is likely not effective as a "breakout  265  warning". In practice, many process variables and upsets impact lubrication and friction, and ultimately billet quality. A force sensor can be used as a design tool for m i n i m i z i n g friction and as an on-line sensor for detecting upsets, and thus preventing the production of sub-standard billets. Process quality can be improved by implementing more appropriate m o u l d taper designs, using results of the billet shrinkage model. Multiple-tapered moulds should be used, using intermediate tapers.  266  Chapter 11  New Knowledge and Recommendations  11.1  New Knowledge  Significant knowledge was obtained i n this research regarding the mechanical response of the mould, and this section highlights the contributions to new knowledge. T h i s research was conducted w i t h two aspects of new knowledge in m i n d : firstly, to provide fundamental knowledge of the process, specifically involving mould-billet friction and m o u l d taper; and secondly, to provide a practical framework for mini-mills to commence on-line monitoring of the process.  1. Simple measurements of m o u l d oscillation have provided important quantitative information regarding the operation of industrial billet machines. M o u l d oscillation is fundamental i n reducing friction and sticking, yet these machines operate w i t h oscillation parameters significantly different from design values.  T h e key parameters of stroke, negative-strip  time and m o u l d lead often operated at unacceptable values. 267  Further,  the machine response appeared to be dynamic, and changed as a function of oscillation frequency and loading. Individual machine design also affected the response, since one machine would increase stroke w i t h i n creasing oscillation frequency while another would decrease stroke w i t h increasing frequency. Oscillation parameters may also be set incorrectly; i n one instance the operating negative-strip time was virtually zero. 2. Machine forces have been measured quantitatively on industrial billet casters, possibly for the first time. Strain sensors installed on the machine drive a r m (for the machines tested), facilitated these measurements.  Thus the drive a r m appears to be an appropriate location for  robust, on-line monitoring of machine forces. T h e casting forces significantly dominated the cold machine forces, indicating that most of the force signal measured was caused by mould-strand friction.  3. Mould-billet friction may be evaluated by estimating the friction coefficient or by calculating the work expended per oscillation cycle, a technique developed at Bethlehem Steel i n research on slab casting [68]. B o t h techniques involve subtraction of the cold machine forces to obtain a more accurate estimate of mould-billet friction. Thus friction can be quantified, and process variables such as lubricants, oscillation parameters and casting speed may be evaluated for their impact on friction. 4. A thermal-stress, elastic-viscoplastic, billet shrinkage model was developed using A B A Q U S commercial finite-element software. Coupled w i t h 268  the results of existing models of m o u l d heat flux and m o u l d distortion, mould-billet binding could be evaluated. Results of these models were used to evaluate m o u l d taper design, and to interpret force sensor results when binding was occurring. T h e m o u l d taper was found to be inappropriate at both companies.  Company A used a shallow  single-tapered m o u l d , and Company D an aggressively tapered parabolic m o u l d . Multiple-tapered moulds should be employed, using an intermediate taper (commencing at approximately 2 pet. m and reducing to 1 pet. m  _ 1  _ 1  at the meniscus,  at the bottom of the 200 m m mould).  