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The measurement of forces in chip refiners Siadat, Seyed Mohammad Ali 2001

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THE MEASUREMENT OF FORCES IN CHIP REFINERS By SEYED MOHAMMAD Al I SIADAT B.Eng. (Mechanical Engineering), McMaster University, 1997  A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR THE D E G R E E OF M A S T E R OF APPLIED SCIENCE In THE F A C U L T Y OF G R A D U A T E STUDIES Department of Mechanical Engineering  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA March 2001 © S. M. Ali Siadat, 2001  In presenting  this  degree at the  thesis  in  partial fulfilment  of  University of  British Columbia,  I agree  freely available for reference copying  of  department  this or  publication of  and study.  thesis for scholarly by  this  his  or  her  Department The University of British Columbia Vancouver, Canada  requirements that the  I further agree  purposes  representatives.  may be It  thesis for financial gain shall not  permission.  DE-6 (2/88)  the  that  advanced  Library shall make it  by the  understood be  an  permission for extensive  granted  is  for  allowed  that without  head  of  my  copying  or  my written  ABSTRACT The purpose o f the chip refining process i n the pulp and paper industry is to produce wood pulps and to enhance certain desirable properties o f the fibres i n the pulp suspension, b y subjecting the wood material to cycles o f shear and compressive stress. This process has commonly been quantified i n terms o f energy-based parameters such as specific energy and refining intensity, but such methods, although useful for establishing energy-pulp  quality relationships,  do  not  describe  the  underlying  fundamental  mechanisms o f the process. It has been suggested that a knowledge o f the stress-strain history o f individual fibres can yield a deeper understanding o f the process [Page, Fundamental Research Symposium (1989)].  W i t h the long-term goal o f such an understanding, the forces experienced b y pulp i n the refining zone are measured i n a laboratory refiner operating at 700 rpm with softwood T M P at 16% consistency. This is done using a two-axis force sensor, originally designed by A . Bankes, P. W i l d and D . Ouellet. The design, i n its original form, did not perform well enough to provide a reliable force measurement under the high excitation frequency o f passing refiner bars, as the sensor's resonant frequency was too low. A modified design with a much higher natural frequency is presented here, along with force measurements i n the refining zone for various plate clearances, and varying dilution flow rate.  From these measurements, we see that both the normal and shear forces contain a component due to the ploughing action o f the corner o f the bar through the floe (termed  ii  the comer force), a phenomenon previously only seen i n the shear force [Batchelor et al. J. Pulp Pap. S c i . 23(1) (1997), Senger et al., Proceedings o f the International Mechanical Pulping Conference, (2001)].  The peak normal force increased with decreasing plate clearance, while the peak shear force measured b y the sensor did not exceed U N , corresponding to a maximum shear force per unit bar length o f 2.2 k N / m . The equivalent tangential coefficient o f friction decreased with decreasing plate clearance, and also decreased upon the addition o f dilution water. The sensor design needs further refinement for testing at higher refiner rotational speeds, as signals acquired at high speeds are distorted b y the sensor's resonant vibrations.  iii  CONTENTS ABSTRACT LIST OF TABLES  ,  LIST OF FIGURES. ACKNOWLEDGEMENT 1.  INTRODUCTION.  2.  REFINING THEORY. 2.1 Energy-Based Refining Theories 2.1.1 Introduction To Energy-Based Refining Theories 2.1.2 L o w Consistency Refining Theory 2.1.3 H i g h Consistency Refining Theory  2.2 Force-Based Refining Theories. 2.2.1 Forces In L o w Consistency Refining 2.2.2 Forces In H i g h Consistency Refining  2.3 Research Objectives 3.  ORIGINAL SENSOR DESIGN 3.1 Design Details 3.2 Impact Tests & Calibration. 3.3 Refiner Tests Using Original Sensor Design 3.4 Discussion Of Preliminary Test Results. 3.4.1 Calibration 3.4.2 Dynamic Behaviour 3.4.3 Sensor Fabrication  iv  4.  MODIFIED SENSOR DESIGN  37  4.1 Design Modifications  37  4.1.1 Machining O f Housing Parts  37  4.1.2 Piezo Ceramic Elements  38  4.1.3 Insulating Material  38  4.1.4 Housing Support  39  4.1.5 Damping Mechanisms  41  4.1.6 Further Stiffening O f Sensor  41  4.2 Impact Tests & Calibration  5.  43  4.2.1 Sensor Response T o Combined Normal A n d Shear Loads  43  4.2.2 Effect O f Impact Position  48  REFINING TRIALS.  50  5.1 Experimental Setup  50  5.2 Refining Force Profiles  51  5.2.1 B a r Passing Events  51  5.3 Data Rejection Criteria  55  5.3.1 Sensor Vibrations  56  5.3.2 C y c l i c Fluctuations In Normal Force W i t h Each Rotation  59  5.4 Analysis & Discussion  62  5.4.1 Impact Statistics  62  5.4.2 Variation O f Shear Force W i t h Plate Clearance  63  5.4.3 Effect O f Injecting Dilution Water  65  5.4.4 Variation o f \k,eq W i t h Plate Clearance & Consistency  v  65  5.4.5 Ranges O f Measured p^eq & Average Pressure  6. CONCLUSIONS  67  71  BIBLIOGRAPHY.  73  NOMENCLATURE  76  APPENDIX A: Specifications O/D2B502 Refiner Plates  79  APPENDIX B: Properties OfPiezo Ceramic Elements  80  APPENDIX C: Calibration Procedure APPENDIX D: Matlab Programs  81 96  APPENDIX E: Estimated Length Of Bars Crossing at Any Given Time  vi  100  LIST OF TABLES 1.1 Differences between chip refiners and pulp refiners  4  4.1 K-Values determined by impacting the sensor at different angles  45  4.2 Variation o f sensitivity (K-values) o f piezo elements 2 and 3 with varying impact position on the top face o f the probe. A l l K-values are i n V / N , and a is the standard deviation  49  5.1 Summary o f impact statistics for refining runs at 700 rpm ( a is the standard deviation)  63  5.2 Values o f constants from different sources for use i n Equation 2.8 (SI and S2 refer to primary and secondary stage processes, respectively) 68  vii  LIST OF FIGURES 1.1 Schematic diagram o f a chip refiner  2  3.1 Components o f the preliminary sensor design  20  3.2 Sensor installed i n refiner plate for measuring forces during refiner operation  21  3.3 Impact testing o f sensor (mounted in jig) using force hammer. Impacts i n the xdirection correspond to the direction o f bar impacts at the leading edge during refiner operation  23  3.4 Force hammer impact i n time and frequency domain  23  3.5 Response o f sensor (from piezo elements 1 & 3) to a normal impact at the probe tip ...24 3.6 Variation o f peak signal voltage from piezos 1, 2 and 3 with impact force for normal impacts 25 3.7 Average transfer functions for piezo elements 1 and 3 i n response to 20 vertical impacts  27  3.8 Signals from piezo elements during refiner operation. B a r passing events cannot be distinguished as vibrations dominate the signal  30  3.9 Refining forces derived from the above signals. The fine line corresponds to the forces calculated from piezo elements 1 and 3, while the bold line uses the combination o f piezo elements 2 and 3  30  3.10 The variation o f the refining forces over a period o f 1 second, as derived from different piezo combinations. The periodic behaviour corresponds to the rotor plate rotation  32  3.11 Comparison o f measured with calculated values o f the normal force for impacts applied to the sensor when mounted i n the plated  33  3.12 Exaggerated diagram showing how the piezo elements deform as the probe is displaced  35  4.1 Sensor housing design changes  38  4.2 Average transfer functions for piezo elements 1 and 3, with the new housing modifications and the 2 mm-wide piezo elements  40  4.3 Sensor used i n conjunction with shims i n order to inhibit deformation o f housing  40  viii  4.4 Effect o f using latex pads in conjunction with layers o f mica i n the shims. The time domain signal o f piezo element 3 is shown in response to an impact from the force hammer  42  4.5 Transfer functions for piezo elements 1 and 3, for revised sensor design with all new modifications 42 4.6 Impacts administered at different angles by using aluminum wedges  44  4.7 A comparison o f the true normal component with values calculated from Equations 4.4a and 4.5a  47  4.8 A comparison o f the true normal and shear components with those calculated from Equations 4.4b and 4.5b  47  4.9 The moving load during a bar passing event. A s the rotor bar moves across the top o f the probe, so does the centre o f pressure  48  5.1 Refining normal force (bold line) and shear force (fine line) at 700 rpm as calculated using piezo combinations 2-3 and 2-4 52 5.2 One o f the three segments o f the D 2 B 5 0 2 rotor plate (the stator plate segments are identical)  53  5.3 The normal (bold line) and shear forces (fine line) due to a typical bar impact  54  5.4 A n illustration o f problematic 30 k H z resonant vibrations o f the sensor  56  5.5 Typical force profiles o f bar impacts at 2560 rpm  57  5.6(a) Sensor vibrations at approximately 2 k H z  58  5.6(b) 2 k H z vibrations grow i n amplitude for five successive bar impacts, until a sixth impact from a wider bar reduces their amplitude. This record shows several successive occurrences o f this phenomenon  58  5.7 C y c l i c fluctuations i n normal force with each rotation at 2560 rpm  60  5.8 Variation o f plate clearance and mean normal force through one full rotation o f the rotor plate  61  5.9 Equivalent tangential coefficient o f friction versus plate clearance  66  5.10 Plot o f the equivalent tangential coefficient o f friction against average mechanical pressure for different refiners  68  ix  ACKNOWLEDGEMENT The author wishes to thank the many people whose help eased the task o f preparing this thesis. T o Dr. D . Ouellet for the priceless guidance provided throughout m y experience as a Masters' student. To J. Senger for the many helpful discussions and valuable feedback, and for generally being a pleasure to work with. T o R. N a g y for the technical support to combat the seemingly endless computer problems. To Dr. P. W i l d , A . Bankes, M . Olmstead and B . Shiari for much helpful input regarding the force sensor. T o P. Taylor for the meticulous fabrication o f sensor parts. T o T. Paterson, K . W o n g , L . Brandly, B . Dutka, J. Marsden, B . M c M i l l a n , R. Penko, J. Mackenzie, G . White, D r . R . Thiruvengadaswamy, and Dr. G . Stewart for providing help i n many areas during m y time at the Pulp & Paper Centre. To the N C E Mechanical W o o d Pulps Network for funding m y project. A n d most o f all, to m y parents for ceaseless love and support throughout m y time as a student (and as a human being, for that matter).  x  1. INTRODUCTION Refiners are used i n the pulp and paper industry to mechanically separate fibres from the wood matrix and to enhance certain pulp properties.  The former o f the two actions,  commonly termed mechanical pulping, is carried out i n chip refiners at high consistency. Here, wood chips are fed into the refiner and fibres are peeled away from the wood structure b y repeated cycles o f shear and compressive stresses. This mechanism affects the physical properties o f the individual fibres, and o f the paper ultimately made from these fibres.  The most common type o f refiner is the disc refiner, illustrated schematically i n Figure 1.1.  Pulp is fed through the inlet, and moves between the two refiner plates, one  stationary and the other rotating at high speed (commonly 1800 rpm i n North America, and 1500 rpm i n Europe). Both plates have a bar and groove pattern, and are separated by a small gap through which the pulp flows. A s the rotor bars pass over the stator bars, agglomerates o f pulp fibres are trapped repeatedly between the passing bars, and i n this way receive the cyclic loading that constitutes the mechanical action o f refining.  These loading events are the topic o f study i n this work, for they are the basic cause o f the changes to the fibre structure.  The nature o f the changes i n the refined pulp is  strongly dependent on the absolute and relative magnitudes o f these loads and the number o f loading cycles received b y each fibre. These factors are influenced b y the plate  1  Outlet Figure 1.1 Schematic diagram of a chip refiner.  pattern, the refiner rotational speed, the pulp consistency, the plate clearance and the residence time o f pulp i n the refining zone. A l l these variables come under consideration depending on the desired result.  A t this point, we must make a distinction between chip refining and pulp refining. Chip refining is the production o f pulp from wood chips b y refining at high consistency, whereas low consistency pulp refining is carried out to develop the properties o f fibres that have already been separated b y chemically dissolving the wood substances that bind them together.  2  In chip refiners, it is desired first to break down the wood chips and free the individual fibres, and then to enhance their  flexibility.  The chips are first impacted at the beginning  o f the refining zone with a coarse bar pattern that becomes progressively finer as we move radially outwards through the refining zone.  The breaker bar section is tapered  slightly to allow for a larger plate gap i n this region, which narrows to a smaller gap at the intermediate bar section, and often continues to narrow all the way to the outer radius o f the refining zone. Due to the high energy mechanical action i n chip refiners, large amounts o f steam are produced between the refiner plates, causing high temperatures and pressures that are not encountered i n the lower consistency pulp refining process.  The purpose o f pulp refining is to alter the properties o f the fibres, which have already been separated from the wood matrix, to a state that best serves the final product. Therefore, the breaker bar section is not required i n this application, and usually there is only one type o f bar that spans the refining zone. A s a result o f the lower consistency, pulp refining is carried out at a much lower plate clearance than chip refining.  The key differences between pulp and chip refiners are summarized i n Table 1.1. Due to these differences (most notably i n the flow o f pulp), the refining action i n the two processes is characterized differently.  O n a very basic level, however, the action o f the  two types o f refiners is similar, as i n both cases the wood material is repeatedly beaten b y passing refiner bars. Therefore, there are some similarities i n the characterization o f the different types o f refiners.  3  Chip Refiners Pulp Refiners High (20-60%) Low (3-5%) 36 to 68 inches (0.91 to 1.73 m) 32 to 48 inches (0.81 to 1.22 m) 1500 rpm in Europe 1200 or 1800 rpm in North America 600 to 900 rpm (although some 1st stage refiners run at up to 2300 rpm) Plate Clearance 0.5 to 3 mm 0.06 to 0.2 mm Specific Energy 1.5to3.5MWh/t 80 to 250 kWh/t Pulp suspension is pumped through refiner Pulp Flow Pulp is propelled by forces inside refiner Table 1.1 Differences between chip refiners and pulp refiners. Consistency Plate diameter Speed  In order to predict the extent o f the refining treatment received b y the fibres, a number o f theories have been put forward. For the most part, these have been based on the net mechanical energy transferred to a unit mass o f pulp, and the "intensity" at which this energy is applied. This approach has proven useful i n developing relationships between key operating variables and the quality o f the resulting pulp suspensions, and the simplicity o f some o f these energy methods has facilitated their widespread use. However, when it comes to understanding the fundamental mechanisms o f refining, such energy-based theories offer limited insight, because they make no attempt to describe the mechanisms b y which the energy was transferred to the fibres.  Refined fibres undergo a variety o f structural changes due to the different modes o f loading they experience. Passing bars cut and bend fibres, and subject them to cyclically varying normal and shear stresses.  Furthermore, the effects also depend on the  combinations o f the modes o f loading and the relative magnitudes o f these loads.  A general objective o f the work presented here is to develop a better understanding o f high consistency refining based on the forces encountered i n the process. This work w i l l  4  focus on measuring the forces that are experienced between refiner bars and examining how they are affected b y operating conditions. The basis o f our approach was to develop a two-axis force sensor capable o f withstanding the harsh conditions present inside an operating refiner, and to use this sensor to measure forces at various plate clearances, consistencies and rotational speeds.  The refiner used i n this study is a 12-inch Sprout Waldron laboratory refiner. The force sensor used was originally designed by A l a n Bankes [1], and was modified i n order to improve its behaviour. The modified design is useful for tests on the laboratory refiner, operating at speeds up to 700 rpm, above which meaningful force measurements are not possible as sensor vibrations dominate the signal.  This thesis begins with a review o f refining theories and previous investigations regarding the refining forces. The focus then shifts to the development, testing and use o f the refiner force sensor.  This is followed b y an analysis o f force measurements made  during refiner operation.  