Control of Cutting Vibration and Machining Instability E-Book

C. Steve Suh

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 319

Veröffentlichungsjahr: 2013

Beschreibung

Presents new developments on machine tool vibration control based on discontinuous dynamical systems

Machining instability is a topical area, and there are a wide range of publications that cover the topic. However, many of these previous studies have started by assuming that the behavior of the system can be linearised. Meanwhile, there are many recent advances in the fields of signal processing, nonlinear dynamics, and nonlinear control, all of which are relevant to the machining stability problem.  This book establishes the fundamentals of cutting mechanics and machine tool dynamics in the simultaneous time-frequency domain.  The new nonlinear control theory developed by the authors that facilitates simultaneous control of vibration amplitude in the time-domain and spectral response in the frequency-domain provides the foundation for the development of a controller architecture universally viable for the control of dynamic instability including bifurcation and chaos.  Once parameters underlying the coupling, interaction, and evolution of different cutting states and between the tool and workpiece are established, they can then be incorporated into the architecture to create a control methodology that mitigate machining instability and enable robust, chatter-free machine tool design applicable in particular to high speed micro- and nano-machining. 

• Presents new developments on machine tool vibration control based on discontinuous dynamical systems
• Provides a clear and concise approach to the understanding and control of machine tool and workpiece vibrations from an alternative view, contributing to an in-depth understanding of cutting dynamics and robust control of machining instability
• Equips the reader with the knowledge to understand the dynamics of cutting and operation of machine-tool systems in different conditions as well as the concept of cutting instability control
• Includes data examples in MATLAB coding

Leseprobe

Contents

Cover

Title Page

Copyright Page

Preface

Chapter 1: Cutting Dynamics and Machining Instability

1.1 Instability in Turning Operation

1.2 Cutting Stability

1.3 Margin of Stability and Instability

1.4 Stability in Fine Cuts

1.5 Concluding Remarks

References

Chapter 2: Basic Physical Principles

2.1 Euclidean Vectors

2.2 Linear Spaces

2.3 Matrices

2.4 Discrete Functions

2.5 Tools for Characterizing Dynamic Response

References

Chapter 3: Adaptive Filters and Filtered-x LMS Algorithm

3.1 Discrete-Time FIR Wiener Filter

3.2 Gradient Descent Optimization

3.3 Least-Mean-Square Algorithm

3.4 Filtered-x LMS Algorithm

References

Chapter 4: Time-Frequency Analysis

4.1 Time and Frequency Correspondence

4.2 Time and Frequency Resolution

4.3 Uncertainty Principle

4.4 Short-Time Fourier Transform

4.5 Continuous-Time Wavelet Transform

4.6 Instantaneous Frequency

References

Chapter 5: Wavelet Filter Banks

5.1 A Wavelet Example

5.2 Multiresolution Analysis

5.3 Discrete Wavelet Transform and Filter Banks

References

Chapter 6: Temporal and Spectral Characteristics of Dynamic Instability

6.1 Implication of Linearization in Time-Frequency Domains

6.2 Route-to-Chaos in Time-Frequency Domain

6.3 Summary

References

Chapter 7: Simultaneous Time-Frequency Control of Dynamic Instability

7.1 Property of Route-to-Chaos

7.2 Property of Chaos Control

7.3 Validation of Chaos Control

References

Chapter 8: Time-Frequency Control of Milling Instability and Chatter at High Speed

8.1 Milling Control Issues

8.2 High-Speed Low Immersion Milling Model

8.3 Route-to-Chaos and Milling Instability

8.4 Milling Instability Control

8.5 Summary

References

Chapter 9: Multidimensional Time-Frequency Control of Micro-Milling Instability

9.1 Micro-Milling Control Issues

9.2 Nonlinear Micro-Milling Model

9.3 Multivariable Micro-Milling Instability Control

9.4 Micro-Milling Instability Control

9.5 Summary

References

Chapter 10: Time-Frequency Control of Friction Induced Instability

10.1 Issues with Friction-Induced Vibration Control

10.2 Continuous Rotating Disk Model

10.3 Dynamics of Friction-Induced Vibration

10.4 Friction-Induced Instability Control

10.5 Summary

References

Chapter 11: Synchronization of Chaos in Simultaneous Time-Frequency Domain

11.1 Synchronization of Chaos

11.2 Dynamics of a Nonautonomous Chaotic System

11.3 Synchronization Scheme

11.4 Chaos Control

11.5 Summary

References

Appendix: MATLAB® Programming Examples of Nonlinear Time-Frequency Control

A.1 Friction-Induced Instability Control

A.2 Synchronization of Chaos

Index

This edition first published 2013 © 2013 John Wiley & Sons, Ltd

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Library of Congress Cataloging-in-Publication Data

