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Modelling of forces and appropriate control strategies in the abrasive machining of wood Reiser, Henry Lawrence 2003

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MODELLING OF FORCES AND APPROPRIATE CONTROL STRATEGIES IN THE ABRASIVE MACHINING OF WOOD by HENRY LAWRENCE REISER B.Sc. The University of Toronto 1992 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF MECHANICAL ENGINEERING We accept this thesis as conforming To the required standard THE UNIVERSITY OF BRITISH COLUMBIA JUNE, 2003 ©Henry Lawrence Reiser, 2003 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Mechanical Engineering The University of British Columbia Vancouver, Canada Date 111 oi*\ 2.003 Abstract This thesis presents an examination of the cutting and machining of Douglas Fir. Wood processing is a major component in the economy and to maximize economic benefit and minimize fibre loss the insights gained from this research have been applied to predict the material removal. The mechanics of cutting solid wood in single point cutting, milling and grinding have been analyzed and presented. Cutting models for abrasive machining of Douglas Fir parallel to the grain based on the analysis of the mechanics of cutting solid wood are proposed and analysed. The use of abrasives in the wood working industry is widely used as a finishing operation. This process is very labour and time intensive requiring highly skilled personnel thus an expensive operation. The automation of the sanding process will benefit the wood working industry in cost savings, uniformity of the piece parts as well as reducing the need for re-work of a work-piece. A simple force controlled edge finishing (grinding) system based on the proposed cutting models has been presented. This grinding system does not require the geometry of the work-piece to be previously defined and can finish parts to a tolerance of +/- 0.0254 mm thus ensuring quality edges with a minimum of fibre loss. Table of Contents A B S T R A C T " T A B L E O F C O N T E N T S »' LIST O F T A B L E S VI LIST O F FIGURES VII LIST O F S Y M B O L S XI A C K N O W L E D G E M E N T S XVI C H A P T E R 1 1 INTRODUCTION 1 1.1 THESIS OBJECTIVES 2 1.2 THESIS OUTLINE 2 C H A P T E R 2 4 LITERATURE REVIEW O F M E T A L AND W O O D CUTTING MECHANICS AND MACHINING P R O C E S S E S 4 2.1 INTRODUCTION 4 2.2 MECHANICS OF METAL CUTTING 5 2.2.1 Introduction 5 2.2.2 Metal Chip Formation 5 2.2.2.1 Continuous Chips 6 2.2.3 Mechanics of Orthogonal Cutting 8 2.2.3.1 Determination of Shear Angle 8 2.2.3.2 Chip Velocity 9 2.2.3.3 Cutting Force Components in Orthogonal Cutting 10 2.2.3.4 Merchant's Model for Orthogonal Cutting 11 2.2.3.5 Lee and Shaffer's Model for Orthogonal Cutting 12 2.2.3.6 Stress Distribution on the Rake Face 14 2.2.3.7 Ploughing or Parasitic Forces 16 2.3 DISCONTINUOUS CUTTING PROCESSES 18 2.3.1 Introduction ! 18 2.3.2 Up-Milling and Down-milling 18 2.3.3 Chip Thickness in Milling 19 2.3.4 Milling Forces and Energy 21 2.4 GRINDING 24 2.4.1 Introduction 24 2.4.2 Grinding Forces and Energy. 26 2.5 WOOD STRUCTURE PARAMETERS AND INFLUENCE ON THE CUTTING PROCESS 29 2.5.1 Introduction 29 2.5.2 Thin Walled/Thick Walled Fibres 30 2.5.3 Softwood Fibre Layered Structure 31 2.5.4 Wood as a Composite Polymer 32 2.6 ORTHOGONAL CUTTING OF WOOD 32 2.6.7 Introduction 32 2.6.2 Factors Affecting the Tool Forces When Cutting Wood 33 2.6.2.1 Grain Direction in Wood 34 2.6.2.2 Chip Type Formation (90-0 Direction) 35 2.6.2.3 Franz Type I Chip Formation 38 2.6.2.4 Franz Type II Chip Formation 39 2.6.4.5 Franz Type III Chip Formation 40 2.6.5 Cutting Velocity Effects 41 2.6.6 Cutting Tool Forces (90-0 Direction) 41 2.7 PERIPHERAL MILLING OF WOOD PARALLEL TO GRAIN 45 2.7.1 Introduction 45 2.7.2 Chip Formation 46 2.7.3 Surface Quality and Power Requirements 46 2.7.4 Cutting Forces in Peripheral Milling of Wood 48 2.8 ABRASIVE MACHINING OF WOOD 51 2.8.1 The Main Physical Parameters Contributing to the Structural Breakdown of Wood in Grinding 51 C H A P T E R 3 53 SOLID W O O D CUTTING EXPERIMENTS 53 3.1 INTRODUCTION 53 3.2 PENDULUM CUTTING EXPERIMENT 53 3.2.1 Introduction 53 3.2.2 Apparatus 54 3.2.3 Three-dimensional Force Dynamometer 55 3.2.4 Tooling 59 3.2.5 Data Acquisition 59 3.2.6 Wood Samples 60 3.2.7 Results and Plots 61 3.2.8 Chip Formation 70 3.3 SINGLE EDGE FLY CUTTER EXPERIMENTS 80 3.3.1 Introduction 80 3.3.2 Apparatus 81 3.3.3 Tooling 82 3.3.4 Results and Plots 83 3.4 SOLID WOOD GRINDING WITH HOLKE MILLING MACHINE 84 3.4.1 Introduction 84 3.4.2 Apparatus 84 3.4.3 Tooling 84 3.4.4 Results and Plots 85 C H A P T E R 4 93 IMPLEMENTATION OF A FORCE CONTROL SOLID WOOD GRINDER 93 4.1 INTRODUCTION 93 4.1.1 Apparatus 94 4.1.2 Grinder Assembly 95 4.1.3 Grinding Apparatus Experiments 98 4.1.4 Results and Plots of Gantry Grinding System Experiments 98 4.1.5 Grinder System Implementation 100 4.2 SYSTEM MODELLING 102 C H A P T E R 5 119 C O N C L U S I O N S A N D R E C O M M E N D E D F U T U R E W O R K 119 Conclusions 119 5.2 Future Work 727 BIBLIOGRAPHY 122 IV APPENDIX A 130 A . 1 DEVELOPMENT OF GRINDING SYSTEM MODEL 130 A. 1.1 Grinding System Block Diagram 130 A. 1.2 Cutting Model 737 A 7.3 Drive Motor 737 A. 1.4 Grinder Assembly Dynamics 733 A. 1.5 Grinder Displacement Feedback 738 A. 1.6 Ball Screw Drive and Work Piece Dynamics 738 A. 1.7 Compumotor Drive Controller 743 A 7.8 Control PC Modeling 743 V List of Tables TABLE 2.1 ABRASIVE GRIT TYPES AND KNOOP HARDNESS 2 5 TABLE 2 . 2 APPROXIMATE PERCENTILE DISTRIBUTION OF THE MOST IMPORTANT CHEMICAL COMPONENTS IN THE DIFFERENT LAYERS OF A SOFTWOOD TRACHEID 3 2 TABLE 2 . 3 CHIP TYPES OF SUGAR PINE AT VARIOUS MOISTURE CONTENTS, CUTTING DEPTHS, AND RAKE ANGLES [FRANZ 3 8 ] 3 6 TABLE 2 . 4 F C AS A FUNCTION TOOL RAKE FACE AND DEPTH OF C U T 4 2 TABLE 2 . 5 F T AS A FUNCTION TOOL RAKE FACE AND DEPTH OF C U T 4 3 TABLE 2 . 6 F C AND F T AS A FUNCTION OF MOISTURE CONTENT 4 3 TABLE 2 . 7 COEFFICIENT OF FRICTION BETWEEN CHIP AND TOOL TO WOOD SPECIES AND MOISTURE CONTENT 4 4 TABLE 2 . 8 NET CUTTERHEAD POWER REQUIRED WITH VARYING NUMBER OF KNIVES, DEPTH OF CUT, FEED RATE 5 0 TABLE 3.1 TRANSDUCER SENSITIVITIES 5 6 TABLE 3 .2 EDGE FORCE COMPONENTS OF F C E AND F T E FOR DOUGLAS FIR 6 5 TABLE 3 . 3 CHIP COMPRESSION RATIO R T W H E N DOUGLAS FIR IS C U T 7 4 TABLE 3 .4 APPARATUS USED IN THE MILLING EXPERIMENT 81 TABLE 3 . 5 VARIABLES USED AND CALCULATED VALUES FOR F X ( A V E ) AND FY(AVE) 9 1 TABLE 3 . 6 COMPARISON BETWEEN MEASURED AND CALCULATED VALUES OF FXJAVE) AND FY<AVE) ••• 9 2 TABLE 4 .1 GRINDER SYSTEM APPARATUS 9 4 TABLE 4 . 2 GRINDER ASSEMBLY APPARATUS 9 6 TABLE 4 . 3 CALIBRATION DATA FOR THE GRINDER ASSEMBLY SPRING 9 7 TABLE 4 . 4 MATERIAL REMOVAL RATIO DOWN-GRINDING 9 9 TABLE 4 . 5 GRINDER SYSTEM FREQUENCY RESPONSE 1 0 9 TABLE A . 1 MOTOR MANUFACTURER MOTOR CONSTANTS DATA 1 3 3 TABLE A . 2 MANUFACTURER'S INERTIA SPECIFICATIONS 1 3 9 vi List of Figures FIGURE 2.1 ORTHOGONAL MACHINING (CUTTING PROCESS) 4 FIGURE 2 . 2 DEFORMATION ZONES [4] 5 FIGURE 2 . 3 METAL CHIP TYPES [3] 7 FIGURE 2 . 4 SHEAR PLANE AND SHEAR PLANE ANGLE [14] 8 FIGURE 2 . 5 VELOCITY RELATIONSHIP IN ORTHOGONAL CUTTING 1 0 FIGURE 2 . 6 FORCE COMPONENTS IN ORTHOGONAL CUTTING [25] 11 FIGURE 2 . 7 LEE AND SHAFFER'S SLIP LINE FIELD FOR ORTHOGONAL CUTTING 1 3 FIGURE 2 . 8 MOHR'S STRESS CIRCLE FOR THE STRESS ZONE 1 4 FIGURE 2 . 9 DISTRIBUTION OF NORMAL AND SHEAR STRESS ON TOOL RAKE FACE [4] 1 5 FIGURE 2 . 1 0 TOOL EDGE RADIUS 1 6 FIGURE 2 . 1 1 VARIATION OF F C AND F T WITH UNCUT CHIP THICKNESS 1 6 FIGURE 2 . 1 2 PARASITIC EDGE FORCES 1 8 FIGURE 2 . 1 3 UP-MILLING AND DOWN-MILLING [14] 1 9 FIGURE 2 . 1 4 VARIATION OF UNCUT CHIP THICKNESS IN SLAB MILLING 2 0 FIGURE 2 . 1 5 A FORCES IN DOWN-MILLING [27] 2 1 FIGURE 2 . 1 5 B FORCES IN UP-MILLING [27] 2 1 FIGURE 2 . 1 6 ABRASIVE CHIP FORMATION [14] 2 4 FIGURE 2 . 1 7 ABRASIVE MACHINING [25] 2 6 FIGURE 2 . 1 8 PLUNGE SURFACE GRINDING USING WORK-PIECE DYNAMOMETER 2 7 FIGURE 2 . 1 9 U P AND DOWN GRINDING [32] 2 8 FIGURE 2 . 2 0 MULTIFIBER STRUCTURE OF SOFTWOOD 2 9 FIGURE 2 . 2 1 THREE PRINCIPAL AXIS OF WOOD 3 0 FIGURE 2 . 2 2 STRUCTURE OF DOUGLAS FIR [33] 3 1 FIGURE 2 . 2 3 THINWALLED-THICKWALLED FIBRES [34] 3 1 FIGURE 2 . 2 4 SOFTWOOD TRACHEID STRUCTURE [35] 3 2 FIGURE 2 . 2 5 MCKENZIE CUTTING NOTATION 3 5 FIGURE 2 . 2 6 FRANZ CHIP TYPE I [52] 3 7 FIGURE 2 . 2 7 FRANZ CHIP TYPE II [52] 3 7 FIGURE 2 . 2 8 FRANZ CHIP TYPE III [52] 3 8 FIGURE 2 . 2 9 FORCE PLOT OF F C AND F T UP-MILLING ( A ) AND DOWN-MILLING ( B ) PALMQVIST ETAL [55] 4 9 FIGURE 2 . 3 0 ELASTIC COMPRESSION AND PLASTIC COMPRESSION OF WOOD STRUCTURES CAUSED BY THE GRITS OF THE GRINDER WHEEL 5 2 FIGURE 3.1 T H E PENDULUM APPARATUS 5 5 FIGURE 3 .2 THREE-DIMENSION FORCE DYNAMOMETER 5 6 vii FIGURE 3 .3 CALIBRATION DATA OF CHARGE A M P OUTPUT ORTHOGONAL AXIS X LOADED 5 7 FIGURE 3 .4 CALIBRATION DATA OF CHARGE A M P OUTPUT ORTHOGONAL Y AXIS LOADED 5 7 FIGURE 3 .5 CALIBRATION DATA OF CHARGE A M P OUTPUT ORTHOGONAL AXIS Z LOADED 5 8 FIGURE 3 .6 KISTLER CHARGE AMPLIFIERS (1 ) AND KROHN-HITE FILTER (2) 5 8 FIGURE 3 . 7 TOOLING USED 3 0 (1) , 0 (2) , AND - 3 0 (3 ) DEGREE RAKE ANGLES 5 9 FIGURE 3 .8 SAMPLE OF DOCUWAVE WAVEFORM USING A + 3 0 ° RAKE ANGLE TOOL 6 0 FIGURE 3 . 9 TYPICAL DOUGLAS FIR SAMPLE USED IN THE CUTTING EXPERIMENTS 6 1 FIGURE 3 . 1 0 DEPTH OF C U T Ho Vs CUTTING FORCE ( F C ) AND THRUST FORCE ( F T ) DOUGLAS FIR + 3 0 ° RAKE ANGLE TOOL 6 2 FIGURE 3 . 1 1 DEPTH OF C U T H O V S CUTTING FORCE ( F C ) AND THRUST FORCE ( F T ) DOUGLAS FIR 0 ° RAKE ANGLE TOOL 6 3 FIGURE 3 . 1 2 DEPTH OF C U T H O V S CUTTING FORCE (F C ) AND THRUST FORCE (F T ) DOUGLAS FIR - 3 0 ° RAKE ANGLE TOOL 6 4 FIGURE 3 . 1 3 DEPTH OF C U T (HO) V S CUTTING PRESSURE ( K ) + 3 0 ° RAKE ANGLE TOOL 6 6 FIGURE 3 . 1 4 DEPTH OF C U T (HO) V S CUTTING PRESSURE ( K ) 0 ° RAKE ANGLE TOOL 6 6 FIGURE 3 . 1 5 DEPTH OF C U T (HO) V S CUTTING PRESSURE ( K ) - 3 0 ° RAKE ANGLE TOOL 6 7 FIGURE 3 . 1 6 ( p - a ) Vs SHEAR ANGLE + 3 0 , 0 , AND - 3 0 DEGREE RAKE ANGLE TOOLS 6 8 FIGURE 3 . 1 7 DEPTH OF C U T V S SHEAR STRESS + 3 0 DEGREE RAKE ANGLE TOOL 6 9 FIGURE 3 . 1 8 DEPTH OF C U T V S SHEAR STRESS 0 DEGREE RAKE ANGLE TOOL 7 0 FIGURE 3 . 1 9 DEPTH OF CUT V S SHEAR STRESS - 3 0 DEGREE RAKE ANGLE TOOL 7 0 FIGURE 3 . 2 0 CHIPS PRODUCED AT DEPTHS OF 0 . 1 0 1 6 MM, 0 . 2 0 3 2 MM, 0 . 2 5 4 MM, 0 . 4 0 6 4 MM AND 0 . 8 1 2 8 MM USING A + 3 0 ° RAKE ANGLE TOOL 7 1 FIGURE 3 .21 CHIPS PRODUCED AT DEPTH OF 0 . 0 5 0 8 MM, 0 . 1 0 1 6 MM, 0 . 2 0 3 2 MM, 0 . 4 0 6 4 MM AND 0 . 8 1 2 8 MM USING A 0 ° RAKE ANGLE TOOL 7 2 FIGURE 3 . 2 2 CHIPS PRODUCED AT H O 0 . 1 0 1 6 MM, 0 . 2 0 3 2 MM, 0 . 2 5 4 MM, AND 0 . 4 0 6 4 MM USING A -3 0 ° TOOL 7 3 FIGURE 3 . 2 3 DEPTH OF C U T Ho Vs CHIP THICKNESS RATIO R T + 3 0 , 0 , AND - 3 0 DEGREE RAKE ANGLE TOOLS 7 5 FIGURE 3 . 2 4 FRICTION AND NORMAL FORCES + 3 0 ° RAKE ANGLE TOOL 7 6 FIGURE 3 . 2 5 FRICTION AND NORMAL FORCES 0 ° RAKE ANGLE TOOL 7 7 FIGURE 3 . 2 6 FRICTION AND NORMAL FORCES - 3 0 ° RAKE ANGLE TOOL 7 8 FIGURE 3 . 2 7 DEPTH OF C U T V S THE COEFFICIENT + 3 0 ° RAKE ANGLE TOOL 7 9 FIGURE 3 . 2 8 DEPTH OF C U T V S THE COEFFICIENT OF FRICTION 0 ° RAKE ANGLE TOOL 7 9 FIGURE 3 . 2 9 DEPTH OF C U T V S THE COEFFICIENT OF FRICTION - 3 0 ° RAKE ANGLE TOOL 8 0 FIGURE 3 . 3 0 PERIPHERAL UP-MILLING (PLANING) 81 FIGURE 3 . 3 1 APPARATUS USED IN THE PERIPHERAL MILLING (PLANING) OF DOUGLAS FIR 8 2 FIGURE 3 . 3 2 SKETCH OF FLYCUTTER USED 8 2 viii FIGURE 3 . 3 3 RADIAL DEPTH OF C U T (D) V S T H E MEASURED VALUES OF F X ( A V E ) AND F Y ( A V E ) FROM THE FLY CUTTER EXPERIMENT USING A 0 ° RAKE ANGLE TOOL 8 3 FIGURE 3 . 3 4 APPARATUS USED IN THE SURFACE GRINDING OF DOUGLAS FIR 8 5 FIGURE 3 . 3 5 FORCES IN UP-GRINDING 8 6 FIGURE 3 . 3 6 FEED-RATE V S F Y ( A V E ) UP-GRINDING HOLKE MILLING MACHINE 8 9 FIGURE 3 . 3 7 FEED-RATE V S F X ( A V E ) UP-GRINDING HOLKE MILLING MACHINE 8 9 FIGURE 3 . 3 8 FEED-RATE V S FY(AVE) W H E N DOWN-GRINDING HOLKE MILLING MACHINE 9 0 FIGURE 3 . 3 9 FEED-RATE V S F X ( A V E ) DOWN-GRINDING HOLKE MILLING MACHINE 9 0 FIGURE 4.1 FORCE CONTROLLED GRINDER ASSEMBLY 9 5 FIGURE 4 . 2 GRINDER ASSEMBLY 9 6 FIGURE 4 . 3 SKETCH OF SPRING DIMENSIONS 9 7 FIGURE 4 . 4 F Y ( A V E ) Vs FEED-RATE GRINDER SYSTEM 9 9 FIGURE 4 . 5 BLOCK DIAGRAM OF P C CONTROL SYSTEM 1 0 1 FIGURE 4 . 6 CONTROL PROGRAM ALGORITHM 1 0 2 FIGURE 4 . 7 GRINDER SYSTEM BLOCK DIAGRAM 1 0 4 FIGURE 4 . 8 SIMULATION OF GRINDER SYSTEM RADIAL DEPTH OF C U T RESPONSE TO A 0.1 MM STEP INPUT W H E N I P C = 1 0 1 0 5 FIGURE 4 . 9 GRINDING SYSTEM RADIAL DEPTH OF C U T RESPONSE TO A 0.1 MM STEP INPUT 1 0 6 FIGURE 4 . 1 0 SIMULATION OF GRINDER SYSTEM RADIAL DEPTH OF C U T RESPONSE TO A 0.1 MM STEP I N P U T W H E N I P C = 3 0 1 0 7 FIGURE 4 . 1 1 SIMULATION OF GRINDER SYSTEM RADIAL DEPTH OF CUT RESPONSE TO A0 . 1 MM STEP INPUT I P C = 8 0 1 0 8 FIGURE 4 . 1 2 MOTOR ROTOR CURRENT RESPONSE TO A 0.1 MM C U T CONTROL STEP W H E N I P C = 1 0 1 1 0 FIGURE 4 . 1 3 MOTOR ROTOR CURRENT RESPONSE TO A 0.1 MM C U T CONTROL STEP W H E N I P C = 3 0 1 1 1 FIGURE 4 . 1 4 MOTOR ROTOR CURRENT RESPONSE TO A 0 .1MM C U T CONTROL STEP W H E N I P C = 8 0 1 1 2 FIGURE 4 . 1 5 FORCE RESPONSE TO A 0.1 MM C U T CONTROL STEP W H E N I P C = 1 0 1 1 3 FIGURE 4 . 1 6 FORCE RESPONSE TO A 0.1 MM C U T CONTROL STEP W H E N I P C = 3 0 1 1 4 FIGURE 4 . 1 7 FORCE RESPONSE TO A 0.1 MM C U T CONTROL STEP W H E N I P C = 8 0 1 1 5 FIGURE 4 . 1 8 SYSTEM FREQUENCY RESPONSE I P C = 1 0 1 1 6 FIGURE 4 . 1 9 SYSTEM FREQUENCY RESPONSE I P C = 3 0 1 1 7 FIGURE 4 . 2 0 SYSTEM FREQUENCY RESPONSE I P C = 8 0 1 1 8 FIGURE A . 1 GRINDER SYSTEM BLOCK DIAGRAM 1 3 0 FIGURE A . 2 WOOD CUTTING MODEL 1 3 1 FIGURE A . 3 DRIVE MOTOR MODEL 1 3 2 FIGURE A . 4 GRINDER ASSEMBLY DYNAMICS 1 3 3 ix FIGURE A . 5 PLOT OF L V D T OUTPUT W H E N GRINDER ASSEMBLY W A S IMPACT TESTED 1 3 4 FIGURE A . 6 GRINDER ASSEMBLY MODEL 1 3 6 FIGURE A . 7 GRINDER ASSEMBLY DYNAMICS SIMULATION 1 3 7 FIGURE A . 8 GRINDER ASSEMBLY CUTTING TORQUE MODEL 1 3 8 FIGURE A . 9 GRINDER DISPLACEMENT L V D T MODEL 1 3 8 FIGURE A . 1 0 IN-FEED BALL SCREW DRIVE 1 3 9 FIGURE A . 1 1 PLOT OF BALL SCREW ROTATIONAL VISCOUS DAMPING TEST 141 FIGURE A . 1 2 BALL SCREW AND WORK PIECE DYNAMICS MODEL 1 4 2 FIGURE A . 1 3 COMPUMOTOR CONTROLLER MODEL 1 4 3 FIGURE A . 1 4 P I D CONTROL BLOCK OF COMPUMOTOR DRIVE 1 4 4 x List of Symbols a is the rake angle P is the chip flow angle r jmax ' s t n e maximum value of normal stress <rn is normal stress d<j> is the tooth spacing is, 0w is the work piece ball screw shaft position 0 is any angle 9 is the angle at center of wheel p is the average coefficient of friction <|> is the instantaneous angle of rotation (J> is the shear plane angle <t>Lee and Shaffer is the Lee and Shaffer shear angle ^Merchant is Merchant shear angle <t>s is the swept angle of the tool x is the shear yield stress x c u t is the cutting torque produced by the grinder assembly xm is the motor output torque rm is the torque applied to the ball screw by the motor T W is the torque applied to the ball screw drive to advance the work piece into the grinder surface. T S is shear stress A is the characteristic decay constant, ^ is the damping ratio co is the damped natural frequency co is the rotational speed con is the natural frequency A is a wood cutting constant xi a is the axial depth of cut a is the damping constant B wood cutting constants D is the damping constant d is the radial width of cut dgct is the amount of stock removed D b is the ball screw damping D e rotational viscous damping D m is the motor damping Dpc is the software differential gain Ea is the net armature voltage (volts) F is the friction force acting along the tool rake face F C is the cutting or power consuming Force F c ,c is the horizontal cutting force component F C ,R is the horizontal rubbing force F c c is the cutting power consuming force caused by cutting action F C E is the power consuming edge force FCut cutting force Ff is a force from the flank face could be decomposed into F T E and FA=. F R instantaneous radial cutting force F s is the shearing force F T is the instantaneous tangential force F T is the Thrust Force F t,c is the thrust cutting force component FT,R is the thrust rubbing force F tc is the cutting thrust force caused by the cutting action F TE is the thrust edge force Fx(ave) is the average force in the X axis Fy(ave) is the average force in the Y axis G is the grinding ratio, h* is the critical chip thickness xii H c is the chip thickness H 0 is the un-deformed chip thickness (depth of cut) Hz is hertz IPC Integral gain Personal Computer Ia is the armature current (amps) IPC is the software integral gain. J b is the ball screw shaft inertia J e is the equivalent load inertia generated by the feed drive, J m is the motor inertia K is the specific cutting pressure K is the spring constant ki is the cutting force constant k2 is the parasitic force constant Kb is the back emf constant relating motor shaft speed to Vb. KD is the programmable differential gain kg is kilogram K| is the programmable integral gain K P is the programmable proportional gain Kt is the torque constant of the motor Kfc is a shearing force cutting coefficient (parallel) K tc is a shearing force cutting coefficient (normal) KtE is an edge tangential force coefficient (parallel) KfE is an edge tangential force coefficient (normal) Kv is the programmable overall gain /„ is natural contact length L is the longitudinal axis lb. is pound m is meter M is mass MHz is mega hertz xiii ML is the lignin rich middle lamella which glues the wood fibres together mm is millimetre n is the number of teeth on the cutter N is Newton N is the force acting perpendicular to the rake face of the tool N is the RPM of the cutter P is the pitch of the ball screw P is the primary cell wall of wood fibre Pave is the specific power pC/V is Pico coulombs/volt PP C is the software proportional gain R is the cutter radius R is the radial axis Ra is the armature resistance (ohms) RCut is the material removal ratio H is the ratio of radial to tangential cutting forces r2 is the ratio of radial to tangential flank forces rt is the chip thickness ratio S1, S2, S3 are the three secondary cell walls of wood fibre S m is the mean chip thickness S t is the cut per tooth T is the tangential axis t is the uncut chip thickness T is torque T a v e is the average value of torque u is the specific grinding energy V is the velocity of the work-piece V is the peripheral velocity v is the feed velocity Va is the DC voltage applied to the motor xiv Vb is the back emf (CEMF) produced by motor generation action V c is the chip velocity V s is the shear velocity W is the central lumen or cavity of wood fibre w is the width of cut w c is the chip width X axis x is the edge force constant. X c u t depth of cut X g is the displacement of the grinder assembly in reaction to the cutting force F c ut X g is the linear displacement of the grinder away from the work piece in reaction to the cutting force. X p is the desired position as commanded by the system control PC X w is the work displacement Y axis. xv Acknowledgements I would like to express my most heartfelt gratitude to my advisor Dr. Ian Yellowley for his encouragement and guidance. His patience and perseverance were instrumental in my completing this work and his candour was most uplifting. I would also wish to acknowledge the continuous support from my colleagues, students and the administration at UCC. Without their assistance and understanding I would have not been able to embark on this voyage of discovery. This work is dedicated to my loving wife Madeleine, my best friend and strongest ally. I want to thank her and my children for their support and patience, during this lengthy and sometimes difficult journey. xvi CHAPTER 1 Introduction Wood harvesting and the production of related products from solid wood and wood fibre are the source of a significant part of the Canadian economy. This renewable material is used in many products ranging from building materials and paper to engineered structures. If the wood is harvested in an environmentally sensitive fashion, wood could be available as a basic material practically indefinitely. With the desire to maintain sustainable harvest levels within the forests of Canada, the amount of wood harvested annually must match the replacement trees grown. Current increasing levels of the harvesting wood in Canada and the world cannot be sustained due to pressure from various stakeholders of the land base and the ability of the forest to regenerate [Mater 1]. As a result there is a need to add value to the wood harvested in order to generate an expanding economy using equivalent quantities of wood and maintain sustainable forestry management. The primary breakdown of logs into dimensional lumber is the mainstay of the wood industry in British Columbia and Canada. This approach to revenue generation requires great quantities of wood and the forests of British Columbia and Canada cannot sustain the increasing levels of harvest required to maintain a growing economy. It is through increased secondary wood processing and adding value to the finished product that the province will maximize the return on the harvested wood fibre beyond primary breakdown. Wood is not a homogeneous material and the cutting and machining of solid wood (as opposed to metals) has traditionally been based on practical experience and a rule of thumb approach. Under specific cutting conditions such as when continuous chips are formed or when wood is machined using abrasives, the insights gained from the research into the machining of wood may be applied to predict the material removal. The use of computer controlled machines allows stock removal to be optimized minimizing fibre loss thus maintaining the accuracy and finish of the machined parts. 