5. M a t h e m a t i c a l models and sensor measurements were used to interpret the m o u l d response during friction changes. Interestingly, the force signal does not necessarily respond to mould-billet binding. If the lubrication is adequate, low forces w i l l be sensed.  Thus friction sensing responds  m a i n l y to lubrication effectiveness. If binding exists however, and lubrication is poor, exceptionally high forces w i l l be measured. 6. A surprising result of this study is that a correlation likely exists between heat extraction and friction when casting w i t h oil lubrication (solid friction).  A rough surface impacts heat transfer and friction negatively.  Thus when casting w i t h oil lubrication, mould-billet contact governs heat transfer and friction. 7. T h e friction response of oil and m o u l d flux lubricants fundamentally differ i n billet casting. T h e difference between solid lubrication and l i q u i d 269  lubrication has been noted in the slab casting literature [69] in reference to evaluating mould flux lubrication. Very little research has been published regarding friction in the field of billet casting. Further, slab casters usually employ only powder lubrication and billet machines typically use oil lubrication. During the course of this work, the two mini-mills participating in the research implemented powder casting practice for certain grades to improve billet quality. This research in evaluating friction on billet machines is timely, as billet producers are now using both lubricant types, as well as casting a large range of grades and sizes. As was evident in one example of high friction using mould powder, significant opportunity exists in billet casting to improve the usage of mould fluxes. The powder in this case was poorly selected, as the liquid flux pool was very small, and insufficient for effective lubrication. Also apparent in this example was the influence of mould oscillation and casting speed on flux consumption. Thus friction needs to be measured and minimized: the use of a force sensor is key in evaluating lubricants for both improving billet quality and increasing productivity.  11.2  Recommendations  As is evident from this research, the mechanical response of the mould is very dynamic, and changes with process variables. Since the mould response is key to both billet quality and productivity, its behaviour should not be presumed or neglected.  Recommendations from this research centre on measurement 270  of m o u l d response.  This work contributes to the concept of the "Intelligent  M o u l d " [16], an on-line monitoring system for billet and process quality. T h e casting machine itself should not be a variable i n the process. T h e machines tested were not operating at design specifications, since measurement of the oscillator response had not previously been conducted during operating conditions.  One would expect that monitoring of the oscillator would  assist i n maintenance, and would flag potential oscillator problems before substandard billets were produced or the machine became damaged. Thus, the oscillator response should be measured at least periodically during casting conditions. A reference performance should be established (i.e. measured stroke and negative-strip time), and deviations from this performance would indicate a need for maintenance. One might not expect that on-line monitoring of the oscillator would be necessary, but "human" upsets also occur. A s was noted during one plant trial, the negative-strip time was zero because of incorrect oscillation settings. Local oscillation practices may vary between grades, l u bricants and m o u l d sizes, and it is understandable that confusion may occur at times given the chaotic environment of the plant floor. On-line monitoring, reporting and alarming would ensure that target oscillation settings were being met. Friction monitoring is an essential tool for evaluating lubrication effectiveness, and for selecting lubricants such as m o u l d powders.  