5  2 . REFINING THEORY Characterization o f the action o f refining has evolved over the years to enable producers of pulp to predict the effects o f different operating conditions. This chapter w i l l review the key theories put forward to characterize the action o f both high consistency and l o w consistency refining. The review w i l l focus first on energy-based theories for the two types o f processes, and then on research into forces experienced b y pulp floes i n refiners. This w i l l set the stage for a summary o f the objectives o f the work presented i n this thesis.  2.1 ENERGY-BASED REFINING THEORIES 2.1.1  INTRODUCTION  TO ENERGY-BASED  REFINING  THEORIES  The most widely used parameter for characterization o f the degree o f refining at both high and low consistency is the specific energy, which is defined as the  energy  transferred per unit mass o f pulp. It is calculated from:  (2.1)  E = —  m  f  where P is the net power transferred to the pulp and m  f  is the oven-dry fibre mass flow  rate through the refiner.  O n its own, the specific energy is not enough to fully characterize the refining action, because o f differences i n types and sizes o f refiner, plate designs and operating conditions.  Therefore, two trials with pulp refined to the same specific energy can  exhibit very different results, as the different effects o f refining on the fibres (internal and external fibrillation, fibre cutting, etc.) can occur to different extents.  This is true for  both high consistency [2] and low consistency processes [3].  It was therefore  necessary to develop a second parameter  which, when used i n  conjunction with the specific energy, would allow us to predict the effects o f refining b y accounting for other important refining conditions. This additional parameter generally attempts to quantify the severity or intensity o f the refining treatment b y estimating the amount o f energy transferred to pulp with every refiner bar impact.  The number o f impacts received b y each fibre is directly dependent on the time it spends i n the refining zone (the residence time). In low consistency refiners, pulp is pumped through b y an external pumping system, and the liquid nature o f the suspension allows a simple calculation o f the residence time based on geometric considerations and the flow rate o f the pulp suspension.  In high consistency chip refiners, the pulp suspension  behaves more like a wet solid than a liquid, and no pump is used. Therefore, the velocity o f the pulp through the refiner is determined b y considering the forces acting on it, such as the centrifugal force, contact forces with the refiner plates, and drag forces from the large amounts o f steam produced during the process.  Because o f these key differences i n the way pulp flows through low and high consistency refiners, the measures o f refining intensity differ i n these two cases. They w i l l therefore be reviewed separately i n the next two sections.  7  2.1.2  LOW  CONSISTENCY  REFINING  THEORY  There have been many suggestions for the form o f the refining intensity parameter at l o w consistency. A s the name suggests, this parameter, i n all its forms, describes the severity with which the energy treatment is imparted to the pulp.  The definitions o f the measures o f intensity discussed here are all i n the form: P  (2.2)  1 =  constant where / is the intensity and P is the net power.  The form o f the constant i n the  denominator distinguishes the different ways o f measuring the intensity.  In l o w consistency processes, the most commonly used intensity measure is the specific edge load  (SEL),  defined as [4]:  P SEL = -^—  CEL  P  (2.3)  = ^ - ^ -  X""»„Aco  The denominator here is known as the cutting edge length  {CEL).  It is the total length o f  bar crossings per second i n the refining zone. The values n and n i are the number o f ri  S  bars on the rotor and stator, respectively, i n a radial increment i, Z,- is the length o f the refiner bar within the radial increment, and co is the rotational speed o f the refiner (revolutions per second). The SEL is therefore a measure o f the energy transferred per unit length o f bar, measured i n J/m.  8  This intensity measure is based on the design o f the plates i n use, but neglects many parameters that are known to have an effect on the mechanical treatment.  A major  criticism o f the SEL theory is that it ignores parameters such as groove depth, bar and groove widths, and bar angle, although it has been suggested that some o f these parameters are indirectly accounted for [5]. In response to these criticisms, extensions to the SEL theory were devised that included some o f these other plate parameters.  Among  these were the Modified Edge Load (MEL) [6] and Specific Surface Load (SSL) [7] theories.  Other theories were not limited to plate design parameters, as factors such as pulp consistency, unrefined fibre properties and plate clearance had yet to be addressed. Possibly the most comprehensive o f all intensity measures to date, i n terms o f accounting for all the relevant factors i n the refining process, comes from Kerekes' C-factor theory [3]. This theory accounts for plate parameters, pulp properties and operating variables, and also allows for an estimation o f the number o f impacts received b y each fibre, as w e l l as the average energy associated with each impact. However, due to its more complex nature than the  2.1.3  HIGH  SEL-type  theories, the C-factor theory is not as widely used i n industry.  CONSISTENCY  REFINING  THEORY  One o f the greatest influences i n the understanding o f high consistency refining came when M i l e s and M a y published their highly successful model o f the flow o f pulp i n chip refiners [8] i n 1990. They followed it up a year later with extensions on the theory and experimental results to support the work [9]. Their approach consists o f considering the  9  forces acting on an element o f pulp i n the refining zone to predict its radial velocity, which is then used to estimate the residence time.  The model predicts that this element o f pulp is acted on b y centrifugal and frictional forces, along with the drag forces exerted b y the copious amounts o f steam generated i n the refiner. The equation derived for the radial velocity o f the pulp, v, as it relates to the radial position i n the refining zone, r, is: dv _ rco dr  v  2  —a  V  Ecjr)  r  (2-4)  + S  II, a > ( r - r , ) 2  2  2  where CO is the refiner's rotational speed, c is the pulp consistency (fraction), \i and  are  the coefficients o f friction i n the radial and tangential directions respectively, r\ and  are  r  the inner and outer radii o f the refining zone, a is a constant that equals 4 for a single-disc refiner and 2 for a double-disc refiner, and S is a term related to the steam flow.  The  steam flows backward (i.e. counter to the flow o f pulp) near the inlet o f the refining zone, and forward near the outlet, exerting no force on the pulp at the stagnation point i n between.  Therefore, b y assuming that the effects o f the backward and forward  flowing  steam cancel each other out, the equation is simplified b y removing the steam flow term [10]. A further simplification can be made b y assuming that the pulp velocity gradient is small relative to other terms i n Equation 2.4, and the differential equation is then reduced to a simple algebraic equation.  The residence time, %, can then be determined using:  (2.5)  10  and the number o f impacts experienced b y each unit o f pulp,  where N  av  n , imp  is:  is the average number o f bars per unit length o f arc. U s i n g this, M i l e s and  M a y then coined an intensity measure for the chip refining process. This is the specific energy per impact, e: F e = —  (2.7)  TV av  Thus, as M i l e s , M a y and associates have shown [8-11], a two-parameter energy-based characterization can be used to predict certain pulp property changes associated with changes i n refining conditions.  2.2 FORCE-BASED REFINING THEORIES To their credit, researchers have come a long way i n predicting the response o f pulp to refining b y quantifying the process i n terms o f energy-based parameters. However, all o f these characterizations possess the common shortcoming that none can describe the exact mechanisms o f the energy transfer.  A variety o f structural changes are experienced b y  the fibres i n the process, among which internal fibrillation, external fibrillation, fibre shortening and the creation o f fines are the main ones. The type o f loading seen b y the fibres  is the direct influence for these changes, but none o f the energy based  characterizations yield an understanding o f these effects.  The following sections are  dedicated to the research that has focused on the refining forces i n order to gain a  11  complete, detailed picture o f the mechanical phenomena occurring inside a refiner. The cases o f high and low consistency are again taken up separately.  2.2.1  FORCES  IN LOW  CONSISTENCY  REFINING  In 1989, Page described his vision o f the forces acting on an agglomerate o f pulp fibres (a floe) as it is trapped between passing bars i n the refining zone [12]. H e envisioned three main forces i n refining: a normal component (perpendicular to the faces o f the bars) due to the compression o f the floe, a shearing component (in the direction tangential to the relative motion o f the bars) due to friction between the pulp and the bars, and a "ploughing" force (also known as the 'corner force') required for the bar corners to plough through the floe. Page himself did no work to measure these forces.  One o f the first attempts to quantify the refining forces was described b y Khlebnikov et al. at the Leningrad Institute for the Pulp and Paper Industry.  They used sensors to  determine the forces i n a conical refiner operating at 2-3 % consistency [13]. They measured forces i n two perpendicular directions on the face o f a refiner bar, those directions being normal to the face o f the bar (the normal force) and tangential to the motion o f the bar (the tangential force, or shear force).  They plotted the shear force  profile that they measured due to individual bar passing events where floes were trapped between opposing refiner bars. The shear force was seen to rise sharply at the start o f the event, then fall sharply to a much lower level where it remained essentially constant until the trailing edges o f the bars i n question parted ways.  12  The sensor designs they used were based on strain gauges, and these designs were revised the following year [14] before being used b y Goncharov, who then implemented their use in a disc refiner [15]. H e reported similar force profiles to those o f Khlebnikov et al.  In retrospect, it seems likely that the initial peak i n the shear force was due to the corner force described b y Page twenty years later, and the lower, constant force regime that followed it was the friction force between the pulp and the metal faces o f the refiner bars.  The initial high force regime was seen to act for a greater portion o f the bar passing event when the plate clearance was decreased. The overall magnitudes o f the forces measured were seen to rise with increasing consistency, increasing operating speed, and decreasing plate gap. Khlebnikov et al. defined the ratio o f the tangential force to the normal force as the coefficient o f refining, and saw that it increased for decreasing plate clearance and for increasing speed. Goncharov reported a coefficient o f refining o f approximately 0.11 for unbleached sulphite pulp at 2.5-3 % consistency refined at 720 rpm. H e also quoted peak pressures at the bar surface o f around 3.4 M P a for the initial high force regime.  In 1981, Nordman et al. measured pressures i n grooves and on bar surfaces i n a disc refiner at l o w consistency, running at 1200 rpm [16]. They registered pressure peaks on the bar surfaces that corresponded to bar passing events, although these were somewhat more erratic i n nature than those depicted b y Khlebnikov et al. Nordman et al. reported peak to peak pressures o f 0.08-0.12 M P a due to bar passing events - more than 20 times lower than those reported b y Goncharov.  13  In 1997, Martinez, Batchelor, Kerekes and Ouellet published work done to characterize and model the forces on pulp floes when trapped between opposing refiner bars at low speed (corresponding to approximately 1 rpm) [17,18]. Their tests were performed on a specially designed machine, called the single-bar refiner. This could compress and shear one floe o f pulp at a time i n the same way as would occur between opposing refiner bars, while measuring forces i n the normal and tangential directions. In this way, they could examine the effect o f single bar passing events on individual floes.  They used spherical nylon floes at a consistency o f 9.5% and assumed linear elastic behaviour to develop and test a force model. These tests showed evidence o f a corner force component i n the shear force. After this initial peak, the shear force dropped to a lower constant value. The normal force profile rose to a peak at the beginning o f the bar passing event, and remained essentially constant until the trailing edges o f the passing bars parted ways.  The model was later modified b y Batchelor and Ouellet to consider previously dried kraft pulp fibres with collapsed lumens.  It was also extended to predict the tensile forces  experienced b y individual fibres. According to the model, the tensile force to which a fibre is subjected depends on the location and orientation o f the fibre within the floe, as well as the size o f the trapped portion o f the floe [19].  14  2.2.2  FORCES  IN HIGH  CONSISTENCY  REFINING  In 1975, Atack et al. measured the temperature and pressure at different locations i n the refining zone i n a single-disc, open-discharge refiner operating at 1800 rpm and discharge consistencies o f 20-50% [20]. Although they could not see the details o f bar passing events, they did see pressure "spikes" at the frequency at which bars passed over the pressure sensor.  These spikes were seen to be as high as 620 k P a at times. Atack  later suggested that the magnitude o f these spikes would be influenced b y the size o f floes [21].  In their pressure measurements, Atack et al. also observed cyclic pressure  fluctuations  (approximately 28 k P a i n magnitude) with each rotation o f the rotor plate, upon which the spikes were superimposed. Having correlated this cyclic variation with variations i n the plate separation due to run-out i n the rotor plate, they concluded that this periodic fluctuation was due to the saturated steam pressure i n the refining zone. In later work, Atack et al. used high-speed photography to show that periodic variations i n the amount o f pulp present at any given area o f the refining zone occur due to that same rotor run-out phenomenon [22].  In 1982, Franzen and Sweitzer studied the variation o f the total axial thrust with varying motor load, specific energy and consistency [23]. They quantified the refining forces i n terms o f the total axial thrust and a tangential friction force (which draws the torque from the motor) between the plates. The latter was defined as proportional to the axial thrust,  15  the constant o f proportionality being a coefficient o f friction. They proceeded to claim (referring to extensive unpublished work b y Fisher) that this coefficient o f friction increased with increasing consistency.  The resultant tangential friction force was  envisioned to act at a certain radial distance from the centre o f the plates, and this distance was shown to vary depending on the operating conditions.  M i l e s and M a y derived the following simple equation for this coefficient o f friction for a non-pressurized refiner [8]:  IP  p:=  (2.8)  —  ha>F (r r ) m  l+  2  where ]i is the tangential coefficient o f friction, P is the motor load, F is the total axial t  m  thrust, rj and o are the inner and outer radii o f the refining zone, respectively, CO is the rotational speed o f the refiner (rad/s) and h is the number o f rotating discs (1 or 2). U s i n g data from a Bauer 914 m m atmospheric double-disc refiner operating at 1200 rpm, they plotted the motor load against the axial thrust for different pulp consistencies (15, 20 and 30%) and found a l l points to fall on the same straight line, indicating that the coefficient o f friction was independent o f consistency. From the slope o f the line, they calculated a value o f 0.75 for  Furthermore, they suggested that \i was independent o f  the radial position i n the refining zone.  t  A s the tangential speed o f a refiner bar is  proportional to the radial position at which the speed is measured, this implies that \i  t  would also be independent o f refiner speed.  16  M o s t recently, Senger and Ouellet used the single bar refiner apparatus o f the work o f Martinez et al. and Batchelor et al. to examine the forces on T M P floes at high consistency and low speed [24].  They showed nonlinear elastic behaviour at high  consistency, and presented clear evidence o f the corner force component i n the shear force. A s the corner force was seen to represent a large part o f the shear force, the ratio o f the shear to the normal force could no longer be considered a true coefficient o f friction, and they coined a new variable, the equivalent tangential coefficient o f friction \i , , t  eq  as this ratio.  \\, , q t  e  was shown to increase with increasing consistency and with  increasing floe grammage, and it was seen to decrease with an increasing extent o f bar wear.  23 RESEARCH OBJECTIVES The fact that energy-based characterizations do not refer directly to the mechanisms b y which refining causes structural changes i n the fibres leaves us i n search o f a force-based theory b y which we can completely quantify and predict the effects o f refining. Such a theory has yet to be developed, and before this can happen much work needs to be done i n understanding the refining forces themselves.  This is not the only reason to study the refining forces. Given that the refining process is energy intensive, it becomes  even more desirable to understand  mechanisms, as it could help to reduce energy costs i n the long run.  17  its underlying  The objectives o f the work presented here can be summarized as follows: -  T o design and implement the use o f a two-axis force sensor for a refiner operating at high consistency  -  T o measure the normal and shear forces experienced b y pulp floes during bar passing events To investigate how these forces are influenced b y operating conditions.  W o r k was begun on the first o f these three objectives b y A . Bankes, P. W i l d , and D . Ouellet prior to the start o f the work presented as part o f this Master's thesis.  The  original design and preliminary testing o f the force sensor comprised the work done as part o f the Master's degree o f A . Bankes. This work is described i n detail i n his Master's thesis [1], and summarized i n the next chapter.  18  3. ORIGINAL SENSOR DESIGN The work o f Bankes included the original design o f the sensor, the building and testing o f a large-scale prototype, and the construction and testing o f a preliminary version o f the force sensor for use inside the laboratory refiner at the U B C Pulp and Paper Centre. The reader is referred to Bankes' Master's thesis for details on the design concept and the large-scale prototype [1]. The testing o f the original design was performed at U B C , and marked the beginning o f the work done as part o f this thesis.  The objectives for the tests described i n this chapter were: to develop and implement a calibration procedure, to examine the sensor's dynamic behaviour, to examine force traces from the refiner and identify bar passing events, to bring to light any other issues involved i n the design, fabrication, assembly and use o f the sensor.  3.1 DESIGN DETAILS The original design o f the sensor is depicted schematically i n Figure 3.1 i n terms o f its separate components, and the assembled item is shown i n Figure 3.2. This design was devised b y A . Bankes i n collaboration with P. W i l d and D . Ouellet [1].  The workings o f the force sensor can be summarized as follows: The sensor's T-shaped probe is held inside the housing, completely supported by the four piezo ceramic  19  elements under preload, such that any displacement o f the probe relative to the sensor housing w i l l deform the piezo elements.  Figure 3.1 Components of the preliminary sensor design.  According to [1], signals from two piezo elements from opposite sides o f the sensor probe tip (one from the left and one from the right, as pictured i n Figure 3.1) can be used to uniquely determine the magnitude and direction o f the force acting on the probe tip. The calculation o f these forces is described i n Section 3.2.  The sensor probe tip has the same shape as a refiner bar, and was designed as such to replace a 5 mm-long section o f a bar. A hole was machined i n the back o f a D 2 B 5 0 2 refiner plate (see Appendix A for specifications) i n which the sensor fits snugly, with the probe tip replacing the removed bar section.  20  T Probe Top Plate  Figure 3.2 Sensor installed in refiner plate for measuring forces during refiner operation.  The piezo ceramic material used for the elements was lead zirconate titanate (PZT), whose ferro-electric behaviour is specified in Appendix B. The piezo elements in the original design were 1 mm X 1 mm X 7 mm in size, and were clamped under preload along the 5 mm length that was in contact with the probe.  A n insulating layer was  required to prevent conduction between the electrodes of the piezo elements and the sensor's metal parts. In the preliminary design, small sheets of paper were glued to the appropriate locations on the sensor probe and housing for this purpose. The adhesive used was a Loctite™ cyano-acrylate product.  To prevent water from entering the sensor housing, it was sealed around the edges at the last step of the assembly using a silicone sealant.  21  3.2 IMPACT TESTS & CALIBRATION The response o f the refiner force sensor was characterized using a P C B 086D80 piezoelectric impact hammer. This device, used i n conjunction with an appropriate signal conditioner, gives an output signal whose voltage is proportional to the magnitude o f the force experienced at the tip o f the hammer head. The impact testing setup is illustrated schematically i n Figure 3.3.  The force hammer reliably measures forces up to 60 N , and the impacts provide excitation up to very high frequencies (see Figure 3.4). A s a result, it is ideal for testing the sensor's response i n both the time domain and the frequency domain.  The original calibration method consisted o f impacting the sensor i n two perpendicular directions, which corresponded to the directions o f the normal (y-direction) and shear (xdirection) refining forces.  However, this method cannot be used when the sensor is  mounted i n the refiner plate, because the neighbouring bars obstruct the hammer's path when trying to apply horizontal impacts. Therefore, the sensor was held i n a vice for the calibration presented i n [1], where it could easily be impacted i n the two directions. It was later noted b y the author o f this work that the vice did not adequately replicate the sensor's mounting conditions i n the refiner plate, and so a specially designed j i g (depicted i n Figure 3.3) was constructed to hold the sensor for the impact testing.  The  geometry o f the j i g ' s contacting surface with the sensor is identical to that o f the refiner plate.  22  y  Figure 3.3 Impact testing of sensor (mounted in jig) using force hammer. Impacts in the x-direction correspond to the direction of bar impacts at the leading edge during refiner operation.  Time (ms)  n 100f 1  80  QL  0  I  10  I  1  I  I  I  I  I  i  20  30  40  50  60  70  80  90  Frequency (kHz)  Figure 3.4 Force hammer impact in time andfrequencydomain.  23  l  100  The sensor was struck with the hammer and the resulting piezo signals were analysed. Piezo elements emit negative signals when compressed, and positive signals when extended . A sample impact with the corresponding sensor output signals is shown i n 1  Figure 3.5.  80 CD  1  I  I  1  1  1.6  1.8  2  2.2  1  1  1  1  1.8  2  2.2  1  1  1  i  /  60 40  S | 20 X  0  1.4  2.4 1  so  3  /  > 1 ^  1.4 2  I  \j\f\^ 1.6 \  2.4 1  0  a -2 -4 o -6 1.4  1.6  1.8  2  2.2  2.4  Time (ms)  Figure 3.5 Response of sensor (from piezo elements 1 & 3) to a normal impact at the probe tip.  The magnitude o f the first peak o f each piezo element signal was seen to be directly proportional to the peak amplitude o f the force hammer signal, for impacts i n both the normal and shear directions. This is expressed mathematically as:  The terms compression and extension, as used here, should be understood as being relative to the preloaded state. As the piezo elements are under preload, they are always under compressive stress. When the preload is applied, the piezo elements emit a signal for a brief period of time and then this signal fades to zero. Subsequently, the piezo elements emit no charge unless further relative deformation takes place. If the elements are then extended relative to the preloaded state, even though they are not experiencing a positive tensile stress, they will emit a positive signal. 1  24  Vi=K F  (3.1a)  VrK F  (3.1b)  iN  iS  N  s  where the subscript i denotes the piezo element number, V is the voltage from piezo t  element i, FM and Fs are the normal and shear force magnitudes, respectively, and KIN and Kis are the normal and shear calibration coefficients (in V / N ) . The former relation, as an example is illustrated graphically i n Figure 3.6.  Piezo Voltage vs Impact Force (y-direction) 4 i  Hammer Force (N) Figure 3.6 Variation of peak signal voltage from piezos 1,2 and 3 with impact force for normal impacts.  A t this point, it was assumed that the response from each piezo element to an impact at an arbitrary angle 0 to the y-direction (a combined normal and shear load) was equal to the sum o f the responses to the normal component  F cos&  and the shear component  F sinQ.  This assumption o f the validity o f linear superposition is tested i n Section 4.2. For now, the following relations are assumed to hold: F  = FcosQ  (3.2a)  F  s  = FsinQ  (3.2b)  F  s  = F(K  N  Vt =K F iN  N  + K  iS  iN  25  cosQ + K  iS  sinQ)  (3.3)  where F is the magnitude o f the resultant force.  It should be noted here that these calibration coefficients KJS and Km were determined b y impacting the sensor i n the aforementioned jig, after which the sensor was transferred to the refiner plate and again impacted i n the normal direction to see h o w the response compared to that i n the j i g .  Invariably, the values o f KJN determined from the plate and  the j i g differed, sometimes b y up to 20%. Due to this discrepancy, the K-values subsequently used for force calculations were not those determined directly from the j i g configuration. Instead, the value o f KIN from the plate was used, and K s was calculated t  using the following equation:  K {jig) iN  This assumes that the normal and shear calibration coefficients change proportionately when the sensor's mounting conditions change.  The validity o f this assumption was  difficult to verify i n practice, and this represents a serious limitation o f this calibration method. A more reliable method o f determining the value o f K s was therefore developed t  and w i l l be presented i n Section 4.2.  U s i n g Equation 3.3, one can derive equations for the forces F and F given the voltage N  s  from any two piezo elements on opposite sides o f the probe tip. These w i l l be i n the form: F =C V C V N  i  i+  j  (3.5a)  J  F =D V +D V s  i  i  J  26  j  (3.5b)  where i and j are the numerical designations o f the piezo elements on either side o f the probe, and the values o f C and D for these piezo elements can be determined using the K values above.  A detailed description o f this calibration procedure, including the  determination o f all relevant constants, is given i n Appendix C .  The average transfer functions o f piezo elements 1 and 3 are depicted i n Figure 3.7 for frequencies up to 15 k H z . Transfer functions were calculated for several impacts and averaged over the range o f frequencies according to:  f  n  .  .  \  J,(\r,(f)'r>(f)\)j H (f) i  = 20log  (3.6)  Piezo E l e m e n t 1  5  Frequency ( k H z ) Piezo E l e m e n t 3  Frequency ( k H z )  Figure 3.7 Average transfer functions for piezo elements 1 and 3 in response to 20 vertical impacts.  27  where H ( / ) is the magnitude (in dB) o f the average transfer function at frequency / a n d i  Vt(f) and Vh(f) are the magnitudes o f the signals from piezo / and the hammer, respectively, at said frequency.  W e can see that the transfer function is markedly different between piezo elements 1 and 3. In both cases, the transfer function exhibits several peaks, first i n the region between 1 and 3 k H z , and then above 8 k H z or so. This behaviour was unexpected, since a finite element analysis o f the system, carried out by Bankes, indicated that the lowest natural frequency should be about 25 k H z . The cause o f this discrepancy was not immediately apparent, but w i l l be examined later i n this chapter.  3.3 REFINER TESTS USING ORIGINAL SENSOR DESIGN The force sensor was used to measure forces i n the U B C Pulp and Paper Centre's SproutWaldron 12-inch laboratory refiner. This refiner is non-pressurized, and is run using a 50 horsepower (35 k W ) motor. The motor load is controlled b y manually varying the plate clearance.  The l o w natural frequency quoted above for the force sensor must be compared with the frequency  at which bars on the refiner's rotor plate pass over the sensor probe during  refiner operation, as this is the major frequency component o f the excitation force. W e calculate the bar passing frequency using the following equation: / J b p  -  J l ^ 60(5 + G)  28  (3.7)  where Q is the refiner speed (rpm), r is the radial position (m) o f the sensor on the refiner s  plate, and B and G are the bar and groove widths (m), respectively, on the rotor plate.  O n the D 2 B 5 0 2 plates used here, the sum B + G is 5.4 m m , and the sensor was at a radial distance o f 14.6 cm from the axis o f rotation o f the rotor plate. Thus, for a speed o f 2560 rpm (full speed), fb  p  is 7.2 k H z , and for 1260 rpm, fi, is 3.6 k H z . p  Under normal  circumstances, the refiner can be run at any desired speed up to 2560 rpm using a variable frequency drive. However, the drive emits large quantities o f electrical noise which interfere with the data acquisition. This drive had to be bypassed as a result, and the refiner speed could only be varied b y changing the configuration o f the pulleys over which the drive belts ran. This allowed us to run the refiner at only two speeds: 1260 rpm and 2560 rpm.  Ideally the sensor should be an overdamped system with a natural frequency much higher than the frequency o f excitation, so that the sensor's natural vibration does not affect its ability to measure the refining forces. However, from the data presented i n Figures 3.5 and 3.7, we can see that this sensor has a low natural frequency and is underdamped. W e could therefore expect that the sensor's vibration behaviour would dominate the signal, and prevent accurate force measurement. Indeed, this is exactly what was observed.  Figure 3.8 shows a 10 ms time trace o f the individual piezo signals during refiner operation, and Figure 3.9 shows the force traces derived from those piezo signals. The signals are clearly dominated b y the sensor's vibration, as can be seen i n their sinusoidal  29  0  -0.1 -0.2  646  647  648  649  650  651  652  653  654  655  646  647  648  649  650  651  652  653  654  655  646  647  648  649  650  651  652  653  654  655  0 S -0.1]  -0.2 0  > ^  o  -0.1  N U £ -i 645  Time (ms)  Figure 3.8 Signals from piezo elements during refiner operation. distinguished as vibrations dominate the signal. 6  H  n  r-  i  r-  j  I  Bar passing events cannot be  r  n  4 o 2 PL, 0 £ i-I o -21 _1  645 1  646  -|  I  647  1  L  648  rr  649 650 651 Time (ms) n  r  L.  652  653  654  1  1  r  652  653  654  655  oo Pi - 1 u eo U  JS  645  646  647  648  649 650 651 Time (ms)  655  Figure 3.9 Refining forces derivedfromthe above signals. Thefineline corresponds to the forces calculated from piezo elements 1 and 3, while the bold line uses the combination of piezo elements 2 and'.  30  nature. W i t h the bar passing frequency at 3.6 k H z , the time between bar passing events is 0.28 ms, and no such events can be distinguished from the trace, neither i n the piezo signals nor i n the force trace.  A n interesting feature can be seen i n Figure 3.10, where the forces are plotted for 1 second o f refiner operation. The periodic variation o f the force trace corresponds exactly to the refiner's rotational speed.  This is due to the run-out on the rotor plate, which  effectively causes a cyclic variation i n the plate clearance. The pulp between the plates thus sees a periodic, varying level o f compressive strain, and this comes through i n the force reading.  It should be noted that the forces calculated from the combination o f piezo elements 1 and 3 differ from those calculated from combination 2 and 3, i n both Figures 3.9 and 3.10. This aspect was not examined i n [1] and is discussed i n the following section.  31  Refining Forces Calculated from Piezo Elements 1 & 3  100  200  300  400  500  J  i_  600  700  800  600  700  800  900  Time (ms)  J  100  200  300  400  500  i_  900  Time (ms) Refining Forces Calculated from Piezo Elements 2 & 3  0  100  200  300  400  500  600  700  800  900  Time (ms)  „  2  S  -1  z  _i  0  100  200  300  400  500  600  i  i  700  800  i_  900  Time (ms)  Figure 3.10 The variation of the refining forces over a period of 1 second, as derived from different piezo combinations. The periodic behaviour corresponds to the rotor plate rotation.  32  3.4 DISCUSSION OF PRELIMINARY TEST RESULTS 3.4.1  CALIBRATION  The equations reported earlier for force determination proved reliable, and the calibration o f the sensor was successful (see Figure 3.11). However, some doubts remained with regard to interpreting the piezo element responses i n terms o f the linear superposition assumption o f Equation 3.3. Impact testing using a large-scale model suggested that the assumption was not valid [1], and such a test had yet to be devised and carried out for the prototype. This test is described i n Section 4.2.  0  10  20  30  40  50  60  70  Measured Force (from force hammer) (N)  Figure 3.11 Comparison of measured with calculated values of the normal force for impacts applied to the sensor when mounted in the plated.  