1 1.1 Thesis Objectives This thesis presents an investigation into the cutting forces and chip formation process when Douglas Fir is machined. The primary objectives of the thesis are: i. ) To analyze the mechanics of cutting solid wood in single point cutting, milling and grinding. ii. ) To develop a model of the grinding process of solid wood. iii. ) To examine the veracity of the developed model in grinding operations. iv. ) To design a simple edge finishing (grinding) system to control edge quality using the knowledge of the mechanics gained from above. 1.2 Thesis Outline This thesis also provides a review of the literature on orthogonal cutting, milling and grinding of metal and wood. The cutting forces and chip types produced in wood cutting were examined experimentally using a pendulum apparatus with single positive, negative and zero degree rake angle HSS tools. In addition the milling and grinding forces encountered when machining Douglas Fir have been measured and correlated with previous work and simple theories. Based on the force model developed, an adaptive computer controlled grinding machine has been designed and implemented. This thesis is organized as follows. Chapter 2 is a review of the literature concerned with the basic mechanics of the metal cutting process with an emphasis on the cutting forces and tool geometry. The use of single point orthogonal tools and more complex operations using mill cutters and abrasive media is reviewed. A literature survey on the properties of solid wood and previous work on solid wood cutting, wood chip formation, cutting force models and wood cutting mechanics is also presented. In Chapter 3, the solid wood cutting experimental procedures used by the author are presented. Experiments were performed in continuous cutting 2 using a single point tool, in milling using a single tooth Fly Cutter, and in abrasive machining using a Grinding Wheel. A Piezo Electric Dynamometer (after Lai [60]) was used to measure the cutting forces in all experiments. The results of the single edge cutting experiments were used to describe the effect of tool rake angle on the cutting forces, chip type formation, and the resulting finish. The results of the Fly Cutter experiments were used to validate the forces measured in the pendulum experiment. The Grinding experiment results are given and a Grinding Force Model is presented. This model is used in the later experimental work. In chapter 4 a discussion of the implementation of a Force Control Solid Wood Grinder is presented. This system uses a simple force sensor attached to the grinder assembly and an X-Y gantry to present the work-piece to the grinder. The system performance and the Cutting Force Models developed previously are analyzed. Chapter 5 outlines the conclusions and makes suggestions for future work. 3 CHAPTER 2 Literature Review of Metal and Wood Cutting Mechanics and Machining Processes 2.1 Introduction The control of any machining process requires first an understanding of the mechanics of the chip formation process. The machining process involves the removal of a thin layer of material from the work-piece by a cutting tool as shown in Figure 2.1. Figure 2.1 Orthogonal Machining (Cutting Process) There has been much research directed towards the metal cutting process, the majority of the work has been directed towards orthogonal cutting. The term orthogonal cutting was first used by Merchant [2] and refers to the case where the cutting edge of the tool is perpendicular to the cutting velocity vector. The resulting system is then 2 dimensional, considerably simplifying analysis. 4 The discussion starts with a consideration of orthogonal cutting with a single cutting edge and constant cutting conditions. Later sections examine the more complex milling and grinding processes. 2.2 Mechanics of Metal Cutting 2.2.1 Introduction During the metal cutting process, the metal ahead of the tool edge deforms plastically as it passes through the shear plane [Merchant 2], [Oxley 3] [Armarego and Brown 4]. This plastic zone is of significant (finite) dimensions compared to the uncut chip thickness. There are two basic approaches to the analysis of the deformation zone. The first is the thin-plane or thin-zone model by Merchant [5], Kobayashi and Thomsen [6] (Figure 2.2 a) and the other the thick deformation region as proposed by Palmer and Oxley [7], Okushima and Hitomi [8] and Lee and Shaffer [9] (Figure 2.2 b). At very slow cutting speeds the thick deformation region analysis is required to describe the cutting process while at high cutting speeds the thin-zone model appears adequate [Armarego and Brown 4]. (o) <b) Figure 2.2 Deformation Zones [4] 2.2.2 Metal Chip Formation All machining processes involve formation of chips by 5 deforming the work material on the surface of the work-piece with a cutting tool. The amount and type of deformation the material is exposed to affects: i. ) The type of chip ii. ) The resulting surface quality iii. ) Cutting forces iv. ) Temperatures developed i.) Dimensional accuracy The chip type formed can provide an indication of the deformation and surface quality produced during cutting [Ernst 10], [Ernst and Merchant 11], [Ernst and Merchant 12]. There are three basic chip types formed in machining processes: i. ) Discontinuous chips (Figure 2.3 a), ii. ) Continuous chips (Figure 2.3 b), and iii. ) Continuous chips with built up edge (Figure 2.3 c) This review will only examine continuous chip formation since it is most pertinent to the machining of wood. 2.2.2.1 Continuous Chips During the cutting of ductile materials like low carbon steel, copper, brass and aluminium alloys a continuous ribbon-type chip is produced. The pressure of the tool plastically deforms the material ahead of the cutting edge in compression as well as shear [Oxley 3]. The chip slides over the tool rake face for some distance and then leaves the tool. Friction between the chip and tool may produce secondary (additional) deformation in the chip material [Sata 13]. The plastic zone ahead of the tool edge is called the primary zone of deformation, and the deformation zone on the rake face is usually referred to as the secondary zone of deformation. Both of these zones and the sliding of the chip on the rake face produce heat, thus increasing the temperature on the tool-chip interface. [Oxley 3]. 6 (b) Id Figure 2.3 Metal Chip Types [3] The extent of primary zone of deformation depends on: i. ) Rake angle of tool, ii. ) Cutting speed, iii. ) Work material characteristics iv. ) Friction on rake face. With large positive rake angle tools, the transition of work material into chip is gradual and the material suffers less overall deformation. Cutting forces are also low. With small positive or negative rake angle tools, the work material suffers a far more severe deformation, and the cutting forces involved are also larger. With higher cutting speeds, the thickness of the primary zone of deformation shrinks, i.e. it becomes narrower. The material characteristics that influence the size of the primary zone are: i.) Strength 7 ii. ) Strain-hardening iii. ) Strain rate iv. ) Heat conductivity. An increase in friction on the rake face tends to increase the size of both the primary and the secondary zones of deformation. 2.2.3 Mechanics of Orthogonal Cutting In thin zone models, it is assumed that the work material shears across a plane and forms the chip. The plane is called the shear plane and the angle that it makes with the cutting velocity vector is called the shear plane angle (Figure 2.4). Figure 2.4 Shear Plane and Shear Plane Angle [14] 2.2.3.1 Determination of Shear Angle The shear plane angle (<j>) is the angle between the cutting velocity vector and the plane (AC) across which the work material suffers shear deformation and forms the chip (see figure 2.7). During the chip formation process there is conservation of mass hence: 8 HQwV = HcwcVc (2.1) Where H 0 , w, and V are the un-deformed chip thickness (depth of cut), width of cut and velocity of the work-piece respectively. H c , wc, and V c are the chip thickness, chip width and chip velocity respectively. When w is comparable to H 0 , there is significant side flow and the chip width w c is greater than w. However when w » H 0 , the side flow is negligible and w = wc. In most cutting processes, this condition is satisfied. Hence HQV = HCVC (2.2) Therefore H V r,= — = — (2.3) ' Hc V where rt is the chip thickness ratio. From the geometry of figure 2.7 Shear plane length = AC= = — ^ (2.4) sin ^ cos(^ - a) where a is the rake angle of the tool. Hence ^ = r,= S l n < * (2.5) Hc cos(</>-a) This equation can then be solved for § rt cosor tan (9 = —-— ; (2.6) 1 — rt sin or allowing <|> to be calculated from measurements of chip thickness. 2.2.3.2 Chip Velocity If it is assumed that the work material is moving against the tool with a velocity V (Fig. 2.4). The surface layer shears across the shear plane AC and becomes part of the chip. The surface layer suffers a velocity discontinuity parallel to the shear plane. As a result of V and the velocity discontinuity Vs (Fig. 2.5) the chip attains a velocity V c along the rake face. From the geometry; 9 thus and sin(90° + a - <f>) sin(90° - a) sin <f> V c = chip velocity = V s i n ^ V. =• cos(^-or) V cos a cos(^-or) 90° + a-<t> (2.7) (2.8) (2.9) Figure 2.5 Velocity Relationship in Orthogonal Cutting 2.2.3.3 Cutting Force Components in Orthogonal Cutting It is commonly accepted that the cutting process is in a state of "quasi static" equilibrium, [Merchant 2]. The tool and shearing forces must then appear as shown in Figure 2.6. Typically F c (Cutting or Power Consuming Force) and F t (Thrust Force) are measured using a Dynamometer. The average coefficient of friction u, at the interface between the chip and the tool can be related in terms of F, N and P (the chip flow angle) as follows: F u. = tan (3 = N or tan (p-a)=-^ F„ (2.10) (2.11) 10 Figure 2.6 Force Components in Orthogonal Cutting [25] 2.2.3.4 Merchant's Model for Orthogonal Cutting One of the earliest analyses of orthogonal cutting is due to Ernst and Merchant [Ernst and Merchant 11]. Their model is based on the minimization of rate of energy dissipation in the cutting process. The basic assumptions in the model are: i) Tool edge is sharp ii) The work material suffers deformation across a thin shear plane iii) There is no side spread (deformation is 2 dimensional) iv) There is uniform distribution of normal and shear forces on the shear plane v) The work material is rigid, perfectly plastic From the geometric relations between forces in orthogonal cutting F c = R cos (p - a) (2.12) 11 and F s = R cos (<|> + B -a) (2.13) where F s = ^ J _ ( 2 1 4 ) s i n ^ where x is the shear yield stress of the material, w is the width and H 0 is the depth of cut. Therefore R = ^ (2.15) sin(^) cos(^ + p — a) Fc = HQ w(j — - ) (2.16a) sin(^) cos(^ + P - a) Ft=H0w(r (2.16b) sin(^) cos(^ + P - y) Merchant's model is based on the minimization of rate of energy consumption. Therefore the value of the Merchant shear angle (^ Merchant) can be determined using: * ^ = ~ \ ( f i - a ) (2-17) If it is assumed that there is only sliding friction on the rake face and that there is a thin shear deformation primary zone, then Eq. 2.16 can be used to calculate the magnitudes of the cutting force (Fc) and the thrust force (Ft) [Seethaler 19]. 2.2.3.5 Lee and Shaffer's Model for Orthogonal Cutting An alternative thick zone (slip line field based) model has been proposed by Lee and Shaffer [9]. The slip line field proposed by them is shown in Figure 2.7. The resultant cutting force R is inclined at an angle p to the normal to the tool rake face. The deformation zone is contained in the triangular region ABC. The line AC is the shear plane across which material suffers a velocity discontinuity. The plane CB is stress free, since there are no external forces acting on the tool or chip boundary and hence the slip lines meet this final 12 boundary at 45°. One set of the slip lines are inclined at (45° -p) to the tool rake face. U Figure 2.7 Lee and Shaffer's Slip Line Field for Orthogonal Cutting From the geometry of the appropriate Mohr circle shown in Fig. 2.8: <))Lee and Shaffer = 45° - (P-a) (2.18) The slip line field inside the zone ABC consists of a straight orthogonal net implying a constantly stressed zone. However the distribution of stress on the rake face has been found to be non constant [Zorev 15]. In addition the applicability of this solution for negative rake angles seems doubtful. For example, for a = -10, and p = 35°, the shear angle <)> would be zero, which is inadmissible. 13 Figure 2.8 Mohr's Stress Circle for the Stress Zone 2.2.3.6 Stress Distribution on the Rake Face In the previous discussion of orthogonal cutting, it has been assumed that the shear and normal stresses are uniformly distributed over the tool rake face. Many investigators [Takeyama and Usui 16], [Sata and Yoshikawa 17], [Zorev 15] have on the other hand approximated the distribution of normal stress by an exponential curve. The shear stress is found to be constant up to a certain portion of contact length from the tool tip, which is called the sticking zone. Beyond this zone, the shear stress decreases to zero. In the latter zone, called the sliding zone (Fig. 2.9), Coulomb's law of friction is considered applicable. Over the length A to F (lst) the normal stress is very high and the metal adheres to the rake face; plastic flow occurs in the work material. From F to B (b) smaller normal stresses exist and sliding friction occurs. These results were determined using experiments involving the use of photoelastic materials and evaluating the fringe patterns. Alternatively two part rake face tools were used and each segment of the tool was attached to 2 separate dynamometers to make comparative measurements. 14 Figure 2.9 Distribution of Normal and Shear Stress on Tool Rake Face [4] The distribution function for the normal stress is typically found to be of the form a n = Ax m (2.19) where A and m are constants and x is the distance from the end of chip-tool contact. If ©-max is the maximum value of normal stress at the cutting edge, then the above distribution may be expressed in the form ^ = f f M ( f ) " (2-20) where cr n is normal stress on the rake face at a distance Xfrom the end of the contact length, and /„ is natural contact length (as opposed to "controlled" contact length). The total normal force N on the rake face is then given by N= l<r„wdx = wl'aBmAmdx (2.21) WCT I N = ==-2- (2.22) (iw + 1) 15 2.2.3.7 Ploughing or Parasitic Forces In the previous discussions, it was assumed that the cutting edge is perfectly sharp but in all practical cases the tool has a finite radius, however small see Fig. 2.10 [Albrecht 18]. This small thickness (or radius) of the cutting edge increases the cutting force. VERY DULL SLIGHTLY DULL Figure 2.10 Tool Edge Radius If a plot is made between the cutting force components and the depth of cut, the lines relating the two variables do not pass through the origin. They make finite positive intercepts on the force axis at zero depth of cut (Fig. 2.11). 0 0-1 0-2 0-3 0-4 Ho (mm) Ho (mm) Figure 2.11 Variation ofFc and Ft with Uncut Chip Thickness 16 The force values given by the intercept are related to the dullness of the tool edge. If the shear angle is kept constant then it maybe argued that the intercept is equal to the edge force. Assuming a constant value of edge force/length of cutting edge, the cutting force components F c and F t may be written as F^KE+F^ (2.23) FT — FLE + F T C (2.24) where F C E and FTE (edge forces) are the components due to the ploughing action of the tool edge and Fee and F tc are those caused by the cutting action. At H 0 = 0, F c E and FTE may be taken equal to the intercept. In practice it is often convenient to avoid formulations containing the shear angle and friction angle, (one will not know these). In such cases a simple cutting pressure is taken from tables and empirical equalities. Thus Fc=H0wK (2.25) F,=H0wKrx (2.26) where K is the specific cutting pressure and n is the cutting force ratio, r2 is the parasitic force ratio. As mentioned earlier the total cutting force has a component proportional to the cross sectional area of the un-deformed chip and a parasitic force (Fig. 2.11) which is proportional to the active cutting edge length thus the total force can be expressed in the form F c + (2-27) Ft=kxrx(H0w) + k2r2w (2.28) where ki, k2, n, and r2 are constants. 17 Figure 2.12 Parasitic Edge Forces 2.3 Discontinuous Cutting Processes 2.3.1 Introduction In milling, the cutting teeth are on the periphery of the cutter. The teeth may be helical or straight (parallel to the axis of the cutter) and each tooth moves in a trochoidal path relative to the work-piece. The resulting chip thickness is variable and the cutting forces are discontinuous due to the intermittent, periodic contact of each tooth of the cutting tool. There are two types of milling, face (or end mill cutting) and peripheral (or slab milling). In this section peripheral milling will be discussed. 