Machining Dynamics (eBook)

Tony L. Schmitz is Professor of Mechanical Engineering and Engineering Science at The University of North Carolina at Charlotte.K. Scott Smith is Professor and Department Chair of Mechanical Engineering and Engineering Science at The University of North Carolina at Charlotte.

Preface 5
Contents 7
Chapter 1: Introduction 11
1.1 The Big Picture 12
1.2 A Brief Review 14
1.3 Road Map 14
References 15
Chapter 2: Modal Analysis 17
2.1 Single Degree of Freedom Free Vibration 18
2.1.1 Free Vibration 18
2.1.2 Forced Vibration 19
2.1.3 Self-Excited Vibration 20
2.1.4 Lumped Parameter Model: No Damping 20
2.1.5 Viscous Damping 23
2.1.6 Coulomb Damping 26
2.1.7 Solid Damping 27
2.1.8 Lumped Parameter Model: Viscous Damping 27
2.2 Single Degree of Freedom Forced Vibration 29
2.3 Two Degree of Freedom Free Vibration 35
2.4 Two Degree of Freedom Forced Vibration 45
2.4.1 Modal Analysis 46
2.4.2 Complex Matrix Inversion 50
2.5 System Identification 52
2.5.1 Modal Fitting 52
2.5.2 Model Definition 57
2.5.3 Modal Truncation 59
2.6 Modal Testing Equipment 62
2.6.1 Force Input 63
2.6.2 Vibration Measurement 64
2.7 Measurement Uncertainties 68
Exercises 69
Appendix: Orthogonality of Eigenvectors 73
References 75
Chapter 3: Turning Dynamics 77
3.1 Turning Description 77
3.2 Regenerative Chatter in Turning 80
3.3 Stability Lobe Diagrams 83
3.4 The Oriented FRF 93
3.5 Turning Time Domain Simulation 101
3.5.1 Chip Thickness Calculation 101
3.5.2 Force Calculation 103
3.5.3 Displacement Calculation 104
3.5.4 Multiple Degree of Freedom Modeling 109
3.6 Modulated Tool Path Turning 111
3.6.1 Stability Analysis 114
3.6.2 Experimental Demonstration 118
3.7 Process Damping 124
3.7.1 Process Damping Description 125
3.7.2 Stability Algorithm 127
Exercises 133
References 136
Chapter 4: Milling Dynamics 139
4.1 Milling Description 139
4.1.1 Tooth Passing Frequency 147
4.1.2 Multiple Teeth in the Cut 150
4.2 Regenerative Chatter in Milling 152
4.3 Stability Lobe Diagrams 155
4.3.1 Average Tooth Angle Approach 155
4.3.2 Oriented FRF 157
4.3.3 Fourier Series Approach 164
4.4 Milling Time Domain Simulation with Straight Teeth 174
4.4.1 Chip Thickness Calculation 174
4.4.2 Force Calculation 177
4.4.3 Displacement Calculation 177
4.4.4 Simulation Summary and Implementation 178
4.4.5 Periodic Sampling 185
4.5 Milling Time Domain Simulation with Helical Teeth 188
4.6 Ball Milling Time Domain Simulation with Helical Teeth 196
4.7 Experimental Cutting Force Coefficients 200
4.7.1 Updated Force Model 200
4.7.2 Linear Regression 203
4.7.3 Nonlinear Optimization 206
4.7.4 Experimental Techniques 208
4.8 Process Damping 209
4.8.1 Process Damping Description 209
4.8.2 Stability Algorithm 210
4.8.2.1 Up Milling 211
4.8.2.2 Down Milling 212
Exercises 217
Appendix: Reformulation of Fourier Series Eigenvalue Problem 219
References 221
Chapter 5: Surface Location Error in Milling 223
5.1 Surface Location Error 223
5.2 Frequency Domain Solution 226
5.2.1 Fourier Force Model 227
5.2.2 Frequency Domain Surface Location Error 229
5.2.3 Variation in Surface Location Error with Axial Location 235
5.2.4 Combining Stability and Surface Location Error in a Single Diagram 238
5.3 Cycloidal Tool Path Time Domain Simulation 239
Exercises 246
Appendix: Fourier Force Series Coefficients 247
References 248
Chapter 6: Special Topics in Milling 250
6.1 Frequency Content of Milling Signals 250
6.2 Runout 265
6.2.1 Simulation Modification 268
6.3 Variable Teeth Spacing 271
6.3.1 Simulation Updating 271
6.4 Period-n Bifurcations 274
6.4.1 Poincaré Maps 279
6.4.2 Bifurcation Diagrams 279
6.4.3 Stability Maps 280
6.5 Uncertainty Propagation 283
Exercises 285
References 287
Chapter 7: Tool Point Dynamics Prediction 291
7.1 Motivation 292
7.2 Basic Receptance Coupling 292
7.2.1 Two Component Rigid Coupling 293
7.2.2 Two Component Flexible Coupling 297
7.2.3 Two Component Flexible, Damped Coupling 304
7.3 Advanced Receptance Coupling 310
7.4 Beam Receptances 316
7.5 Assembly Receptance Predictions 324
7.6 Tool-Holder-Spindle-Machine Receptance Predictions 330
7.6.1 Spindle-Machine Receptances 335
7.7 Accelerometer Mass Compensation 339
7.8 Thin Rib Dynamics 341
Exercises 346
References 348
Chapter 8: Machining Tribology 352
8.1 Geometry, Forces, and Temperature 354
8.2 Tool Life 366
8.3 Cutting Fluids 377
8.4 Relationship to Machining Dynamics 380
Exercises 381
References 382
Index 384