Since casting  w i t h m o u l d fluxes has only recently been employed i n the m i n i - m i l l industry, this research on friction monitoring is timely. Friction sensing can be used as  271  a design tool for selecting lubricants and setting m o u l d oscillation parameters. Friction sensing also responds well to some process upsets, and is an excellent on-line tool for detecting problems. In the case of a lubrication upset, the shell may stick, reducing surface quality, crack under high axial forces, or cause a breakout as an extreme case. Reduced lubrication w i l l also cause premature m o u l d wear. M o u l d taper design varies significantly i n the billet industry, as was evident i n a survey of billet producers [3]. M a t h e m a t i c a l modelling of billet shrinkage w i l l greatly assist i n m o u l d taper design. A l t h o u g h the o p t i m u m m o u l d taper, for a given m o u l d size, w i l l depend on steel grade and casting speed, some guidelines exist for taper design. Single-tapered moulds are i n appropriate because of m o u l d distortion at the meniscus and greater billet shrinkage i n the upper portion of the mould. Thus multiple-tapered moulds should be used. Parabolic moulds which are steeply tapered (5 pet. m  _ 1  at the  meniscus) have been shown to be too aggressive. If peritectic steels are to be cast i n a 200 m m m o u l d , intermediate tapers are appropriate (say 2 pet. m at the meniscus, and 1 pet. m  _ 1  _ 1  lower i n the mould). Further, billet producers  must measure the m o u l d dimensions to confirm the operating m o u l d taper. This would ensure that moulds were supplied to the correct tolerances, and moulds which have distorted are removed from service. T h e issue of process control i n billet casting is very important, especially w i t h respect to m o u l d flux lubrication and high speed casting. A s was seen i n this research, casting speed upsets may cause high friction when using m o u l d  272  fluxes.  In this context, the implementation of steel flow rate control would  be advantageous, as the casting speed would remain fixed. T h e disadvantages include cost and design of such equipment, since it is rarely used (if at all) i n the m i n i - m i l l industry. If flow rate control, and hence casting speed control, is available to the researcher, the impact of lubrication and friction can be further studied. For a given lubricant and mould oscillation settings, friction versus casting speed curves can be generated. Thus lubricants may be selected, and casting speed targets set for m i n i m i z i n g friction. M o u l d response should be measured quantitatively  to assist i n oscilla-  tor maintenance, the setting of oscillation parameters, evaluating lubricants, and identifying upsets on-line. Ultimately, the industry needs robust, precise oscillation, and low mould-billet friction to reduce billet defects and facilitate high speed casting.  11.3  A Primer for Billet Producers  If you own a billet machine read this.  1. M o u l d oscillation • Measure it. It's not what you think it is. 2. Process control • Casting speed may vary significantly, by greater than 30 pet., because of lack of steel flow control. This may be unacceptable for  273  m o u l d flux lubrication practice and high speed casting.  