2.3.2 Up-Milling and Down-milling Depending upon the relationship between the feed motion of the work-piece and the cutter rotation, two types of arrangements can result. They 18 are commonly known as up-milling and down-milling (fig. 2.13). (Up milling) conventional cut Figure 2.13 Up-milling and Down-milling [ 14] In the case of up-milling (or conventional milling), the cutter starts with zero chip thickness and rubs against the work-piece surface before actually beginning to cut. The rubbing action generates considerable heat at the interface. As a result a newly formed chip may be welded on to the rake face of the cutter tooth. In down (or climb) milling, the chip thickness is maximum at the beginning of the cut and is gradually reduced to zero [Degarmo et al 14]. Relative power consumption is chip thickness dependent. 2.3.3 Chip Thickness in Milling Figure 2.14 shows two consecutive relative positions of the cutter with centers at C and C They correspond to a time interval during which the work-piece moves by a distance equal to the feed per tooth of the cutter (St) [Martellotti 20] and d the radial depth of cut. 19 Figure 2.14 Variation of Uncut Chip Thickness in Slab Milling In the usual case where the feeding speed is much less than the peripheral velocity then the path is approximately circular and the uncut chip thickness (t) at any angle 0 is given by t = S, sin0 (2.29) The feed per tooth (St) can be determined by where v is the feed of the table, N is the RPM of the cutter, and n is the number of teeth on the cutter. In peripheral milling, the resulting surface finish will comprise of washboarding (waviness) and a resulting instability or chatter is produced from the cutter vibrations [Koenigsberger and Sabharwal 21], [Montgomery and Altintas 22]. 20 2.3.4 Milling Forces and Energy The cutting forces in peripheral milling have been investigated by many authors [Martellotti 20], [Koenigsberger and Sabharwal 23], [Pandey and Shan 24], and [Yellowley 25] etc. A force model based on an orthogonal cutting data base where the milling force component coefficients can be predicted has also been developed [Budak et al 26]. Average values of milling cutting forces and parasitic forces are useful in adaptive control strategies when both radial width and axial depth of cut are to be controlled. A suitable force model is available that considers both rake face and parasitic forces of the cutting tool in the determination of expressions for average values of force, torque and specific power [Yellowley 25] [Yellowley 27]. Figure 2.15A Forces in Down-milling [27] R Figure 2.15B Forces in Up-milling [27] 21 The tangential force is a function of mean chip thickness, specific cutting pressure K and the force ratio r, thus including the edge forces (nose and flank) contributions, the instantaneous cutting forces FT and FR can be calculated from the following. FT =KaStsin0 + xa (2.31) Where K is the specific cutting pressure, a is the axial depth of cut, S t is the feed per tooth, § is the instantaneous angle of rotation and x is the edge force constant. If the cutting force has equal components of cutting and parasitic forces then a critical chip thickness (h) is used to characterize the chip thickness, then Kah'=xa (2.32) or x = Kh* (2.33) then equation (2.35) can be re-written as h* FT = KaSt (sin </> + —) (2.34) h' and FR=KaSl(rlsin0 + r2—) (2.35) where KaS, s i n^ is the cutting and KaS,h*/St is the parasitic force component respectively and ^ is the ratio of radial to tangential cutting forces and r2 is the ratio of radial to tangential flank forces. Typical values for the cutting force ratio ^ are 0.2< n<0.5 and for the edge force ratio r2 are 1<r2<4. When the geometry in Figures 2.15A and 2.15B is considered, then T = FTR (2.36) where T is torque and R is the cutter radius. Then in up-milling Fx = FT cos (/> + FR sin <j> (2.37) Fy - FR cos<j) -FT sin<j> (2.38) and in down-milling Fx = FR sin (j>-Ft cos <j> (2.39) 22 FY = FR cos <j> + FT s i n </> (2.40) The instantaneous values of force and torque are linearly dependent on axial depth of cut. Average values of torque (T a v e) and specific power (Pave) can be expressed as 2n Sm where N is the number of teeth on the cutting tool, S m is the mean chip thickness given by S _ = M ^ ) ( 2 4 2 ) R is the radius of the cutting tool, and (j) s is the swept angle of the tool where c o s ^ - ' = ( l - % ) (2.43) then KaNS, t t i / r ) ... Tm = - id +—</>sR) (2.44) where d is the radial width of cut. In terms of the radial width of cut, then r „ = ^ « * A ( i + f ) (2.45) The average power (P a Ve) is given by Pave= TgveCO (2.46) where co is the rotational speed thus KaNRa> h \ Pm = —z <f>sSm (1 + —) (2.47) 2n Sm or Pave=Kadv(\ + ^ -) (2.48) where v is the feeding velocity. The average value of force in the x direction Fx(ave) in up milling can be derived from the expression Fx(aVe) = ^r-St[ j(sin^cos0 + rx s i n 2 <j> + ^-(cos<j> + r2 sin^))<ty] (2.49) 2n I St Now average values of forces in up-milling can be expressed as 23 Fx(ave) = ^ ^ [ ( l - c o s 2 ^ ) + r 1 ( 2 ^ - s i n 2 ^ ) + ^ - ( s i n ^ + r 2 ( l -cos# , ) ) ] (2.50) Fy(ave) = El (1 - cos2^ s)- (2#, - sin 2£ )+^ - ( r 2 s in^ -(1 - cos<j,s))] (2.51) and for down-milling ^c(-) = Ws - sin2£) - (1 - cos 2*y+^-(r 2 (1 - cos<j>s) - sin £)] (2.52) on o , = ^ J - [ r I 0 - c o s 2 # 1 ) + (2#I - s i n 2 ^ ) + ^ ( ( l - c o s ^ ) - r 2 s i n ^ ) ] (2.53) 2.4 Grinding 2.4.1 Introduction Grinding is a form of abrasive machining, where the abrasive grits are embedded in a bonded wheel or belt and thus act as the cutting teeth. Chips are formed by the edges of the abrasives (figure 2.16). The abrasive grain edges can have a positive, zero or negative rake angles (on average negative). The abrasive grits are usually mounted on a disk or a belt as a mounted product, or close packed into wheels or stone then called a bonded product. The abrasive grits are generally very hard materials and can be natural or man made [Degarmo et al 25]. Typical grits used are given in Table 2.1. The abrasive grit size affects the size of the chip formed, it follows that the larger the grit, the larger the chip formed. Approximately 2 to 5% of the grits are in the contact area any one time [Degarmo et al 14]. Figure 2.16 Abrasive Chip Formation [14] 24 Abrasive Grit Type Knoop Hardness Quartz (Si0 2) sand 320 Aluminium Oxide (AI2O3) 2100 Silicon Carbide (SiC) 2400 Cubic Boron Nitride (CBN) 4700 Diamonds (man made) 7000 Table 2.1 Abrasive Grit Types and Knoop Hardness However the cuts become finer as the grain size is reduced and grain size is the controlling factor in finish (roughness), so the resulting Material Removal Rate (MRR) will decrease with a decrease in grit size. In addition to grit size, the shape of the grit will determine the geometry of the cutting edge (rake and flank angles). Grits can have a range of the rake angles from +45° to -60° or greater, where large negative rake angles typically do not cut the material but either rub over or plough through the surface. Thus grinding is a combination of cutting, plowing and rubbing (Figure 2.17) As the abrasion process continues, the abrasive grits are themselves being continuously abraded, fractured or dislodged from the bond resulting in a continuous change to the proportions of each of the basic processes (rubbing, ploughing and cutting). In the grinding of metal the chip formation process is again one of compression and shear. In some cases the chips absorb enough heat energy to burn or melt in the atmosphere, yielding the typical sparks observed while grinding. 25 Cutting Grinding chip Plowing (no chips) Rubbing (no chip) Side view Workpiece End view Side view Loaded workpiece material Attritious wear of grit Loading Figure 2.17 Abrasive Machining [25] As the grinding process progresses, the grains wear and become dull, and when the resulting cutting forces exceed the strength of the bond, grits are pulled free. This in turn changes the diameter of the grinding wheel over time and this phenomena is explained in practical terms through the grinding ratio, G. Where mm3 metalremoved G = mm wheellost As the grinding wheel is used, metal chips sometimes accumulate in the voids causing it to become loaded and/or glazed. This results in a need for the wheel to be dressed to maintain sharpness. 2.4.2 Grinding Forces and Energy In the process of grinding, forces are generated between the wheel and the work-piece. A work-piece dynamometer is used to measure the horizontal (Fc) and vertical (Ft) forces (Fig. 2.18). In surface grinding, the total force vector exerted by the work-piece against the wheel can be separated into a 26 tangential component FT and a radial component FR as shown in Figure 2 . 19 . These forces can be measured directly by using a work-piece dynamometer. DYNAMOMETER " 1 " Figure 2.18 Plunge Surface Grinding Using Work-piece Dynamometer The specific grinding energy (u), (the energy spent in removing a unit volume of material), can be expressed as u = (FTV)/(vwd) ( 2 .54 ) where FT is the mean tangential force on the wheel, V is the wheel speed, v is the work speed, a is the axial width of cut and d is the radial depth of cut [Brach et al 28 ] . The specific grinding energy tends to be a constant for a specific material, a specific grinding wheel and un-deformed chip thickness. The fracture stress of the grits (which sharpens the grinding wheel) is a constant for a material being machined and the type of loading. However the specific grinding energy varies significantly with the un-deformed chip thickness, and the condition of the wheel face [Brach et al 28 ] . For fine plunge grinding of steel F C = 2 F T ( 2 . 55 ) and as long as F C and F T are approximately equal (< 2 X ) , typical for conventional fine grinding then u = (FcV)/(vctd) ( 2 .56 ) 2 7 When F c and F t are significantly different or when the ratio of d to the diameter is large, then the spindle torque or power may have to be measured directly or F c and F t via a dynamometer. Figure 2.19(a) is a graphical representation of up grinding and figure 2.19(b) of down grinding. 6> = c o s _ 1 ( 2 / D ) = cos"1 (1 -2dID) (2.57) / 2~ where 9 is the angle at center of wheel corresponding of arc of wheel work contact, D is the wheel diameter, and d is the wheel depth of cut. The value of the specific grinding energy in up grinding will be greater than for down grinding. This is because in the case of up grinding, chip formation does not occur immediately but only after the wheel has reached the Figure 2.19 Up and Down Grinding [32] full depth of cut. Initially only rubbing will occur, but when FR is of a sufficient value, then rubbing is changed to chip formation. In the case of down grinding, the transition is from chip formation to rubbing and this occurs at a much lower value of d. Therefore the minimum chip thickness that may be cut will be smaller for down grinding than for up grinding. 28 The grinding forces can be broken down into a cutting component and a sliding (rubbing) component [Handigund and Miller 29]. FC=FC<C+FC,R (2.58) and Ft=Ftfi+FttR (2.59) where F c,c and F t,c represent the horizontal and vertical cutting forces respectively and F C,R and FT,R the horizontal and vertical rubbing forces. As in milling, there is a component of edge force (parasitic) in the measured forces. 2.5 Wood Structure Parameters and Influence on the Cutting Process 2.5.1 Introduction Softwood has a very complex structure both macroscopically and microscopically. Wood is anisotropic [McKenzie 30] and is comprised of macroscopic elements (growth rings, knots, heart wood, sap wood, etc) and microscopic elements (fibres, cells, pits, resin channels, rays, etc) as can be seen in Fig. 2.20 [Koponen et al 31]. Wood is a visco elastic material [McKenzie 30] and orthotropic in nature [Green et al 32]. Due to its orthotropic nature wood has unique and independent mechanical properties in the direction of three mutually perpendicular axes: longitudinal, radial and tangential (Figure 2.21). T Figure 2.20 Multi'fiber Structure of Softwood 29 Longitudinal Figure 2.21 Three Principal Axis of Wood As shown Fig. 2.21; the longitudinal axis L is parallel to the fibre (grain); the radial axis R is normal to the growth rings (perpendicular to the grain in the radial direction): and the tangential axis T is perpendicular to the grain but tangent to the growth rings. 2.5.2 Thin Walled/Thick Walled Fibres As softwood grows under normal seasonal conditions, annual growth rings are formed. Each growth layer comprises the wood produced by the cambium in a single growth season. The cambium is the outermost surface under the bark in the tree stem or bole. There are two types of wood growth in each ring, earlywood and latewood. Earlywood is softer with thin cell walls and more porous than thick walled latewood [Desch 33]. Fig. 2.22 shows the growth rings where the earlywood is lighter and the latewood is darker. Also shown in figure 2.22 are vertical resin canals (which can contain 30 Figure 2.22 Structure of Douglas Fir [33] Eartywood Latewood Figure 2.23 Thinwalled-Thickwalled Fibres [34] silicates) another sub structure of softwoods. Figure 2.23 clearly demonstrates the earlywood-latewood boundary in addition to the thin-walled early wood tracheids and the thick-walled late wood tracheids [llvessalo-Pfaffli 34]. 2.5.3 Softwood Fibre Layered Structure Softwood fibres are comprised of up to 4 sets of cell wall layers as can be seen in figure 2.24 [llvessalo-Pfaffli, Laamanen 35]. There is the primary (P) wall and three secondary (S1, S2, S3) walls. In addition there is a lignin rich 31 middle lamella (ML) which glues the cells together and a central lumen or cavity (W). Figure 2.24 Softwood Tracheid Structure [35] 2.5.4 Wood as a Composite Polymer There are basically three polymers in wood: i) Cellulose a linear macro-molecule (principally crystalline in nature). ii) Linear amorphous polyoses molecules called hemicellulose. iii) Lignin, a crosslinked amorphous polymer. The distribution of the polymers in softwood is outlined in the Table 2.2 [Panshin and DeZeeuw 36]. Tracheid Layer Lignin Hemicelluloses Cellulose Middle Lamella 70% 10-20% 10-20% S1 Layer 40-60% 5-20% 20-40% S2 Layer 15-30% 30% 40-55% S3 Layer 15% 30% 55% Table 2.2 Approximate Percentile Distribution of the Most Important Chemical Components in the Different Layers of a Softwood Tracheid 2.6 Orthogonal Cutting Of Wood 2.6.1 Introduction 32 The two most common methods of machining wood are by sawing (single edge constant chip thickness) and peripheral milling or planing (variable chip thickness, multiple teeth). Although the cutting mechanics of metal has been studied extensively, the cutting mechanics of wood has received much less attention [Dippon et al 37]. Franz [38] investigated the wood cutting process, Kivimaa [39] cutting forces and the effect of tool geometry and McKenzie [40] the relationship between the cutting properties of wood and its physical and mechanical properties. Stewart [41, 42] investigated the cutting of wood at various grain angles. Chip swelling in orthogonal cutting of wood has been investigated by Ozaki et al [43], and the mechanics of orthogonal cutting of medium density fiberboard has been investigated by Dippon et al [37] and Stewart [44]. Measuring and modeling wood cutting forces has been investigated by Gronlund [45], Sawada et al [46, 47] and Ohta [48] have developed simulations of the chip formation in the orthogonal cutting of wood by the Extended Distinct Element Method. Komatsu [49] and Huang [50, 51] investigated peripheral milling of wood and the effect of rake angles on the cutting forces and surface quality. The majority of the research has been directed towards orthogonal cutting with a single cutting edge. 2.6.2 Factors Affecting the Tool Forces When Cutting Wood The tool forces developed in the orthogonal cutting of wood are affected by the combined influence of the following factors [Koch 52] (it might be noted that these [(i and ii) also apply to metal cutting]: i) Cutting tool factors: • Rake angle • Clearance angle (flank face) • Sharpness • Friction between chip and tool face • Tool obliquity • Induced lateral vibration 33 ii) Feed factors: • Width of cut • Depth of cut, i.e., chip thickness • Feed speed, i.e., cutting velocity in orthogonal cutting • Grain orientation relative to cut iii) Work-piece factors: • Species • Specific gravity • Moisture content • Work-piece temperature • Mechanical properties 2.6.2.1 Grain Direction in Wood In order to separate a chip from the work-piece failure must be induced at the juncture of the chip and the work-piece. The strength of wood varies with grain direction and chip configuration, thus cutting power and surface quality are all affected by the direction of cut with respect to the grain direction. McKenzie [52] used a notation to describe the orientation of the grain of the wood relative to the cutting vector in orthogonal cutting. A two number notation is used in this convention. The first number represents the angle of the cutting edge with respect to the grain of the wood and the second number is the angle between the cutting vector direction and the grain see Fig. 2.25. In this thesis only the 90-0 cutting orientation will be examined. 34 90-0 Figure 2.25 McKenzie Cutting Notation 2.6.2.2 Chip Type Formation (90-0 Direction) Large deformations occur in the work-piece before a chip separates from the work-piece due to the properties of wood. In some cases cracks propagate ahead of the chip and tool interface below the surface being created causing a poor chip and surface finish. In the case of dull tools or tools with a negative rake angle, the wood is compressed during the cutting process and does not recover immediately, but later produces raised grain or spring back [McKenzie 30, 40] [Dippon et al 37]. In orthogonal wood cutting there are 3 chip types formed and they are called Type I, II, and III [Franz 36]. Franz Type I chips are formed when the wood splits ahead of the tool by cleavage and fails finally in bending. See Fig. 2.26. Sawada et al [46, 47] have modeled this behaviour using the Extended Distinct Element Method. Franz Type II chips are formed when there is a shear failure in the wood see Fig. 2.27. Franz Type III chips are formed due to severe compression parallel to the grain, (analogous to discontinuous chip formation in metal cutting) due to a cyclic build up of force till the chip breaks free, see Fig. 2.28. Although there are three basic chip types, under certain conditions it is possible to get abrupt changes from one chip type to another, with no 35 appreciable transition phase. It is also possible to get cyclic transitions from one chip type to another, but this depends on the instantaneous stress situation. Franz [38] reported the following chip types formed as a function of tool rake angle, depth of cut, and moisture content of the wood, see Table 2.3. Type of Chip Formed Chip Thickness (mm) Tool Rake Angle 5° 10° 15° 20° 25° 30° @1.5 Percent Moisture Content .0508 III Ill II II II II .127 III III II II II II .254 III III III I I I .381 III III III I I I .508 III III III I I I .635 III III III I I I .762 III III III I I -@8.0 Percent Moisture Content .0508 III II II II II II .127 III II II II I I .254 III II II II I I .381 III II II I I I .508 III III II I I I .635 III III III I I I .762 III III III I I -©Saturated With Moisture .0508 - - - - - II .127 Ill Ill Ill Ill II II .254 III III III III III II .381 III III III III III II .508 - III III III III II .635 - III III III III II .762 - III III III III III Table 2.3 Chip Types of Sugar Pine at Various Moisture Contents, Cutting Depths, and Rake Angles [Franz 38] 36 Figure 2.26 Franz Chip Type I [52] Figure 2.28 Franz Chip Type III [52] 2.6.2.3 Franz Type I Chip Formation The formation of Franz Chip Type I is cyclical in nature. Initially when the tool makes contact with the work-piece, the wood is stressed and shears ahead of the tool edge. As the tool moves forward, the wood ahead of the tool is strained in compression parallel to the grain and in tension at the tool edge. As the tool continues to move a crack propagates starting at the tool edge and proceeds rapidly in the direction of the grain ahead of the current location of the tool. With additional movement of the tool the chip slides up the rake face of the tool and the cleavage continues to advance till the bending stresses on the chip cause the chip to fail. When the tool reaches the point where the chip separated from the work-piece, the tool encounters un-deformed material and the process begins another cycle. Chip Type I form under the following conditions [Koch 52]: I. Low resistance to cleavage (high stiffness and strength in bending). 