A Study of the Cutting Performance in Abrasive Waterjet Contouring of Alumina Ceramics and Associated Jet Dynamic Characteristics

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1 A Study of the Cutting Performance in Abrasive Waterjet Contouring of Alumina Ceramics and Associated Jet Dynamic Characteristics By Hua Liu B. Eng. (Mech.) A thesis submitted to the Queensland University of Technology for the degree of Doctor of Philosophy. School of Mechanical, Manufacturing and Medical engineering Queensland University of Technology 2004

2 KEYWORDS Abrasive waterjet contouring, dimensional analysis, cutting performance model, dynamic characteristics of abrasive waterjet, computational fluid dynamics, jet characteristics model II

3 Abstract Abrasive waterjet (AWJ) cutting is one of the most recently developed nontraditional manufacturing technologies. It has been increasingly used in industry owing to its various distinct advantages over the other cutting technologies. However, many aspects of this technology require to be fully understood in order to increase its capability and cutting performance as well as to optimize the cutting process. This thesis contains an extensive literature review on the investigations of the various aspects in AWJ machining. It shows that while considerable work has been carried out, very little reported research has been found on the AWJ contouring process although it is a common AWJ cutting application. Because of the very nature of the AWJ cutting process, the changing nozzle traverse direction involved in AWJ contouring results in kerf geometrical or shape errors. A thorough understanding of the AWJ contouring process is essential for the reduction or elimination of these shape errors. It also shows that a lack of understanding of the AWJ hydrodynamic characteristics has limited the development of cutting performance models that are required for process control and optimization. Accordingly, a detailed experimental investigation is presented in this thesis to study the various cutting performance measures in AWJ contouring of an 87% alumina ceramic over a wide range of process parameters. For a comparison purpose, the study also considers AWJ straight-slit cutting. The effects of process parameters on the major cutting performance measures in AWJ contouring have been comprehensively discussed and plausible trends are amply analysed. It finds that the taper angles on the two kerf walls are in different magnitudes in AWJ contouring. The kerf taper on the outer kerf wall increases with the arc radius (or profile curvature), while that on the inner kerf wall decreases. Moreover, the depth of cut increases with an increase in arc radius and approaches the maximum in straight cutting for a given combination of parameters. The other process variables affect the AWJ contouring process in a way similar to that in straight cutting. The analysis has provided a guideline for the selection of process parameters in the AWJ contouring of alumina ceramics. III

4 In order to predict the cutting performance in process planning and ultimately optimize the cutting process, mathematical models for the major cutting performance measures in both straight-slit cutting and contouring are developed using a dimensional analysis technique. The models are then verified by assessing both qualitatively and quantitatively the model predictions with respect to the corresponding experimental data. It shows that the models can adequately predict the cutting performance measures and form the essential basis for developing strategies for selecting the optimum process parameters in AWJ cutting. To achieve an in-depth understanding of the jet dynamic characteristics such as the velocity and pressure distributions inside a jet, a Computational Fluid Dynamics (CFD) simulation is carried out using a Fluent6 flow solver and the simulation results are validated by an experimental investigation. The water and particle velocities in the jet are obtained under different input and boundary conditions to provide an insight into the jet characteristics and a good understanding of the kerf formation process in AWJ cutting. Various plausible trends and characteristics of the water and particle velocities are analysed and discussed, which provides the essential knowledge for optimizing the jet performance through optimizing the jetting and abrasive parameters. Mathematical models for the water and particle velocity distributions in an AWJ are finally developed and verified by comparing the predicted jet characteristics with the corresponding CFD simulation data. It shows that the jet characteristics models can yield good predictions for both water and particle velocity distributions in an AWJ. The successful development of these jet dynamic characteristics models is an essential step towards developing more comprehensive mathematical cutting performance models for AWJ cutting and eventually developing the optimization strategies for the effective and efficient use of this advanced manufacturing technology. IV

5 TABLE OF CONTENTS KEYWORDS... II ABSTRACT..... III LIST OF FIGURES...IX LIST OF TABLES...XIII STATEMENT OF ORIGINAL AUTHORSHIP...XIV ACKNOWLEDGMENTS... XV NOMENCLATURE...XVI CHAPTER 1 INTRODUCTION... 1 CHAPTER 2 LITERATURE REVIEW INTRODUCTION THE AWJ MACHINING TECHNOLOGY Characteristics of AWJ cutting technology Abrasive waterjet systems Entrainment system Direct pumping system Working principle of entrainment AWJ machine Parameters involved in AWJ cutting JET CHARACTERISTICS Characteristics of waterjet Jet structure along the jet flow direction Jet structure along the jet radial direction Characteristics of abrasive waterjet Estimation of particle velocity The effect of process parameters on the particle velocity Models for particle acceleration Phase distribution within the jet Velocity measurement Inductive method Photography method Laser-based method Jet impact force measurement MICRO CUTTING MECHANISMS Micro cutting mechanism of ductile material Micro cutting mechanism of brittle material MATERIAL REMOVAL PROCESS Two-dimensional model Stages of the cutting process Cutting zones Two stage impact zone models Three stage impact zone models KERF CHARACTERISTICS Kerf profile V