Consider  installing flow control. • The meniscus is, at times, excessively turbulent due to poor stream quality. If the meniscus cannot be stabilized, m o u l d flux lubrication practice should be implemented for depression-prone grades. Friction and lubrication • Friction may be quantified by installing a strain sensor on the m a chine drive arm. • O i l and m o u l d flux friction responses fundamentally differ. • W h a t impacts measured friction w i t h oil lubrication? — Peritectic steel surface roughness — Surface defects like depressions — O i l supply and distribution • W h a t impacts measured friction w i t h flux lubrication? — Casting speed — M o u l d oscillation • W h a t can you see w i t h a friction sensor? — Overall mould-billet interaction: lubrication effectiveness. — Gross process upsets like strand plugging and breakouts. — Billet jerking caused by a lubrication problem.  274  — Mould-billet binding i n the presence of poor lubrication. • W h a t can't you see w i t h a force sensor? — Single, local events like meniscus sticking, or transverse depressions forming. • W h a t else likely affects friction? — M o u l d taper. Impacts contact w i t h o i l lubrication; flux thickness w i t h powders. — T y p e of mould flux: break-point temperature and viscosity.  11.4  Simple Tools for On-Line Monitoring  T h e following section lists some simple features that an on-line system could use to monitor m o u l d response. This work complements the research of K u m a r [13], who studied the m o u l d thermal response i n the context of billet defects. A prototype of such an on-line system has been under development at U B C [98, 118], which is capable of most of these features.  11.4.1  Sensors  T h e system must be capable of measuring friction and m o u l d oscillation. Strain gauge and L V D T sensors are appropriate. T h e system must also log casting speed, metal level and mould thermocouple signals i f available.  275  11.4.2  Features  Oscillator • M o u l d stroke • Negative-strip time • M o u l d lead • Oscillation frequency  Process C o n t r o l • M e t a l level • Casting speed • M e t a l level stability (standard deviation of the meniscus thermocouple signal).  Lubrication • R a w force range • Effective friction coefficient (including the rejection of the cold machine forces)  11.4.3  Display  Table 11.1 presents a list of process parameters and how they may be presented by an on-line system. The process parameter attributes used i n the table are: 276  Operating T h e actual sensor reading or calculated process parameter. Set point T h e target process parameter. Heat average T h e process parameter averaged on a per heat basis. Extrema T h e history of m a x i m u m and m i n i m u m values of the parameter taken over a specified time period. E x t r e m a may be reported on a per heat basis, or trended on a per minute basis to visualize the operating range of a process variable. T h e graphical displays (raw signal versus time) would assist i n the assessment of oscillation condition and friction regime. T h e system could alarm when a process parameter was out of a specified range.  For example, i f the casting speed became excessive, the heat could  be aborted.  T h e system could also report process parameters as part of a  management information system. T h e parameters could be reported on a per heat basis, including average, set point, and extrema values.  277  Table 11.1: Suggested methods for displaying process parameters on an on-line system. Process Parameter Stroke  M o u l d velocity Negative-strip time  M o u l d lead  Oscillation frequency  Casting' speed  M e t a l level  Meniscus stability Raw force range Friction coefficient  Attribute operating set point heat average extrema operating operating set point heat average extrema operating set point heat average operating set point heat average operating set point heat average extrema operating set point heat average extrema operating heat average operating heat average operating heat average extrema  278  Numeric X X X X  Trend X  X X X X X X X X X X X X X X X X X X X X X X X X X  X  Graphical X  X X  X X  X  X  X X  X X X X X  Bibliography [1] Iron and Steel Institute. Statistical Information.  