There was also the noted shortcoming o f using the mounting j i g to calibrate the sensor, when K-values differed significantly between cases where the sensor was mounted i n the j i g and those where it was mounted i n the refiner plate. It thus became necessary either to verify Equation 3.4, or to devise a method b y which the K-value for shear forces could be determined with the sensor mounted i n the plate. The latter o f the two options was selected, and this is also described i n Section 4.2.  33  3.4.2  DYNAMIC  BEHAVIOUR  O f all the aspects o f sensor behaviour that were studied i n these tests, its vibration characteristics emerged as the area most i n need o f improvement.  The sensor's l o w  natural frequency was the reason for the vibration problems, as explained earlier. G i v e n that the bar passing frequency was 3.6 k H z , and higher frequency components were present i n the excitation, a sensor capable o f measuring forces i n such an environment would need a significantly higher natural frequency than that o f this design. Ideally, an overdamped system would also be desirable.  The forces experienced could not be determined with any certainty, neither qualitatively nor quantitatively, not only due to the vibrations, but also due to the fact that signals from piezo elements on vertically opposite sides o f the sensor probe were not consistent with expectations.  T o clarify this point, consider the case shown i n Figure 3.12. Assuming  that the dominant factor controlling the piezo signal is the normal stress i n the ydirection, as piezo element 1 is extended (relative to the preloaded state), its signal should be positive, while piezo element 2, being compressed, should give a negative signal. Therefore, we would expect piezo elements 1 and 2 to exhibit signals o f opposite sign at all times (and the same would be expected o f piezo elements 3 and 4). In reality, this was not the case (see, for example, Figure 3.8 i n previous sections).  34  Bottom Plate  Figure 3.12 Exaggerated diagram showing how the piezo elements deform as the probe is displaced. One possible explanation for this is that the piezo signals are not only dependent on the normal stress experienced by the elements, but also on shear stresses to a significant extent. Although such a ferro-electric material behaving ideally would not respond to shear stress, it was confirmed that the elements used here were not behaving ideally, as the polarization direction o f some parts o f the crystal structure were not perfectly aligned with the poling direction [1]. Another possible explanation for the discrepancy between piezo element pairs is that the sensor housing was not perfectly rigid, contrary to earlier assumptions. Relative deformation o f the top and bottom plates o f the housing would not only explain this, but would also account for the discrepancy between the natural frequency predicted by the finite element model and the value observed experimentally. Subsequent testing confirmed this suspicion, as w i l l be explained i n the following chapter.  3.4.3  SENSOR  FABRICATION  Piezo ceramic elements would often crack during sensor assembly, and imperfections i n the machined finish o f the sensor housing were seen as the root o f the problem.  35  The  piezo elements would effectively rest on ridges left by the machining tools, and would thus bend and break when the preloading screws were tightened.  The lack o f good  contact between the piezo surfaces and the top and bottom plates was also suspected to reduce the stiffness o f the assembly.  To compound the problem, the piezo elements' dimensions (most importantly the thickness i n the y-direction) varied significantly from one element to the next.  This  caused further difficulties i n keeping the top and bottom plates parallel during assembly, and made it hard to ensure that all piezo elements saw the same preload.  A l l o f the issues explained above led to the conclusion that significant modifications to the sensor were required before a reliable refiner force measurement would be possible. The following chapter is dedicated to the necessary modifications and their effects on the sensor's behaviour.  36  4. MODIFIED SENSOR DESIGN In an effort to address the problems with sensor performance that were outlined i n the previous section, several design modifications were examined. Considerable efforts were also devoted to finding the cause o f the l o w natural frequency o f the sensor. These steps led to an improved sensor design which is presented i n this chapter. Improvements to the calibration procedure were also necessary, as was the testing o f certain assumptions. The impact tests to this end and a new calibration method are also presented here.  4.1 DESIGN MODIFICATIONS 4.1.1  MACHINING  OF HOUSING  PARTS  In order to improve the surface finish o f the sensor housing, a new housing design was proposed i n which the square recesses i n the top and bottom plates were replaced b y circular recesses. This was done after noting that the surface finish defects were largely tool marks left b y the passage o f the small end m i l l used to machine the square recesses. This problem is avoided with the new design, as the circular recesses can be bored directly with one pass using a large end m i l l o f the desired diameter.  This change is  illustrated i n Figure 4.1. W i t h this modification, it also became more practical to use four screws to hold the top and bottom plates together.  This would also stiffen the housing  and help ensure that the top and bottom plates were parallel during sensor assembly.  37  Top Plate  Top Plate  Old Sensor Housing  Revised Sensor Housing Bottom Plate  Bottom Plate  Figure 4.1 Sensor housing design changes.  4.1.2  PIEZO  CERAMIC  ELEMENTS  To increase the stiffness o f the sensor system, and thus raise the sensor's natural frequency, it was decided to use wider piezo elements. The new piezo elements were 2 m m wide (twice the original width i n the x-direction according to Figure 3.1), and identical to the original elements i n other dimensions.  For each sensor built, careful  attention was given to the selection o f the piezo elements prior to sensor assembly to ensure that each piezo element's thickness (dimension along the y-axis) was within ± 0 . 0 1 m m o f the others.  4.1.3  INSULATING  MATERIAL  Attention was also given to the selection o f material used to insulate the piezo elements from the metal parts o f the sensor. The different materials considered were scotch tape, mica and alumina coating. The first, a 3 M ™ - b r a n d scotch tape, had the advantages o f being a cheap, effective and quick solution. The tape layer provided ample insulation, but its stiffness was unknown and subject to some doubt.  Layers o f mica were also considered for insulation, but were rejected, as their use required a greater amount o f glue. The added thickness due to the extra glue and m i c a  38  layers was deemed too large, and was difficult to control precisely.  This caused  difficulties i n ensuring that the top and bottom plates o f the housing were parallel, and also lowered the stiffness o f the system.  It was postulated that using a thinner, stiffer insulation layer could improve the vibration characteristics o f the sensor.  To this end, an alumina coating was applied to a set o f  sensor parts. This coating is expected to have a higher modulus o f elasticity than the tape and was about half as thick, both contributing to higher support stiffness for the probe. However, using the tape instead o f the coating did not appear to reduce the first natural frequency at all, and so it was concluded that the choice between these two was not a limiting factor i n the design's lowest mode o f vibration.  The changes described up to this point shifted the sensor's first natural frequency from 2.5 k H z to 8 k H z (see Figure 4.2).  4.1.4  HOUSING  SUPPORT  A s explained i n section 3.4, the individual piezo element signals did not behave as expected, and we suspected that this might be due to deformation o f the sensor housing. To determine whether such deformation was taking place, shims were used to obstruct any deflection o f the top and bottom plates. These shims (made from mica) were used as shown i n Figure 4.3, to sandwich the sensor.  A side effect i f this modification was to  increase the preload on the piezo elements, which reduced the sensor's sensitivity, but not to a problematic extent. The addition o f shims alone raised the natural frequency  39  Piezo 1  Frequency (kHz) Figure 4.2 Average transfer functions for piezo elements 1 and 3, with the new housing modifications and the 2 mm-wide piezo elements.  Shims  Refiner Back Plate  Figure 4.3 Sensor used in conjunction with shims in order to inhibit deformation of housing.  o f test sensors to the 12-15 k H z range. The effect o f placing shims against the top plate was greater than that achieved by placing shims against the bottom plate, implying that  40  the top plate deformed more readily than the bottom plate. This explains w h y transfer functions o f piezo elements 2 and 3 (which are between the probe and the bottom plate) were generally better than those o f 1 and 4 (which were against the top plate). Although transfer functions o f piezo elements 1 and 4 were improved with the use o f shims, they still did not behave as well i n the frequency domain as piezo elements 2 and 3, which generally  exhibited smoother  transfer  functions  and higher  natural  frequencies.  Therefore the piezo element combination 2-3 is preferred for force measurement.  4.1.5  DAMPING  MECHANISMS  Attempts were made to add a damping mechanism to the system i n different ways. The void regions o f the sensor housing were filled with different combinations o f latex and silicone, but none o f these attempts at internally damping the system made much difference.  However, when external damping mechanisms were employed, a considerable effect was seen i n the free vibration behaviour. Latex pads were added to the shims to dampen the vibrations due to the deformation o f the housing, and the effects are shown i n Figure 4.4. The damping factor increased from approximately 1% to 7% upon adding the latex pads.  4.1.6  FURTHER  STIFFENING  OF  SENSOR  Finally, we tried filling the void regions i n the sensor housing with epoxy, to stiffen the system even further. This last modification, i n combination with all the others mentioned above, gave test sensors whose first natural frequencies were i n the range 25-30 k H z (see Figure 4.5).  41  No latex pads present 0.4 ^0.2  2.5  3  T i m e (ms)  4  4.5  Latex pads used as part of shims 3 2 u B  "o  1h  >  3.5  4.5  T i m e (ms)  Figure 4.4 Effect of using latex pads in conjunction with layers of mica in the shims. The time domain signal of piezo element 3 is shown in response to an impactfromthe force hammer. Piezo 1  25  30  35  Frequency ( k H z )  Figure 4.5 Transfer functions for piezo elements 1 and 3, for revised sensor design with all new modifications.  42  4.2 IMPACT TESTS AND CALIBRATION Aside from the work summarized i n the previous section, other aspects o f the sensor's behaviour were examined. The objectives o f the tests presented i n this section were: -  T o test the response o f the sensor to combined normal and shear loads, To examine how the sensor's response changes when varying the position o f impact on the probe, To develop a more reliable calibration procedure, i n which all calibration coefficients are determined with the sensor mounted i n the refiner plate.  4.2.1  SENSOR  RESPONSE  TO COMBINED  NORMAL  AND  SHEAR  LOADS  W h e n pulp floes are impacted b y bars during refiner operation, the resultant force is a combination o f a normal and a shear component. Thus far, it has been assumed that the sensor's response to such a force would be the sum o f its response to the pure vertical component plus the response to the pure horizontal component o f the force. This was mathematically stated as: Vi =K F iN  N  + K  iS  F  s  = F(K  iN  cosQ + K  iS  sinQ)  (3.3)  where F is the magnitude o f the resultant force and 9 is the angle that its line o f action makes with the perpendicular to the top face o f the probe (i.e., the angle made with the ydirection, as defined i n Figure 3.1). If the refining forces are to be calculated as such, then a confirmation o f the above equation is required.  43  To this end, wedges o f different geometries were constructed from aluminum and glued to the top face o f the probe, so that repeatable impacts could be applied to the sensor at precise angles (see Figure 4.6).  A s the wedges were made from aluminum, their  individual masses were very small (ranging from 0.02 to 0.05 g), generally below 3% o f that o f the sensor probe (weighing 2 g), and so any effects o f having increased the probe mass were not significant.  Figure 4.6 Impacts administered at different angles by using aluminum wedges.  For every angle 8 at which the probe was impacted, the piezo elements responses were seen to be proportional to the magnitude o f the impact force, V =K F t  (4.1)  m  where K,e is the experimentally determined constant o f proportionality.  KfN was determined as before, b y impacting the sensor vertically (0 = 0°), and i f the assumption o f linear superposition holds, then K;s could be determined from:  44  Kjq = K  IN  cos 9 +  K  JS  sin 9  (4.2)  or, rearranging, K  -K cosQ  n  iN  (4.3)  sin 9  If the assumption o f linear superposition is valid, the values o f K;s calculated from Equation 4.3 for different angles should all be the same. The results are summarized i n Table 4.1. It should be noted that piezo element 2 cracked during the assembly o f this sensor, and so no signals from this piezo element are included i n this analysis. Aside from the values i n the shaded regions o f the table, the KJS values calculated for different angles are close. The exception to this are those values i n the shaded regions, which were inaccurate because at this particular angle, the sensor response was small (Kie changes sign i n these regions) and the signal-to-noise ratio was low, hence the discrepancies i n the K J S values.  Angle (°) 0  Piezo 1 Kie Kis (mV/N) (mV/N) 43.3 57.0  82.7  20  71.8  91.0  16  30  86.4  97.8  26.9  40  94.6  95.6  50.9  K  1 S  =91.8 mV/N  KIN =43.3 mV/N  28.3  -112.7  242.3  -S 4  -161.0  175.4  -18.9  -122.0  162.8  -31.3  -106.6  3  10  Ave  48.6  Piezo 4 K4S (mV/N) -  Piezo 3 Ke K3S (mV/N) (mV/N) -70.2 -42.1  155.7  O  Ave K3S= 164.6 mV/N K3N =-70.2 mV/N  K49 (mV/N)  Ave K4S=-113.7 mV/N K4N =48.6 mV/N  Table 4.1 K-Values determined by impacting the sensor at different angles  U s i n g the method outlined i n Appendix C , the average K-values can be used to derive equations to calculate the normal and shear forces from a combination o f two piezo elements. For the piezo combinations 1-3 and 1-4, these are:  45  F  =12.12F, - 6 . 7 6 F  F  = 5.17F, +3.I9F3  Na  su  F  m  4  = 12.12F, +9.78F  3  4  7^=5.18^-4.61^  (4.4a,b)  (4.5a,b)  where V i , V3 and V are the magnitudes o f the piezo element signals i n volts. 4  The true normal and shear forces on the sensor probe, as measured b y the hammer, are: FN = F cosQ  (3.2a)  Fs =  (3.2b)  FsinQ  W e can now compare these true forces with those calculated from the sensor signals using Equations 4.4 and 4.5.  Figures 4.7 and 4.8 show the calculated forces plotted  against the actual forces for 100 impacts at the different angles listed i n the table above. A linear regression performed on the two sets o f data gave slopes and correlation coefficients very close to 1 for both graphs, indicating that a measure o f the forces with the assumption o f linear superposition is reliable. Comparing the data to the equal-value lines i n the figures, piezo combination 1-3 appears to slightly overestimate the normal force and underestimate the shear force. These deviations from the equal value lines on the graphs are explained by the fact that piezo elements 1 and 4 are i n use here, and they are known to give less accurate results than piezo elements 2 and 3, as explained earlier. Another source o f error was the difficulty i n ensuring that the line o f action o f the impact forces passed through the centre o f the probe tip. This caused more significant errors i n the impacts at the larger angles, as is evident from the string o f points that lie below the equal value line i n Figure 4.7, which represent the data for 0 = 4 0 ° .  46  Actual Normal Component (F cosG) (N) Figure 4.7 A comparison of the true normal component with values calculated from Equations 4.4a and 4.5a.  Actual Shear Component (F sinG) (N) Figure 4.8 A comparison of the true normal and shear components with those calculatedfromEquations 4.4b and 4.5b.  47  The validity o f the linear superposition assumption can now be used in order to calibrate the sensor i n the plate, as both KJN and K , s can be determined with the sensor mounted i n the refiner plate, thus solving the problem o f having to use the mounting jig.  4.2.2  EFFECT  OF  IMPACTPOSITION  One o f the major objectives o f this work is to examine the refining forces and their variation over the duration o f a bar passing event when a floe is trapped between the sensor and a rotor bar. During such an event, a rotor bar passes over the sensor, trapping a floe at the leading edge o f the probe where the forces begin to act. A s the rotor bar moves over the probe, the centre o f pressure moves away from the leading edge, right across the width o f the probe's top face, to end up at the trailing edge o f the probe tip. It is therefore important that the sensor response does not change significantly with the point o f application o f the loads, so that a meaningful force profile over the bar passing event can be acquired.  