38 II. Deep depth of cut. III. Larger positive rake angles. IV. Low coefficient of friction between chip and rake face of the tool. The resulting surface finish on the work-piece is affected by the nature of the wood failure. A chipped grain surface will result where crack extends below the plane generated by the cutting tool. In cases where the crack propagates above the plane generated by the tool, the tool then has an effective depth of cut that is less than the original and the resulting surface finish is of good quality. When Type I chips are formed there is usually slight wear on the cutting edge as the chip makes contact only for a small part of the total tool travel. 2.6.2.4 Franz Type II Chip Formation Franz Type II chips are formed when specific conditions allow for a steady state of continuous wood shearing in front of the cutting edge with respect to the work surface [Koch 52]. A Type II chip is continuous in nature, and when formed, is the result of a strain induced by the rake face of the cutting tool. The wood elements fail along the shear plane and the chip slides upward along the rake face of the tool. The stresses are transferred continuously to the un-deformed wood in the work-piece. The chips formed are continuous smooth spirals whose radius is affected by the depth of cut and rake face geometry. The resulting work-piece surface is smooth and free of defects. In terms of quality of finish, Type II chips result in a surface free of raised grain and rough spots and there is no damage below the cutting plane. Factors that lead to the formation of Type II chips are: i. ) Small depth of cut. ii. ) Intermediate moisture content. iii. ) Intermediate rake angles of the cutting tool. 39 Since the chip is in intimate contact with the tool for longer periods of time the tool will become dull more quickly. 2.6.4.5 Franz Type III Chip Formation Franz Type III chips are formed due to cyclical series of compression and shear failures ahead of the tool in the work-piece [Koch 52]. The cycle can be described as follows. When the tool engages the work-piece the material is compressed parallel to the grain, and as the tool continues to move the wood is further strained until rupture occurs in shear parallel to the grain. The deformed material is compacted against the rake face of the tool. Stresses are continued to be applied to the wood ahead of the tool until the accumulation of compressed material becomes critical and buckling results, forcing the chip upwards along the rake face of the tool. When using negative rake angle tools, friction between the chip and rake face can be quite high. A build up of compacted material can develop as in cutting with a Built Up Edge in metal cutting. The accumulated compacted material on the rake face can affect the geometry of the tool and act as a Positive rake angle. When the size of the mass becomes critical or when then tool acts as a positive rake angled tool and a Type I chip is formed, this can induce instability and the compacted material breaks free of the rake face. The Type III chip failures result in a surface commonly referred to having fuzzy grain. This is due to the fact that there have been failures along and below the cutting plane. Factors that lead to the formation of Type III chips are: i. ) Cutting tool factors: Low positive to negative rake angle Dull tool. High coefficient of friction Induced lateral vibration ii. ) Feed factors: 40 Width of cut Small depth of cut Feed speed Grain orientation relative to cut iii.) Work-piece factors: Species High moisture content Work-piece temperature 2.6.5 Cutting Velocity Effects Cutting velocity at low feed speeds affects the cutting forces by a factor of 2.5 times, but in higher cutting speed ranges (300 to 2743 meters per min.) the cutting forces are unaffected [Koch 52]. Ohta and Kawasaki [48] noted that increased cutting speeds improved the surface quality. They also noted that there was a reduction in the typical split along the fibres as is seen in Franz Type I chips. Koch [52] suggests that the factors that may alter the cutting resistance of wood as a function of increasing the cutting velocity are as follows: i. ) Increase in force required to accelerate the chip at higher cutting velocities. ii. ) The strength of wood increases with increased rate of deformation. iii. ) Strength of wood decreases as temperature increases (localized temperature variations at chip-work-piece juncture). iv. ) Coefficient of friction between the tool and chip may change as the cutting velocity is varied v. ) When cutting wet wood, hydraulic action of water in proximity to the tool may alter with varying velocities 2.6.6 Cutting Tool Forces (90-0 Direction) 41 The two basic methods of measuring tool forces when cutting wood are using a force sensor (typically a dynamometer) located between the work-piece holder and a fixed base or to place the force sensor between the tool and tool holder. Early work by Franz [38], Kivimaa [39] measured tool forces when cutting wood in the 90-0 orientation and McKenzie [40] measured tool forces when cutting wood in the 90-90 orientation. The following section reviews the forces when the 90-0 direction is used. As shown in the Merchant force diagram (Fig. (2.6), the forces investigated are F c and F t as these forces are directly measured using a force dynamometer. When the cutting tests were performed the following variables must be considered: i. ) Tool rake face angle ii. ) Tool flank face angle iii. ) Species of wood iv. ) Moisture content of the wood v. ) Width of Cut vi. ) Depth of cut In general low and negative tool rake face angles induce higher parallel tool forces and as the tool rake face angle is increased, the parallel forces drop. In addition low positive and negative tool rake angles cause an increase in the normal tool forces, see Table 2.4 and Table 2.5. A positive tool rake face angle may often yield negative normal tool forces as the tool tends to lift the work-piece into the cutting edge. F c of Sugar Pine @ 1.5% Moisture Content and a 6.35 mm Width of Cut Tool Rake Face Angle Depth of Cut (mm) Fc(N) 5U .254, .508, .762 88.96, 164.58, 240.2 10u .254, .508, .762 84.51, 146.79, 195.72 15u .254, .508, .762 71.17, 102.31, 115.65 20u .254, .508, .762 62.28, 75.62, 106.76 25u .254, .508, .762 44.48, 66.72, 80.07 30u .254, .508, .762 35.58, 53.38, 57.83 Table 2.4 Fc as a Function Tool Rake Face and Depth of Cut 42 F t of Sugar Pine @ 1.5% Moisture Content and a 6.35 mm Width of Cut Tool Rake Face Angle Depth of Cut (mm) Ft (N) 5U .254, .508, .762 19.57, 25.58, 31.14 10° .254, .508, .762 13.34, 13.12, 12.45 15u .254, .508, .762 8.89, 8.45, 8.01 20° .254, .508, .762 4.45, 2.22, -1.78 25u .254, .508, .762 -1.33, -2.85, -5.56 30° .254, .508, .762 -2.78, -5.56, -8.45 Table 2.5 F t as a Function Tool Rake Face and Depth of Cut When the effect of moisture content of the wood on F c and F t is considered, an increase in both the cutting forces will result with an increase in moisture content [Franz 36], see Table 2.6. Koch [42] used the following relationship to calculate F c for shallow depths of cut K = KHcmw (2.60) Where K is a constant, H c is the chip thickness, m is a constant between 1 and 0 (generally observed to be from 0.25 to 0.67), w is the width of chip. When cutting larger chips then F c can be calculated from the following Fc=(A + BHc)w (2.61) Where A and B are experimentally determined and suitably chosen. The tool flank face angle has reported to be optimized at 15° by both Franz and Kivimaa, as when it is lower there is considerable rubbing between the tool flank face and the freshly cut surface. F c and F t of Sugar Pine as a Function of Moisture Content With a 6.35 mm Width of Cut, .762 mm Depth of Cut, and 10° Rake and 15° Flank Angle Moisture Content % Ft (N) Fc (N) 1.5 12.45 195.72 8.0 21.35 209.07 Saturated 48.93 11.21 Table 2.6 F c and F t as a Function of Moisture Content 43 Tool sharpness, has a direct effect on the tool forces when cutting wood as well. As the tool loses its sharp edge, the tool forces increase and the tool wear is rapid. As the tool wears the tool flank face becomes negative and ploughing forces are introduced. This has the effect of changing the chip types formed and increasing the tool forces. Koch [52] reports that a critical sharpness angle of 45 degrees is a reasonable angle to minimize tool wear and maintain sharpness. Friction between the chip and tool affects the force distribution and chip formation. The friction forces are affected by the moisture content and species of the work-piece. As in metal cutting the coefficient of friction is determined using the following F F ju = — = tan(arctan + a) (2.62) Where p is the coefficient of friction, F is the friction force acting along the tool rake face, and N is the force acting perpendicular to the rake face of the tool. Franz [38] reported the following coefficients of friction as a function of moisture content, see Table 2.7. Relation of Coefficient of Friction Between Chip and Tool to Wood Species and Moisture Content Moisture Content Species Sugar Pine Yellow Birch 1.5 percent 0.35 0.45 8.0 percent 0.35 0.41 Saturated 0.69 0.48 Table 2.7 Coefficient of Friction Between Chip and Tool to Wood Species and Moisture Content Dippon et al [37] investigated the orthogonal cutting mechanics of Medium Density Fiberboard (MDF). They developed a Mechanistic cutting model 44 where the cutting forces were decomposed into tool rake and flank face components. In their findings it was concluded that when cutting MDF, there was very little friction on the tool rake face and that the pressure from the uncut chip dominates the force on the rake face. They also concluded that the shear laws used in metal cutting are not directly applicable to the cutting of MDF due to the non-uniform nature of the material and as a result their cutting model was proposed. The cutting force F c resulted from the contact between the rake face and the chip and could be decomposed into F c C and a normal component Ffc. Also a force from the flank face Ff could be decomposed into F t E and FfE. When H 0 represents the uncut chip thickness and w the width of cut, then w*H 0 is the uncut chip area. The tangential and feed forces can be calculated from the relationship Ft= F t c + F t E = K t c wH 0 + K t Ew (2.63) and Ff = Ffc + FfE = KfcwHo + KfE (2.64) where K tc and Kfc are the shearing force cutting coefficients and K tE and KfE are the edge force coefficients. To determine the cutting constants a series of orthogonal cutting tests were made and from the plot of the cutting forces and depth of cut, when h=0 at the Y intercept, the edge force constants Kt£ and KfE were determined. After subtracting the edge force component from the measured cutting forces, K tc and Kfc were determined. This is similar to the edge effects reported by Albrecht [18], Yellowley [25], Budak [26], and Handigund [29] when metals are cut, milled and ground. 2.7 Peripheral Milling of Wood Parallel to Grain 2.7.1 Introduction The most common application of peripheral milling of wood is planing [Koch 52]. Material is removed as single chips from the work-piece by the successive intermittent engagement of the knives of the cutter-head. As in 45 metal cutting this process can be either conventional milling (up-milling) or down-milling. 2.7.2 Chip Formation In peripheral milling of wood the chip formation process is similar to that described by Franz in the orthogonal cutting of wood. The ideal elastic chip has been modeled by Phalitzsch et al [53] from experimental evidence using a high-speed camera and a cutter head with two knives separated by 180°. Phalitzsch observed that in down-milling there is less crack propagation when compared to up-milling conditions. In addition Phalitzsch observed that the chip velocity was typically 50% greater than the cutter speed and this was attributed to high centrifugal forces. As described in the milling of metals, in the peripheral milling operation the knife edge travels in a circular motion hence the relationship of the knife edge to the grain changes with the position of the knife. In addition the rake and clearance angles will change with position as will the depth of cut. The resulting chips will be all three Franz chip types which will form sequentially depending upon the instantaneous conditions [Koch 52]. For up-milling the initial cut conditions are selected to favour the formation of Franz Chip Type II and in the case of down-milling the cut conditions are selected to favour the formation of Franz Chip Type II as well. 2.7.3 Surface Quality and Power Requirements The factors affecting the surface and power required when milling wood are: i.) Work-piece factors • Species • Moisture content • Specific gravity 46 • Grain orientation ii. ) Cutterhead factors • Cutting velocity • Cutting-circle diameter • Number of jointed knives cutting • Rake angle • Clearance angle • Sharpness of cutting edge • Width of joint • Knife extension beyond face of gib • Shape of gib face • Obliquity of cutters iii. ) Feed factors • Feed speed • Depth of cut • Direction of cutterhead rotation with relation to direction of feed The surface quality should be free of waves caused by the intermittent cutting process. Fuzzy grain should as a function of the chip type formed, and "chip marks" on the surface caused by up-milling (i.e. the chip not fully clearing the cutting edge of the knife) should all be minimized by optimizing the above factors. Heisel and Krondorfer [54] investigated the effects of vibrations developed between the work-piece and the cutting tool. They used a surface probe (contact stylus probe) during the cutting process and experimentally determined the induced periodic changes on the work-piece surface by the cutter knives. 47 2.7.4 Cutting Forces in Peripheral Milling of Wood Table 2.8 outlines the net cutterhead power requirements when the depth of cut, nominal feed speeds, and number of jointed knives in the cutter-head are varied [Koch 52]. The species used in this experiment was Douglas fir, with a moisture content of 7.33%, specific gravity of 0.0445, milled parallel to the grain, rake angle of 27.5°, clearance angle of 22.5°, knife extension beyond gib 6.35 mm, width of joint 0.254 mm, and cutter-head rpm of 3600. In the peripheral milling of wood the power requirement increases as a function of an increased number of knives. This is because the material removal rate (MMR) is increased and more work is performed. In addition as the feed speed is increased this will again result in an increase in the MMR thus an increase in work. As the depth of cut is increased the cutting forces will increase, and this also will require more power. Palmqvist et al [55] investigated cutting forces in peripheral milling of wood using an ATI Gamma force/torque sensor bolted to a 3 axis NC router table. The work-piece was placed above the sensor that has a maximum output frequency of 7,000 Hz. This allowed the investigators to make up to 7-8 readings per cut and measure F c and F t directly. It should be noted that these investigators suggest that the spring back effect of wood after cutting is due to the large negative normal forces F t. These negative forces compress the wood during the cut then the wood springs back as raised grain and similar defects. Also during the cut positive values of F t were observed and it is suggested that this is responsible for torn or chipped grain. When Palmqvist cut pine using a 0° rake angle knife, a feed rate of 2.5 m/min, a cutterhead speed of 5000 rpm, with 3 cutting inserts, and a depth of cut at 2.0 mm, the results in Figure 2.33 were observed. It should be noted from the results shown in Fig. 2.29 that F t is initially negative (due to work piece lifting) then becomes positive. Also when the magnitude of F t is compared in up-milling to down-milling, F t is greater in down-48 milling during the initial phase of cutting. In addition, the value of F c is lower in down-milling when compared to up-milling. This can be attributed to the fact that in up-milling it takes longer for the chip to form as reported by many authors. 150 100 | 5 0 e .? 0 -50 -100 1 FC : F c \j \ .'A l"\/s 11 16 21 26 31 36 41 46^5^ » Sample Number A 150 100 | 5 0 o 0 u. -50 -100 :.Fc :Fc \ * . ' A •'' 1 \ 6/ 11 16 21 26 31 36 41 44 61 56 6 /ft \ /Ft Sample Number B Figure 2.29 Force Plot ofFc and Ft Up-milling (A) and Down-milling (B) Palmqvist et al [55] 49 Number of knives 12 6 4 2 Depth of Cut (mm.) Net Power (watts) Feed Speed (M/min) Net Power (watts) Feed Speed (M/min) Net Power (watts) Feed Speed (M/min)) Net Power (watts) Feed Speed (M/min) 0.397 924.67 182.88 581.66 186.23 626.39 186.53 559.27 185.31 0.794 1379.54 182.27 1155.83 184.4 1208.03 185.31 827.73 183.49 1.588 2117.79 178.31 1826.96 181.66 1931.36 183.49 2244.56 181.05 2.381 2870.94 163.68 2677.06 178 3154.31 174.04 3012.63 169.77 3.175 3519.7 163.68 3251.25 171.6 3706.13 166.73 3378.02 167.64 0.397 812.81 156.67 521.99 158.5 626.39 156.97 402.68 157.28 0.794 1304.97 155.75 760.61 158.19 1133.46 156.97 827.73 156.67 1.588 2005.93 150.57 1797.14 157.28 1841.88 155.14 1521.23 155.45 2.381 2460.81 152.7 2259.47 155.14 2378.78 155.45 2729.26 154.53 3.175 3139.4 149.05 3169.22 153.92 3497.33 152.09 3698.67 151,49 0.397 723.33 126.8 454.88 127.71 492.16 127.41 387.76 128.41 0.794 1163.29 126.19 775.53 127.1 857.55 126.8 693.5 128.32 1.588 1715.11 126.19 1185.66 127.1 1543.6 126.19 1372.09 127.1 2.381 2155.07 124.36 1797.14 126.8 2155.07 126.49 2087.96 126.49 3.175 2602.49 123.14 2356.41 125.58 2781.46 125.27 2975.34 124.36 0.397 760.61 93.57 350.48 95.1 305.74 93.88 268.45 93.88 0.794 1036.52 93.27 589.1 94.49 761.13 93.88 522 93.88 1.588 1603.25 92.05 887.38 94.18 1029.07 93.27 939.58 93.88 2.381 1923.91 92.66 1334.8 94.18 1521.23 93.57 1588.34 93.57 3.175 2214.73 98.45 1707.65 93.57 1961.19 92.96 2058.13 92.96 0.397 574.19 32.92 260.99 32.92 231.17 33.22 141.68 32.92 0.794 775.53 32.92 350.48 32.92 313.19 33.22 201.34 32.92 1.588 1103.64 32.92 551.82 32.92 492.16 33.22 268.45 32.92 2.381 1304.97 32.92 686.04 32.92 626.39 33.22 477.25 32.92 3.175 1513.77 32.92 812.81 32.92 745.7 33.22 596.56 32.92 Table 2.8 Net Cutterhead Power Required With Varying Number of Knives, Depth of Cut, Feed Rate. 50 2.8 Abrasive Machining of Wood There has been little research on the topic of the abrasive machining of wood. Typically the research that has been conducted has used mounted product (abrasive) on belts. Taylor et al [56] experimentally investigated the relationship between species, orientation of the grain, abrasive used, pressure applied to the work-piece and grit size on material removal rate (MRR) and quality of the resulting surface. The authors noted that there are innumerable overlapping grooves on the finished surface and that the cutting occurs usually with negative rake angles producing the finest chips They concluded that the pressure applied to the work-piece had the major influence on stock removal rates for all grit sizes. They also concluded that the MRR was affected inversely as the grit size decreased and that the quality of the work-piece surface improved with decreasing grit sizes. The authors suggested that an automated, sanding system of complex contours would be highly desirable. 