6 2.6.2 Surface characteristics Kerf characteristics in contouring Effect of process parameters on kerf characteristics Effect of process parameters on the kerf taper angle Effect of process parameters on the top kerf width Effect of process parameters on the bottom kerf width Effect of process parameters on the depth of cut Effect of process parameters on the surface roughness Effect of process parameters on the surface waviness Concluding comments on kerf characteristics AWJ CUTTING PERFORMANCE MODELS Models for the depth of cut Mathematical models based on erosion theories Fracture mechanics-based model Models based on energy-conservation Models for kerf geometrical features Models for surface characteristics TECHNIQUES FOR ENHANCING THE CUTTING PERFORMANCE Multipass cutting operations Controlled cutting head oscillation Forward angling the AWJ Increasing machine capability CONCLUDING REMARKS CHAPTER 3 A STUDY OF ABRASIVE WATERJET CONTOURING INTRODUCTION EXPERIMENTAL WORK Experimental design Experimental procedure and set-up Data acquisition KERF CHARACTERISTICS EFFECT OF PROCESS PARAMETERS ON THE KERF TAPER ANGLES Statistical analysis The effect of arc radius The effect of traverse speed The effect of abrasive flow rate The effect of standoff distance The effect of water pressure Summary of the trends of kerf taper angles EFFECT OF PROCESS PARAMETERS ON THE TOP KERF WIDTH Statistical analysis The effect of arc radius The effect of traverse speed The effect of abrasive flow rate The effect of standoff distance The effect of water pressure Summary of the trends of top kerf width EFFECT OF PROCESS PARAMETERS ON THE DEPTH OF CUT Statistical analysis The effect of arc radius VI

7 3.6.3 The effect of traverse speed The effect of standoff distance The effect of water pressure Summary of the trends of depth of cut EFFECT OF PROCESS PARAMETERS ON THE SMOOTH DEPTH OF CUT Statistical analysis The effect of arc radius The effect of traverse speed The effect of abrasive flow rate The effect of standoff distance The effect of water pressure Summary of the trends of smooth depth of cut CONCLUDING REMARKS CHAPTER 4 DEVELOPMENT OF PREDICTIVE CUTTING PERFORMANCE MODELS IN AWJ MACHINING INTRODUCTION PREDICTIVE MODELS FOR THE DEPTH OF CUT Model formulation Model assessment PREDICTIVE MODELS FOR KERF TAPER ANGLES Model formulation Model assessment PREDICTIVE MODELS FOR TOP KERF WIDTH AND SMOOTH DEPTH OF CUT CONCLUDING REMARKS CHAPTER 5 A CFD STUDY OF THE DYNAMIC CHARACTERISTICS OF ABRASIVE WATERJET INTRODUCTION CFD MODEL FORMULATION Geometry and boundary conditions Selection of the models Governing equations Evaluation of grids Test of inlet boundary conditions Flat inlet boundary condition at nozzle exit Flat inlet boundary condition inside nozzle One-seventh law inlet profiles Remarks on the inlet conditions CFD SIMULATION OF WATER JET CHARACTERISTICS Water jet structure Flow velocities along the jet centreline Downstream jet velocity profiles Characteristics of jet dynamic pressure CFD SIMULATION OF PARTICLE VELOCITIES Particle velocities along the jet axial direction Downstream particle velocity profiles EXPERIMENTAL VALIDATION Experimental apparatus and set-up Experimental design and procedure VII

8 5.5.3 Data acquisition and analysis CONCLUDING REMARKS CHAPTER 6 MATHEMATICAL MODELS FOR WATER AND PARTICLE VELOCITY IN ABRASIVE WATERJET INTRODUCTION MATHEMATICAL MODELS FOR WATERJET VELOCITY Model formulation Model for waterjet velocity along the jet centreline Model for the waterjet velocity profile in radial direction Model assessment MATHEMATICAL MODELS FOR PARTICLE VELOCITY Theoretical particle motion models Particle velocity models Model assessment CONCLUDING REMARKS CHAPTER 7 FINAL CONCLUSIONS AND FUTURE WORK FINAL CONCLUSIONS PROPOSED FUTURE WORK REFERENCES APPENDIX A: EXPERIMENTAL RESULTS OF AWJ CONTOURING AND STRAIGHT CUTTING ON ALUMINA CERAMICS APPENDIX B: RESULTS OF ANOVA FOR THE DETERMINATION OF THE SIGNIFICANCE OF INDIVIDUAL PROCESS VARIABLES APPENDIX C: SUMMARY OF CFD MODELS APPENDIX D: RESULTS OF EXPERIMENT FOR CFD VALIDATION APPENDIX E: LIST OF PUBLICATIONS FROM THE PROJECT VIII