Rotor b ai  Sensor probe tip  Figure 4.8 The moving load during a bar passing event. As the rotor bar moves across the top of the probe, so does the centre of pressure. The experiment conducted to study this aspect o f the sensor behaviour consisted o f dividing the top face o f the probe into a grid o f 15 squares, each 1 m m x 1 m m i n size,  48  and vertically impacting the centre o f each square several times with the force hammer to determine a K - v a l u e for each piezo element i n each location.  The results for piezo elements 2 and 3 are shown i n Table 4.2. A s one w o u l d expect, there is a small variation i n the voltage o f the signal per unit force o f impact along the width o f the probe (as the moment arm o f the impact relative to each piezo element changes along the x-direction). There is little effect o f moving the impact position along the length o f the probe (z-direction), as shown b y the l o w standard deviations reported i n the table.  Thus we can conclude that K J N undergoes only small changes with varying  impact position (mostly within 10% o f the mean), and that the value measured i n the centre o f the probe is representative o f the mean value.  Similar results were seen when K-values were measured for impacts applied at 3 0 ° at different positions on the grid. The sensitivity o f the sensor did not vary greatly for the different impact positions, suggesting that KJS is affected i n the same way as K J N , and that neither are significantly sensitive to the point o f application o f the forces i n question. Piezo 3 K-Values  Piezo 2 K-Values  X  X  z  1  2  3  O(x)  0.084  0.079  0.008  2  0.095 0.092  0.086  0.078  0.007  3 4  0.093 0.095  0.084  0.078  0.088  0.007 0.009  5  0.092  0.087  0.077 0.074  a(z)  0.001  0.002  0.002  1  2  3  <J(X)  1  0.139  0.145  0.152  0.007  1  2  0.140  0.148  0.149  0.005  3 4  0.142  0.151  0.152  0.138 0.143  0.148 0.153  0.005 0.006  5  0.149 0.152  o(z)  0.002  0.003  0.002  z  0.006  0.009  K3 (mean) = 0.085 V/N  K N(mean) = 0.147 V/N  N  2  Table 4.2 Variation of sensitivity (K-values) of piezo elements 2 and 3 with varying impact position on the top face of the probe. All K-values are in V/N, and a is the standard deviation.  49  5. REFINING TRIALS 5.1 EXPERIMENTAL SETUP Refining trials with the improved sensor were performed using the same Sprout Waldron 12-inch atmospheric discharge laboratory refiner that was used for the tests described i n Chapter 3. N e w pulleys and drive belts were purchased to be able to run the refiner at different speeds. Trials were conducted with the refiner running at speeds o f 700 rpm and 2560 rpm (full speed) using softwood T M P at an inlet consistency o f 16%. F o r the high speed runs, the pulp was continuously fed into the refiner using a plunger-style feeder, thus maintaining a reasonably stable motor load. This method could not be used for the low speed runs, as the refiner's ability to propel pulp outwards through the refining zone is greatly reduced at lower speeds. Therefore, the pulp was fed i n small quantities (about 0.3 k g at a time), and dilution water was injected intermittently v i a the eye o f the refiner to ensure that pulp passed through and exited the refining zone.  The consistency was varied during the low speed tests b y adding dilution water.  Pulp  samples taken from inside the refiner after adding dilution water had an average consistency o f 13%. This value is, o f course, only approximate, and the technique is useful only for distinguishing between a high consistency (16% without addition o f dilution water), and a lower consistency (upon addition o f dilution water).  In the high-speed tests, pulp was fed at two different inlet consistencies: 2 5 % and 12%.  50  A l l trials were performed using D2B502 plates, which gave a bar passing frequency over the sensor probe o f 2 k H z for the low speed runs, and 7.4 k H z at high speed. acquisition was carried out on a state-of-the-art 4-channel digital oscilloscope.  Data We  sampled 3 piezo signals (from piezo elements 2,3 and 4) and one signal from a tachometer measuring the refiner's rotational speed. The sampling rate was 250 k H z for the low speed tests and 1 M H z for the high-speed tests.  The objectives for these tests were: to isolate bar passing events and examine their force profiles -  to observe the variation o f normal and shear forces and their relative magnitude upon changing the plate clearance, refiner speed, and consistency.  5.2 REFINING FORCE PROFILES 5.2.1  BAR  PASSING  EVENTS  Figure 5.1 shows a 5 ms force trace representing the normal and shear forces during refiner operation at 700 rpm. In all such diagrams i n this chapter, the normal force is depicted b y the bold line, and the shear force by the fine line. Several interesting features are present here. The sharp spikes, occurring at approximately 0.5 ms intervals, are the force profiles o f bar passing events.  The first and seventh spikes are impacts that last  slightly longer than the others. This is a feature o f the D2B502 plate pattern (see Figure 5.2), on which all bars have a width o f 2.8 m m , except every sixth bar, which has a width o f 5.5 m m over the location o f the sensor probe.  51  The radial position o f the probe  corresponds to the streak visible on the left half o f the segment near the outer radius. This is a scratch left b y the sensor probe. The larger width o f some o f the bars at this radial position explains w h y some peaks are wider i n the force profile.  In the case depicted i n Figure 5.1, the peak magnitude o f the forces varies when we look at successive impacts. This is typical o f what was generally observed.  The peak levels were seen to vary quite erratically depending on how the pulp was feeding. This was to be expected, since the magnitude o f the forces depends on factors  417  418  419  420  421  422  Time (ms)  Figure 5.1 Refining normal force (bold line) and shear force (fine line) at 700 rpm as calculated using piezo combinations 2-3 and 2-4.  52  Figure 5.2 One of the three segments of the D2B502 rotor plate (the stator plate segments are identical).  such as the floe size, floe position relative to the bars and floe strength, all o f which can vary greatly during normal refiner operation.  Forces calculated from the combination o f signals from piezo elements 2 and 4 agree well with those from the combination o f 2 and 3 i n terms o f the magnitudes o f the forces. However, as we can see from Figure 5.1, the profiles from the 2-4 combination are somewhat more adversely affected b y vibrations, and so the combination 2-3 was regarded as correct, and the 2-4 combination was not used for any force data.  Figure 5.3 shows a close-up o f one bar impact.  In general, the force profiles o f individual bar impacts were quite clearly defined and were a l l quite similar i n shape.  Both the normal and shear forces rise sharply to a  53  maximum early i n the impact, and then fall to a lower level that gradually drops off to zero as the impact ends.  The shear force profiles measured here were similar to those shown b y Senger et al. on their low-speed single bar refiner [24], but we saw important differences between the normal force profile measured i n the two cases. In the work o f Senger et al., the normal  78.9  79  79.1  79.2  79.3  79.4  79.5  79.6  Time (ms) Figure 5.3 The normal (bold line) and shear forces (fine line) due to a typical bar impact.  force profile was essentially triangular and symmetric about the peak value, as the compressive force on the floe rose steadily to reach a maximum when the rotor and stator bars were centred over each other, then dropped steadily to zero as the bars departed each other [24]. In contrast, they also observed that the shear force profile was asymmetric, and attributed this to the action o f the corner force. This force component, acting on the leading edge o f the bar, rose sharply at the start o f the impact, and dropped to zero  54  halfway through the impact, when the leading edge o f the rotor bar reached the trailing edge o f the stator bar. Senger et al. observed that the corner force acted almost entirely i n the tangential direction. The overall shear force during a bar crossing was thus the sum o f the corner force and the friction force (proportional to the normal force), which explained the asymmetry o f the shear force profile.  The profiles shown here suggest that the corner force has a component i n the normal as well as i n the tangential direction. The fact that the corner force has a normal component i n our results and did not display one i n the measurements performed b y Senger [24] at l o w speed may be an indication that the direction o f action o f the corner force is influenced b y speed. Our results are not sufficient to reach a definite conclusion on this aspect, however, and a more detailed investigation o f the effect o f refiner speed w i l l be required.  5.3 DATA REJECTION CRITERIA To investigate how refiner operating conditions affected the forces between bars, we recorded signals representing thousands o f bar impacts.  Sensor vibrations and other  phenomena detrimental to the force measurement were sometimes seen to affect the signals adversely.  W e therefore had to reject some signals when analyzing records o f  data, and the criteria used for rejecting such signals are described i n this section.  55  5.3.1  SENSOR  VIBRATIONS  The sensor's vibration problems encountered i n these tests can be split into two categories: Vibrations at 30 k H z , corresponding to the peaks i n the transfer functions i n Figure 4.5 (resonant vibration). -  Vibrations at 2 k H z , set up by bar passing events at this frequency,  Although some low-magnitude 30 k H z vibrations were present i n most signals, these were not often a cause o f a loss o f accuracy. In some cases, however, the shear force profile was significantly affected b y these vibrations. Signals where the amplitude o f these vibrations exceeded 10% o f the peak magnitude o f the shear force were rejected. A n example o f such a signal is shown i n Figure 5.4.  30  25  r  20 -  10  5  0 711  711.2  711.4  711.6  711.8  712  712.2  712.4  712.6  Time (ms) Figure 5.4 An illustration of problematic 30 kHz resonant vibrations of the sensor.  56  712.8  Figure 5.5 shows typical bar passing events at an operating speed o f 2560 rpm. Although bar impacts are clearly distinguishable, the true peak magnitude o f the forces is subject to some doubts, as the resonant response o f the sensor affects the measurement to a significant degree. This is particularly true for the shear force because o f its lower peak magnitude. A s a result o f this problem, none o f the signals we collected at high refiner rotational speed could be used for quantitative analysis. This is clearly a shortcoming o f the force sensor that needs to be addressed i n subsequent design refinements.  i  i  i  i  i  i  i  59.3  59.4  59.5  59.6  59.7  59.8  59.9  i  60  Time (ms) Figure 5.5 Typical force profdes of bar impacts at 2560 rpm.  In some cases during the tests at 700 rpm, the sensor was seen to vibrate at a frequency close to that o f the bar passing events. This is shown i n Figures 5.6 (a) and (b), where the five consecutive 2.8 m m bars begin to excite the sensor into vibration at approximately 2  57  30 I  1  1  1  1  1  I  I  r  1  25 20 15 -  _ -j  Q| 378  I  380  j ,  382  , ,  i  i  384  386 388 Time (ms)  I  I  |  390  392  394  1  |  396  Figure 5.6(a) Sensor vibrations at approximately 2 kHz.  1  1  1  50  40  ^ 30 < D O  1  20  10  0  lrJttl|||l|Pl i  i  i  475  480  485  w <  490 Time (ms)  i  i  495  500  Figure 5.6(b) 2 kHz vibrations grow in amplitude for five successive bar impacts, until a sixth impact from a wider bar reduces their amplitude. This record shows several successive occurrences of this phenomenon.  58  k H z . A s the sensor starts to vibrate i n this way, the normal force reading after the bar impact dips down to a negative value, instead o f reading zero normal force.  This dip  increases i n magnitude with each bar passing, until the passing o f the sixth bar, which is wider than the previous five on the D2B502 plate pattern.  The impact with this bar  serves to dissipate the energy o f the vibration i n two ways. A s the pulp between this wider bar and the sensor probe is held against the probe for a longer time, this provides a damping mechanism. A l s o , the passage o f the wider bar effectively breaks the periodicity o f the excitation, thus temporarily counteracting the vibration (before it is set up again b y the next five bars).  It should be noted that these vibrations are only present i n the normal force and not i n the shear force, suggesting that the sensor probe is vibrating purely with linear motion along the y-axis (as defined i n Figure 3.1). These vibrations sometimes become severe enough to significantly affect the force measurement, as shown i n Figure 5.6(a), and so all force signals displaying vibrations whose amplitudes were over 10% o f the magnitude o f the peak force were rejected.  5.3.2  CYCLIC  FLUCTUATIONS  IN NORMAL  FORCE  WITH  EACH  ROTATION  In some o f the signals, particularly at high speed, another problem began to appear i n the normal force signal. Figure 5.7 shows a part o f a signal that seems to be comprised o f a low frequency cyclic variation i n the normal force upon which the spikes (bar impacts) are superimposed. This cyclic variation corresponds exactly to the period o f rotation o f the refiner, and again only appears i n the normal force.  59  Figure 5.7 Cyclicfluctuationsin normal force with each rotation at 2560 rpm.  Figure 5.8 is a plot o f the average normal force and the varying plate clearance over one rotation, and there is a clear relationship between the two. A s it was not possible to measure the exact plate clearance at the location o f the sensor during normal refiner operation, the clearance was estimated b y measuring the height o f each bar with a dial gauge when the refiner was off. Zero plate clearance was determined with the refiner i n operation, b y narrowing the plate gap until the highest point on the rotor plate was contacting the highest point on the stator (the sensor probe tip) once per revolution. Thus, the plate clearance setting on the refiner applies to the gap between the highest bar on the rotor and the sensor probe. The clearance associated with other bars passing over the sensor probe can be determined relative to that using the bar heights measured with the dial gauge.  Although the determination o f the plate clearance using the static  60  measure o f rotor bar heights is not exactly representative o f the actual plate clearance during operation, it serves here for a qualitative comparison o f the varying plate clearance and the mean normal force. The mean normal force was calculated b y taking a moving average o f entire revolutions o f the rotor during operation, and the similarity i n the shapes o f the two curves was used to align them with each other i n Figure 5.8.  Bar# 20  40  60  80  100  120  140  • Plate Gap O Average Normal Force  2.0 1.8 1.6 1.4 1.2  o  1.0 0.8 0.6 0.4 0.2 0.0  Figure 5.8 Variation of plate clearance and mean normal force through one full rotation of the rotor plate.  The regions o f smaller plate gap are associated with higher normal force. This trend most likely occurs because o f higher compressive stresses imposed on the pulp network at lower plate gaps. This phenomenon was not restricted to the high speed tests, but was more pronounced there than i n the 700 rpm runs.  This phenomenon was considered a problem, as the offset i n the normal force could have been due to a change i n the sensor preload, with the sensor housing compressed between the refiner plate segment and the back plate (see Figure 4.3). Such circumstances would  61  skew the  force measurement.  Pending further  tests to determine  whether  this  phenomenon was indeed problematic, signals showing such a shift i n the baseline force were excluded from further analysis.  5.4 ANALYSIS AND DISCUSSION 5.4.1  IMPACT  STATISTICS  In order to analyze several signals, each containing hundreds o f bar impacts (those satisfactorily free o f the rejection criteria outlined i n the previous section), the signals were processed using M A T L A B 5 for Windows. M A T L A B programs were used at all stages o f signal analysis - for the calibrations and impact testing described earlier, as w e l l as for the calculation o f the refining forces from piezo signals and the subsequent analysis o f these measured forces.  A l l M A T L A B programs (m-files) used i n this work are  included i n Appendix D .  To  analyze the force signals from the refiner, a program was designed to isolate  individual bar passing events i n the signal. This program also extracted the normal and shear force profiles o f the events, recorded the peak values o f these forces, and calculated the equivalent tangential coefficient o f friction as the ratio o f these forces. The latter was calculated using two different methods; first b y taking the ratio o f the peaks o f the shear and normal forces (called u, (peaks)), and second b y calculating the ratio o f these forces tei7  at each point i n time during the impact and then taking the average (p.,, (ave)) o f these e?  values. The beginning and the end o f each impact were defined by the points at which the normal force rose above 1 N and fell below it, respectively. The region i n between  62  was extracted from the force signal as the bar passing event. Strictly speaking, the event starts when the force rises from zero and ends when the force falls back down to zero, but a threshold value o f 1 N had to be used to prevent falsely registering impacts due to noise or small vibrations i n the signal.  