2.8.1 The Main Physical Parameters Contributing to the Structural Breakdown of Wood in Grinding There has been substantial research conducted in the abrasive machining (grinding in the 0-90 direction) of wood in the field of mechanical pulping and this work may provide insight into the grinding mechanism in the 90-0 grinding of wood. Atack [57, 58] proposed a mechanistic model of the grinding process. Atack suggests that the grinding process is a two stage process, where in the first stage (preliminary breakdown), the wood structure is loosened, then in the second stage the fibres are removed in a combing action. Lucander [59] suggests that during the grinding process the wood experiences elastic and plastic compression (see Figure 2.30). It is during the plastic compression phase that the wood structure suffers fatigue changes as a 51 result of the stress pulses generated by the grit. This causes fatigue changes in the wood structure that loosen the fibres which are then peeled away by the grit of the stone in subsequent interactions. Elastic Compression Plastic Compression Figure 2.30 Elastic Compression and Plastic Compression of Wood Structures Caused by the Grits of the Grinder Wheel 52 CHAPTER 3 SOLID WOOD CUTTING EXPERIMENTS 3.1 Introduction The experimental work discussed in this Chapter is aimed at the generation of a thorough understanding of the wood cutting process. The investigation included the measurement and analysis of cutting forces, chip type formation, peripheral milling and grinding in a series of three experiments. i. ) A Pendulum Cutter assembly was used to investigate orthogonal cutting forces and resulting chip types. ii. ) A single tooth Fly Cutter was used on a Holke Vertical Milling Machine to investigate the average cutting forces during peripheral milling. iii. ) A Grinding Wheel was used on the Holke Vertical Milling Machine to investigate average cutting forces when grinding wood. 3.2 Pendulum Cutting Experiment 3.2.1 Introduction The objective of this experiment was to gain insight on the influence of rake angle and depth of cut on the wood cutting process and chip types formed. Three depths of cut were used 0.1016 mm (0.004"), 0.2032 mm (0.008"), and 0.464 mm (0.016"). At each depth three HSS tools with a clearance angle of 15° and rake angles of +30°, 0°, and -30° were used to examine the mechanics of the process. To simplify analysis all cuts were made in the 90-0 direction. Douglas Fur was selected as the wood type and all the wood samples were maintained at <3% moisture content (measured using a Protimeter Mini III Moisture Content Meter). 53 3.2.2 Apparatus A Pendulum apparatus was used to provide the tool holding and cutting velocity (see (Figure 3.1)). The average velocity during cutting was 137.16 M/min (90 in/sec). The procedure used to make the cuts is as follows: • The tool was adjusted to the appropriate depth using the depth adjustment screw and a dial gauge then secured in place using the set screws. • The height of the surface of the sample was measured using a dial gauge. • The pendulum arm was lifted and released, and when the tool made contact with the sample a cut was made. The forces were measured using a three-dimensional dynamometer [Lai 60]. The depth of cut was measured using a dial gauge placed in a jig to maintain the same measurement point and the chips were collected and measured using a 4 digit digital calliper. Figure 3.1 illustrates the following components: 1. The Mintoyo 0.0001" Dial Gauge. 2. The 3-dimensional Force Dynamometer. 3. The Tool Holder. 4. Pendulum Arm Support Bearings. 5. The Pendulum Frame. 6. The Pendulum Arm 54 Figure 3.1 The Pendulum Apparatus 3.2.3 Three-dimensional Force Dynamometer A 3-dimensional force dynamometer [Lai 66] was used to measure the cutting forces in X, Y, and Z directions as illustrated in Figure 3.2. As can be seen in Figure 3.2, the work-piece holder (3) is mounted to the upper surface of the dynamometer (4) . Also illustrated are the zero crossing sensors (2) and the tool holder (1). Also the orthogonal axis X, Y, and Z of the 3-dimensional force dynamometer are illustrated. 55 Figure 3.2 Three-dimension Force Dynamometer The dynamometer was calibrated using weights with a range of .4535-13.607 kg (1 - 30 lb.). During the calibration process the three orthogonal axis were loaded simultaneously and measurements were made on a Tektronix 420A, 200 MHz, 4 channel oscilloscope. The plots of the outputs of the charge amplifiers for the X, Y, and Z axis can be seen in figures 3.3, 3.4, and 3.5 respectively. The active components in the 3-dimensional dynamometer are Kistler piezo electric force cells and these are connected to Kistler 5004 charge amplifiers. The transducer sensitivities were set as shown in Table 3.1. Orthogonal Axis X Y Z pC/V Setting 2.225 2.225 2.225 Table 3.1 Transducer Sensitivities 56 During the pendulum cutting experiments there was no need to monitor the Y axis, the principal cutting forces F c and F t being in the XZ plane. Output of Charge Amp with X Cjrthogonal Axis Loaded I a 8 l Load Applied to X Axis (kg) Figure 3.3 Calibration Data of Charge Amp Output Orthogonal Axis X Loaded Output of Charge Amp Wrth Y Orthogonal Axis Loaded §• 0.8 Load Applied to Y Axis (kg.) Figure 3.4 Calibration Data of Charge Amp Output Orthogonal Y Axis Loaded 57 Output of Charge Amps With Z Orthogonal Axis Loaded (0 Q_ 0.8 -I 0.6 'ge Am n _ I 0.4 ^000Q * o 2 O 0.2 ^ y = 0.0492x - 0.0005 a n ^ ^ ^ ^ ^ r\ — u . y y o i -o 0 2 4 6 8 10 12 14 16 Load Applied to Z Axis (kg) Figure 3.5 Calibration Data of Charge Amp Output Orthogonal Axis Z Loaded The charge amplifiers were connected to a Krohn-Hite Model 3905B Multichannel filter that was used to apply a Butterworth low pass filter. The break frequency of this filter was set to 100Hz. The Kistler charge amplifiers and Krohn-Hite multichannel filter are illustrated in Figure 3.6. Figure 3.6 Kistler Charge Amplifiers (1) and Krohn-Hite Filter (2) 58 3.2.4 Tooling The tools used in this series of cutting experiments are illustrated in Figure 3.7; they are made of 12.7 mm (1/2") X 12.7 mm (1/2") X 47.625 (1-") M2 8 High Speed Steel (HSS) and there is a 15° clearance angle on all tools. The rake angle is +30° (1), 0° (2), and -30° (3) respectively. Figure 3.7 Tooling Used 30 (1), 0 (2), and-30 (3) Degree Rake Angles 3.2.5 Data Acquisition The data was collected using a Tektronix TDS 420A 200 MHz 4 Channel oscilloscope and the stored waveforms were analyzed using Tektronix Docuwave software. A typical waveform for a 30° rake angle tool, 15° clearance angle, 0.1041 mm (0.0041") depth, and 6.35 mm (0.250") width of cut is 59 illustrated in Figure 3.8. Using the output of the filter (X and Z) the force components in the normal and friction direction on the rake face can then be estimated as follows; F = (Ft *cosa) + (Fc *sinor) (3.1) N = (FC *cosor) - (F , * s ina ) (3.2) where a is the tool rake face angle. Figure 3.8 Sample of Docuwave Waveform Using a +30° Rake Angle Tool 3.2.6 Wood Samples A typical example of the work material used in this series of cutting experiments is illustrated in Figure 3.9. All the samples were 209.55 mm (8%") 60 long, 50.8 mm (2") high and 6.35 mm (%") thick. The wood type is Interior Douglas Fir taken from the same piece, and clear of knots. The samples were prepared so that the direction of the fibre ran parallel to the surface. These parameters were maintained for all the cuts to ensure uniformity of the results. Figure 3.9 Typical Douglas Fir Sample Used in the Cutting Experiments 3.2.7 Results and Plots Numerous cuts were made using the Pendulum apparatus. Using the measured outputs for axis X and Z, the values of the parallel cutting force F c and the thrust force F t were determined. Figures 3.10, 3.11, and 3.12 show the relationships of the depth of cut (H0) and the cutting forces for +30°, 0°, and -30° tools respectively. As can be seen from the figures, F c is a function of depth of cut (Ho) and the rake angle. As the depth of cut increases and the rake angle becomes more negative, F c increases. These values agree with cutting data of Kivimaa [39] as reported in Table 2.4. From the plots of F t is also a function of depth of cut and the rake angle of the tool. As the depth of cut increases or as the tool rake angle becomes more negative F t increases. These values agree with the cutting data for F t as reported by Kivimaa [39] in Table 2.5. 61 Depth of Cut Vs Forces Fc and Ft +30 Degree Rake Angle Tool Figure 3.10 Depth of Cut Ho Vs Cutting Force (FJ and Thrust Force (F,) Douglas Fir +30° Rake Angle Tool 62 Depth of Cut Ho Vs Forces Fc and Ft 0 Degree Rake Angle Tool 300 250 A 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Depth of Cut Ho (mm) Figure 3.11 Depth of Cut Ho Vs Cutting Force (Fc) and Thrust Force (FJ Douglas Fir 0° Rake Angle Tool 63 Depth of Cut Vs Forces Fc and Ft -30 Degree Rake Angle Tool 300 y = 653.92x + 59.248 250 / m • / 200 orces (N) orces (N) 150 • Ft (N) • Fc(N) U . 100 50 n y =401.76x+41.319 0 0.05 0.1 i i 1 — n 1 0.15 0.2 0.25 0.3 0.35 Depth of Cut Ho (mm) Figure 3.12 Depth of Cut Ho Vs Cutting Force (Fc) and Thrust Force (Ft) Douglas Fir-30° Rake Angle Tool 64 The negative values for F t when a +30° rake angle tool is used infer that the tool lifts the work piece during the cutting process. Referring to Figure 3.8 waveform 2, it can be seen that the value measured is negative (-0.040 Volts). In the figures of H 0 versus the cutting forces (F c and Ft) the Y intercept indicates the edge force components of the cutting process as determined from the trend-line expressions in the figures (see Table 3.2) and the values are consistent with equations 2.24 and 2.25. Edge Force Components of F c E and F tE as a Function of Rake Angle Rake Angle (a) Degrees Edge Force F c E (N/m) Edge Force F t E (N/m) +30 degrees 22.005 0.09446 0 Degrees 41.223 4.4254 -30 Degrees 59.248 41.319 Table 3.2 Edge Force Components of F c E and FtE for Douglas Fir Figures 3.13, 3.14, and 3.15 are plots of the depth of cut (Ho) versus the cutting pressure (K) for +30°, 0°, and -30° rake angle tools: where K = ^ - (3.3) H0w and w is the width of cut. As can be seen from the plots K decreases with respect to the depth of cut. It also can be observed that K for the 30° tool is less than for the 0° tool and K is less for the 0° tool than the -30° tool. This is expected as the cutting forces are less when a positive rake angle tool is used compared to when a tool with zero or a negative rake angle is used during cutting. In addition as the tool becomes less positive the edge forces become larger. It should also be noted that as the rake angle becomes less positive the shear angle decreases. Figure 3.16 is a plot of shear angle ((j>) as a function of the Friction Angle (P) minus the Rake Angle (a) [Eggleston et al 67]. 65 Depth of Cut Ho v s Cutting P ressure K +30 Degree Rake Angle T o o l S! 3 in -p in E £ & o> z 3 o 60000000 50000000 40000000 30000000 20000000 10000000 0 0.0001 0.0002 0.0003 Depth of C u t H o (m) 0.0004 Figure 3.13 Depth of Cut (Ho) Vs Cutting Pressure (K)+30° Rake Angle Tool Depth of Cut Ho vs Cutting Pressure K 0 Degree Rake Angle Tool 300000000 ^ 250000000 a> 3 ^ 200000000 in c tn t £ 8" 150000000 •S 100000000 3 ° 50000000 0 0.0001 0.0002 0.0003 0.0004 D e p t h of C u t H o (m) 0.0005 Figure 3.14 Depth of Cut (Ho) Vs Cutting Pressure (K) 0° Rake Angle Tool 66 Depth of Cut Ho vs Cutting Pressure K -30 Degree Rake Angle Tool 250000000 * 200000000 a> $ E" 150000000 o>Z 100000000 c O 50000000 • • • 0 5E-05 0.0001 0.0002 0.0002 0.0003 0.0003 0.0004 Depth of Cut Ho (m) Figure 3.15 Depth of Cut (Ho) Vs Cutting Pressure (K )-30° Rake Angle Tool As can be seen in Figure 3.16, the Shear Angle is a function of the Rake angle (a) of the tool used. As the rake angle is decreased from a positive to a negative value the shear angle decreases. This is consistent with the observations of Eggleston [61]. The averaged shear angle for the tools used is; • +30° rake angle tool -> .83 rad (47.5°) • 0° rake angle tool -> .57 rad (32.65°) • -30° rake angle tool -> .48 rad (27.5°) It should be noted that the slope of the shear angles do not correspond with the slopes of the Lee and Shaffer and Ernst and Merchant solutions. It would appear that neither the Ernst and Merchant minimum-energy criterion nor the ideal plastic-solid solution of Lee and Shaffer is in agreement with the experimental results. 67 Friction Angle Minus Rake Angle vs Shear Angle 0.9 Beta Minus Alpha (rad) Figure 3.16 (fi-a) Vs Shear Angle +30, 0, and-30 Degree Rake Angle Tools 68 Figures 3.17, 3.18, and 3.19 are plots of the Shear Stress (T s) as a function of the depth of cut (H 0). The shear stress (x s) appears to be a function of rake angle as the shear stress increases with a zero rake angle tool. This could be attributed to a decreasing rake angle and an increasing chip thickness ratio (rt). The decrease in shear stress observed with respect to the other tools used may be due to the significant edge forces ( F C E and FTE) in addition the value of rt was very difficult to determine with the chip produced from the -30 degree rake angle tool. The average shear stress for the tool used is; • +30 degree rake angle tool -> 3.202 x 107 N / m 2 • 0 Degree rake angle tool-> 4.489 x 107 N / m 2 • -30 Degree rake angle tool-> 2.624 x 107 N / m 2 £ E (O cr i - to (0 7 to 40000000 30000000 20000000 10000000 0 0 Depth of Cut (Ho) v s Shear S t ress +30 Degree Tool 0.0001 0.0002 0.0003 Depth of Cut Ho (m) 0.0004 Figure 3.17 Depth of Cut Vs Shear Stress +30 Degree Rake Angle Tool 69 Depth of Cut Ho vs Shear Stress 0 Degree Tool | ? 60000000 ? J 40000000 | §- 20000000 w 0 0 0.0001 0.0002 0.0003 0.0004 0.0005 Depth of Cut Ho (m) Figure 3.18 Depth of Cut Vs Shear Stress 0 Degree Rake Angle Tool co 40000000 £ g. 20000000 >- w CD z . c CO 0 Depth o f Cu t Ho v s S h e a r S t r e s s -30 D e g r e e T o o l 0.0001 0.0002 0.0003 Depth of Cut Ho (m) 0.0004 Figure 3.19 Depth of Cut Vs Shear Stress -30 Degree Rake Angle Tool 3.2.8 Chip Formation Figures 3.20, 3.21, and 3.22 respectively illustrate the chips formed using +30°, 0°, and -30° rake angle tools. The chip type formed is a direct function of the rake angle of the tool and depth of cut. As can be seen in Figure 3.20, a Franz Chip Type 2 is formed when the depth of cut is between 0.1016 mm (.004") and 0.2032 mm (0.008") while Franz Chip Type 2-1 is formed when the depth of cut is 0.254 mm (0.010"). This chip type has segments that are Chip Type 1 (that are fractured due to 70 crack propagation ahead of the tool chip interface) joined by Chip Type 2 segments. When the depth of cut is 0.4064 mm (0.016") a Franz Chip Type 1 is formed. Upon close examination it can be seen that the chip is comprised of segments that form due to crack propagation. When the depth of cut is 0.8128 mm (0.032"), the chip breaks apart into many segments of various thickness. Figure 3.20 Chips Produced at Depths of 0.1016 mm, 0.2032 mm, 0.254 mm, 0.4064 mm and 0.8128 mm Using a +30° Rake Angle Tool The resulting surface finish is a function of the chip type formed. In the case where Franz Chip Type 2 chips are formed, the surface finish is smooth with no raised grain. In the case where Franz Chip Type 1 are formed the resulting surface finish is poor. There are many pockets left on the surface where the chip segments broke free of the parent material, and these pockets are of various depths depending upon the chip thickness. In the case of Franz Chip Type 2-1, the resulting surface finish is better than when Type 1 chips are formed but not a smooth as when only Type 2 chips are formed. There are shallow pockets formed where the chip separates due to crack propagation but smooth sections where Chip Type 2 are formed. Figure 3.21 illustrates the types of chips formed when a zero degree rake angle tool is used. As can be seen in Figure 3.20, a Franz Chip Type 2 is formed when the depth of cut is 0.002". When the depth of cut is between 0.1016 mm (0.004") and 0.4064 mm (0.016") a Franz Chip Type 2-3 is 71 formed. It is interesting to note that upon close examination, the early wood forms a Franz Chip Type 2 and the Late Wood forms a chip type 3 and this may be influenced by the increased density of the early wood. However when a 0.8128 mm (0.032") cut is made the chip becomes more Franz Chip Type 3 in character. When a zero degree rake angle tool is used, under very shallow depths of cut a Chip Type 2 is formed and the resulting surface finish is quite smooth. However when Chip Types 2-3 are formed the "raised grain" finish results. This could be due to the fact that the late wood undergoes a continuous shear from the parent material and the early wood behaves in a typical cyclical fashion as described in Chapter 2. As a result the surface finish of the late wood of the sample is rough and there are many levels below the surface of the early wood in the sample. Figure 3.21 Chips Produced at depth of 0.0508 mm, 0.1016 mm, 0.2032 mm, 0.4064 mm and 0.8128 mm Using a 0° Rake Angle Tool Figure 3.22 illustrates the chip types formed when a -30° tool is used. As can be seen in Figure 2.21, the chips formed are predominately Franz Chip Type 3 at all depths of cut. However upon close investigation the early wood of the sample in the 0.1016 mm (0.004") and 0.2032 mm (0.008") cut still forms a Chip Type 2. It can be suggested that due to the increased density of the early wood, it undergoes a more continuous shearing that does the late wood. 72 The resulting surface finish exhibits the "raised grain" profile, and the pockets left in the early wood were of various depths. This finish is better than the resulting surface finish when a Chip Type 1 is formed and poorer than when a Chip Type 2 is formed. When machining wood it is most desirable to form Chip Type 2. Figure 3.22 Chips Produced at Ho 0.1016 mm, 0.2032 mm, 0.254 mm, and 0.4064 mm Using a -30° Tool Figure 3.23 is a plot of depth of cut (Ho) versus the Chip Thickness Ratio (rt). It would appear from the plot that the chips formed are thicker than the depth of cut as all the chip thickness ratios are <1. In addition as the rake angle is decreased to zero degrees and then to negative rake angles, rt becomes larger. This suggests that the chip thickness increases with both depth of cut and tool geometry. It should be noted that measuring the chip thickness using a digital calliper (0.00254mm resolution) was very difficult with Chip Types 1 and 3. These measurement errors could lead to misleading results and should be used as only a rough guide on the relationship between the depth of cut (H0) and the thickness of the resulting chip formed. Table 3.3 illustrates the Chip Compression Ratios (rt) when cutting Douglas Fir with +30, 0, and -30 degree tools. The decreasing trend in rt is consistent with the decreasing shear angles observed. 