9 LIST OF FIGURES Figure 2.1. Principle of entrainment system Figure 2.2. Principle of ASJ generation... 9 Figure 2.3. Major components of AWJ machine Figure 2.4. Structure of high speed waterjet Figure 2.5. Particle distribution across the jet Figure 2.6. Mechanism of material removal by solid particle erosion Figure 2.7. Incident two-dimensional erosive particle cutting into a ductile surface at an angle of attack α Figure 2.8. Ploughing and cutting by solid particle Figure 2.9. Lateral cracking of brittle material Figure Stages of the cutting process Figure The cutting wear and deformation wear Figure Two stage impact zone model Figure Schematic of through cut kerf Figure Relative strength zone in a waterjet Figure Schematic of non-through cut kerf Figure Schematic description of striation formation mechanism Figure (a) Jet lag, (b) bottom view of sharp corner, and (c) skirt-shaped geometry Figure Kerf profile in multipass AWJ cutting Figure Schematic of oscillation technique Figure Schematic of jet forward angle technique Figure 3.1. Kerf layout on specimens Figure 3.2. Schematic of kerf geometry and measurement methodology Figure 3.3. Surface characteristics generated in AWJ contouring Figure 3.4. Depths of cut generated at the different traverse speeds Figure 3.5. The effect of arc radius on the kerf taper angles Figure 3.6. The effect of traverse speed on kerf taper angles Figure 3.7. The effect of abrasive flow rate on kerf taper angles Figure 3.8. The effect of standoff distance on the kerf taper angles Figure 3.9. The effect of water pressure on kerf taper angles IX

10 Figure The effect of arc radius on the top kerf width Figure The effect of traverse speed on the top kerf width Figure The effect of abrasive flow rate on the top kerf width Figure The effect of standoff distance on the top kerf width Figure The effect of water pressure on the top kerf width Figure The effect of arc radius on the depth of cut Figure The effect of traverse speed on the depth of cut Figure The effect of standoff distance on the depth of cut Figure The effect of water pressure on the depth of cut Figure The effect of arc radius on the smooth depth of cut Figure The effect of traverse speed on the smooth depth of cut Figure The effect of abrasive flow rate on the smooth depth of cut Figure The effect of standoff distance on the smooth depth of cut Figure The effect of water pressure on the smooth depth of cut Figure 4.1. Predicted trends of depth of cut with respect to water pressure Figure 4.2. Predicted trends of depth of cut with respect to traverse speed Figure 4.3. Predicted trends of depth of cut with respect to abrasive flow rate Figure 4.4. Predicted trends of depth of cut with respect to arc radius Figure 4.5. Percentage deviations of the model predictions from the experimental data Figure 4.6. Predicted and experimental depth of cut for straight cutting Figure 4.7. Predicted and experimental depth of cut for AWJ contouring Figure 4.8. Predicted trends of kerf taper angles with respect to water pressure Figure 4.9. Predicted trends of kerf taper angles with respect to traverse speed Figure Predicted trend of kerf taper angls with respect to standoff distance Figure Predicted trend of kerf taper angles with respect to abrasive flow rate Figure Predicted trend of kerf taper angles respect to arc radius Figure Percentage deviations of model predicted kerf taper angles from the corresponding experimental data Figure Predicted and experimental kerf taper angle for straight cutting Figure Comparison of predicted and experimental kerf taper angles under different water pressures X

11 Figure Comparison of predicted and experimental kerf taper angles under different traverse speeds Figure Comparison of predicted and experimental kerf taper angles under different standoff distances Figure Comparison of predicted and experimental kerf taper angles under different abrasive flow rates Figure Comparison of predicted and experimental kerf taper angles under different arc radii Figure Predicted and experimental top kerf width Figure Predicted and experimental smooth depth of cut Figure Percentage deviations of model predictions from the experimental data Figure 5.1. Overview of the procedures in the jet characteristics study Figure 5.2. Schematic of the computational domain with boundary conditions Figure 5.3. Non-uniform grid Figure 5.4. Jet velocities with different grid resolutions Figure 5.5. Geometry and boundary conditions for the test of flat inlet boundary Figure 5.6. Jet velocity and dynamic pressure along the jet centreline Figure 5.7. Jet velocities and dynamic pressure profiles Figure 5.8. Geometry and boundary conditions for the test of the flat inlet velocity boundary at 2mm inside nozzle Figure 5.9. Jet velocity and dynamic pressure along the centre line Figure Jet velocities and dynamic pressure profiles Figure Geometry and boundary conditions for the one seventh law inlet velocity profile Figure Jet velocities and dynamic pressure along the axial direction Figure Jet velocities and dynamic pressure profiles Figure Structure of water flow Figure Water volume fraction at downstream cross-sections Figure Jet velocities along the jet centreline Figure Jet velocity profiles at different downstream locations Figure Jet velocity profiles for the different nozzle diameters Figure Dynamic pressure decay along the jet centreline Figure Jet dynamic pressure profiles XI