Iron and  Steelmaker,  23(13), J u l y 1996. [2] J . K . Brimacombe, E . B . Hawbolt, F . Weinberg. Metallurgical Investigation of Continuous Casting Billet Moulds - I. Distortion, Fouling and Wear. ISS Transactions,  1:29-40, 1982.  [3] I . V . Samarasekera, J . K . 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K o z l o w s k i , B . G . Thomas, J . A . A x x i , H . Wang. Simple Constitutive Equations for Steel at H i g h Temperature. Met. Trans. A, 23A:903-917, M a r c h 1992. [114] J . Szekely. Rate Phenomena  in Process Metallurgy.  Wiley-Interscience,  New York, 1974. [115] H i b b i t t , Karlsson and Sorensen Inc., Pawtucket, R L Verification  Manual,  ABAQUS/Standard  1995.  [116] S. K u m a r . T r i a l D I Internal Report, 1993. Unpublished, University of B r i t i s h C o l u m b i a , Vancouver, Canada. [117] C . A . Pinheiro. Private communication, University of B r i t i s h C o l u m b i a , Vancouver, Canada. [118] B i l l K i e l h o r n . Work i n progress. Centre for Metallurgical Process E n g i neering, University of B r i t i s h C o l u m b i a , Vancouver, Canada.  289  Appendix A Strain Gauge Force Calculation  Strain on the drive arm was calculated from the strain gauge bridge voltage using E q u a t i o n 4.1. Stress was calculated from the elastic stress-strain relationship, a — Ee, and force was simply F =  crA . arm  where: a = stress (Pa) E = elastic modulus (Pa) F = force (N)  A  = cross-sectional area of drive arm (m ) 2  arm  T h e variable values used i n the calculations were:  v = 0.3 E = 200-10 P a 9  GF = 2 Substituting the variable values into Equation 4.1, the strain gauge force was  290  F = EA e arm  = arm( EA  )  r 13  +  07Vr  (A.l)  For Machine B (trials A l and A 2 ) , the oscillator a r m was made of 101.6 m m square steel tubing, w i t h a wall thickness of 9.53 m m . T h e corresponding area was 0.0035 m . For Machine C (trials D 2 and D 3 ) , the oscillator 2  a r m was a tapered steel box. T h e dimensions of the box at the strain gauge location was 255 x 100 m m , w i t h a 15 m m wall thickness. T h e area of the box was 0.00975 m . 2  291  Appendix B Mould Thermocouple Layout  292  Distance from mould top (mm)  95  O 1  04 08 Oil  0 24  O O O O O O O O  2 3 5 7 9 12 14 15  O O O O O O O  16 17 18 19 20 21 22  290 315 335 385 435 485 535  O 23  630  O 25  730  06 O10 013  130 145 160 175 190 205 220 235  Figure B . l : Layout of m o u l d thermocouples on the east face; used for plant trials D I and D 2 .  293  Table B . l : M o u l d thermocouple depths used i n plant trials D I and D 2 .  Thermocouple Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25  294  Depth (mm) 7.81 7.79 7.77 7.78 7.74 7.74 7.63 7.69 7.70 7.85 7.77 7.86 7.71 7.76 7.76 7.48 7.66 7.78 7.69 7.68 7.64 7.60 7.62 7.56 7.49  Appendix C Calibration Data  T h i s appendix contains calibration equations to convert logged voltages to SI units. T h e equations are linear, of the form:  output unit = ao + a\ * voltage  (C.l)  Table C . l : Sensor calibration data for plant trial D I . Signals logged i n m i l l i volts.  Sensor load cell 1 load cell 2 load cell 3 L V D T 1 (cam) L V D T 2 (table) casting speed  Unit N N N mm mm mm s  a  _ 1  295  0  -0.0203  «i 2162 2071 2007 0.981 0.967 -0.00959  Table C.2: Sensor calibration data for horizontal m o u l d movement test during plant t r i a l D I . A l l L V D T s were short stroke.  Sensor short L V D T short L V D T short L V D T short L V D T  Unit mm mm mm mm  1 2 3 4  a  a  0  x  5.00 3.60 3.98 12.19  Table C . 3 : Sensor calibration data for plant trial A l . Signals logged i n volts.  Unit mm s mm s mm mm s A N  Sensor P C B accelerometer 531 P C B accelerometer 532 LVDT Casting Speed motor current strain gauge  a  ai  0  9869 9869 5.484 20.31 4.63 82840  - 2  - 2  _ 1  0.07  Table C.4: Sensor calibration data for plant trial D 2 . Signals logged i n m i l l i volts.  