73 Chip Compression Ratio For Douglas Fir Using Tools With a Clearance Angle of +15 Degrees Rake Angle of Tool Chip Compression Ratio (rt) +30 Degree .75 - .79 0 Degree .62 - .68 -30 Degree .55-.59 T a b l e 3.3 C h i p C o m p r e s s i o n Rat io r T W h e n D o u g l a s F i r is C u t Figures 3.24, 3.25 and 3.26 illustrate the relationship between F and N as the depth of cut increase from 0.1016 mm (0.004") to 0.4064 mm (0.016"). The Chip Friction force F and the Normal force N increase as result of the decreasing shear angle. In the case of the +30° tool, the ratio of the Chip Friction force (F) to the Normal Friction force (N) is the highest and this is consistent with the highest coefficient of friction reported in this experiment. If the Chip Types 1 and 3 are compared to Chip Type 2, these chips have discontinuities in their structure, resulting in less overall contact with the tool rake face. In addition, Chip Type 1, separates from the parent material as a result of crack propagation. This behaviour is described in Chapter 2 but when the cracked chip segments are lifted, they act as cantilevers and do not interact with the tool rake face in any significant manner. The Coefficient of friction when cutting Douglas fir can be determined using Equation 2.8. The experimental results for the Coefficients of friction, (as illustrated in Figures 3.27, 3.28, and 3.29 for +30°, 0°, and -30° tools respectively) do not agree with the results obtained by Franz [38]. 74 Depth of Cut Ho Vs Chip Thickness Ratio 0.85 0.8 S 0 7 5 c o + 3 (0 * 0.7 (0 (0 a> c | 0.65 l -Q . " 0.6 0.55 0.5 • v +30 Degree Tool $ i 0 Degree Tool • • • • ^ • • * • • > f - 30 Degree Tool 0.1 0.2 0.3 0.4 Depth of Cut Ho (mm) 0.5 Figure 3.23 Depth of Cut Ho Vs Chip Thickness Ratio rt +30, 0, and 30 Degree Rake Angle Tools 75 Depth of Cut Ho Vs Chip Friction Force F and Normal Force N +30 Degree Tool (Douglas Fir) 35 30 25 — 20 (0 5 o O 15 10 5 0 0.05 0.1 0.15 0.2 0.25 Depth o f Cut H o (mm) F(N) 'N (N) 0.3 0.35 Figure 3.24 Friction and Normal Forces +30° Rake Angle Tool 76 Depth of Cut Ho Vs Chip Friction Force F and Normal Force N 0 Degree Tool (Douglas Fir) 300 250 200 © 150 u 100 50 ..I • • • • • F(N) • N(N) 0.1 0.2 0.3 0.4 Depth of Cut Ho (mm) 0.5 Figure 3.25 Friction and Normal Forces 0° Rake Angle Tool 77 Depth of Cut Ho Vs Chip Friction Force F and Normal Force N -30 Degree Tool (Douglas Fir) 350 300 250 200 (0 .__ g 150 100 50 0 -50 • • 0.05 0.1 0.15 0.2 0.25 0.3 Depth of Cut Ho (mm) • F(N) • N(N) 0.35 Figure 3.26 Friction and Normal Forces -30° Rake Angle Tool 7 8 Franz predicts that when the Coefficient of friction is low this would favour the formation of Franz Chip Type 1 and a higher Coefficient of friction would favour a Chip Type 3. However this series of experiments demonstrated that when the Coefficient of friction was between .5 and .6, Franz Chip Type 2 were produced. This effect could be due to the roughness of the rake face of the cutting tool but more than likely the formation of the chip types has more to do with the geometry of the tool and depth of cut. In the formation of Franz Chip Type III, there is a cyclical build up of pressure on the rake face until the wood elements fail in shear. There can be build up of wood elements on the face of the tool and when this build up reaches a critical state the chip is separated with little sliding on the rake face. Depth of Cut Ho Vs Coefficient of Friction +30 Degree Rake Angle Tool 0.57 2 c 0.56 o o 0.54 £ jf 0.53 § 0.52 O 0.51 0.00005 0.0001 0.00015 0.0002 0.00025 D e p t h o f C u t H o ( m ) 0.0003 0.00035 Figure 3.27 Depth of Cut Vs the Coefficient +30° Rake Angle Tool *- 0.3 o 1 .1 0.2 o o * if 0.1 o o 0 Depth of Cut Vs Coefficient of Friction 0 Degree Rake Angle Tool • • 0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004 0.00045 D e p t h o f C u t H o ( m ) Figure 3.28 Depth of Cut Vs the Coefficient of Friction 0° Rake Angle Tool 79 «_ 0.08 r = 0.06 § .2 •5 tS 004 E •= <5 u - 0.02 o o o Depth of Cut Vs Coefficient of Friction -30 Degree Rake Angle Tool • • 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 D e p t h o f C u t H o ( m ) Figure 3.29 Depth of Cut Vs the Coefficient of Friction -30° Rake Angle Tool 3.3 Single Edge Fly Cutter Experiments 3.3.1 Introduction The purpose of this experiment was to investigate the Average Forces during peripheral milling (planing) of Douglas Fir and contrast these forces with the forces measured in the Pendulum cutting experiment. In this experiment the samples were the same type used as described in Section 3.2.6. The cutting tool used was the 0° rake angle tool used in the pendulum cutting experiment as described in Section 3.2.4. The data acquisition system was the same as was used in the pendulum cutting experiments as described in Section 3.2.5. The samples were cut in a planing operation (Fig. 3.30) and were up-milled. The sample feed rate was set at 203.2 mm (8.0") per minute and the spindle speed was set to 2000 RPM. The measurements made were of the average cutting forces in the X and Y axis. 80 Figure 3.30 Peripheral Up-Milling (Planing) 3.3.2 Apparatus The apparatus used in this experiment is illustrated in Figure 3.31 and described in Table 3.4. Equipment Used Description Milling Machine (1) Holke Vertical Milling Machine Tooling (2) Single tooth fly cutter attached to the milling machine spindle. Work piece holder (3) work piece (sample) holder mounted to the 3-D dynamometer [Lai 60] used in previous experiments mounted to the milling table Data Acquisition hardware (4) Tektronix TDS 420 Digital Storage Oscilloscope Filter (5) A Krohn-Hite Model 3905B Multichannel filter was used in the Butterworth low pass configuration and set at a break frequency of 100Hz to filter the output of the charge amplifiers Charge Amplifiers (6) The dynamometer was attached to the filter to capture the process data and save it floppy disk.. Kistler 5004 charge amplifiers were used in combination with the 3-D dynamometer. Table 3.4 Apparatus Used in the Milling Experiment 81 Figure 3.31 Apparatus Used in the Peripheral Milling (Planing) of Douglas Fir 3.3.3 Tooling The cutterhead used in this experiment was a single tool fly cutter (Fig. 3.32) with an attached 0 degree rake angle, 15 degree clearance angle, HSS tool mounted in the spindle of the Holke Vertical Milling Machine. The spindle speed used was 2000 RPM and the diameter of the cutting circle was a 101.6 mm (4.0"). ^925 mm n' Shaft Figure 3.32 Sketch ofFlycutter Used 82 3.3.4 Results and Plots A series of 6 cuts were made with a radial width of cut (w) of 6.35 mm (0.25"), and the depths of cut (d) of 2 at 0.1143 mm (0.0045"), 2 at 0.07366 mm (0.0029"), 1 at 0.14986 mm (0.0059"), and 1 at 0.1524mm (0.006"). The data was collected using the filter to measure the average forces. Peripheral Milling with Flycutter Radial Depth of Cut (d) Vs Measured Values of Fx and Fy Ave. 0 Degree Rake Angle Tool 120 100 £ 8 0 § 60 40 20 0 y = 620.05x + 17.39 R 2 = 0.9769 y= 153.76X +7.3409 R 2 = 0.9852 • Fy(ave) (N) • Fx(ave) (N) 0.05 0.1 0.15 Radial Depth of Cut ( d (mm)) 0.2 Figure 3.33 Radial Depth of Cut (d) Vs The Measured Values ofFx(ave) and Fy(ave) From the Fly Cutter Experiment Using a 0° Rake Angle Tool The measured values of FX(a Ve) and F y( a Ve) are shown in Fig. 3.33. are in good agreement with the measured values of the cutting forces (Ft) and (Fc) forces as shown in Fig. 3.10. 83 3.4 Solid Wood Grinding With Holke Milling Machine 3.4.1 Introduction The purpose of this experiment is to investigate the forces during grinding of Douglas Fir. In this experiment the samples were the same type used as described in Section 3.3.2. The samples were surface ground and both up-cut and down-cut. The width of cut was 6.35 mm (0.25") on all cuts, the grinding wheel was dressed with a single point diamond dressing tool when required. The feed rates used where 50.8 mm/min (2.0"), 203.2 mm/min (8.0"), and 406.4 mm/min (16"). The spindle speed was set to 2000 RPM and the measurements made were of the average cutting forces in the X and Y axis. The forces were measured using the three-dimensional dynamometer [Lai 60] and stored in the TDS 420 oscilloscope. The stored results were analyzed and the process was repeated as necessary 3.4.2 Apparatus The apparatus used for this experiment is illustrated in Fig. 3.34. This is the same apparatus as outlined in Section 3.3.2 used in the fly-cutter experiment with the exception of the tooling used. The data acquisition system was the same as was used in the pendulum cutting experiments as described in Section 3.2.5. 3.4.3 Tooling The cutting tool used was a Straight shape Norton 253871 4X2X20mm 3/8R 1/2B 38A80 JV8BE grinding wheel. This grinding wheel has fine Aluminium Oxide grits with a grain size of 80. The grinding wheel is J grade (soft hardness) and the Bond Type is vitrified. 84 Figure 3.34 Apparatus Used in the Surface Grinding of Douglas Fir 3.4.4 Results and Plots A series of 9 cuts were made with an axial of cut (a) of 6.35 mm (0.25"), and the radial depth of cut (d) of 3 @ 0.127mm (0.005"), 3 @ 0.254 mm (0.010"), and 3 @ 0.508 mm (0.020"). The data was collected using the filter to measure the average forces. Equations 2.52, 2.53, 2.54, and 2.55 cannot be used in their current form to calculate FX(ave) or Fy(ave) in this experiment. This is because the feed per tooth (St) cannot be calculated directly. As described in section 2.4.1 the number of active grits on the grinding wheel is unknown at any specific time. Assume tooth spacing is d<j>, and cut force and a constant force. 85 Figure 3.35 Forces in Up-grinding and then or so and Consider Fig. 3.35; 2n v = dd[—][RPS] (3.4) dtp V = 2n[RPS] (3.5) 2n dd V v = 8dA[RPS] = ^ L ( 3 . 6 ) W d</>R _ , Rv _ , dd = —d<f> (3.7) Rv dFT = a[Kx — sin^ + K2 ]d<j> (3.8) Rv dFR = a[K,ri — s i n ^ + r2K2 ]8</> (3.9) To find Fxovg) and FY(avg) for Up-grinding, integrate the following expressions; 86 8FX = 8FT cos </> + 8FR sin ^  (3.10) dFY = dFR cos^ - 8FT sin^ (3.11) SO ^ ( o v , ) = cos^ + a ^ s i n ^ (3.12) 0 then FX(ave) = j[a(K1—sm^ + K2)cos^ + a(Klrl—sm^ + r2K2)sm^]d^ (3.13) o V V and FX(ave) = 4 ^ ( 2 s i n 2 ^ s + r 1(2^ -s in2^)) + K 2 [s in^ + r 2( l-cos^)] (3.14) Similarly using Eq. 3.11 then; ^(ove) = cos^ - dFT sm<j>)8</> (3.15) o SO r Rv Rv Fn a v e ) = jlaiK^—sm^ + ^K^cos^-aiK.—sm^ + K ^ s m ^ (3.16) and o r v FY{ave) = a [ - ^ [ r 1 2 s i n 2 ^ - ( 2 ^ - s i n 2 ^ ) ] + i : 2 ( r 2 s in^- ( l -cos^) ) ] (3.17) .KjRv. 4V For down-grinding; 8FX = dFR sin ^  - dFT cos ^  (3.18) dFY = 8FR cos ^  + 8FT sin ^  (3.19) To find the values Fx(ave) and FY(ave) for down-grinding the procedure is similar so only the final result is given. K Rv FX{ave) = 4 - ^ r ( l ( 2 6 - s i n 2 ^ ) - 2 s i n 2 ^ ) + ^ 2 ( r 2 ( l - cos^ ) -s in^ ) ] (3.20) and K Rv FY(me) = a [ - ^ - ( ( 2 £ - s i n 2 ^ ) + r 1 2s in 2 ^) + /i : 2(r 2sin^ +(l-cos^))] (3.21) 87 where d is the radial depth of cut, a is the axial depth of cut, (j)s is the swept angle, V is the peripheral velocity of the grinding wheel, R is the radius of the grinding wheel, and v is the feed velocity. Figures 3.36 and 3.37 illustrate the relationship of Fx(ave) and Fy(ave) to feed speed when up-grinding. Figures 3.38 and 3.39 illustrate the relationship of Fx(ave) and FY(ave> when down-grinding. Using simultaneous methods, K2 and r2 can be determined when v equals 0 m/sec, and when v equals the feed speed, K1 and ri can be 1 determined. Then the equations can be solved using Eq. 3.14 and 3.17 for up-grinding and Eq. 3.20 and 3.21 for down-grinding. Typically FX(ave) and FY(ave) are measured using a force sensor (e.g. dynamometer), and with a knowledge of the feed speed and the direction of rotation of the grinding wheel, the radial and axial depth of cut can be calculated thus allowing adaptive control. The values for FX(ave) and FY(ave) were calculated using Eq. 3.16, 3.17, 3.20, and 3.21 respectively are illustrated in Table 3.4. The samples used are as shown in Fig.3.8, and a peripheral velocity of the grinder wheel was 2000 RPM. Various radial depths of cut (d) were used as illustrated in Table 3.5 and the axial depth of cut (a) was 6.35 mm. Table 3.6 illustrates a comparison of the calculated and measured values for FX(ave) and FY(ave) and as can be seen there is very good agreement between the two values. It should be noted that the values for the cutting force ratio (n) and the edge force ratio (r2) are not in agreement with the values stated by Yellowley [25]. This could be the result that when cutting wood the thrust force (Ft) is lower than when metals are cut. In addition the parasitic forces are higher when wood is cut when compared to metal. 88 F Y ( a v g ) Grinding Vs. Feed-rate Up-grinding • 0.127 mm • 0.254 mm A 0.508 mm 0 0.02 0.04 0.06 0.08 0.1 Feed-rate (m/sec) Figure 3.36 Feed-rate Vs FY(ave) Up-grinding Holke Milling Machine Fxovg) Grinding Vs. Feed-rate Up-grinding & .4 £ 2 ^ ^ 0.04 0.06 0.08 0 y = -37.3x - 0.0592 1 y = - 5 2 . 8 2 2 x - 1 . 4 1 0 9 • 0.127 mm • 0.254 mm A 0.508 mm y = - 6 5 . 2 2 9 x - 3 . 1 8 Feed-rate (m/sec) Figure 3.37 Feed-rate Vs FX(aVe) Up-grinding Holke Milling Machine 89 FY(avg) Grinding Vs . Feed-rate Down-grinding • 0.127 mm • 0.254 mm A 0.508 mm 0 0.02 0.04 0.06 0.08 0.1 Feed-rate (m/sec) Figure 3.38 Feed-rate Vs FY(ave) When Down-grinding Holke Milling Machine Fx(avg) Grinding v s Feed-rate Down-grinding ) 0.02 0.04 0.06 0.08 0 y = -27.902x-1.1469 1 y = -65.282X - 2.1434 • 0.127 mm • 0.254 mm A 0.508 mm y = -77.729x-4.1573 Feed-rate (m/sec) Figure 3.39 Feed-rate Vs FX(ave) Down-grinding Holke Milling Machine 90 Calculated Values for F X ( a v e) and F Y ( a V e) Up/ Down V (m/sec) K i (N/m2) K 2 (N/m2) ri r 2 d (mm) <t>s (rad) Fx(ave) (N) FY(ave) (N) U 9.9683 -509216000 -145.943 -1.91 -3.980 0.127 0.0730 -0.43671 1.0940 U 9.9683 -509216000 -145.943 -1.91 -3.980 0.127 0.0730 -1.57345 3.5612 u 9.9683 -509216000 -145.943 -1.91 -3.980 0.127 0.0730 -3.0891 6.8507 u 9.9683 -361623000 -2342.29 -1.82 -1.968 0.254 0.1033 -1.89612 4.2228 u 9.9683 -361623000 -2342.29 -1.82 -1.968 0.254 0.1033 -3.45056 7.5962 u 9.9683 -361623000 -2342.29 -1.82 -1.968 0.254 0.1033 -5.52314 12.094 u 9.9683 -228570000 -3807.82 -1.65 -1.614 0.508 0.1461 -3.73267 7.2518 u 9.9683 -228570000 -3807.82 -1.65 -1.614 0.508 0.1461 -5.61305 11.175 u 9.9683 -228570000 -3807.82 -1.65 -1.614 0.508 0.1461 -8.12022 16.407 D 9.9683 351968300 2541.73 2.50 1.3537 0.127 0.0730 -1.38217 2.3705 D 9.9683 351968300 2541.73 2.50 1.3537 0.127 0.0730 -2.16973 4.5695 D 9.9683 351968300 2541.73 2.50 1.3537 0.127 0.0730 -3.21981 7.5015 D 9.9683 441549600 3510.137 1.55 1.7361 0.254 0.1033 -2.75849 5.2698 D 9.9683 441549600 3510.137 1.55 1.7361 0.254 0.1033 -4.7562 8.7489 D 9.9683 441549600 3510.137 1.55 1.7361 0.254 0.1033 -7.41982 13.387 D 9.9683 267900000 5017.909 1.21 1.7099 0.508 0.1461 -4.8586 9.4047 D 9.9683 267900000 5017.909 1.21 1.7099 0.508 0.1461 -7.25318 12.789 D 9.9683 267900000 5017.909 1.21 1.7099 0.508 0.1461 -10.4459 17.302 Table 3.5 Variables used and Calculated Values for FX(ave) and FY(ave) 91 Comparison of Measured and Predicted Values of FX(ave) and FY(ave) d (mm) a (mm) Measured Forces Fx(ave) Fy(ave) Ratio (N) (N) Calculated Forces Fy(ave) FX(ave) Ratio (N) (N) 0.127 6.35 1.201019 -0.48041 -0.4 -0.43671 1.094069 -0.39916 0.127 6.35 3.302803 -1.50127 -0.45455 -1.57345 3.561208 -0.44183 0.127 6.35 6.805777 -3.12265 -0.45882 -3.0891 6.850727 -0.45092 0.254 6.35 4.32367 -1.92163 -0.44444 -1.89612 4.222874 -0.44901 0.254 6.35 7.806626 -3.60306 -0.46154 -3.45056 7.596285 -0.45424 0.254 6.35 12.41053 -5.68483 -0.45806 -5.52314 12.09417 -0.45668 0.508 6.35 7.206116 -3.74318 -0.51944 -3.73267 7.251843 -0.51472 0.508 6.35 11.81002 -6.0051 -0.50847 -5.61305 11.17582 -0.50225 0.508 6.35 16.6141 -8.40714 -0.50602 -8.12022 16.40778 -0.4949 0.127 6.35 2.522141 -1.36116 -0.53968 -1.38217 2.370575 -0.58305 0.127 6.35 4.403738 -2.40204 -0.54545 -2.16973 4.569561 -0.47482 0.127 6.35 7.606456 -3.36285 -0.44211 -3.21981 7.501544 -0.42922 0.254 6.35 5.404587 -2.80238 -0.51852 -2.75849 5.26981 -0.52345 0.254 6.35 9.007646 -4.80408 -0.53333 -4.7562 8.748911 -0.54363 0.254 6.35 13.81172 -7.44632 -0.53913 -7.41982 13.38771 -0.55423 0.508 6.35 9.407985 -4.96421 -0.52766 -4.8586 9.404776 -0.51661 0.508 6.35 14.01189 -7.28618 -0.52 -7.25318 12.78962 -0.56711 0.508 6.35 18.21546 -10.4088 -0.57143 -10.4459 17.30274 -0.60372 Table 3.6 Comparison Between Measured and Calculated Values of F X (ave) and F Y(ave) 92 CHAPTER 4 Implementation of a Force Control Solid Wood Grinder 4.1 Introduction Abrasive finishing processes are a very important operation for the removal of unwanted material. The use of abrasives in the wood working industry is widely used as a finishing operation. This process is very labour and time intensive thus requiring highly skilled personnel. This results in making the sanding operation an expensive process. The automation of the sanding process will benefit the wood working industry in cost savings, uniformity of the piece parts as well as reducing the need for re-work of a work-piece. This need has been identified by Taylor et al [56] who investigated the input parameters of the sanding process and the effects on the MMR and resulting finish. In this chapter a discussion of the implementation of an automated force controlled solid wood grinder system is presented. A simple cutting model was developed for the grinder system and is presented and analyzed. This cutting model was experimentally determined and is based on the previous experimental work outlined in chapter 3. The grinding system uses a simple force sensor attached to the grinder assembly and a X-Y gantry is used to present the work-piece to the grinder assembly. The grinding system is unique in that the geometry of the work-piece does not have to be previously defined. The system can scan for the surface of the work-piece and once identified will follow the surface and remove the desired amount of material. If there are any changes to the cutting force the system responds with an appropriate control action. The development of the grinder system model is presented and the model is analyzed. A wood simple grinding cutting model is proposed based on the ratio of stock removed for a known feed-rate and grinder peripheral velocity. 