12 Figure Jet dynamic pressures for different nozzle diameters Figure Particle velocities at jet centreline Figure Particle velocities at different radial locations Figure Particle velocities at jet centreline for different nozzle diameters Figure Particle velocity profiles Figure Particle velocity distributions for the different particle sizes Figure Experimental apparatus and set-up Figure Measured jet diameter (slot width) vs jet travel distance Figure Comparison of average jet velocities from CFD simulation and experiments Figure 6.1. Water velocities along the jet centreline with different initial peak velocities Figure 6.2. Water velocities along the jet centreline Figure 6.3. Velocity profile at different jet downstream cross-sections Figure 6.4. Dimensionless velocity profiles with different nozzle diameters Figure 6.5. Dimensionless velocity profiles with different initial peak velocities Figure 6.6. Predicted trends of water velocity along the jet centreline Figure 6.7. Predicted trends of water velocity profile Figure 6.8. Percentage deviations of the model predictions from the CFD simulated data Figure 6.9. Particle velocity along the jet centreline with respect to ~ x Figure Particle velocity ratio u p( x~,r ~ ) / u p( x~,0 ) along the radial direction Figure The effect of dimensionless particle diameter on the particle velocity Figure Predicted trends of particle velocity along jet centreline Figure Predicted trends of particle velocity profiles Figure Particle velocity vs dimensionless particle diameter Figure Percentage deviations of the model predictions from the CFD simulation data for particle velocities XII

13 LIST OF TABLES Table 3.1. Physical and mechanical properties of the test specimens Table 3.2. The levels of parameters used in the experiment Table 3.3. Analysis of variance on the inner kerf taper angle Table 3.4. Analysis of variance on the outer kerf taper angle Table 3.5. Analysis of variance on the top kerf width Table 3.6. Analysis of variance on the depth of cut Table 3.7. Analysis of variance on the smooth depth of cut Table 3.8. Summary of the effect of process parameters on the kerf characteristics in AWJ contouring Table 4.1. Process parameters associated with material volume removal by a single particle Table 4.2. Variables associated with particle impact angle Table 4.3. Variables involved in kerf taper angle Table 4.4. Coefficients of determination of the possible models Table 5.1. Grid resolution schemes Table 5.2. Input parameters for CFD simulations Table 5.3. Experimental parameters Table 6.1. Variables with dimensions associated with water velocity XIII

14 The work contained in this thesis has not been previously submitted for a degree or diploma at any other higher education institution. To the best of my knowledge and belief, the thesis contains no material previously published or written by another person except where due reference is made. Signed: Date: XIV

15 ACKNOWLEDGMENTS The author wishes to express her sincere gratitude to her supervisor Dr. Jun Wang for his valuable guidance, constructive suggestions and expert supervision throughout the course of this work. The author also desires to acknowledge her associate supervisors Dr. Richard Brown and Dr. Neil Kelson for their valuable assistance and advice. Their support helped a lot when sometimes things did not evolve as wanted. The author wishes to express her thanks to her fellow research scholars, Mr. Wenge Song and Mr. Shunli Xu who worked with the author on different aspects of abrasive waterjet cutting, and gave enthusiastic assistance. Many thanks also due to the author s friends, for their friendship and moral support. Without these friends, the author would not have been here and fulfilled the thesis. Last but not least, the author wishes to express her gratitude to her sister and brotherin- law for their moral and financial support during this period. Especially, the author would like to express her profound gratitude to her parents. It is because of their moral support and encouragement that the author has been able to go through some difficult periods of time and complete this thesis. The author dedicates this thesis to her beloved parents. XV

16 NOMENCLATURE Symbol a A b b c C D C f C k C v C y C µ, C 1ε, C 2ε d j d p D D t e E f w F G k h h c h d h r h s H k 1 k d Quantity flaw distribution parameter axial surface area impacted by the waterjet jet width in the main region jet width in shear zone at initial region drag coefficient coefficient of fraction on the kerf wall characteristic factor that combines the particle and material characteristics orifice efficiency compressibility coefficient constants in transport equations jet diameter particle diameter nozzle diameter distance from the top kerf geometrical error modulus of elasticity of the target material proportional factor for the fraction of effective stress wave energy measured jet impact force by a piezoelectric force dynamometer generation of turbulent kinetic energy due to the mean velocity gradients depth of cut depth of cutting wear zone depth of deformation wear zone depth of cut in AWJ contouring smooth depth of cut hardness of target material factor to consider the momentum transfer efficiency function of the drag coefficient and the insert diameter XVI

17 K c m a m p m w n P critical stress intensity factor abrasive flow rate particle mass water mass flow rate number of particles supplied to the jet water pressure P 0 P c P m P (x,y) q r r a r p jet dynamic pressure at nozzle exit and in the jet centre minimum water pressure required to remove the material jet centreline dynamic pressure dynamic pressure at point (x,y) function of the abrasive velocity and the threshold velocity radial distance in a jet the abrasive/water mass flow ratio particle radius ~ r represents r/d R R a R a (0) R e R ep R f Rw S d t t n Y Y c u u a u j u 0 u e profile radius surface roughness surface roughness close to the top kerf Reynolds number relative Reynolds number particle roundness factor surface waviness standoff distance time workpiece thickness distance from jet axis in the main region distance from jet axis in the initial region nozzle traverse speed average waterjet velocity at a cross-section jet velocity initial peak velocity in the jet centre at the nozzle exit threshold particle velocity for removing material XVII