Sensor load cell 1 load cell 2 load cell 3 LVDT motor current strain gauge casting speed metal level  Unit N N N mm A N mm s mm  a  ai  -0.0203 -335  2162 2071 2007 1.47 2.606 156250 -0.00959 26.265  0  _ 1  296  Table C.5: Sensor calibration data for plant trial D3, force sensor test. Signals logged in volts.  Sensor LVDT accelerometer strain gauge temperature casting speed metal (171 mm metal (194 mm metal (200 mm metal (200 mm  mould) mould) Concast) Steltek)  Unit mm mm s N °C mm s mm mm mm mm  a -15 -7.401 -250000 -75 -21.25 -223.2 -151.3 -120 -150 0  - 2  _1  «i 7.77 2.467 88315 75 21.25 90.71 74.1 63.5 69.2  Table C.6: Sensor calibration data for plant trial A2, force sensor test. Signals logged in volts.  Sensor LVDT accelerometer strain gauge casting speed metal level  Unit mm mm s N mm s mm  297  a  0  - 2  -74.01  _1  152.4 185  «i 12.96 24.67 454000 -152.4 -29  Appendix D Plant Trial Sensor Schematics  298  Figure D . l : Electrical schematic for plant trial D I .  299  c 2§  JSTTOflUOO UIOJT  aojnos aSujiOA  •O T3 U  <u Oh  .5 <^ UJ9ui[dure  uopBjuauirujsui  jauonipuoo JBUglS  ^1  H Q >  jauonipuoo JBUSIS  I Figure D . 2 : Electrical schematic for plant trial A l .  300  <0 o o  jgijiidure UOpBTOSJ  A\rarreg  1  i"  •C  /trarjeg  /{jddns j 9 A \ o d p3JBIIl§3J  UOA 01  japiAip  J9UOTJipUOO  IBUSIS  Figure D . 3 : Electrical schematic for plant trial D 2 .  301  u  /(jddns  K M O j  puonipuo3  JSUOlJipUCQ  reuSis  •• •  Figure D.4: Electrical schematic for on-line force sensor test  302  u  jaijijcluiv  /(iddns J9M0J  puopipucQ I'BUSIS  jauonipucQ reu§TS  J3IJI[dlUB  u >  /(jddns  o  Figure D.5: Electrical schematic for on-line force sensor test 303  Appendix E Chemical Compositions of Heats Monitored  T h i s appendix contains the chemical analyses of heats monitored during the m a i n experimental plant trials.  304  Table E . l : C h e m i c a l composition, i n weight percent, of heats monitored at plant t r i a l A l .  Heat 708 709 710 711 712 713 714 715 716 717 718 719 720 727 728 729 730 737 738 743  Lub. flux flux flux flux flux flux flux flux flux flux flux oil oil oil oil oil oil oil oil oil  c  .43 .31 .19 .19 .19 .19 .19 .16 .41 .88 .93 .90 .88 .71 .72 .68 .67 .79 .81 .93  Mn 0.67 0.74 0.53 0.46 0.48 0.50 0.50 0.84 0.83 0.75 0.70 0.68 0.75 0.82 0.81 0.83 0.79 0.83 0.79 1.14  S .025 .023 .022 .015 .017 .016 .041 .024 .023 .031 .026 .020 .020 .024 .016 .015 .011 .016 .017 .016  P .014 .010 .008 .008 .007 .008 .015 .016 .012 .019 .020 .011 .020 .014 .015 .014 .014 .011 .015 .021  Si .19 .20 .22 .21 .17 .18 .19 .27 .24 .19 .21 .20 .20 .24 .16 .15 .11 .16 .17 0.16  Cu .21 .19 .27 .23 .17 .22 .24 .20 .21 .32 .29 .24 .26 .23 .22 .23 .24 .24 .22 .27  Cr .20 .16 .13 .13 .14 .12 .12 .15 .86 .24 .22 .15 .16 .88 .89 .23 .27 .59 .61 .25  Ni .11 .10 .09 .11 .08 .08 .08 .08 .12 .14 .11 .09 .11 .11 .16 .12 .16 .13 .12 .13  Mo .44 .028 .026 .028 .027 .021 .035 .023 .196 .050 .039 .028 .037 .049 .065 .185 .186 .056 .081 .046  V .001 .001 .001 .001 .001 .000 .001 .001 .004 .002 .000 .000 .001 .003 .003 .001 .002 .002 .001 .004  Nb .031 .001 .023 .023 .025 .026 .023 .026 .034 .003 .002 .002 .002 .019 .021 .024 .022 .025 .021 .001  Sn .012 .009 .011 .009 .007 .008 .008 .009 .010 .011 .013 .017 .020 .012 .009 .011 .016 .014 .014 .014  Table E . 2 : C h e m i c a l composition, i n weight percent, of heats monitored at plant t r i a l D I .  Heat 142 146 147 148 149  Lub. oil oil oil oil oil  C .12 .32 .32 .32 .84  Mn 0.84 0.71 0.86 1.31 0.71  S .028 .023 .009 .006 .022  P .019 .023 .022 .022 .023  Si .21 .20 .24 .24 .24  Cu .26 .30 .27 .29 .35  305  Cr .10 .10 .09 .24 .09  Ni •Mo .02 .10 .10 .02 .10 .02 .10 .02 .02 .10  Ti  B  .33 .33  .0020 .0032  Sn .016 .024 .016 .022 .026  N  Ca  Al  .001 .002  .010 .005  Table E . 