93 4.1.1 Apparatus The apparatus used in the experiment and implementation of the grinder system is illustrated in Figure 4.1 and described in Table 4.1. Equipment Used Description Xaxis(1) Parker Compumotor Plus Brushless DC Servo motor (Model 23 CPL57-120) and drive, and a fully supported Thompson 2EB Superslide Ball Screw Assembly (Model 2EB-08-FTB 12mm X 5mm NP) Y axis (2) Parker Compumotor Plus Brushless DC Servo motor (Model 23 CPL57-120) and drive , and a fully supported Thompson 2EB Superslide Ball Screw Assembly (Model 2EB-08-FTB 12mm X 5mm NP) Work piece holder (3) Same as used in the previous experiments. Spindle assembly (4) 500 W. permanent magnet DC motor with tacho-generator controlled by a DC Servo Drive (not shown) Grinding wheel (5) Described in Section 3.4.3 Spring position sensor (6) Lucas-Schaevitz Linear Voltage Displacement Transducer (Model GPD 121-1000) Spring (7) 87.563 N/mm spring Table 4.1 Grinder System Apparatus The samples used were the same as in the pendulum cutting, fly cutter, and grinding experiments as described in Section 3.2.6. The data acquisition system for the cutting experiments consisted of a B&K 0-60 V., 6 A., DC Power Supply Model 1050 to power the LVDT and the data was collected using a Tektronix TDS 420A 200 MHz 4 Channel oscilloscope. The stored waveforms were analyzed using Tektronix Docuwave software as described in Section 3.2.5. 94 Figure 4.1 Force Controlled Grinder Assembly 4.1.2 Grinder Assembly The grinder assembly used is illustrated in Figure 4.2. The components identified in Fig. 4.2 are listed in Table 4.2. The grinder assembly spring was fabricated in a brake from a 180 mm X 25.4 mm X 6.35 mm sheet of mild steel. The spring dimensions are illustrated in Figure 4.3. The spring was manufactured to have a Spring Constant of 500 Ibs./in. The calibration of the spring in the grinder assembly was accomplished by loading the grinder assembly with known forces and measuring the displacement with a 0.0001" dial gauge. The spring material was removed with a Dremel tool until the correct 95 displacement for the load was achieved. The calibration data for the spring can be seen in Table 4.3 and Figure 4.3. Equipment Description Spindle Motor Assembly (1) Fabricated from 3A" Al. stock Spring position sensor (2) LVDT described in Table 4.1 Linear bearing assembly (3) damping air cylinder American Pneumatics Double Acting (2" extension, 1" bore) Thompson V2" and linear bearing assembly Spring (4) Force spring the 87.563 N/mm spring Spindle Motor (5) Spindle motor and Tachometer as described in Table 4.1 Table 4.2 Grinder Assembly Apparatus Y Axis Figure 4.2 Grinder Assembly 96 60 mm 10 mm Side V iew 7T\ 25.4 mm - 65 mm . Top View 3 Spring Dimensions Made of Mild Steel S h e e t Metal 6.35 mm Thick Figure 4.3 Sketch of Spring Dimensions Calibration Data For Grinder Assembly Spring Force Applied (N) Displacement (mm) 4.44822 0.0127 8.89644 0.0254 22.2411 0.0635 44.4822 0.127 88.9644 0.254 133.4466 0.381 Table 4.3 Calibration Data for the Grinder Assembly Spring 97 4.1.3 Grinding Apparatus Experiments Numerous down-cutting operations were made with the grinding wheel set to a constant spindle speed of 2000 RPM with an axial depth of cut (a) of 6.35 mm (0.25") The radial depth of cut (d) used were 0.1016 mm (0.004"), 0.2032 mm (0.008"), and 0.3048 mm (0.012"). Various feed-rates 50.8 mm/min (2.0in/min), 203.2 mm/min (8.0 in/min) and 406.4 mm/min (16.0 in/min) were used as required The procedure used for the cutting experiments was to measure the sample surface with a gauge and Mintoyo 0.0001" dial gauge at a known position and measure and record the output of the LVDT (10 mV/0.0254 mm). The radial depth of cut was set and the sample was cross feed at velocity (v) in the X axis direction and down-cut by the grinding wheel as illustrated in Figure 4.1. During the cutting process the output of the LVDT was measured and acquired. This data reflected the cutting force as a function of the spring displacement. After the cut was made the sample was moved to a known position and the amount of stock removed was measured using the gauge and the Mintoyo 0.0001" dial gauge. 4.1.4 Results and Plots of Gantry Grinding System Experiments Fig. 4.4 illustrates the results of down-grinding experiments using the grinding system. There is very good agreement with the results show in Fig. 3.8. Table 4.4 illustrates the ratio of desired radial depth of cut and the actual depth of cut after the sample was ground. As can be seen by the results the ratio of stock removed is a function of feed-rate and this is attributed to spring back. With a feed rate of 6.773 mm/sec, the ratio is 0.5. The desired cut at the selected feed-rate results in half of the desired being stock removed. As reported by Ohta [48] the amount of spring back is inversely proportional to the 98 Fvove) vs Feedrate Grinder Systen Down-grinding i Figure 4.4 Fy(ave) Vs Feed-rate Grinder System Material Removal Ratio as a Function of Feed -rate Feed-rate Material Removal (mm/sec) Ratio 0.00847 0.378 0.006773 0.5 0.003387 0.65 Table 4.4 Material Removal Ratio Down-grinding cutting speed and an analysis of the results shown in Table 4.4 verify this. Dippon et al [37] reported spring back in their investigation when cutting of MDF. Spring back has been described by Lucander [59] as the result of Elastic compression of the wood. The grits protruding from the grinding wheel generate cyclic shear and compression on the wood surface. The compression is either elastic (reversible) or plastic (irreversible) due to the visco-elastic nature of the wood matrix. The plastic compression deforms the wood fibres by softening the lignin sufficiently to cause fatigue changes in the wood. The elastic compression 99 is reversible and the fibres return to their original size after the stress has been removed. Lucander reports that only 10%-50% of the compression is plastic so what fibres are not sheared after they have been loosened from the wood matrix would remain on the sample. In the experiment performed on the grinding system, it was demonstrated that the desired axial depth of cut over the feed-rate tested varied from 38.7% to 65%. This allows for a simplified cutting model; dac,=d*Rcut (4.1) where d a ct is the amount of stock removed, R c ut is the material removal ratio, and d is the radial depth of cut. R c ut can now be treated as a constant and can be determined experimentally. The material removal ratio is a function of feed-rate, and to remove 0.1016 mm of material (clear Douglas Fir, parallel to the grain, moisture content < than 3%) at a feed-rate of 4.064 m/sec, it was experimentally determined that 8.896 N of force (FY(ave)) is required. Attention must be paid to the data reported, since with a radial depth of cut set at a given value, in fact the amount of material removed would not equal the value desired. 4.1.5 Grinder System Implementation The developed grinder system incorporated a Pentium (800 MHz) personal computer (PC) as the control platform. The control code was written in Borlan C++, and a Metrabyte DAS 20 was used to acquire the force sensor output. A Parker PC23 was installed in the PC to co-ordinate the X and Y axis, refer to Fig. 4.5 the PC control block diagram of the system 100 Block Diagram of PC Control DAS20 PC Control Program PC23 Force Sensor Compumotor Controller Axto'X ii Axis Y Figure 4.5 Block Diagram of PC Control System When the grinder assembly starts the grinding process, the output of the force sensor is recorded and compared to the desired force (depth of cut). The grinder assembly is stepped into the work-piece until the desired force is sensed and the desired amount of stock is removed. In the implementation of the grinder system, the cross feed-rate was selected to get a R c u t of 0.5. The value of the force sensor was continuously polled and compared to the desired force necessary to remove the required amount of stock. If there was a difference then the error was integrated and the grinder assembly was moved in the appropriate direction until the correct force ( F Y ( a V e)) was detected. This would allow for a contouring algorithm to be developed. The control program algorithm is outlined in Figure 4.6. Using Eq. 3.21, the radial depth of cut d can be calculated once the constants r-i, r2, rC|, and K 2 have been experimentally determined. In the cutting model proposed in Eq. 4.1, the variable R c u t can be determined dynamically if it is assumed that the initial contact point on the work-piece is clear Douglas Fir. The set (desired) radial depth of cut (d) could be compared to the LVDT output and the actual radial depth of cut (dac t) can be determined. Then R c u t is d/d a ct and the value for R c u t then can be used in the control program independent of the cross-feed rate. This would allow for the implementation of an adaptive control strategy. 101 Step in .0127mm Step out :0127mm: Addl toR1 Subtract 1 from RV •Control Program Algorithm. Call T/D Call.T/D Figure 4.6 Control Program Algorithm System Modelling 102 The development of the grinder system model is outlined in Appendix A and the system model illustrated in Fig.4.7. The grinder system was modelled as a 3 r d order system, however the s 3 term (jerk) can be ignored as it is 100x less than any of the other coefficients. Matlab [64] R12 was used to simulate the grinder system model and three cases are presented with the Control Program Integration gain changed from 10 to 30 and finally to 80. The implemented grinding system was determined to be over damped, however the simulation indicates that the system response can be improved to an 8 fold increase in the integral gain and keep the overshoot within acceptable levels to maintain the desired accuracy Case 1 is a simulation of the system response to a 0.1016 mm (0.004") cut control step with the PC control algorithm implementing integral action only with integral gain IPC =10. The resulting closed loop system transfer function is: H ( s ) = 2.795*004 = W * ) ( 4 2 ) 1.267s3 +119.75 2 + 57445 + 1.397e004 x^is) The grinder system simulated response is illustrated in Figure 4.8. Illustrated in Figure 4.9 is the response of the grinder system to a 0.1.mm step input. The response time agrees with the simulated response time very well. It can also be seen that it took 7 control actions to remove the additional material. The control program for this operation was set to remove 0.1 mm of material at a cross-feed rate of 4.064 x 10"2 m/sec. Since each pulse represents a 0.0254mm radial depth of cut then the grinding cut ratio R c u t is in very good agreement with the results of the grinding experiments. The system has a repeatability of +/- 0.0254 mm. 103 Grinder Depth Response to 0.1 mm Cut Control Step (IPC = 10) 0:25r T — ] j (7 j 1 2 f 0 0.5 "1 1.5 r2 2.5 :3 -3:5- A -AS Time (sec) Figure 4.8 Simulation of Grinder System Radial Depth of Cut Response to a 0.1 mm Step Input When IPC = 10 105 Figure 4.9 Grinding System Radial Depth of Cut Response to a 0.1 mm Step Input Case 2 is a simulation of a response to a 0.1 mm cut control step with the PC control algorithm implementing integral action only with integral gain IPC = 30. The resulting closed loop system transfer function is: H(s) = 8.384e004 grind (s) 1267s 3 +119.7 s2 + 57445 + 4.192e004 x m (s) (4.3) Case 3 is a simulation of response to a 0.1 mm cut control step with the PC control algorithm implementing integral action only with integral gain IPC = 80. The resulting closed loop system transfer function is: H(s) = 2.236e005 grind 1.267s 3119.7s 2 + 5744s +1.118e005 (4.4) 106 Grinder Depth Response to 0.1 mm Cut Control Step (IPC = 30) O.25; c _ , , , . , , r « U - 4 0 Oil: 0.2 03- 'OA- 0:5 0.8 .0:7 0.8 >0.S 1 Time (sec) Figure 4.10 Simulation of Grinder System Radial Depth of Cut Response to a 0.1 mm Step Input When IPC = 30 107 Grinder Depth Response to 0.1 mm Cut Control Step (IPC = 80) 0;25; &2+-Q:T5 0:1: 0,05 :0.2 0.3 • M 0:5 Time(secS 0.6. 0.7 0.8 ^0:9-Figure 4.11 Simulation of Grinder System Radial Depth of cut Response to a0.1 mm Step Input IPC = 80 108 4.2.2 System Analysis Matlab was used to simulate the grinder system response and cutting force, motor rotor current, and Bode plots were generated. Figures 4.12, 4.13 and 4.14 illustrate the simulation of the grinder system rotor current response to a 0.1 mm radial depth of cut response when changes in the IPC value was set to 10, 30 and 80 respectively. The motor used was a Compumotor 23-CPL57-120 brushless DC Servo motor with a rated maximum pulse current of 28 Amperes. When the simulation was executed with IPC = 80, the peak current was 7.3 Amperes, well with in the specification and the response time is consistent with the positioning response time. Figures 4.15, 4.16 and 4.17 illustrate the simulation of the cutting force generated in response to a 0.10 mm radial depth of cut response. The force response is consistent independent of the IPC gain setting. However the response time is dependent upon the gain setting as would be expected. Figures 4.18, 4.19, and 4.20 are bode plots of the grinder system frequency response with IPC set to 10, 30, and 80 respectively. The figures illustrate that the closed loop frequency response improves as illustrated in table 4.5. Grinder System Frequency Res ponse PC Integral Gain Frequency Response rad/sec Frequency Response Hz 10 3.0 0.477 30 10.5 1.67 80 50 7.95 Table 4.5 Grinder System Frequency Response With improvements to the control program PID gains, the grinder system can be implemented to be responsive and maintain the desired accuracy demanded of a finishing operation. 109 Motor Response to 0.1 mm Cut Control Step (IPC = 10) T i m e ( s e c ) Figure 4.12 Motor Rotor Current Response to a 0.1mm Cut Control Step When IPC = 10 110 Motor Response to 0.1 mm Cut Control Step (IPC = 30) E Q.5 0,4; 0.5 0.6 Time (sec) 0.8 0.9 Figure 4.13 Motor Rotor Current Response to a 0.1mm Cut Control Step When IPC = 30 111 Motor Response to 0.1 mm Cut Control Step (IPC = 80) 0 Oi l 0:2 0.3: 0V»i 0 5 . 0.6 0.7: 0.8 0:9- :i Time jseci Figure 4.14 Motor Rotor Current Response to a 0.1mm Cut Control Step When IPC = 80 112 Cutting Force Response to 0. 1 mm Cut Control Step (IPC = 10) 0.5 1 1:5 2: 2.5 -3 -33:' 4 4.5, Time(sec) Figure 4.15 Force Response to a 0.1mm Cut Control Step When IPC = 10 113 Cutting Force Response to 0.1 mm Cut Control Step (IPC = 30) t 1 j r T " " r — T t i m e ( s e c ) Figure 4.16 Force Response to a 0.1mm Cut Control Step When IPC = 30 114 Gutting Force Response to 0. 1 mm Cut Control Step (IPC = 80) 0.4: 0.5 0\$ Time (sec) 0,7: 0:8 Figure 4.17 Force Response to a 0.1mm Cut Control Step When IPC = 80 115 System Frequency Response (IPC = 10) io° i61, . 'icf if Frequency (radfeec) Figure 4.18 System Frequency Response IPC = 10 116 System Frequency Response (IPG = 30) .. 0 .1 1. o to .. io- it Frequency (radfeec) Figure 4.19 System Frequency Response IPC = 30 117 System Frequency Response (IPC = 80) 118 CHAPTER 5 CONCLUSIONS AND RECOMMENDED FUTURE WORK Conclusions As W. McKenzie said "wood is difficult to cut". Although the cutting forces are typically low when compared to metal, due to the complex nature of the wood matrix, chip formation is very difficult to control. The constraints of variations in grain direction, moisture content, density, temperature, and species all make the prediction of the cutting forces very difficult. In addition the choice of cutting tools is restricted to mainly positive rake angle tools with a flank face of typically 15 degrees. Edge force losses are significant and the sharpness of the tools must be rigorously maintained. Friction between the chip and rake face varies from species to species and the chips types formed in general are combinations of the three basic types and can change instantly depending on the substructure of the wood matrix the tool encounters. These issues present many obstacles to the practicing engineer in the design computer controlled machinery for the wood processing industry. When cutting and machining clear Douglas Fir even with careful attention to instrumentation the forces measured from sample to sample varied by as much as 25%. However when the forces were averaged trends emerged. When a positive rake angle single point tool was used the thrust cutting force was very low and usually negative and the slope of the power consuming force over a variety of depths of cut did not increase dramatically. When a zero degree rake angle tool was used the thrust cutting force became positive and the slope of the main cutting forces increased more dramatically. When a negative rake angle tool was used the trust force nearly mirrored any increase in the power consuming force and the slope of the forces with respect to depth of cut increased significantly. This was probably due to the significant increase in edge forces and a decrease in the shear angle. Cutting pressures were highest with positive rake angle tool and in all cases decreased with depth of cut as is expected. Shear angle decreased as 119 the tools became less positive and the shear forces remained constant for all tools used. The chip types formed varied as a function of rake angle and depth of cut. To maintain a good finished surface, shallow cuts can only be used with all the tools investigated and the positive rake angle tool consistently yielded continuous chips with the best resulting surface finish. However when the depth of cut exceeded 0.2032 mm cracks would propagate ahead of the +30 degree rake angle tool and Franz Chip Type 1 would form. Chip compression ratios and the coefficient of friction was highest with the positive rake angle tools. There was no apparent advantage to use any tool other than a positive rake angle tool, as the resulting finish was very poor, and the forces were significantly higher. Two cutting models were developed for the grinding process. The first considers the effect of edge forces and the average cutting forces in the grinding operation. When the force ratios and specific cutting pressures were experimentally determined, the radial depth of cut can be calculated directly from the average forces in the X and Y axis typically measured using a dynamometer. This would allow the use of a computer to control the grinding operation. The feed-rate needs to be defined as the main average cutting forces affected directly. The second grinding cutting model presented can dynamically determine the stock removal ratio. Since wood is visco elastic in nature, spring back presents difficulty in ensuring the desired amount of stock is removed from the surface. This model generates a grinding cut ratio that can be used to maintain dimensional accuracy. In addition there is no need to define the geometry of the work-piece for the edge grinding system. This model also requires knowledge of the feed rate. A novel force controlled edge grinding system was developed to validate the grinding cut ratio model. The grinding system scans for the work-piece and will remove the desired amount of stock with a tolerance of +/-0.0254mm. A force sensor was constructed and interfaced to the controlling computer. The system would remove stock based on a model of the average 120 force in the Y axis only. This system can also dynamically calculate the cutting ratio to overcome spring back and ensure dimensional accuracy. 