18 u i u n u p u p0 velocities in the x i coordinate directions velocities in the x n coordinate directions the particle velocity particle initial velocity u p1(x,0) velocity for a certain sized particle at the point (x, 0) u p(0,0) particle initial velocity at location (0,0) x~,r ~ u 1 velocity of a certain sized particle at the point ( ) p ( ) x~,r ~ u r u t u ( x ~,0) water velocity along the inlet boundary and at a radial direction r velocity of the abrasive at the top of the kerf water velocity in the jet centre at a downstream location (x/d) from u ( x, ~ r the nozzle exit ~ ) water velocity at the dimensionless point ( ~ x, ~ r ) u Reynolds stress. U k i u n kinetic energy V c V M V s V t w b w m w t W e x i and x n critical particle velocity volume of material removed volume of material removed by individual particles total material removal rate bottom kerf width minimum kerf width top kerf width Weber number coordinate directions x distance from the nozzle exit along the jet axial direction x c length of initial region ~ x represents x/d XVIII

19 Greek symbols Symbol α α 0 α e α q α t β γ Quantity particle attack angle critical impact angle at which the maximum erosion occurs attack angle at kerf exit q th phase volume fraction angle of impingement (or attack) at top of cutting surface function of Poisson's ratio of the workpiece material fracture energy per unit area γ 1 and γ 2 two solutions for the right hand side of equation (6.30) ε energy required to remove a unit volume of material ε d ε c ε e η θ θ c θ inner θ outer deformation wear factor cutting wear factor specific energy for deformation wear mode momentum transfer efficiency kerf taper angle angle of the slope of the striation curve at the jet exit kerf taper angle on the inner kerf wall in AWJ contouring kerf taper angle on the outer kerf wall in AWJ contouring µ dynamic viscosity σ target material flow stress σ k and σ ε turbulent Prandtl numbers for k and ε respectively σ j water surface tension µ momentum-transfer coefficient considering the velocity loss due to friction between the water flow and the orifice wall ρ ρ p ρ w flow density particle density water density XIX

20 A Study of the Cutting Performance in Abrasive Waterjet Contouring of Alumina Ceramics and Associated Jet Dynamic Characteristics By Hua Liu B. Eng. (Mech.) A thesis submitted to the Queensland University of Technology for the degree of Doctor of Philosophy. School of Mechanical, Manufacturing and Medical engineering Queensland University of Technology 2004

21 KEYWORDS Abrasive waterjet contouring, dimensional analysis, cutting performance model, dynamic characteristics of abrasive waterjet, computational fluid dynamics, jet characteristics model II

22 Abstract Abrasive waterjet (AWJ) cutting is one of the most recently developed nontraditional manufacturing technologies. It has been increasingly used in industry owing to its various distinct advantages over the other cutting technologies. However, many aspects of this technology require to be fully understood in order to increase its capability and cutting performance as well as to optimize the cutting process. This thesis contains an extensive literature review on the investigations of the various aspects in AWJ machining. It shows that while considerable work has been carried out, very little reported research has been found on the AWJ contouring process although it is a common AWJ cutting application. Because of the very nature of the AWJ cutting process, the changing nozzle traverse direction involved in AWJ contouring results in kerf geometrical or shape errors. A thorough understanding of the AWJ contouring process is essential for the reduction or elimination of these shape errors. It also shows that a lack of understanding of the AWJ hydrodynamic characteristics has limited the development of cutting performance models that are required for process control and optimization. Accordingly, a detailed experimental investigation is presented in this thesis to study the various cutting performance measures in AWJ contouring of an 87% alumina ceramic over a wide range of process parameters. For a comparison purpose, the study also considers AWJ straight-slit cutting. The effects of process parameters on the major cutting performance measures in AWJ contouring have been comprehensively discussed and plausible trends are amply analysed. It finds that the taper angles on the two kerf walls are in different magnitudes in AWJ contouring. The kerf taper on the outer kerf wall increases with the arc radius (or profile curvature), while that on the inner kerf wall decreases. Moreover, the depth of cut increases with an increase in arc radius and approaches the maximum in straight cutting for a given combination of parameters. The other process variables affect the AWJ contouring process in a way similar to that in straight cutting. The analysis has provided a guideline for the selection of process parameters in the AWJ contouring of alumina ceramics. III

23 In order to predict the cutting performance in process planning and ultimately optimize the cutting process, mathematical models for the major cutting performance measures in both straight-slit cutting and contouring are developed using a dimensional analysis technique. The models are then verified by assessing both qualitatively and quantitatively the model predictions with respect to the corresponding experimental data. It shows that the models can adequately predict the cutting performance measures and form the essential basis for developing strategies for selecting the optimum process parameters in AWJ cutting. To achieve an in-depth understanding of the jet dynamic characteristics such as the velocity and pressure distributions inside a jet, a Computational Fluid Dynamics (CFD) simulation is carried out using a Fluent6 flow solver and the simulation results are validated by an experimental investigation. The water and particle velocities in the jet are obtained under different input and boundary conditions to provide an insight into the jet characteristics and a good understanding of the kerf formation process in AWJ cutting. Various plausible trends and characteristics of the water and particle velocities are analysed and discussed, which provides the essential knowledge for optimizing the jet performance through optimizing the jetting and abrasive parameters. Mathematical models for the water and particle velocity distributions in an AWJ are finally developed and verified by comparing the predicted jet characteristics with the corresponding CFD simulation data. It shows that the jet characteristics models can yield good predictions for both water and particle velocity distributions in an AWJ. The successful development of these jet dynamic characteristics models is an essential step towards developing more comprehensive mathematical cutting performance models for AWJ cutting and eventually developing the optimization strategies for the effective and efficient use of this advanced manufacturing technology. IV

