Control of Cutting Vibration and Machining Instability: A Time–Frequency Approach for Precision, Micro and Nano Machining

Presents new developments on machine–tool vibration control applicable to nonlinear and discontinuous dynamical systems Cutting instability is a temporal–spectral aberration in the simultaneous time–frequency domain.  This aberration is particularly prominent at high machining speeds as it is nonlinear, nonstationary, and characteristically broadband. Irrespective of cutting speed, proper mitigation of cutting requires that vibration amplitudes in the time domain and vibration spectra in the frequency domain be simultaneously suppressed. Micro–machining is operated in a speed range that is at least one order of magnitude higher than conventional cutting operations. As cutting at higher speeds is inherently unstable, mitigating dynamic instability in micro–machining is a pressing issue in the industry.  In this book, the authors develop powerful analytical tools essential for the characterization of cutting instability, which is inherently complex and often chaotic. It also provides effective measures for instability control, system identification, and signal processing – the three components fundamental to machine–tool design. The strategy formulated in the book, along with the control and design methodologies, is novel and unique in that it deploys simultaneous vibration and frequency control in real–time to negate manufacturing instability including machine–tool chatter. Key features:– supports interdisciplinary engineering curricula in nonlinear dynamics, wavelet signal processing, control, engineering design, and manufacturing integrates both basic and advanced topics from several engineering disciplines into the creation of an innovative, new control theory incorporates nonlinear dynamics and nonlinear time–frequency control into the design of high–speed, high–precision machine–tools

Preface ix 1 Cutting Dynamics and Machining Instability 1 1.1 Instability in Turning Operation 2 1.1.1 Impact of Coupled Whirling and Tool Geometry on Machining 3 1.2 Cutting Stability 10 1.3 Margin of Stability and Instability 12 1.4 Stability in Fine Cuts 23 1.5 Concluding Remarks 31 References 32 2 Basic Physical Principles 33 2.1 Euclidean Vectors 33 2.2 Linear Spaces 34 2.3 Matrices 36 2.3.1 Eigenvalue and Linear Transformation 37 2.4 Discrete Functions 38 2.4.1 Convolution and Filter Operation 39 2.4.2 Sampling Theorem 40 2.4.3 z–Transform 41 2.5 Tools for Characterizing Dynamic Response 42 2.5.1 Fourier Analysis 49 2.5.2 Wavelet Analysis 51 References 54 3 Adaptive Filters and Filtered–x LMS Algorithm 55 3.1 Discrete–Time FIR Wiener Filter 55 3.1.1 Performance Measure 56 3.1.2 Optimization of Performance Function 58 3.2 Gradient Descent Optimization 60 3.3 Least–Mean–Square Algorithm 62 3.4 Filtered–x LMS Algorithm 64 References 68 4 Time–Frequency Analysis 71 4.1 Time and Frequency Correspondence 72 4.2 Time and Frequency Resolution 75 4.3 Uncertainty Principle 76 4.4 Short–Time Fourier Transform 77 4.5 Continuous–Time Wavelet Transform 79 4.6 Instantaneous Frequency 81 4.6.1 Fundamental Notions 82 4.6.2 Misinterpretation of Instantaneous Frequency 85 4.6.3 Decomposition of Multi–Mode Structure 90 4.6.4 Example of Instantaneous Frequency 94 4.6.5 Characteristics of Nonlinear Response 97 References 100 5 Wavelet Filter Banks 101 5.1 A Wavelet Example 101 5.2 Multiresolution Analysis 104 5.3 Discrete Wavelet Transform and Filter Banks 112 References 116 6 Temporal and Spectral Characteristics of Dynamic Instability 117 6.1 Implication of Linearization in Time–Frequency Domains 118 6.2 Route–to–Chaos in Time–Frequency Domain 125 6.3 Summary 134 References 134 7 Simultaneous Time–Frequency Control of Dynamic Instability 137 7.1 Property of Route–to–Chaos 137 7.1.1 OGY Control of Stationary and Nonstationary H´enon Map 139 7.1.2 Lyapunov–based Control of Stationary and Nonstationary Duffing Oscillator 140 7.2 Property of Chaos Control 144 7.2.1 Simultaneous Time–Frequency Control 145 7.3 Validation of Chaos Control 155 References 162 8 Time–Frequency Control ofMilling Instability and Chatter at High Speed 165 8.1 Milling Control Issues 165 8.2 High–Speed Low Immersion Milling Model 167 8.3 Route–to–Chaos and Milling Instability 168 8.4 Milling Instability Control 170 8.5 Summary 175 References 176 9 Multidimensional Time–Frequency Control of Micro–Milling Instability 177 9.1 Micro–Milling Control Issues 177 9.2 Nonlinear Micro–Milling Model 179 9.3 Multivariable Micro–Milling Instability Control 181 9.3.1 Control Strategy 183 9.4 Micro–Milling Instability Control 186 9.5 Summary 193 References 197 10 Time–Frequency Control of Friction Induced Instability 199 10.1 Issues with Friction–Induced Vibration Control 199 10.2 Continuous Rotating Disk Model 201 10.3 Dynamics of Friction–Induced Vibration 206 10.4 Friction–Induced Instability Control 208 10.5 Summary 214 References 215 11 Synchronization of Chaos in Simultaneous Time–Frequency Domain 217 11.1 Synchronization of Chaos 217 11.2 Dynamics of a Nonautonomous Chaotic System 219 11.3 Synchronization Scheme 222 11.4 Chaos Control 223 11.4.1 Scenario I 223 11.4.2 Scenario II 227 11.5 Summary 227 References 229 Appendix: MATLAB® Programming Examples of Nonlinear Time–Frequency Control 231 A.1 Friction–Induced Instability Control 231 A.1.1 Main Program 232 A.1.2 Simulink® Model 236 A.2 Synchronization of Chaos 239 A.2.1 Main Program 239 A.2.2 Simulink® Model 244 Index 245

Dr C. Steve Suh, Director, Institute for Innovation and Design in Engineering, Department of Mechanical Engineering, Texas A&M University, USA . Dr Suh obtained his PhD in Mechanical Engineering from Texas A&M University in 1997. He has co–authored numerous journals articles and a book, and was Guest Editor of the Journal of Vibration and Control in 2007. Dr Suh’s research interests include Nonlinear control theory; Laser ultrasonic thermometry; Characterization and control of dynamic manufacturing instability; Engineering design theory; MEMS and NEMS fabrication; High–performance 3D microelectronic packaging; Dynamic system diagnostics and prognostics; Wave propagation; Thermo–Elasto–Viscoplastodynamics. Dr Meng–Kun Liu, Lecturer, Department of Mechanical Engineering, Texas A&M University, USA . Dr.Liu obtained his PhD in Mechanical Engineering from Texas A&M University in 2012.   He has two–years senior design instructor experience in system engineering, project management and design optimization, and four years hands–on experience in industrial projects with focuses on design innovation. He was the recipient of the 2012 Departmental Graduate Student Teaching Award, and has co–authored numerous journal articles and conference proceedings. This is his first book.