3 : C h e m i c a l composition, i n weight percent, of heats monitored at plant t r i a l D 2 .  Heat 277 278 279 280 281 282 286 297 298 299 300 311 312 313 314 315 316 333 334 351 352 353  Lub. flux flux flux flux flux flux flux oil oil oil oil flux flux flux flux flux flux flux flux oil oil oil  c  .14 .13 .14 .13 .13 .13 .14 .12 .13 .12 .13 .33 .30 .33 .31 .32 .32 .32 .32 .80 .81 .80  Mn 0.84 0.82 0.85 0.89 0.86 0.88 0.82 0.86 0.82 0.84 0.88 1.29 1.33 1.29 1.26 1.36 1.31 1.28 1.26 0.65 0.65 0.63  S .020 .021 .019 .020 .021 .024 .017 .018 .018 .019 .020 .007 .009 .011 .008 .006 .007 .005 .008 .012 .017 .024  P .010 .010 .010 .009 .012 .015 .006 .010 .008 .008 .010 .011 .010 .009 .009 .010 .008 .007 .009 .009 .007 .013  Si .17 .17 .18 .18 .20 .19 .17 .16 .17 .16 .19 .18 .20 .18 .17 .19 .20 .18 .19 .18 .20 .20  Cu .28 .30 .27 .29 .26 .30 .30 .31 .33 .35 .33 .29 .31 .30 .30 .25 .24 .30 .33 .28 .27 .29  306  Cr .09 .09 .09 .09 .10 .09 .07 .10 .08 .08 .09 .24 .24 .23 .24 .25 .26 .24 .23 .07 .08 .10  Ni .09 .09 .08 .10 .09 .08 .10 .09 .09 .09 .09 .10 .09 .09 .12 .09 .08 .09 .09 .08 .08 .09  Mo .02 .02 .02 .02 .02 .01 .02 .02 .02 .02 .02 .01 .01 .02 .03 .02 .02 .01 .01 .01 .01 .01  Ti  B  .038 .038 .038 .036 .035 .040 .038 .035  .0027 .0037 .0028 .0025 .0024 .0027 .0023 .0028  Sn .014 .015 .015 .017 .015 .014 .013 .012 .014 .017 .016 .016 .016 .015 .014 .014 .014 .015 .015 .014 .015 .016  N  Ca  Al  .0094 .0086 .0086 .0095 .0081 .0079 .0087 .0081  .002 .002 .002 .002 .002 .002 .003 .003  .007 .007 .006 .006 .007 .007 .007 .006  Appendix F Contour Plots of Surface Defects  307  (mm)  Billet Width (mm)  Figure F . l : Longitudinal midface depression believed to be caused by excessive mould taper. Sample 1, trial D I , 0.3 pet. C + B , 203 mm mould, oil lubrication, north face.  308  Figure F.2: Longitudinal midface depression believed to be caused by excessive mould taper. Sample 2, trial D 2 , 0.14 pet. C, 203 mm mould, powder lubrication, north face.  309  Figure F.3: Transverse depression, sample 1. Trial D2, 0.14 pet. C, 203 mm mould, powder lubrication, east face.  310  depth (mm) -0.15  50  100  150  Billet Width (mm)  Figure F.4: Transverse depression, sample 2. Trial D2, 0.14 pet. C, 203 mm mould, powder lubrication, south face.  311  depth (  CD C GO CO  o  0.83 0.23 -0.38 -0.98 -1.59 -2.19 -2.79 -3.40 -4.00 -4.61 -5.21 -5.82  100 Billet Width (mm)  Figure F . 5 : Transverse depression, sample 3. T r i a l D 2 , 0.3 pet. C + B , 203 m m mould, o i l lubrication, east face.  312  CD CO CC  0  50  100  depth ( 0.33 -0.00 -0.34 -0.68 -1.02 -1.35 -1.69 -2.03 -2.37 -2.71 -3.04 -3.38  150  Billet Width (mm)  Figure F.6: Transverse depression, sample 4. Trial D I , 0.3 pet. C + B , 203 mm mould, oil lubrication, west face.  313  Figure F.7: Transverse depression, sample 5. Trial D2, 0.3 pet. C + B , 203 mm mould, oil lubrication, south face.  314  Appendix G Thermomechanical Tests of Boron Steels  The simple tests described i n Table G . l were conducted on as-cast samples to determine if the boron steels exhibited increased hot strength.  Further  metallurgical research must be conducted to test samples at in-situ conditions.  Table G . l : Thermomechanical tests. Steel  Sample  (°C) Trial Trial Trial Trial  DI, DI, DI, DI,  heat heat heat heat  146 146 148 148  0.32 0.32 0.32 0.32  pet. pet. pet. pet.  C C C + B,Ti C + B,Ti  315  1300 1300 1300 1300  Tdeform  Strain R a t e  (°C) 1200 1300 1200 1300  0.01 0.01 0.01 0.01  0.30%C 0.30%C + B,Ti 10  1  0.1  0.2 Strain  Figure G . l : Thermornechanical tests of 0.32 pet. C and 0.32 pet. C + B as-cast samples at a strain rate of 1 0 s at 1200°C. - 2  _ 1  0.30%C 0.30%C + B,Ti 0.0  0.1  0.2 Strain  0.4  Figure G.2: Thermomechanical tests of 0.32 pet. C and 0.32 pet. C + B as-cast samples at a strain rate of 10~ s at 1300°C. 2  _ 1  316  

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