24 TABLE OF CONTENTS KEYWORDS... II ABSTRACT..... III LIST OF FIGURES...IX LIST OF TABLES...XIII STATEMENT OF ORIGINAL AUTHORSHIP...XIV ACKNOWLEDGMENTS... XV NOMENCLATURE...XVI CHAPTER 1 INTRODUCTION... 1 CHAPTER 2 LITERATURE REVIEW INTRODUCTION THE AWJ MACHINING TECHNOLOGY Characteristics of AWJ cutting technology Abrasive waterjet systems Entrainment system Direct pumping system Working principle of entrainment AWJ machine Parameters involved in AWJ cutting JET CHARACTERISTICS Characteristics of waterjet Jet structure along the jet flow direction Jet structure along the jet radial direction Characteristics of abrasive waterjet Estimation of particle velocity The effect of process parameters on the particle velocity Models for particle acceleration Phase distribution within the jet Velocity measurement Inductive method Photography method Laser-based method Jet impact force measurement MICRO CUTTING MECHANISMS Micro cutting mechanism of ductile material Micro cutting mechanism of brittle material MATERIAL REMOVAL PROCESS Two-dimensional model Stages of the cutting process Cutting zones Two stage impact zone models Three stage impact zone models KERF CHARACTERISTICS Kerf profile V

25 2.6.2 Surface characteristics Kerf characteristics in contouring Effect of process parameters on kerf characteristics Effect of process parameters on the kerf taper angle Effect of process parameters on the top kerf width Effect of process parameters on the bottom kerf width Effect of process parameters on the depth of cut Effect of process parameters on the surface roughness Effect of process parameters on the surface waviness Concluding comments on kerf characteristics AWJ CUTTING PERFORMANCE MODELS Models for the depth of cut Mathematical models based on erosion theories Fracture mechanics-based model Models based on energy-conservation Models for kerf geometrical features Models for surface characteristics TECHNIQUES FOR ENHANCING THE CUTTING PERFORMANCE Multipass cutting operations Controlled cutting head oscillation Forward angling the AWJ Increasing machine capability CONCLUDING REMARKS CHAPTER 3 A STUDY OF ABRASIVE WATERJET CONTOURING INTRODUCTION EXPERIMENTAL WORK Experimental design Experimental procedure and set-up Data acquisition KERF CHARACTERISTICS EFFECT OF PROCESS PARAMETERS ON THE KERF TAPER ANGLES Statistical analysis The effect of arc radius The effect of traverse speed The effect of abrasive flow rate The effect of standoff distance The effect of water pressure Summary of the trends of kerf taper angles EFFECT OF PROCESS PARAMETERS ON THE TOP KERF WIDTH Statistical analysis The effect of arc radius The effect of traverse speed The effect of abrasive flow rate The effect of standoff distance The effect of water pressure Summary of the trends of top kerf width EFFECT OF PROCESS PARAMETERS ON THE DEPTH OF CUT Statistical analysis The effect of arc radius VI

26 3.6.3 The effect of traverse speed The effect of standoff distance The effect of water pressure Summary of the trends of depth of cut EFFECT OF PROCESS PARAMETERS ON THE SMOOTH DEPTH OF CUT Statistical analysis The effect of arc radius The effect of traverse speed The effect of abrasive flow rate The effect of standoff distance The effect of water pressure Summary of the trends of smooth depth of cut CONCLUDING REMARKS CHAPTER 4 DEVELOPMENT OF PREDICTIVE CUTTING PERFORMANCE MODELS IN AWJ MACHINING INTRODUCTION PREDICTIVE MODELS FOR THE DEPTH OF CUT Model formulation Model assessment PREDICTIVE MODELS FOR KERF TAPER ANGLES Model formulation Model assessment PREDICTIVE MODELS FOR TOP KERF WIDTH AND SMOOTH DEPTH OF CUT CONCLUDING REMARKS CHAPTER 5 A CFD STUDY OF THE DYNAMIC CHARACTERISTICS OF ABRASIVE WATERJET INTRODUCTION CFD MODEL FORMULATION Geometry and boundary conditions Selection of the models Governing equations Evaluation of grids Test of inlet boundary conditions Flat inlet boundary condition at nozzle exit Flat inlet boundary condition inside nozzle One-seventh law inlet profiles Remarks on the inlet conditions CFD SIMULATION OF WATER JET CHARACTERISTICS Water jet structure Flow velocities along the jet centreline Downstream jet velocity profiles Characteristics of jet dynamic pressure CFD SIMULATION OF PARTICLE VELOCITIES Particle velocities along the jet axial direction Downstream particle velocity profiles EXPERIMENTAL VALIDATION Experimental apparatus and set-up Experimental design and procedure VII