A summary o f our results is shown i n table 5.1. Peak  F,m  Mean Gap Mean Gap  Peak p. ,(peaks) r W Fm Max Mean a Max Mean o Mean  a v e  te  No. of ) o Impacts  (0.001")  (mm)  Mean  a  No  18  0.46  1.61  0.69  3.86  0.59 0.19 0.55 0.20  210  Dilution  8  0.21  3.63  3.56 26.14 0.99 0.90 6.32  0.29 0.09 0.36 0.11  1302  Water  5  0.13  4.17  4.43 34.96 0.96  1.01  8.52  0.23 0.06 0.27 0.09  1873  3  0.08  5.19  6.65 46.42 0.92 1.19  8.32  0.18 0.04 0.20 0.06  1557  Dilution  8  0.21  4.17  4.35 38.99 0.96  1.03 10.39 0.23 0.06 0.27 0.09  2716  Water  5  0.13  7.83  6.74 37.67 1.40  1.22  0.05 0.21 0.08  716  Added  3  0.08  13.58 11.57 55.33 2.06 1.86 10.83 0.16 0.04 0.18 0.08  996  5.24  1.00 0.68  9.13  0.18  Table 5.1 Summary of impact statistics for refining runs at 700 rpm (a is the standard deviation).  A s expected, the data shows a clear trend o f increasing force with decreasing plate clearance.  Lowering the plate clearance causes an increase i n the axial thrust on the  plates due to an increased reaction force from the pulp between the plates.  This also  increases the shear force and thus the power consumption.  5.4.2 VARIATION OF SHEAR FORCE WITH PLATE CLEARANCE W h i l e the peak normal force keeps increasing with decreasing plate gap, the peak shear force seems to level off at about 11 N . Noting from the force profiles that the peak shear force is reached very shortly after the start o f the impact, it seems reasonable to suggest that the peak is due mostly to the corner force. The ceiling o f approximately U N would  63  therefore correspond to the maximum shear force per unit length o f bar that can possibly be attained at this speed and range o f consistency, which is calculated at 2.2 k N / m . This suggests that there may also be a ceiling i n the motor load, which can be estimated using:  (5.1)  where co is the refiner speed (in radians per second), a is the fraction o f the refining zone area that is packed with pulp, rj and r2 are the inner and outer radii o f the refining zone, respectively, FSL is the shear force per unit length, and Lb is the total length o f rotor and c  stator bar edges crossing at any time during refiner operation. This equation assumes that the torque on the refiner's shaft is equal to the moment exerted b y the resultant shear force (calculated based on the average shear force per unit length o f bar edge) acting at a radial distance halfway between the inner and outer radii o f the refining zone.  Lb is c  estimated at 2.3 m (details o f this estimate are given i n Appendix E ) , which is approximately half o f the total bar length o f each o f the plates, and a is estimated at 0.76 [26].  Equation 5.1 predicts the aforementioned ceiling i n the motor load to be 44 k W for the lab refiner when operating at 700 rpm. For the Sprout-Waldron 60-inch refiner i n [25], is estimated at 116 m (using to the method i n Appendix E ) , and this leads to an upper limit i n the motor load o f 19 M W for the refiner running at 1500 rpm.  These values are somewhat higher than the rated capacity o f the motor i n each o f the two cases, which for the laboratory refiner is 35 k W , and for the 60-inch refiner is 10 M W for  64  a single refining zone.  This estimate o f the ceiling i n the motor load is nevertheless  expected to be higher than anything achieved under normal conditions, as the maximum shear force per unit length was used i n the calculation, and this was assumed to act uniformly on all bars under load.  In reality, the average shear force per unit length  throughout the refining zone w i l l likely always be lower than this, thus drawing less power. The bar coverage fraction a also has a significant effect on this measure, and the value quoted above is a rough estimate at best.  5.4.3 EFFECT OF INJECTING DILUTION WATER The addition o f dilution water at constant plate gap seems to cause an increase i n the peak magnitude o f the forces, but this trend must be interpreted with caution. The refiner does not feed w e l l at 700 rpm and, prior to the addition o f dilution water, relatively few impacts are registered before the pulp fills the grooves and forms a mat on the surface o f the plates.  The addition o f dilution water washes away the pulp on the surface o f the  plates, which causes a surge i n the flow o f material through the refiner and, i n turn, leads to an increase i n both the number and the peak magnitude o f impacts measured shortly after.  Thus, the effect observed here might be due to an increased capacity to feed  material through the refiner, rather than an intrinsic increase i n the reaction force o f the pulp mat as a result o f a change i n consistency.  5.4.4 VARIATION OF \i  teq  WITH PLATE CLEARANCE AND CONSISTENCY  The equivalent tangential coefficient o f friction, \i  , taken as the average ratio o f the  tfeq  shear to the normal force, are plotted for the different test conditions i n Figure 5.9. These values are close to those calculated from the peak values o f the shear and normal force  65  from each impact, and qualitatively behave i n the same way, although | i i ^ ( a v e ) is generally slightly higher than |i,, (peaks). The value o f \i , e9  t  eq  decreases with decreasing  gap, because the shear force starts to level off at the lower plate gaps while the normal force continues to rise.  A d d i n g dilution water decreases the consistency o f the pulp suspension between the plates, and this results i n a lower value o f \i,,  eg  at a given plate gap. This is consistent  with a trend that has been observed b y Isaksson et al. i n an industrial refiner, where  Effect of Plate Gap and Consistency on p ^ 0.6 0.5  1  °-  t  0.3  9 I.S  4  0.2 0.1  • No Dilution A Dilution Water Added  0.0 0.00  0.10  0.20 0.30 Mean Plate Clearance (mm)  0.50  0.40  Figure 5.9 Equivalent tangential coefficient of friction vs plate clearance  dilution was seen to reduce \x. _ t  eq  [25]. A similar dependence on consistency was also  observed b y Senger et al. [24] for measurements carried out on a single-bar refiner at very l o w speeds and at consistencies ranging from 5% to 80%. However, the effect he observed i n this consistency range was less pronounced than the one depicted b y our results i n Figure 5.9. In contrast, M i l e s and M a y reported that \i  t>eq  66  was unaffected b y  consistency,  based  on  tests performed  using  a pilot-scale refiner  at  discharge  consistencies i n the range o f 15-30% [8].  Although the differences i n \i  for the different consistency cases are barely within the  t>eq  calculated standard deviation, a student's t-test showed that the differences are significant at a 99.9% confidence limit.  5.4.5 RANGES OF MEASURED \l,, AND A VERAGE PRESSURE eq  For the purpose o f comparing the range o f measured values o f mechanical pressure (due to compressive stress on the pulp between the plates) and the equivalent tangential coefficient o f friction, a graph o f \i  t>eq  against average mechanical pressure is plotted i n  Figure 5.10. This graph includes data from this work and from several other sources.  The average mechanical pressure for our data was calculated as the ratio o f the average peak normal force (from Table 5.1) to the area o f the sensor probe tip (15 m m ) . For all 2  data aside from that o f this work, \i , was calculated using Equation 2.8, t  eq  2P  M=  *  (2.8)  —  hmF (r r ) m  l+  2  and the average mechanical pressure was determined from:  p  where A  M  - = t  =  4 M  '  (5 2)  is the area o f the refiner plates bearing the thrust load o f the pulp between the  plates. This is calculated using the bar coverage fraction, a , along with the proportion o f the total refining zone area {A^ constituted by bar surfaces, represented b y the fraction X.  67  Assuming identical rotor and stator geometries in all cases, and that bar and groove widths are equal, a value of 0.50 is used for the fraction k. The values of the constants used for each of the different data sets are given in Table 5.2. h 0) n (rad/s) (m) (m) Atack etal. (SI & S2) 189 0.376 0.533 1 Isaksson et al. S1 157 0.45 0.785 1 Isaksson et al. S2 157 1 0.51 0.785 Miles & May 126 0.355 0.457 2 Table 5.2 Values of constants from different sources for use in Equation 2.8 (SI and secondary stage processes, respectively). INVESTIGATORS  A (%) 75.6 75.6 75.6 16  and S2 refer to primary  0.1 0.0 -I 0  1 500  1 1000  1 1500  1 2000  1 2500  1 3000  1 3500  Pressure (kPa)  Figure 5.10 Plot of the equivalent tangential coefficient of friction against average mechanical pressure for different refiners.  The dark shaded area represents the data from this work, where the bar coverage fraction a is expected to lie somewhere between 30% and 80%. These values were used to estimate the high and low pressure bounds for this shaded region. For the data of Miles and May a = 16% is used based on measurements made using that refiner [27]. For all other data, a is estimated at 0.76, based on an average value calculated from data published in [26].  68  In the case o f Isaksson et al., the steam thrust for the data published i n [25] was calculated improperly.  Corrected data was obtained from the authors [28], but an  uncertainty remained, i n that pressure measurements were taken at the refiner inlet and also at the inner radius o f the refining zone, but nothing is known about the pressure profile i n the breaker bar region between those two points.  T w o possibilities were  considered: that the pressure increased linearly with radial position from the value measured at the inlet to the higher value at the end o f the breaker bar region, and secondly that the pressure remained constant at the inlet level throughout the breaker bar region. The nature o f the true pressure profile is expected to be somewhere i n between these two cases.  The shaded region encompasses the range o f pressure and \i  tieq  calculated assuming the two cases described above.  In all cases, the value o f \i , increases as the pressure decreases. This is not a surprising t  eq  result, as the calculation o f \i , t  eq  was performed using F  m  i n the denominator, and the  calculation o f the average pressure used F i n the numerator. The only exception to this m  is the data from our work, which used the normal force i n this same way instead o f F . m  This explains the general shape o f the trend seen with increasing pressure.  It should  therefore be re-emphasized that the purpose o f plotting this graph was to compare the ranges o f our measured values with those from other sources, and not to investigate the relationship between \i  t>eq  and mechanical pressure. Such a relationship would have to be  examined under conditions o f constant throughput and motor load, as these are known to have an effect on the variables under consideration. Furthermore, the calculated values o f pressure would be affected b y the bar coverage fraction, a , which is unknown here.  69  The values used are estimates at best, and could also be affected b y the mass flow rate o f pulp fed through the refiner.  It is interesting to note that for all data sets, except for that o f the primary stage refiner o f Isaksson et al., the curves for different refiners lie very close to each other, suggesting that they were operating i n a range o f conditions i n which the equivalent tangential coefficient o f friction for a given pressure was similar for all o f those refiners.  The  difference between the first and second stage refiners from the data o f Isaksson et al. reflects the lower motor load o f the latter case, as a lower [i , (and hence, for a given t  eq  pressure, a lower shear force) is associated with a decrease i n the power consumption. The two points i n the data o f Atack et al. with the lowest values o f \i  tieq  from a second stage refiner.  were also taken  These two points were refined at a l o w specific energy  (unlike the third point with \i , =0.48, which was refined at a specific energy comparable t eq  to the first stage trials). Our trials were performed by refining softwood T M P , effectively making it a second stage process. This would explain w h y our points lie i n the lower region relative to the others.  The fact that the range values o f \i  tfeq  and pressure measured here are similar to those  reported b y the other sources, coupled with the fact that the values o f \i  tieq  for a given  pressure are also similar, indicates that experiments carried out on the laboratory refiner can be useful for investigating the phenomena observed i n larger refiners. Further testing is necessary to determine the exact nature o f the relationship between the variables i n question.  70  6. CONCLUSIONS Energy-based methods are commonly used to characterize the action o f refiners b y quantifying the energy transferred to pulp fibres that pass through the refining zone. However, these methods fail to give insight into the real physical mechanisms acting i n the process.  In the refining zone, pulp floes experience cyclically varying loads i n  directions normal and tangential to the motion o f the refiner bars that impact them, and it is these forces that cause the structural changes induced b y refining.  Therefore, an  understanding o f these forces is a prerequisite to an understanding o f the refining process.  A two-axis force sensor was developed for use i n a 12-inch laboratory refiner to measure the normal and shear forces during refiner operation.  Although the sensor response  presented some limitations when operating the refiner at full speed (2560 rpm), these were not a great detriment when running the refiner at 700 rpm. The magnitudes o f the normal and shear forces were seen to rise sharply at the start o f bar impacts on pulp floes, then to fall sharply again to a lower level before tapering off to zero as the bar impacts came to an end.  This profile suggests that the normal force is made up o f two  components, these being the compressive force on the pulp floe (the lower level regime) and the corner force required to plough through the floe (the initial peak i n the force profile). The shear force on the refiner bar also contains a corner force component, along with a component due to friction between the pulp and the bar's top face. force appears to be the major component i n both cases.  The corner  Previous work, based on  measurements made at low speed i n a single-bar refiner, had suggested that the corner force only affected the shear force i n refining [24].  71  W h i l e the normal force was seen to increase as the plate clearance decreased, the shear force measured b y the sensor reached a maximum at approximately U N . If the corner force is the major component o f the refining forces, then the forces essentially act at the leading edge o f the refiner bars. This suggests an upper limit to the shear force reaction o f the pulp per unit bar length o f approximately 2.2 k N / m , for the 16% inlet consistency and 700 rpm conditions tested here.  The equivalent tangential coefficient o f friction was seen to decrease with decreasing plate gap, due primarily to the leveling off o f the shear force while the normal force continued to rise.  A d d i n g dilution water also lowered the equivalent tangential  coefficient o f friction slightly, suggesting that consistency may have an effect, although more testing needs to be done over a greater range o f consistency to confirm this.  Further work must be carried out to improve the vibration characteristics o f the sensor, as its resonant vibrations dominated the signals collected during refining trials at full speed. The lowest natural frequency o f the sensor must be raised and its damping characteristics enhanced i n order to implement its use at speeds closer to those used industrially.  72  BIBLIOGRAPHY 1. A . Bankes, "Design and development o f a mechanical wood pulp refiner force sensor", Master's Thesis, Queen's University (Jan. 2000). 2. M . I . Stationwala, K . B . M i l e s , A . Karnis, "The effect o f first stage refining conditions on pulp properties and energy consumption", Journal ofPulp and Paper Science, 19(1) (1993). 3. R . J . Kerekes, "Characterization o f pulp refiners b y a C-factor", Nordic Pulp and Paper Research Journal, 5(l):3-8 (1990). 4. W . Brecht, " A method for the comparative evaluation o f bar equipped beating devices", Tappi Journal, 50(8):40A (1967). 5. C.F. Baker, "Specific edge load theory - Applications and limitations" Pira International Refining Conference, Paper 02 (1991). 6. F . P . Meltzer, P. Sepke, " N e w ways to forecast the technological results o f refining", Proceedings o f the International Refining Conf. & Exhibition, Atlanta (1995). 7. J. Lumiainen, "Specific surface load theory", Proceedings o f the International Refining Conf. & Exhibition, Atlanta (1995). 8. K . B . M i l e s , W . D . M a y , "The flow o f pulp i n chip refiners", Journal ofPulp and Paper Science, 16(2):J63-71 (1993). 9. K . B . M i l e s , W . D . M a y , "Predicting the performance o f chip refiners; A constitutive approach", Journal ofPulp and Paper Science, 19(6):J268-274 (1993). 10. K . B . M i l e s , " A simplified method for calculating the residence time and refining intensity i n a chip refiner", Paperija Puu, 73(9):852-857 (1991). 11. K . B . M i l e s , A . Karnis, "The response o f mechanical and chemical pulps to refining", Tappi Journal, 74(1):157-164 (1991). 