5.2 Future Work In this work only orthogonal cuts with the single point tools were made and further work needs to done on the influence of obliquity of the tool on the cutting forces and chip formation. Some promising preliminary investigations were made and the resulting surface after cutting was very good. In addition the mechanism of the shearing process should be further investigated. There is a demand for computer controlled sanding systems and refining the force controlled edge grinder system developed would prove to be beneficial. The contouring algorithm should be further developed and optimized. In addition an implementation of a 3 axis system would allow for wider use in many applications. Further investigation on the average cutting forces when grinding across the grain would also be very useful in expanding applications for the force controlled grinding system. Scanning Electron Microscope images of the ground surface and chips would be very useful in explaining the grinding mechanism of Douglas Fir. 121 Bibliography [1] Mater, J , "Preparing For Growth: New Challenges And Opportunities For The World's Forest Industry," Proceedings of the 13th International Wood Machining Seminar, vol. 1, pp3-14, July (1997) [2] Merchant, M.E., "Basic Mechanics of the Metal Cutting Process," J. of Appl. Mech., vol. 15, pp. A-168-A171 (1944) [3] Oxley, P.L.B., "The Mechanics of Machining: An Analytical Approach to Assessing Machinability," Ellis Horwood Ltd., Chichester, (1989) [4] Armarego, E.J.A., and R.H. Brown, "The Machining of Metals," Prentice-Hall, New Jersey, (1969) [5] Merchant, M.E., "Mechanics of the Metal Cutting Process, " J . Appl. 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Yoshikawa, "A New Expression for the Shear Angle in Metal Cutting," - see "Recent Developments Concerning Cutting Mechanics" by T. Sata in International Research in Production Engineering. Amer. Soc. Mech. Engrs., New York, (1963) 123 [18] Albrecht, P., "New Development in Theory of Metal Cutting Processes," Trans. ASME, Ser. B, vol. 82, p. 348, (1969) [19] Seethaler, R.J. "Integrated Planning, Monitoring, and Control of Milling Operations," Ph.D. Thesis, University of British Columbia, Vancouver, British Columbia, Canada, (1997) [20] Martellotti, M., "Analysis of Milling Process," Trans. ASME, vol. 63, p.677 (1941) and vol. 67, p.233 (1945) [21] Koenigsberger, F., and A.J.P. Sabharwal, "An Investigation into Cutting Pulsations during Milling Operations," Intl. J. Machine Des. Res., vol. 1, p.15, (1961) [22] Montgomery, D., and Y. Altintas, "Mechanism of Cutting Force and Surface Generation in Dynamic Milling," Trans. ASME: J. Eng. 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Miller," Abrasive Wear and Forces in Grinding of Silicon Carbide", Michigan Technological University, p. 6, Houghton, Michigan, (2002) [30] McKenzie, W.M., "Wood is Easy to Cut - Or Is It?," 11th International Wood Machining Seminar, p.33, (1995) [31] Koponen, S., T. Toratti, and P. Kanerva. Wood Science Technol., vol. 25, p.25, (1991) [32] Green, D.W., J.E. Winandy, and D.E. Kretschmann, "Mechanical Properties of Wood," Wood Handbook- Wood as an Engineering Material, Forest Products Laboratory Gen. Tech. Rep. FPL-GTR-113, Madison, WL, pp. 4-1 - 4 -2 , (1999) [33] Desch, H.E., "Timber its Structure and Properties 4 t h Ed.," Macmillan, Toronto, pp. 25-33, (1968) [34] llvessalo-Pfaffli, M.S.," Fibre Atlas, Identification of Papermaking Fibres," Springer-Verlag, Heidelberg, Berlin, (1995) 125 [35] llvessalo-Pfaffi, M.S., and J . Laamanen, KCL internal report. [36] Panshin, A.J. , and C. DeZeeuw," Textbook of Wood Technology. Vol. 1: Structure, Identification, Uses and Properties of the Commercial Woods of the United States and Canada, 3 r d Ed.," McGraw-Hill, New York, (1970) [37] Dippon, J. , H. Ren, F. Ben Amara, Y. Altintas, "Orthogonal Cutting of Medium Density Fiberboards," 14th International Wood Machining Seminar Proceedings,''Vol. 1, p. 31, Paris, France, (1999) [38] Franz, N.C., "An Analysis of Chip Formation in Wood Machining," Forest Products Journal, Vol. 10, No. 3 pp. 332-336, (1955) [39] Kivimaa, E., "Cutting Force in Woodworking," The State Inst. For Tech. Res., Pulb. No. 18, (1950) [40] McKenzie, W.M.," Fundamental Aspects of Wood Cutting Process," For. Prod. Jour., Vol. 10, No. 9, pp. 447-456, (1960) [41] Stewart, H.A.," Effect of Cutting Direction With Respect to Grain Angle on the Quality of Machined Surface, Tool Force Components, and Cutting Friction Coefficient," Forest Prod. Jour., Vol. 41, No. 10, pp. 43-46, (1969) [42] Stewart, H.A.," A Model Predicting Wood Failure With Respect to Grain Angle in Orthogonal Cutting," Wood and Fiber Science, Vol. 15, No. 4, pp. 317- 325, (1983) [43] Ozaki, S., X. Chen, H. Yonenobu, S. Kimura," Chip Swelling in Orthogonal Cutting of Wood" Proc. Of the 14th International Wood Machining Seminar," Vol. 1, (1999) 126 [44] Stewart, H.A., "Analysis of Tool Force sand Edge Recession after Cutting Medium Density Fiber Board," Proc. 9 t h International Wood Machining Seminar, pp. 320-341, (1988) [45] Gronlund, A., "Measuring and Modeling of Cutting Forces - Progress Report on an Ongoing Project," Proceedings of the 10th International Wood Machining Seminar,''Vol. 1, pp. 342-350, (1991) [46] Sawada, T., and M. Ohta, "Simulation of the Chip Formation in the Orthogonal Wood Cutting by the Extended Distinct Element Method," Proc. of the 13th International Wood Machining Seminar, Vol. 1, pp.525-533, (1997) [47] Sawada, T., and M. Ohta, "Simulation of the Wood Cutting Parallel or Perpendicular to the Grian by the Extended Distinct Element Method," Proc. of the 12th International Wood Machining Seminar, pp. 49-45 (1995) [48] Ohta, M., and B. Kawasaki," The Effect of Cutting Speed on the Surface Quality in Wood Cutting. - Model Experiments and Simulations by the Extended Distinct Element Method," Proc. of the 12th International Wood Machining Seminar, pp. 56-62, (1995) [49] Komatsu, M., "Machine Performance of a Router Bit in the Peripheral Milling of Wood 1 - Effects of the Radial Rake Angle of the Peripheral Cutting-Edge on the Cutting Force and Machined-Surface Roughness," Makuzai Gakkaishi, Vol. 39, No. 6, pp. 628-635, (1993) [50] Huang, Y . , " Cutting Force Components in Orthogonal Cutting Parallel to the Grain (90-0) 1 - Effects of the Rake Angles," Mokuzai Gakkaishi, Vol. 40, No. 10, pp. 1134-1140, (1994) 127 [51] Huang, Y . , " Cutting Force Components in Orthogonal Cutting Parallel to the Grain (90-0) 1 - Effects of Feed Lengths," Mokuzai Gakkaishi, Vol. 40, No. 10, pp. 1059-1066, (1994) [52] Koch, P., "Wood Machining Process," Ronald Press Co., New York, (1964) [53] Pahlitzsch, G., K. Dziobek, and K. Puttkammer," Chip Formation and Chip Flow in Milling of Wood and Wood-Based Materials," Proceedings from the 11th International Wood Machining Seminar, pp. 111-124, (1993) [54] Heisel, U., and H. Krondorfer," Surface Method for Vibration Analysis in Peripheral Milling of Solid Wood," Proc. from the 12'th International Wood Machining Seminar, (1995) [55] Palmqvist, J . , G. Johansson," Cutting Forces in Peripheral Milling of Wood," Proc. of the 14th International Wood Machining Seminar, Vol. 1, pp. 91-100, (1999) [56] Taylor, J.B., A.L. Carrano, R.L. Lemaster," Experimental Modeling of the Sanding Process: The Relationship Between Input and Output Parameters," Proc. of the 14th International Wood Machining Seminar, Vol. 1, pp. 73-82, (1999) [57] Atack, D., and W.D. May, Pulp Paper Mag. Can., Vol 63, No. 1, :T10 (1962) [58] Atack, D.," Mechanics of Wood Grinding Trend," The Activities of the Pulp and Paper Research Institute of Canada, Report No. 19, pp. 6-11, (1971) 128 [59] Lucander, M., KCL internal report. [60] Lai, T.C. , ' The Influence of Wear Breakage on Forces in Bar Turning," Masters of Engineering Thesis, McMaster University, Hamilton, Ont., Canada, (1986) [61] Eggleston, D.M., R. Herzog, E.G. Thomsen, "Observations on the Angle Relationships in Metal Cutting", Trans. Of the ASME, J. ofEngr. Ind. Pp. 263-279, (1959) [62] Compumotor, "The Application of an Adaptive Tuning Algorithm to an Industrial Servo System," Compumotor Co. Internal Publication, pp. 1-13, (1998) [63] Goodwin, G.C., "Control System Design," Prentice Hall, Upper Saddle River, New Jersey, (2001) [64] Matlab® for Windows, Copyright© 1984-2002, The MAthWorks, Inc., All Rights Reserved, R12. 129 Appendix A A. 1 Development of Grinding System Model A.1.1 Grinding System Block Diagram The constituent elements of this experimental machinery are given in the block diagram below (Fig. A.1). Where; • T w is the torque applied to the ball screw drive to advance the work piece into the grinder surface. • T C U T is the cutting torque produced by the work being forced against the grinder assembly. • X w is the linear displacement of the work piece into the grinder surface. • X g is the linear displacement of the grinder away from the work piece in reaction to the cutting force. Grinder System Block Diagram Positional Feedback Figure A.1 Grinder System Block Diagram The work piece position is feedback continuously to the Compumotor controller by a motor shaft position encoder. Grinder displacement is feedback 130 continuously via a dedicated LVDT. The depth of cut (Xc ut) can thus be known continuously as Xcut=Xw-Xg (A.1) A.1.2 Cutting Model Experimentally, the relationship between grinder displacement and depth of cut for the tested wood type is known to be Xg=2Xcut (A.2) Combining Eq. A.1 and Eq. A.2 yields the following Xw x Xcut xg Xw 2/3 Xg Figure A.2 Wood Cutting Model A. 1.3 Drive Motor The Compumotor drive can be represented using a classical DC motor model as justified by [Compumotor 62] and described in section 3.7 [Goodwin 63]. The drive motor model is given below in figure A.3: 131 Figure A.3 Drive Motor Model Where: Va is the DC voltage applied to the motor Vb is the back emf (CEMF) produced by motor generation action Ea is the net armature voltage (volts) Ra is the armature resistance (ohms) Ia is the armature current (amps) K, is the torque constant of the motor Kb is the back emf constant relating motor shaft speed to Vb. Vb=Kbdw (A.3) Note that 0W is the work piece ball screw shaft position rm is the torque applied to the ball screw by the motor rcul is the cutting torque loading the motor due to grinder cutting force TW is the net torque applied to the ball screw to advance the work. Note that t w = T m - T c u l (A.4) Constants provided by the motor manufacturer are summarized below in Table A.1 132 Motor Manufacturer Motor Constants Data 22.6 oz-in-amp"1 0.0955 volt-sec-rad"1 Ra 1.5 Q Table A.1 Motor Manufacturer Motor Constants Data A.1.4 Grinder Assembly Dynamics The grinder assembly can be viewed as a second order mechanical system consisting of mass (M), spring (K), and dashpot (D) as outlined in Figure A.4. Fcut Work M -*• K - 0 * LVDT Figure A.4 Grinder Assembly Dynamics As the work is pressed against the grinder by advancing the ball screw, a cutting force is produced on the work. In turn the grinder assembly is displaced by Xg in response to the cutting force F c u t . The differential equation describing this interaction is; Fcul=KXg+DXg + MXg (A.5) where: K is the grinder spring constant (lbs-in"1) M is the mass of the grinder assembly (lbs-in"1-sec"2) D is the equivalent viscous damping of the grinder assembly 133 (Ibs-in"1-sec1) provided by the dashpot cylinder X g is the displacement of the grinder assembly in reaction to the cutting force F c u t (in). The resulting transfer function relating cutting force (F c u t) and grinder displacement (Xg) is then; 1 1 M 2 D K s +s— + — (A.6) F^s) s2M + sD + K ' " M M The spring was manufactured to provide a constant K of 8000 oz-in"1 (500 lbs-in). Since the grinder displacement is directly measured by an LVDT, the mass and viscous damping could be determined by experiment. The following plot (Figure A.5) shows the grinder assembly displacement measured in response to a sudden impulse. Tek gjsjgi Single Seq 2kS/s Function Off —rime Units seconds M 25ms Chi / 820mV Cursor Function H Bars V Bars .11. Paired Figure A.5 Plot of LVDT Output When Grinder Assembly Was Impact Tested The grinder displacement is closely approximated by an under-damped second order function of the form; 134 X(s) = K f 2 = - 2 K * a 2 2 (A.7) (s + a) +6) s +2as + (co +a) where; a is the damping constant O J is the damped natural frequency whose Leplace transform is given by; X(S)= K f 2 = - 2 (A.8) (s + a) +co s +2as + (co +a) The characteristic polynomial for the grinder assembly is then; s2 +2as + (o>2 +a2) (A.9) which control engineers often express in the form; s2 +2%o)ns + 6)2 (A. 10) where; £ is the damping ratio con is the natural frequency By inspection and comparison to the cutting force: grinder displacement transfer function. a = frn=-£- (A.11) 2M a2+co2=a>2=^ (A.12) M If a and co are measured by experiment, D and M can be deduced since K is known. M=. 2 K 2. (A.13) (a +0) ) D = 2aM = — — (A. 14) (a2+co2) After several repetitions of the impulse test, a was determined from the damped envelope of the peaks and from the zero crossings. a = 17.15 sec"1 co = 74.8 rad/sec 135 These yield using Equ. 4.13 and 4.14 respectively; 8000 , 2 . , M = — = 1.358oz-sec -in ((17.15) 2+(74.8) 2) _ 2x8000 . _, D = = 46.59oz - sec- w ((17.15)2 +(74.8) 2 from which K 8000 co =J— = J = 76.8raa/sec " V M V1.358 ^ - g - g - ^ = / 6 - 5 9 = 0 . 2 2 3 2M®„ 24MK 2 V l .358x8000 The grinder assembly dynamics may then be modeled as shown in Figure A.6. Figure A.6 Grinder Assembly Model With M = 1.358 oz-sec"2-in"1 D = 46.59 oz-sec-in"1 K = 8000 oz-in"1 The model was run on Matlab (see Figure 4.12) and the results of the simulation agree with the plot shown in Fig. A.7. 136 t'Ttfse Response Figure A.7 Grinder Assembly Dynamics Simulation The work done in advancing the work piece a distance X w against the force F c u t is; W = FcutXw (A. 15) This work done by the ball screw rotating through an angle 0 W against an opposing torque T c u t; W = rcutew (A. 16) The relationship between cutting torque and cutting force is thus if the ball screw losses are neglected; X... T c u ^ F ^ (A. 17) However X w and 9W are directly related by the pitch of the ball screw as follows; (A. 18) 2x The grinder assembly model can hence be modified (as shown in Figure A.8) to represent cutting torque against which the ball screw motor must work. 137 Grinder Assembly 4 - — Figure A.8 Grinder Assembly Cutting Torque Model Where P = 0.1968 in-rev"1 for system at hand. A.1.5 Grinder Displacement Feedback The PC providing system control receives feedback of the grinder displacement via an LVDT mounted on the grinder assembly. The LVDT has a sensitivity of 1 V-in"1 and a Bandwidth of at least 100X that of the system overall. The LVDT was accordingly modeled as a simple gain feedback as shown in Figure A.9 below. Figure A.9 Grinder Displacement LVDT Model A.1.6 Ball Screw Drive and Work Piece Dynamics The mechanical elements of the ball screw drive and work piece include • Motor armature • Ball Screw Shaft 138 • Ball Screw Nut • Ball screw load consisting of the feed drive assembly, work piece tooling, and the work piece itself. These components translate motor shaft angular displacement and torque into work piece linear displacement and torque and cutting force. Neglecting torsional spring action this mechanism can be thought of as having both inertia and viscous rotational friction consisting of; • Motor inertia and damping (J m , Dm) • Ball screw shaft inertia and damping (J b, DD) • Equivalent ball screw load inertia (Je) generated by the feed drive, tooling, and work piece loading of the linear motion of the ball screw nut. Figure A. 10 In-Feed Ball Screw Drive The motor and ball screw inertia provided by the manufacturer are listed in Table A.2 below. Motor Ball Screw Ball Nut Manufacturer's Inertia Specifications ~Jin I 4.249 x 10"3 oz-in-secz J b 2.562 x 10"* oz-in-sec* Table A.2 Manufacturer's Inertia Specifications 139 The mass of the ball nut load consists of cross-feed drive, tooling, and work piece was measured to be 1.583 oz-in"1-sec2. Using the ball screw pitch, the equivalent inertia of the ball screw load is. )2 J, = ^ - r - = 1.553x10"3 oz - in - sec2 (A. 19) (2nf An applied torque should generate ball screw rotation, if shaft torsion is neglected, given by; T=J0+D0 (A.20) where; where; J e is the combined inertia of motor and ball screw shafts and the equivalent inertia of ball screw load D e is the combined rotation viscous damping of the above elements. Je=Jm+Jb+J, (A.21) J e = 3.1422 x 10"2 oz-in-sec"2 The rotational viscous damping D e of the system was estimated by experiment. Giving the ball nut and its load a sudden but gentile push, sets the motor, ball screw shaft, and ball screw load momentarily into motion. By monitoring the shaft speed of the ball screw as the system coasts to a stop, the viscous damping, D e, of these combined components can be deduced. When the system is coasting down with no torque applied 0 = w (A.22) Je0+De0 = O or Jea>+Deco = 0 (o = -(o^- (A.23) 140 where co is the shaft speed. Using a tachometer attached to the motor shaft, an output voltage proportional to the shaft speed was recorded as the ball screw was jogged and allowed to coast down, (see Figure A.11 below). The above first order differential equation for shaft speed during coast down has a solution of the form; co(t) = o)0e-M (A.24) where A = ^ - (A.25) Figure A.11 Plot of Ball Screw Rotational Viscous Damping Test The DC output of the motor during coast down will be proportional to O J and have the same characteristic decay constant, A. Several coast down tests were performed and the ratio — estimated to range between 50 to 70 sec"1. 141 A transfer function relating torque and ball screw angle can thus be determined as; T(S)=:JeS 20(S) + DeS0(s) or where and 1 m = J, J e has been calculated to equal 3.142 x 10" (A.26) (A.27) measured as 50-70 sec"1 Application of the ball screw pitch to generate work displacement X w from 9 yields the following ball screw drive and work piece dynamic model (see Figure A. 12 below); Figure A.12 Ball Screw and Work Piece Dynamics Model Note that T w represents the net torque advancing the work piece. ^ = r m - T a a (A.28) where xm is the motor output torque T C U T is the cutting torque produced by the grinder assembly. 142 A.1.7 Compumotor Drive Controller The Compumotor drive controller provides closed loop programmable PID control action to accurately control the ball screw position. The controller can be modeled as (see Figure A. 13 below); Figure A. 13 Compumotor Controller Model where; K v is the programmable overall gain KD is the programmable differential gain K p is the programmable proportional gain K | is the programmable integral gain X w is the current work piece position feedback X p is the desired position as commanded by the system control PC V a is the Controller output voltage to the motor terminals. For all system tests, the Compumotor driver controller settings were; K v = 1 K D = 0 K P = 300 K, = 0 A.1.8 Control PC Modeling The control PC uses a high speed data acquisition board to monitor 143 The grinder displacement fed back by the grinder assembly LVDT. The software control algorithm accepts the grinder displacement, compares to a desired reference unit depth (which corresponds to the desired cutting force), and takes control action to change the position command to the Compumotor drive controller as required. The control algorithm can implement proportional, integral, and or derivative action as required and may be represented as in Fig. A. 14; Z) .v2 + Ppcs + / s C o m p u m o t o r D r i v e C o m m a n d 0.5 Figure A. 14 PID Control Block of Compumotor Drive where; Dpc is the software differential gain PPC is the software proportional gain IPC is the software integral gain. 144 

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