27 5.5.3 Data acquisition and analysis CONCLUDING REMARKS CHAPTER 6 MATHEMATICAL MODELS FOR WATER AND PARTICLE VELOCITY IN ABRASIVE WATERJET INTRODUCTION MATHEMATICAL MODELS FOR WATERJET VELOCITY Model formulation Model for waterjet velocity along the jet centreline Model for the waterjet velocity profile in radial direction Model assessment MATHEMATICAL MODELS FOR PARTICLE VELOCITY Theoretical particle motion models Particle velocity models Model assessment CONCLUDING REMARKS CHAPTER 7 FINAL CONCLUSIONS AND FUTURE WORK FINAL CONCLUSIONS PROPOSED FUTURE WORK REFERENCES APPENDIX A: EXPERIMENTAL RESULTS OF AWJ CONTOURING AND STRAIGHT CUTTING ON ALUMINA CERAMICS APPENDIX B: RESULTS OF ANOVA FOR THE DETERMINATION OF THE SIGNIFICANCE OF INDIVIDUAL PROCESS VARIABLES APPENDIX C: SUMMARY OF CFD MODELS APPENDIX D: RESULTS OF EXPERIMENT FOR CFD VALIDATION APPENDIX E: LIST OF PUBLICATIONS FROM THE PROJECT VIII

28 LIST OF FIGURES Figure 2.1. Principle of entrainment system Figure 2.2. Principle of ASJ generation... 9 Figure 2.3. Major components of AWJ machine Figure 2.4. Structure of high speed waterjet Figure 2.5. Particle distribution across the jet Figure 2.6. Mechanism of material removal by solid particle erosion Figure 2.7. Incident two-dimensional erosive particle cutting into a ductile surface at an angle of attack α Figure 2.8. Ploughing and cutting by solid particle Figure 2.9. Lateral cracking of brittle material Figure Stages of the cutting process Figure The cutting wear and deformation wear Figure Two stage impact zone model Figure Schematic of through cut kerf Figure Relative strength zone in a waterjet Figure Schematic of non-through cut kerf Figure Schematic description of striation formation mechanism Figure (a) Jet lag, (b) bottom view of sharp corner, and (c) skirt-shaped geometry Figure Kerf profile in multipass AWJ cutting Figure Schematic of oscillation technique Figure Schematic of jet forward angle technique Figure 3.1. Kerf layout on specimens Figure 3.2. Schematic of kerf geometry and measurement methodology Figure 3.3. Surface characteristics generated in AWJ contouring Figure 3.4. Depths of cut generated at the different traverse speeds Figure 3.5. The effect of arc radius on the kerf taper angles Figure 3.6. The effect of traverse speed on kerf taper angles Figure 3.7. The effect of abrasive flow rate on kerf taper angles Figure 3.8. The effect of standoff distance on the kerf taper angles Figure 3.9. The effect of water pressure on kerf taper angles IX

29 Figure The effect of arc radius on the top kerf width Figure The effect of traverse speed on the top kerf width Figure The effect of abrasive flow rate on the top kerf width Figure The effect of standoff distance on the top kerf width Figure The effect of water pressure on the top kerf width Figure The effect of arc radius on the depth of cut Figure The effect of traverse speed on the depth of cut Figure The effect of standoff distance on the depth of cut Figure The effect of water pressure on the depth of cut Figure The effect of arc radius on the smooth depth of cut Figure The effect of traverse speed on the smooth depth of cut Figure The effect of abrasive flow rate on the smooth depth of cut Figure The effect of standoff distance on the smooth depth of cut Figure The effect of water pressure on the smooth depth of cut Figure 4.1. Predicted trends of depth of cut with respect to water pressure Figure 4.2. Predicted trends of depth of cut with respect to traverse speed Figure 4.3. Predicted trends of depth of cut with respect to abrasive flow rate Figure 4.4. Predicted trends of depth of cut with respect to arc radius Figure 4.5. Percentage deviations of the model predictions from the experimental data Figure 4.6. Predicted and experimental depth of cut for straight cutting Figure 4.7. Predicted and experimental depth of cut for AWJ contouring Figure 4.8. Predicted trends of kerf taper angles with respect to water pressure Figure 4.9. Predicted trends of kerf taper angles with respect to traverse speed Figure Predicted trend of kerf taper angls with respect to standoff distance Figure Predicted trend of kerf taper angles with respect to abrasive flow rate Figure Predicted trend of kerf taper angles respect to arc radius Figure Percentage deviations of model predicted kerf taper angles from the corresponding experimental data Figure Predicted and experimental kerf taper angle for straight cutting Figure Comparison of predicted and experimental kerf taper angles under different water pressures X