12. D . H . Page, "The beating o f chemical pulps - The action and effects", In F . Bolam, editor, Fundamentals o f Papermaking: Transactions o f Fundamental Research Symposium held at Cambridge, volume 1, pages 1-38. Fundamental Research Committee, British Paper and Board Makers' Association (Sept. 1989).  73  13. A . A . Khlebnikov, V . F . Pashinski, V . N Goncharov, E . A . Smimova, "Analysis o f forces involved i n the operation o f a conical refiner", Bum Promst. No.22:12913 6 (English Translation) (1969). 14. V . N . Goncharov, E . A . Smirnova, E . V . Shemyakin, "Method for the determination o f stresses between refiner blades", Bum Promst. No.27:134-138 (1970). 15. V . N . Goncharov, "Force factors i n the disc refiner and their effect on the beating process", Bum Promst. No.5:12-14 (English Translation) (1971). 16. L . Nordman, J.E. Levlin, T. Makkonen, H . Jokisalo, "Conditions i n an L C refiner as observed b y physical measurements", Paperi Ja Puu 63(4) 169-180(1981). 17. D . M . Martinez, W . J . Batchelor, R.J. Kerekes, D . Ouellet, "Forces on fibres i n low consistency refining: Normal force", Journal of Pulp and Paper Science, 23(1):J11-18 (1997). 18. W . J . Batchelor, D . M . Martinez, R.J. Kerekes, D . Ouellet, "Forces on fibres i n l o w consistency refining: Shear force", Journal of Pulp and Paper Science, 23(1):J4045 (1997). 19. W . J . Batchelor, D . Ouellet, "Estimating the forces on fibres i n refining", 4 International Refining Conference, Fiuggi, Italy, Paper 2 (March, 1997).  t h  Pira  20. D . Atack, M . I . Stationwala, " O n the measurement o f temperature and pressure i n the refining zone o f an open discharge refiner", Transactions o f the Technical Section o f the Canadian Pulp and Paper Association (3):71-76 (1975). 21. D . Atack, "Towards a theory o f refiner mechanical pulping", Appita Journal, 34(3):223-227 (1980). 22. D . Atack, M . I . Stationwala, A . Karnis, "What happens i n refining" Pulp and Paper Canada, 85(12):T303-308 (1984). 23. R . Franzen, R . Sweitzer, "Refining forces in high stock concentration pulping", Appita Journal 36(2): 116-121 (1982). 24. J. Senger, D . Ouellet, "Factors affecting the shear forces i n high-consistency refining", Proceedings o f the International Mechanical Pulping Conference, Helsinki, Finland, In Press (2001). 25. A . J . Isaksson, A . H Horch, B . A l l i s o n , A . Karlstrom, L . Nilsson, " M o d e l l i n g o f mechanical thrust i n T M P refiners", Proceedings o f the International Mechanical Pulping Conference, Stockholm, Sweden, pages 87-93 (1997).  74  26. D . Atack, M . I . Stationwala, A . Karnis, "Distribution A n d motion o f pulp fibres on refiner bar surface" Journal ofPulp and Paper Science, 18(4):J131-J137 (1992). 27. W . D . M a y , M . R . M c R a e , K . B . Miles, W . E . Lunan, " A n approach to the measurement o f pulp residence time i n a chip refiner", Journal ofPulp and Paper Science, 14(3):J47-J53 (1988). 28. A . J . Isaksson, B . A l l i s o n , Personal communication o f corrected tangential coefficient o f friction data o f reference [25].  75  NOMENCLATURE a  constant equal to 4 for a single disc-refiner and 2 for a double-disc refiner  a  bar coverage fraction  A  area o f refiner plates experiencing thrust load (m )  Arz  total area o f refining zone (m )  B  refiner bar width (m)  c  pulp consistency (fraction)  Q  normal force coefficient for piezo element /, ( N / V )  CEL  cutting edge length (m/s)  Di  shear force coefficient for piezo element /, (N/V)  e  specific energy per impact (J/kg impact)  E  specific energy (J/kg)  f  frequency (Hz)  fbp  frequency o f bar passing events (Hz)  F  magnitude o f resultant force on sensor probe tip (N)  2  m  F  mechanical thrust (N)  F  normal force (N)  Fs  shear force (N)  FSL  shear force per unit length (N/m)  G  groove width (m)  h  constant equal to 1 for a single-disc refiner and 2 for a double-disc refiner  H  refiner bar height (m)  m  N  76  Hi  average transfer function for piezo element i (dB)  I  refining intensity (units depend on definition o f intensity used)  KIN  sensitivity o f piezo element / to a normal force on the sensor probe tip ( V / N )  Kis  sensitivity o f piezo element / to a shear force on the sensor probe tip ( V / N )  KIQ  sensitivity o f piezo element / to a force acting at angle 0 to the y-axis ( V / N )  Lbc  total length o f bar edges crossing  Lj  length o f refiner bar within radial increment i (m)  X  fraction o f refining zone area constituted b y bar surfaces  m  oven-dry fibre mass flow rate through refiner (kg/s)  p  radial coefficient o f friction  f  r  [i  t  tangential coefficient o f friction  \\, ,eq  equivalent tangential coefficient o f friction  Nov  average number o f bars per unit length o f arc on refiner plate (m" )  n  number o f impacts  riimp  number o f impacts experienced b y pulp i n one pass through the refining zone  riri  number o f bars on rotor plate  ni  number o f bars on stator plate  0  angle between the line o f action o f impact force and the y-axis (°)  t  S  1  Pa e  average mechanical pressure on refiner plates (Pa)  P  net refining power (W)  n  inner radius o f the refining zone (m)  r2  outer radius o f the refining zone (m)  r  radial position o f sensor on stator plate (m)  V  s  77  R  regression correlation coefficient  S  steam flow term (s" )  SEL  specific edge load (J/m)  x  residence time (s)  v  radial velocity o f pulp i n the refining zone (m/s)  Vh  peak voltage o f hammer signal ( V )  Vi  peak voltage o f signal from piezo element i ( V )  CO  refiner rotational speed (rad/s)  Q  refiner rotational speed (rpm)  1  78  APPENDIX A SPECIFICATIONS OF D2B502 REFINER PLATES Rotor and stator plates are identical. Inner radius o f refining zone, r i = 12.25 cm Outer radius o f refining zone, X2 = 15.25 cm Bar width, B = 2.8 m m Bar Height, H = 3.7 m m Groove Width, G = 2.6 m m Number o f bars per segment at radial position o f sensor (14.6 cm) = 48 Number o f segments on rotor = 3 Number o f segments on stator = 3  Figure A l . A segment of the rotor plate  79  APPENDIX B PROPERTIES OF PIEZO CERAMIC ELEMENTS Property  Piezo Elements in Original Design Piezo Elements in Modified Design Units  Material  Lead Zirconate Titanate 1 mm x 1 mm x 7 mm 7.65  Dimensions  1 mm x 2 mm x 7 mm 7.7  g/cm  360  350  °C  1750  1800  1.6  1.5  %  0.62 0.37  0.6  —  31  0.34  —  k»  0.72  0.69  —  d  31  -160  -175  10- C/N  33  365  Density Curie Temperature  Lead Zirconate Titanate  T  c  3  Electrical Dielectric Constant  K T 33  Dissipation Factor Piezoelectric Coupling Factor  kp k  Charge Constant  400  10 C/N  &i  -11.5  -11  10- Vm/N  &  3  25  25.1  10' Vm/N  N  d Voltage Constant Frequency Constants  I2  12  3  3  P  2050  2057  Hz.m  N,  1400  1359  Hz.m  N,  1800  1857  Hz.m  15.5  15.4  10" m /N  19  18.4  10- m /N  Elastic Modulus Compliance  S„ S  E  E 33  80  12  12  2  2  APPENDIX C CALIBRATION PROCEDURE This section provides details o f the calibration procedures employed w i t h the sensors used i n this project.  The section is split into two parts, the first explaining the original  calibration method, which involved the use o f the mounting j i g , and the  second  explaining the revised calibration method, which involved impacting the sensor i n the plate only.  CI. ORIGINAL CALIBRATION METHOD This method consisted o f impacting the sensor (mounted i n the jig) with the forcemeasuring hammer along the x- and y-directions, as shown i n Figure 3.3. This leads to the determination o f K-values (the sensor response i n V / N ) for both normal and shear impacts i n the j i g . The sensor is then installed i n the refiner plate, and impacted normally (along the y-direction) thus determining the actual sensitivity to normal impacts (as this is generally different from the K-value observed with the sensor i n the jig). The K-value for shear impacts i n the plate is then calculated by appropriate scaling according to Equation 3.4.  Equations for calculating the forces from the piezo signals are derived  from these K-values. This process is shown i n detail below for the sensor used for the data i n chapter 3.  81  The results o f impacting the sensor i n the j i g i n the normal and shear directions are shown i n Figures C I and C 2 , while Figure C 3 shows the results o f impacting the sensor i n the normal direction while mounted in the plate.  • Piezo 1 O Piezo 2 A Piezo 3  V, = 0.0509F 2 = 0.9492  N  R  V = -0.0419F  .£* -1  :  §<u -2 -3 -4 V, = -0.0786F R = 0.992  -5  2  -6  Magnitude of Normal Force, FN (N) Figure C I . Piezo voltage vs normal impact force (impacts applied in mounting jig).  15 if  • Piezo 1 (V)  V =0.1783F 3  • Piezo 2 (V) 10  S  R = 0.9921 2  A Piezo 3 (V)  DC i  >  eN «  o c  -10  -15  Magnitude of Shear Force, Fs(N) Figure C2. Piezo voltage vs shear impact force (impacts applied in mounting jig).  82  N  N  • Piezo 1 (V) • Piezo 2 (V) A Piezo 3 (V)  es 0 >  e  Tto  -1  N - 2  V = -0.0705F 3  -5  N  R' = 0.9935  -6  Magnitude of Normal Force, F (N) N  Figure C3. Piezo voltage vs normal force (impacts applied with sensor mounted in plate). The results o f linear regressions are shown on the graphs, and the K-values are determined from the slopes o f these graphs. The summarized results o f the above are: KjNO'ig) = 0-0509 V / N  KisQig) = 0.170 V / N  K (plate) = 0.0570 V / N IN  K (jig) = -0.0419 V / N  K (jig) = -0.176 V / N  K (plate) = -0.0473 V / N  AjArf/'fe) = -0.0786 V / N  /vjstf/g) = 0.178 V / N  K (plate) = -0.0705 V / N  2N  2S  2N  iN  K-values for shear impacts i n the plate are now calculated b y applying Equation C I (same as Equation 3.4) below:  K (jig) iN  The use o f this equation marks a slight departure from the calibration method used i n [1], i n which the discrepancy between the K-values from the j i g and plate mounting conditions was not addressed.  83  Equation 3.4 yields: K (plate) = 0.190 V / N ls  K (plate) = -0.199 V / N 2S  Kss(plate) = 0.160 V / N N o w we can state that:  (C2a)  Rearranging the above equation then gives: (F ) N  iN  ^iS  \  (C2b)  [ s) F  This equation thus gives the normal and shear forces calculated using any desired pair o f piezo elements. A s explained i n [1] and chapter 3 o f this work, pairs o f piezo elements must be chosen such that they are on opposite sides o f the probe, and so only piezo pairs 1-3 and 2-3 are used for force calculations. (F ,\ m  S13  F,N23 523  (6.96 - 8.69^V \ X  3.28 2.58 (-7.39  (C3a)  A  I  -9.3lYV } 2  3.47 2.29  V,  (C3b)  These equations were used to back-calculate the forces from the piezo responses. A l l the data are shown i n the following tables, with the calculated forces and their respective errors shown i n the four columns on the right.  84  Table CI. Data for normal impacts applied with sensor in mounting jig. Fj^measured) V, Fhll3 Error(13) v2 v3 (N) (V) (V) (N) (V) (%) 6.26 0.28 -0.26 -0.60 7.12 13.66 7.79 0.32 -0.34 -0.72 8.53 9.44 9.63 0.43 -0.42 -0.79 9.83 2.10 11.16 0.54 -0.50 -0.97 12.22 9.50 0.32 12.08 -0.42 -1.07 11.50 4.80 15.15 0.56 -0.58 -1.26 14.80 2.27 15.45 0.62 -0.62 14.41 -1.16 6.78 16.37 0.68 -0.64 -1.32 16.18 1.16 -0.62 16.14 17.29 0.71 -1.29 6.68 18.82 -0.72 -1.44 0.85 18.47 1.86 20.66 1.01 -0.83 -1.44 19.56 5.33 20.97 0.95 -0.86 -1.60 20.48 2.31 1.32 -0.92 23.11 -1.69 23.90 3.38 23.11 1.53 -0.94 -1.66 25.08 8.53 24.03 1.65 -1.06 -1.76 26.73 11.25 27.10 1.21 -1.12 -2.04 26.12 3.61 1.14 26.44 28.93 -1.28 -2.13 8.60 31.69 1.98 -1.36 -2.35 34.19 7.89 32.30 1.43 -1.38 -2.35 30.37 5.98 -1.41 35.26 1.87 -2.88 38.03 7.85 0.74 36.03 1.78 -1.48 -2.76 36.29 0.94 38.33 1.96 -1.61 -2.88 38.69 41.19 5.35 39.09 2.09 -1.83 -3.07 2.12 41.95 5.24 39.86 -1.76 -3.13 45.22 2.15 -1.80 -3.57 45.97 1.65 46.75 2.21 -1.92 -3.57 46.40 0.75 1.99 47.52 2.28 -1.95 -3.76 48.46 2.62 51.94 7.58 48.28 -2.16 -3.88 49.82 2.62 -4.01 53.03 6.45 -2.23 2.84 56.72 7.27 52.88 -2.19 -4.26 54.41 2.49 -2.11 -4.44 55.96 2.85 55.18 3.03 -2.31 -4.32 58.57 6.15 3.06 -2.42 -4.76 62.59 8.90 57.48 Mean =5.42  85  Error(23) (N) (%) 7.52 20.14 9.27 18.87 10.42 8.22 12.75 14.18 13.04 7.94 15.94 5.25 15.42 0.25 16.99 3.75 16.58 4.12 18.73 0.51 19.54 5.45 21.22 1.21 22.56 2.41 22.43 2.97 24.18 0.60 27.26 0.59 1.21 29.29 31.90 0.65 32.06 0.74 37.23 5.58 36.60 1.60 38.69 0.95 42.05 7.57 42.17 5.81 46.48 2.78 47.40 1.39 49.38 3.91 52.08 7.86 53.78 7.97 55.79 5.50 4.72 56.98 57.25 3.75 8.14 62.15 Mean =5.05 FN23  Table C2. Data for normal impacts applied with sensor in mounting jig. Fs(measured) (N) 1.8689 2.1752 2.3284 4.0135 4.3199 4.3199 4.7794 5.6985 7.0772 8.1495 8.3027 9.2218 9.6814 11.5196 11.826 12.4387 13.6642 14.1238 15.0429 15.8088 16.0662 16.4216 17.0343 17.1875 20.9681 22.1936 23.4191 27.0956 28.6275 32.3039 34.4975 35.2635 35.3676 36.0294 37.5613 40.625 43.6887 47.5184 48.2843 53.6456 55.1775 55.4534 57.4755 62.0711 63.1127 64.6446 69.2402 69.2402  v,  (V) 0.3688 0.4 0.4313 0.7125 0.6813 0.7438 0.9375 1.1938 0.9812 1.6062 1.4 1.4187 1.5875 1.9 2.9312 2.0875 2.8687 2.275 2.1312 2.6187 2.7125 2.3187 2.4687 2.9437 3.4 3.5875 3.9625 4.525 4.5875 4.9625 6.6188 6.15 5.4625 6.6188 7.0875 7.4 7.0875 8.025 8.65 8.8063 9.5875 9.275 10.3687 10.3687 11.15 10.3687 11.3062 11.3062  v  2  (V) -0.4512 -0.4512 -0.4825 -0.8263 -0.8263 -0.8575 -0.92 -1.1075 -1.2637 -1.2637 -1.4825 -1.7012 -1.6387 -1.9512 -2.0137 -2.0137 -2.4512 -2.295 -2.295 -2.5137 -2.92 -2.6075 -2.7637 -2.5762 -3.3575 -3.67 -3.92 -4.545 -4.545 -5.3325 -6.4625 -6.4938 -5.995 -6.9063 -7.1313 -7.4438 -7.275 -8.3688 -8.6813 -8.9938 -10.0875 -9.775 -10.8688 -10.7125 -11.9625 -10.8688 -12.1188 -12.1188  v  3  (V) 0.37 0.4013 0.4325 0.7763 0.7763 0.8388 0.8388 1.0888 1.3075 1.37 1.5575 1.745 1.745 2.0888 2.1513 2.2138 2.5888 2.5263 2.62 2.8388 2.995 2.87 3.0888 2.9013 3.6825 3.995 4.3075 4.87 4.995 5.1825 7.1312 6.6625 5.745 7.1312 7.6 8.0687 7.2875 8.5375 8.85 9.1625 9.9437 9.475 10.5688 10.9 11.2625 11.2125 11.9938 11.9938  Error(li) Fsis (N) (%) 2.16 15.80 7.91 2.35 2.53 8.68 4.34 8.13 4.24 1.91 6.57 4.60 5.24 9.62 6.72 18.01 6.59 6.86 8.80 8.02 8.61 3.71 9.16 0.72 9.71 0.29 11.62 0.88 15.16 28.23 12.56 0.96 17.74 16.09 13.98 1.02 8.60 13.75 15.91 0.66 16.62 3.47 15.01 8.60 16.07 5.68 17.14 0.27 1.50 20.65 22.07 0.54 24.11 2.95 27.41 1.15 2.42 27.93 8.22 29.65 40.11 16.26 37.36 5.95 32.74 7.43 11.32 40.11 42.86 14.09 45.09 10.99 42.05 3.75 48.35 1.75 51.21 6.05 52.52 2.09 57.10 3.49 54.87 1.06 6.61 61.28 62.13 0.10 3.99 65.63 2.64 62.94 1.75 68.03 68.03 1.75 Mean = 6.05  86  Error(23) (N) (%) 2.41 29.11 2.48 14.23 2.66 14.44 4.64 15.73 4.64 7.53 13.34 4.90 5.11 6.99 6.34 11.19 7.38 4.27 7.52 7.70 8.71 4.92 9.90 7.35 9.68 0.01 11.55 0.30 11.91 0.74 12.06 3.07 14.43 5.63 13.75 2.65 13.96 7.18 15.22 3.70 16.99 5.76 15.62 4.88 16.66 2.18 15.58 9.33 20.08 4.22 21.88 1.40 23.47 0.20 26.92 0.64 27.21 4.95 30.37 5.98 38.76 12.34 37.79 7.17 33.96 3.98 11.84 40.30 12.22 42.15 9.06 44.31 4.02 41.93 48.59 2.26 50.39 4.36 52.19 2.71 4.71 57.77 55.62 0.30 61.92 7.73 0.10 62.13 6.64 67.30 1.94 63.39 69.52 0.40 69.52 0.40 Mean = 6.08  Table C3. Data for normal impacts applied with sensor mounted in plate. Fnfmeasured)  v,  v  Vj  (N) 4.93 7.38 8.46 8.76 9.94 12.44 12.59 13.66 13.66 14.28 16.12 16.68 17.60 18.52 20.97 21.48 22.81 24.03 24.64 25.26 28.63 29.85 32.61 33.73 35.26 37.56 40.63 47.52 48.28 50.58 51.35 59.01 62.84 62.84 63.60 64.37 65.13  (V) 0.22 0.38 0.44 0.41 0.51 0.59 0.59 0.84 0.75 0.69 0.75 0.75 0.78 0.91 1.33 1.06 1.25 1.22 1.72 1.34 1.32 1.69 1.48 1.75 1.81 2.06 2.25 2.69 2.79 3.12 3.08 3.29 3.48 3.48 3.87 4.26 3.78  (V) -0.31 -0.37 -0.39 -0.54 -0.37 -0.54 -0.67 -0.78 -0.66 -0.58 -0.68 -0.78 -0.82 -0.78 -1.05 -1.09 -1.09 -1.07 -1.22 -1.15 -1.37 -1.39 -1.48 -1.57 -1.70 -1.75 -2.00 -2.25 -2.33 -2.45 -2.47 -2.75 -2.93 -2.94 -2.99 -3.08 -3.12  (V) -0.50 -0.63 -0.63 -0.78 -0.66 -0.88 -1.00 -0.78 -0.91 -1.03 -1.13 -1.22 -1.28 -1.34 -1.50 -1.75 -1.53 -1.72 -1.69 -1.75 -2.00 -2.16 -2.47 -2.56 -2.48 -2.63 -2.91 -3.38 -3.28 -3.75 -3.69 -4.03 -4.30 -4.30 -4.44 -4.40 -4.75  2  Error Fm3 (N) (%) 5.87 18.96 8.04 8.91 8.48 0.24 9.62 9.76 9.27 6.73 11.74 5.64 12.82 1.83 12.66 7.33 13.10 4.16 13.75 3.71 6.94 15.00 15.81 5.20 16.56 5.88 17.99 2.87 22.29 6.31 5.24 22.60 22.01 3.51 23.42 2.55 26.69 8.30 24.56 2.76 26.57 7.20 30.48 2.11 2.62 31.75 2.12 34.45 34.12 3.23 37.17 1.05 40.97 0.85 48.03 1.08 47.86 0.88 54.30 7.36 53.45 4.09 57.86 1.95 61.51 2.11 1.99 61.59 65.50 2.98 5.46 67.89 3.71 67.55 Mean =3.93  FN23  Error  (N) (%) 6.96 41.19 8.59 16.29 8.74 3.32 11.23 28.13 8.88 10.68 12.11 2.60 14.28 13.40 13.04 4.58 13.31 2.61 13.85 2.99 15.52 3.71 17.11 2.59 17.99 2.22 18.27 1.31 21.69 3.43 13.21 24.31 22.33 2.10 23.87 0.66 24.75 0.44 24.81 1.76 28.71 0.30 30.33 1.59 33.88 3.91 35.48 5.19 35.57 0.86 37.39 0.46 41.90 3.13 48.05 1.12 47.67 1.27 53.02 4.82 52.56 2.36 2.04 57.80 61.66 1.88 61.73 1.77 63.41 0.30 63.69 1.05 67.25 3.25 Mean =3.14  The mean percentage errors in all cases are quite low, and the graph o f Figure C 4 shows a good agreement between the force measured by the impact hammer, and that calculated using the magnitudes o f the piezo signals. These two facts suggest that the calibration procedure here is reliable.  87  Measured Force (from force hammer) (N) Figure C4. Calculated force vs. Measured force for normal impacts with sensor mounted in plate.  C2. NEW CALIBRATION METHOD A s explained i n section 3.4, the original calibration was modified, as it did not account for the change i n the sensor's response to impacts i n the shear direction when it was transferred from the j i g to the plate. It was seen, time and time again, that the response o f the sensor was extremely sensitive to the mounting conditions. This became an even more significant issue when the use o f shims was employed to stiffen the sensor housing, as there was no way to ensure that the preload on the piezo ceramic elements i n the j i g was the same as that i n the plate.  