30 Figure Comparison of predicted and experimental kerf taper angles under different traverse speeds Figure Comparison of predicted and experimental kerf taper angles under different standoff distances Figure Comparison of predicted and experimental kerf taper angles under different abrasive flow rates Figure Comparison of predicted and experimental kerf taper angles under different arc radii Figure Predicted and experimental top kerf width Figure Predicted and experimental smooth depth of cut Figure Percentage deviations of model predictions from the experimental data Figure 5.1. Overview of the procedures in the jet characteristics study Figure 5.2. Schematic of the computational domain with boundary conditions Figure 5.3. Non-uniform grid Figure 5.4. Jet velocities with different grid resolutions Figure 5.5. Geometry and boundary conditions for the test of flat inlet boundary Figure 5.6. Jet velocity and dynamic pressure along the jet centreline Figure 5.7. Jet velocities and dynamic pressure profiles Figure 5.8. Geometry and boundary conditions for the test of the flat inlet velocity boundary at 2mm inside nozzle Figure 5.9. Jet velocity and dynamic pressure along the centre line Figure Jet velocities and dynamic pressure profiles Figure Geometry and boundary conditions for the one seventh law inlet velocity profile Figure Jet velocities and dynamic pressure along the axial direction Figure Jet velocities and dynamic pressure profiles Figure Structure of water flow Figure Water volume fraction at downstream cross-sections Figure Jet velocities along the jet centreline Figure Jet velocity profiles at different downstream locations Figure Jet velocity profiles for the different nozzle diameters Figure Dynamic pressure decay along the jet centreline Figure Jet dynamic pressure profiles XI

31 Figure Jet dynamic pressures for different nozzle diameters Figure Particle velocities at jet centreline Figure Particle velocities at different radial locations Figure Particle velocities at jet centreline for different nozzle diameters Figure Particle velocity profiles Figure Particle velocity distributions for the different particle sizes Figure Experimental apparatus and set-up Figure Measured jet diameter (slot width) vs jet travel distance Figure Comparison of average jet velocities from CFD simulation and experiments Figure 6.1. Water velocities along the jet centreline with different initial peak velocities Figure 6.2. Water velocities along the jet centreline Figure 6.3. Velocity profile at different jet downstream cross-sections Figure 6.4. Dimensionless velocity profiles with different nozzle diameters Figure 6.5. Dimensionless velocity profiles with different initial peak velocities Figure 6.6. Predicted trends of water velocity along the jet centreline Figure 6.7. Predicted trends of water velocity profile Figure 6.8. Percentage deviations of the model predictions from the CFD simulated data Figure 6.9. Particle velocity along the jet centreline with respect to ~ x Figure Particle velocity ratio u p( x~,r ~ ) / u p( x~,0 ) along the radial direction Figure The effect of dimensionless particle diameter on the particle velocity Figure Predicted trends of particle velocity along jet centreline Figure Predicted trends of particle velocity profiles Figure Particle velocity vs dimensionless particle diameter Figure Percentage deviations of the model predictions from the CFD simulation data for particle velocities XII

32 LIST OF TABLES Table 3.1. Physical and mechanical properties of the test specimens Table 3.2. The levels of parameters used in the experiment Table 3.3. Analysis of variance on the inner kerf taper angle Table 3.4. Analysis of variance on the outer kerf taper angle Table 3.5. Analysis of variance on the top kerf width Table 3.6. Analysis of variance on the depth of cut Table 3.7. Analysis of variance on the smooth depth of cut Table 3.8. Summary of the effect of process parameters on the kerf characteristics in AWJ contouring Table 4.1. Process parameters associated with material volume removal by a single particle Table 4.2. Variables associated with particle impact angle Table 4.3. Variables involved in kerf taper angle Table 4.4. Coefficients of determination of the possible models Table 5.1. Grid resolution schemes Table 5.2. Input parameters for CFD simulations Table 5.3. Experimental parameters Table 6.1. Variables with dimensions associated with water velocity XIII

33 The work contained in this thesis has not been previously submitted for a degree or diploma at any other higher education institution. To the best of my knowledge and belief, the thesis contains no material previously published or written by another person except where due reference is made. Signed: Date: XIV

34 ACKNOWLEDGMENTS The author wishes to express her sincere gratitude to her supervisor Dr. Jun Wang for his valuable guidance, constructive suggestions and expert supervision throughout the course of this work. The author also desires to acknowledge her associate supervisors Dr. Richard Brown and Dr. Neil Kelson for their valuable assistance and advice. Their support helped a lot when sometimes things did not evolve as wanted. The author wishes to express her thanks to her fellow research scholars, Mr. Wenge Song and Mr. Shunli Xu who worked with the author on different aspects of abrasive waterjet cutting, and gave enthusiastic assistance. Many thanks also due to the author s friends, for their friendship and moral support. Without these friends, the author would not have been here and fulfilled the thesis. Last but not least, the author wishes to express her gratitude to her sister and brotherin- law for their moral and financial support during this period. Especially, the author would like to express her profound gratitude to her parents. It is because of their moral support and encouragement that the author has been able to go through some difficult periods of time and complete this thesis. The author dedicates this thesis to her beloved parents. XV

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