88  It was therefore decided that calibration had to be performed with the sensor installed i n the plate, to ensure that mounting conditions did not change between the time o f calibration and refining trials. This section provides the impact data and details o f the calibration for the sensor used for the data i n section 4.2, where the calibration method is outlined.  The sensor was impacted at various angles (as described i n section 4.2), and K-values (KJQ) were determined for different angles, 0, to the normal direction (as shown i n Figure 4.6). KIN was determined as before, by impacting the sensor i n the normal direction. Kis was then determined using:  cose  sin0  This was done for all angles, 0, at which the sensor was impacted, and the mean value o f Kis found i n this way was taken as the true Kis-  Table C 4 shows all the impact data (magnitude o f impact force F from force hammer, and piezo voltages Vj, V3 and V4), along with the true normal and shear forces associated with each impact (F cos0 and F sin0, respectively), and the back-calculated normal and shear components from the piezo signals. Figures C5 through C 9 are graphs o f the impact data, with linear regressions from which the K-values were determined. These K values are summarized i n Table C 5 , which is identical to Table 4.1.  89  Table C4. Data for impacts administered at different angles.  e o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  F (N) 9.19 11.80 15.01 15.47 17.16 17.46 22.06 22.37 22.98 24.51 25.12 26.96 28.80 29.41 31.25 33.70 35.54  V, (V) 0.41 0.52 0.67 0.67 0.75 0.77 0.97 0.97 1.02 1.06 1.09 1.13 1.23 1.30 1.33 1.47 1.52  (V) -0.56 -0.77 -0.94 -1.02 -1.09 -1.14 -1.45 -1.53 -1.63 -1.67 -1.73 -1.94 -2.06 -2.09 -2.22 -2.56 -2.53  Vs (V) 0.47 0.58 0.72 0.76 0.83 0.83 1.04 1.08 1.13 1.19 1.21 1.32 1.41 1.44 1.58 1.58 1.74  F cosQ (N) 9.19 11.80 15.01 15.47 17.16 17.46 22.06 22.37 22.98 24.51 25.12 26.96 28.80 29.41 31.25 33.70 35.54  FsinQ (N) 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00  Fmi (N) 8.73 11.42 14.48 15.01 16.48 16.99 21.56 22.09 23.29 24.18 24.98 26.73 28.90 29.87 31.10 35.12 35.48  Fsi3 (N) 0.31 0.22 0.48 0.23 0.39 0.32 0.37 0.12 0.07 0.16 0.12 -0.36 -0.20 0.03 -0.21 -0.58 -0.24  Ff/N (N) 9.47 11.97 15.19 15.62 17.16 17.35 21.87 22.30 23.31 24.47 25.14 26.54 28.75 29.80 31.50 33.21 35.39  Fsu (N) -0.04 -0.03 0.16 -0.05 0.08 0.16 0.25 0.04 0.07 0.04 0.07 -0.26 -0.11 0.08 -0.38 0.35 -0.17  10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10  6.59 7.20 9.65 10.72 11.64 12.56 14.09 15.32 20.53 20.53 22.06 24.20 25.74 27.57 27.57 27.88 29.87 32.78 32.78  0.39 0.43 0.56 0.62 0.66 0.73 0.80 0.88 1.19 1.16 1.25 1.39 1.47 1.63 1.53 1.64 1.69 1.86 1.83  -0.25 -0.29 -0.35 -0.39 -0.41 -0.43 -0.59 -0.56 -0.75 -0.88 -0.91 -0.98 -1.05 -0.98 -1.34 -1.17 -1.47 -1.38 -1.48  0.17 0.19 0.23 0.27 0.28 0.28 0.40 0.36 0.50 0.63 0.64 0.69 0.73 0.69 0.78 0.83 0.86 0.97 1.05  6.49 7.09 9.50 10.56 11.47 12.37 13.88 15.09 20.22 20.22 21.72 23.84 25.34 27.15 27.15 27.46 29.42 32.28 32.28  1.14 1.25 1.68 1.86 2.02 2.18 2.45 2.66 3.56 3.56 3.83 4.20 4.47 4.79 4.79 4.84 5.19 5.69 5.69  6.46 7.14 9.11 10.16 10.74 11.74 13.63 14.37 19.46 19.93 21.28 23.51 24.88 26.35 27.64 27.81 30.38 31.83 32.19  1.24 1.26 1.76 1.94 2.08 2.42 2.25 2.75 3.75 3.19 3.57 4.05 4.25 5.26 3.63 4.74 4.04 5.23 4.72  6.45 6.98 9.04 10.10 10.70 11.61 13.56 14.12 19.28 20.13 21.41 23.58 24.99 26.42 26.20 27.98 28.86 32.01 32.40  1.25 1.34 1.80 1.98 2.10 2.49 2.29 2.88 3.85 3.11 3.52 4.03 4.22 5.25 4.33 4.68 4.78 5.17 4.64  20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20  4.29 4.37 5.13 5.36 9.50 10.11 11.18 13.17 14.71 17.46 19.00 23.59 23.59 24.51 25.74 28.34 29.41  0.30 0.29 0.32 0.37 0.65 0.68 0.73 0.89 1.03 1.17 1.29 1.62 1.68 1.79 1.86 2.06 2.10  0.07 0.06 0.08 0.09 0.14 0.16 0.19 0.22 0.24 0.31 0.34 0.41 0.43 0.40 0.45 0.38 0.55  -0.03 -0.03 -0.04 -0.04 -0.08 -0.08 -0.10 -0.11 -0.14 -0.16 -0.17 -0.21 -0.22 -0.26 -0.24 -0.27 -0.29  4.03 4.10 4.82 5.04 8.92 9.50 10.51 12.38 13.82 16.41 17.85 22.17 22.17 23.03 24.18 26.63 27.64  1.47 1.49 1.76 1.83 3.25 3.46 3.82 4.51 5.03 5.97 6.50 8.07 8.07 8.38 8.80 9.69 10.06  3.19 3.13 3.28 3.89 6.95 7.18 7.53 9.33 10.90 12.05 13.32 16.82 17.51 18.95 19.44 22.43 21.72  1.79 1.71 1.90 2.21 3.83 4.02 4.38 5.33 6.09 7.04 7.75 9.66 10.08 10.52 11.04 11.87 12.59  3.36 3.24 3.47 4.14 7.17 7.48 7.87 9.73 11.15 12.62 13.94 17.48 18.26 19.12 20.15 22.40 22.63  1.71 1.66 1.81 2.09 3.74 3.89 4.23 5.15 5.98 6.78 7.47 9.36 9.74 10.46 10.72 11.91 12.18  30 30 30  5.90 6.28 7.81  0.49 0.54 0.65  0.11 0.13 0.14  -0.08 -0.09 -0.11  5.11 5.44 6.77  2.95 3.14 3.91  5.17 5.72 6.91  2.87 3.22 3.82  5.08 5.73 6.78  2.91 3.22 3.89  v  2  90  e (°) 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30  F (N) 7.97 8.73 9.11 11.80 15.78 15.78 16.54 17.46 17.62 18.84 19.30 20.83 22.37 24.51 25.43 25.74 31.56  V, (V) 0.67 0.73 0.78 1.00 1.33 1.34 1.45 1.52 1.55 1.66 1.67 1.80 1.91 2.09 2.22 2.19 2.78  v, (V) 0.15 0.16 0.20 0.24 0.36 0.38 0.33 0.40 0.39 0.47 0.46 0.63 0.64 0.77 0.69 0.83 0.95  V, (V) -0.12 -0.12 -0.13 -0.21 -0.29 -0.30 -0.27 -0.33 -0.33 -0.36 -0.36 -0.42 -0.43 -0.49 -0.48 -0.52 -0.61  FcosQ (N) 6.90 7.56 7.89 10.22 13.66 13.66 14.33 15.12 15.26 16.32 16.72 18.04 19.37 21.23 22.02 22.29 27.33  FsinQ (N) 3.98 4.37 4.56 5.90 7.89 7.89 8.27 8.73 8.81 9.42 9.65 10.42 11.18 12.25 12.71 12.87 15.78  (N) 7.07 7.71 8.06 10.51 13.65 13.71 15.37 15.67 16.13 16.91 17.14 17.55 18.77 20.20 22.24 20.91 27.27  Fsn (N) 3.95 4.26 4.63 5.93 8.02 8.16 8.57 9.11 9.23 10.06 10.12 11.28 11.90 13.27 13.66 13.95 17.42  (N) 6.94 7.59 8.08 10.04 13.22 13.35 14.98 15.19 15.57 16.53 16.72 17.68 18.95 20.61 22.18 21.44 27.72  (N) 4.01 4.32 4.63 6.16 8.23 8.34 8.77 9.35 9.51 ' 10.25 10.33 11.24 11.83 13.09 13.71 13.72 17.23  40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40  6.20 6.28 7.35 7.51 7.51 10.26 14.09 17.00 17.16 19.61 22.98 23.90 24.51 25.74 25.74 30.94 32.48 34.62 36.00 39.06  0.52 0.51 0.61 0.61 0.65 0.89 1.24 1.55 1.58 1.80 2.08 2.19 2.22 2.39 2.33 3.04 3.04 3.32 3.54 3.94  0.20 0.19 0.27 0.29 0.26 0.34 0.50 0.83 0.83 0.95 1.01 1.26 1.32 1.39 1.34 1.45 1.64 1.78 2.00 2.16  -0.14 -0.14 -0.17 -0.17 -0.18 -0.28 -0.38 -0.52 -0.50 -0.59 -0.63 -0.77 -0.80 -0.83 -0.83 -0.91 -1.00 -1.09 -1.20 -1.33  4.75 4.81 5.63 5.75 5.75 7.86 10.80 13.03 13.14 15.02 17.60 18.31 18.78 19.71 19.71 23.70 24.88 26.52 27.58 29.92  3.99 4.04 4.73 4.82 4.82 6.60 9.06 10.93 11.03 12.60 14.77 15.36 15.75 16.54 16.54 19.89 20.87 22.25 23.14 25.11  4.92 4.95 5.56 5.51 6.11 8.41 11.63 13.13 13.47 15.39 18.40 18.08 18.02 19.58 19.22 27.02 25.74 28.18 29.46 33.11  3.31 3.24 3.99 4.08 4.16 5.68 7.99 10.65 10.79 12.34 13.98 15.36 15.69 16.79 16.35 20.33 20.93 22.84 24.69 27.25  4.93 4.86 5.71 5.78 6.13 7.99 11.33 13.71 14.20 16.01 19.11 19.10 19.14 20.88 20.19 27.95 27.03 29.53 31.18 34.73  3.31 3.29 3.93 3.95 4.16 5.89 8.14 10.39 10.46 12.06 13.66 14.89 15.18 16.20 15.91 19.91 20.34 22.23 23.90 26.52  91  FN13  Fm4  FSH  0° (Normal direction)  Force (N)  Figure C5. Impacts applied in the normal direction.  10°  R = 0.9464 Force (N)  Figure C6. Impacts applied at 10° to the normal direction.  92  20° • Piezo 1 • Piezo 3 A Piezo 4  V, =0.0718F IT = 0.9958  es  a .3° 1 e  V = 0.0169F = 0.9591 3  N  " * <S0 V = -0.0094F 4  -1 J  Force (N)  = 0.9834  Figure C7. Impacts applied at 20° to the normal direction.  30° • Piezo 1 • Piezo 3 A Piezo 4  V, = 0.0864F R = 0.9984 z  es  a  .3° 1  0.0269F  s« o  R =0.9118  R' = 0.975 Force(N)  Figure C8. Impacts applied at 30° to the normal direction.  93  40° • Piezo 1 • Piezo 3 A Piezo 4  05  e Sf 53 o N ii  4B V = -0.0313F 4  Force (N)  R = 0.9783  Figure C9. Impacts applied at 40° to the normal direction.  Angle (°) 0 10 20 30 40  Piezo 3  Piezo 1 Kie Kis (mV/N) (mV/N) 43.3 82.7 57.0 71.8 91.0 86.4 97.8 95.6 94.6 Ave K =91.8 mV/N KIN =43.3 mV/N 1S  K39  Piezo 4 K 3 S  (mV/N) (mV/N) -70.2 155.7 -42.1 16.9 242.3 175.4 26.9 50.9 162.8 Ave K =164.6 mV/N K 3 N =-70.2 mV/N 3S  K»e (mV/N) (mV/N) 48.6 -112.7 28.3 -9.4 -161.0 -18.9 -122.0 -31.3 -106.6 Ave Kis =-113.7 mV/N K 4 N =48.6 mV/N K 4 S  Table C5. K-Values determined by impacting the sensor at different angles  A s a validation o f the calibration procedure, the following two graphs (Figures 4.7 and 4.8) show plots o f the measured forces from the force hammer signal against the calculated forces from the piezo signals. The graphs show more scatter than Figure C 4 , which is the equivalent graph for the old calibration method.  This is because o f the  difficulty i n administering angled impacts i n such a way that the line o f action o f the  94  applied force passed through the center o f the probe tip. Regardless, the agreement was judged to be sufficiently good for a reliable determination o f the forces.  0  5  10  15  20  25  30  35  40  Actual Normal Component (F cosq) (N)  Figure CIO. (Same as Figure 4.7) Comparison of calculated and measured normal forces.  Actual Shear Component (F sinq) (N)  Figure C l l . (Same as Figure 4.8) Comparison of calculated and measured shear forces.  95  APPENDIX D MATLAB PROGRAMS DL CALIBRATION "Calibn.nf clear load c:\lecroy\calibn\scl000.dat load c:\lecroy\calibn\sc2000.dat load c:\lecroy\calibn\sc3000.dat load c:\lecroy\calibn\sc4000.dat c l e a r sclOOO  sc2000 sc3000  cl(1)=max(scl000) c2(1)=min(sc2000) c3(l)=min(sc3000) h(l)=max(sc4000) ;  % % % %  % Piezo 1 s i g n a l % Piezo 2 s i g n a l % Piezo 3 s i g n a l % Hammer s i g n a l  sc4000;  Maximum Minimum Minimum Maximum  piezo 1 voltage piezo 2 voltage piezo 3 voltage hammer v o l t a g e  load c:\lecroy\calibn\scl001.dat load c:\lecroy\calibn\sc2001.dat load c:\lecroy\calibn\sc3001.dat load c:\lecroy\calibn\sc4001.dat cl(2)=max(scl001) c2(2)=min(sc2001) c3(2)=min(sc3001) h(2)=max(sc4001) ; clear  % % % %  Maximum Minimum Minimum Maximum  s c l O O l sc2001 sc3001  piezo 1 voltage piezo 2 voltage piezo 3 voltage hammer v o l t a g e  sc4001;  % The program p r o c e e d s i n t h i s way u n t i l a l l r e l e v a n t i m p a c t s a r e p r o c e s s e d . The % v e c t o r s c l , c 2 , c3 and h a r e t h e n e x p o r t e d t o M i c r o s o f t E x c e l f o r t h e l i n e a r % r e g r e s s i o n , k - v a l u e d e t e r m i n a t i o n and d e r i v a t i o n o f f o r c e e q u a t i o n s .  D2. TRANSFER FUNCTIONS TF.rrT clear w=hanning(50002);  % D e f i n e Hanning window  load d:\lecroy\calibn\scl000.dat load d:\lecroy\calibn\sc4000.dat tfn=tfe(sc4000,sclOOO,65536,10000000,w) , tfl(l,:)=abs(tfn(l:750)'); c l e a r sclOOO sc4000;  % % % %  load d:\lecroy\calibn\scl001.dat load d:\lecroy\calibn\sc4001.dat  96  Piezo signal Hammer s i g n a l Calculate transfer function C a l c u l a t e magnitude o f t r a n s f e r f u n c t i o n  tfn=tfe(sc4001,scl001,65536,10000000,w); tfl(2,:)=abs(tfn(l:750)'); c l e a r s c l O O l sc4001; % The program p r o c e e d s i n t h i s way u n t i l a l l r e l e v a n t i m p a c t s a r e p r o c e s s e d , and t h e % a v e r a g e t r a n s f e r f u n c t i o n i s t h e n c a l c u l a t e d a s f o l l o w s ( u s u a l l y f o r 10 i m p a c t s ) : tfavl=sum(tf1)/ll; tfdbl=20*logl0(tfavl); f=(0:65535)*10000000/65536; fr=f(1:750);  % C a l c u l a t e average t r a n s f e r % Convert t o d e c i b e l s % Define frequency s c a l e  function  figure(1) plot(fr,tfdbl); g r i d on; h o l d on; t i t l e ( ' A v e r a g e T r a n s f e r F u n c t i o n f o r P i e z o 1' ) ; x l a b e l ( ' f r e q (Hz)'); y l a b e l ( ' T F (dB) ') ;  D3. REFINER FORCE SIGNAL ANALYSIS "Getstats.m" % % % % %  T h i s program l o a d s p i e z o s i g n a l s , c a l c u l a t e s t h e s h e a r and normal f o r c e s , r e g i s t e r s t h e b e g i n n i n g and end o f a l l i m p a c t s , and computes t h e d e s i r e d s t a t i s t i c s s u c h a s peak f o r c e s , c o e f f i c i e n t o f f r i c t i o n (as a v r a t i o and p e a k r a t i o ) , and impact d u r a t i o n . These a r e t h e n s a v e d a s column v e c t o r s t h a t a r e e x t r a c t e d and c o m p i l e d f o r s e v e r a l s i g n a l s b y t h e program named " C o m p i l e s t a t s . m " .  clear load d:\lecroy\d4ref\scl003.dat load d:\lecroy\d4ref\sc2003.dat V2=scl003; V3=sc2003;  % Piezo 2 Voltage % Piezo 3 Voltage  c l e a r s c l 0 0 3 sc2003; Fn=-4.40*V2-10.67*V3; Fs=-1.68*V2+2.52*V3; c l e a r V2 V3; % FORCE PROFILE ANALYSIS % Peak C o u n t e r ( s e t a t 2 t o s t a r t w i t h because (peakcount-1) % a s u s e d below would o t h e r w i s e g i v e a n e g a t i v e i n d e x . avrange=2; % Number o f p o i n t s e i t h e r s i d e o f p o i n t ' i ' u s e d f o r mean v a l u e thresh=1.0; % T h r e s h o l d f o r c e v a l u e (1 N) f o r r e c o g n i z i n g i m p a c t s impstart(1)=-150; % A v o i d s m i s h a n d l i n g t h e f i r s t impact impfinish(l)=-150; buffer=100; % Number o f p o i n t s n e g l e c t e d a f t e r an impact ( t o h e l p % prevent r e g i s t e r i n g v i b r a t i o n s as impacts) impswitch=l; peakcount=2;  % N o i s e Compensation b y mean c a l c u l a t i o n for i=l:avrange meanFn(i)=Fn(i); meanFs ( i ) =Fs ( i ) ,end for i=length(Fn)-avrange:length(Fn)  97  meanFn(i)=Fn(i) ; meanFs(i)=Fs(i); end for  i=l+avrange:length(Fn)-avrange-1 meanFn(i)=mean(Fn(i-avrange:i+avrange)); meanFs(i)=mean(Fs(i-avrange:i+avrange));  end c l e a r Fn F s ; % F i n d l o c a t i o n o f s t a r t and end o f impacts for i=2:length(meanFn) i f ( m e a n F n ( i - l ) < t h r e s h ) & (meanFn(i)>=thresh) l)>buffer) impstart(peakcount)=i; impswitch=i; else i f (meanFn(i-1)>thresh) & (meanFn(i)<=thresh) l)>buffer) & impstart(length(impstart))>0 impfinish(peakcount)=i; peakcount=peakcount+l ; end end end IMPSTART=impstart/250; IMPFINISH=impfinish/250;  % C o n v e r t i n d i c e s t o time  & (i-impstart(peakcount-  & (impswitch-impstart(peakcount-  (ms)  t=(0:4e-3:1000.004); % Compute Impact S t a t i s t i c s f o r j=2:peakcount-l flocsizeindex(j)=IMPFINISH(j)-IMPSTART(j); Fnprofile(1:impfinish(j)-impstart(j)+1,j)=meanFn(impstart(j):impfinish(j))'; Fsprofile(1:impfinish(j)-impstart(j)+1,j)=meanFs(impstart(j):impfinish(j) ) ' ; m a x F n ( j ) = m a x ( F n p r o f i l e ( :, j ) ) ; maxFs (j ) = m a x ( F s p r o f i l e (:, j ) ) ,peakratio(j)=maxFs(j)/maxFn(j); avratio(j)=mean(Fsprofile(1:impfinish(j)-impstart(j)+1,j)./Fnprofile(1:impfinish (j)impstart(j)+1,j)); end  % Save a l l s t a t s 'Impact* Fn F s R(pk) R(av) F l o e S i z e Index(ms) impstart impfinish [(3:j)' maxFn(3:j)'maxFs(3:j)'peakratio(3:j)' avratio(3:j) ' flocsizeindex(3:j)' IMPSTART(3:j)' IMPFINISH(3:j)'] 1  stats003=[(3:j)' maxFn(3:j) ' m a x F s ( 3 : j ) ' p k r a t i o ( 3 : j ) ' flocsizeindex(3:j)' IMPSTART(3:j)' IMPFINISH(3:j)'];  avratio(3:j)'  meanfnO 03 =meanFn; save d : \ r e s e a r c h \ d a t a \ d 4 r e f \ s t a t s 0 0 3 ; save d : \ r e s e a r c h \ d a t a \ d 4 r e f \ m e a n f n 0 0 3 ;  D4. COMPILA TION OF IMP A CT ST A TISTICS "Compilestats.m" % T h i s program p r o v i d e s a p l o t o f t h e s i g n a l showing t h e s t a r t and end o f i m p a c t s % a s r e c o g n i z e d b y " G e t s t a t s . m " , and o u t p u t s a l l t h e impact d a t a a s s o c i a t e d w i t h % t h e s i g n a l i n q u e s t i o n . T h i s data i s then exported t o M i c r o s o f t Excel manually. clear load d:\research\data\d4ref\stats003  98  t=(0:l/1000:50000/1000) ; % P l o t o f f o r c e s and s t a r t X f i n i s h p o i n t s f o r t h e p u r p o s e o f c h e c k i n g how w e l l % i m p a c t s were r e c o g n i s e d b y t h e p r e v i o u s program. % The g r e e n l i n e s s i g n i f y t h e s t a r t o f t h e e x t r a c t e d i m p a c t s and t h e r e d l i n e s % s i g n i f y t h e end o f t h e i m p a c t s . figured) c l f ; h o l d on; plot(t,meanFn,'b',t,meanFs,' r ' ) ; f o r j=2:peakcount-l p l o t ( [ I M P S T A R T ( j ) IMPSTART(j)] , [-2 50] , ' g-', [IMPFINISH(j) IMPFINISH(j)] , [-2 end x l a b e l ( ' T i m e (ms)'); y l a b e l (' F o r c e (N) ) ,t i t l e ( ' I m p a c t s a t 700RPM, Dec 4, s c * 0 1 6 b ' ) ; 1  % Display vectors containing stored variables 'maxFn' maxFn' 'maxFs' maxFs 'pkratio pkratio' 'avratio' avratio 'impdur' flocsizeindex' n=' 1 eng t h (maxFn) 1  1  1  1  99  50], ' r -  APPENDIX E ESTIMA TED LENGTH OF BARS CROSSING A TANY GIVEN TIME  This quantity was estimated i n chapter 6 to estimate the total shear force acting on the rotor plate.  Assuming equal bar and groove widths, the surfaces o f the bars constitute approximately half o f the total area o f the refining zone. That is:  A=4r  ( ) E1  where Ab is the total area o f bar surfaces and An is the area o f the refining zone. The total bar length is then given b y the total bar area divided b y the bar width, B, and the total length o f bars crossing is estimated to be half o f the total bar length. Therefore: 2 bc  AB  2  AB  where r/ and r are the inner and outer radii o f the refining zone, respectively, and Lb is 2  C  the total length o f bars crossing at any given time.  For the Sprout-Waldron 12-inch laboratory refiner with the D 2 B 5 0 2 plates, rj is 12.25 cm, r is 15.25 cm, and B is 2.8 mm, giving a value o f 2.3 m for Lb - For the Sprout2  C  Waldron T W I N 60 refiner i n [25], ri is 45 c m and r is 78.5 cm, and B is assumed to be 2  2.8 m m , giving a value o f 116 m for Lb c  100  

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