Suh, C. Steve Control of cutting vibration and machining instability: a time-frequency approach for precision, micro and nanomachining / C. Steve Suh and Meng-Kun Liu.  pages cm Includes bibliographical references and index. ISBN 978-1-118-37182-4 (cloth) 1. Cutting–Vibration. 2. Machine-tools–Vibration. 3. Machining. 4. Machinery, Dynamics of.5. Time-series analysis. 6. Microtechnology 7. Nanotechnology. I. Liu, Meng-Kun. II. Title. TJ1186.S86 2013 671.3’5–dc232013014158

A catalogue record for this book is available from the British Library

ISBN: 9781118371824

Preface

Controllers are either designed in the frequency domain or time domain. When designed in the frequency domain, it is a common practice that a transfer function is derived from the corresponding governing equation of motion. Frequency response design methods, such as bode plots and root loci, are usually employed for the design of frequency domain based controllers. When designed in the time domain, the differential equation of the system is described as a state space model by the associated state variables. The controllability and observability of the design are then investigated using state feedback or other time domain control laws. Controllers designed in either domain have their advantages. Controllers designed in the frequency domain provide adequate performance with uncertainties. Estimating the output phase and amplitude in response to a sinusoidal input is generally sufficient to design a feedback controller, but the system has to be linear and stationary. Controllers designed in the time domain can accommodate multiple inputs-outputs and correlate internal and external states without considering the requirements in the frequency domain. Proven feasible for linear, stationary systems, both types of controllers can only be applied independently either in the frequency domain or the time domain.

For a linear time-invariant system, only the amplitude and phase angle of the input are changed by the system. The output frequency remains the same as the input frequency, and the system can be stabilized by applying a proper feedback gain. Both the time domain and frequency domain responses are bounded at the same time. However, this is not the case for the chaotic response generated by a nonlinear system. A chaotic response is naturally bounded in the time domain while becoming unstably broadband in the frequency domain, containing an infinite number of unstable periodic orbits of all periods in the phase portrait, called strange attractors. It does not remain in one periodic orbit but switches rapidly between these unstable periodic orbits. If the chaotic response is projected onto the Poincaré section, a lower dimensional subspace transversal to the trajectory of the response, numerous intersection points would be seen densely congregating and being confined within a finite area. This unequivocally implies that the chaotic response is bounded within a specific range in the time domain and dynamically deteriorates at the same time with a changing spectrum of broad bandwidth as the trajectory switching rapidly between infinite numbers of unstable periodic orbits. This phenomenon is prevalent in high-speed cutting operations where strong nonlinearities including regenerative effects, frictional discontinuity, chip formation, and tool stiffness are dominant.

For a nonlinear, nonstationary system, when it undergoes bifurcation to eventual chaos, its time response is no longer periodic. Broadband spectral response of additional frequency components emerge as a result. Controllers designed in the time domain contain time-domain error while being unable to restrain the increasing bandwidth. On the other hand, controllers designed in the frequency domain restrict the bandwidth from expanding while losing control over the time domain error. Neither frequency domain nor time domain based controllers are sufficient to address aperiodic response and route-to-chaos. This is further asserted by the uncertainty principle, which states that the resolution in the time- and frequency-domain cannot be reached arbitrarily. However, as Parseval's Theorem implies that the energies computed in the time- and frequency-domains are interchangeable, it is possible to incorporate and meet the time and frequency domain requirements together and realize the control of a nonlinear response with reconciled, concurrent time-frequency resolutions.

The above is a concise version of what was on our mind when we contemplated many years ago the following two questions: (1) Why is it that a dynamic response could be bounded in the time domain while in the meantime becoming unstably broadband in the frequency domain simultaneously? and (2) Why is it that the control of a nonlinear system has to be performed in the simultaneous time-frequency domain to be viable and effective? The wavelet-based time-frequency control methodology documented in this monograph is the embodiment of our response to these particular questions.

The control methodology is adaptive in that it monitors and makes timely and proper adjustments to improve its performance. Plant parameters in the novel control are identified in real-time and are used to adjust and update the control laws according to the changing system output. Its architecture is inspired by active noise control in which one FIR filter identifies the system and another auto-adjustable FIR filter rejects the uncontrollable input. Analysis wavelet filter banks are incorporated in the control configuration. The analysis filter banks decompose both input and error signals before the controlled signal is synthesized. As a dynamic response is resolved by the discrete wavelet transform into components at various scales corresponding to successive octave frequencies, the control law is inherently built in the joint time-frequency domain, thus facilitating simultaneous time-frequency control. Unlike active noise control whose objective is to reduce acoustic noise, the wavelet-based time-frequency control is designed to minimize the deterioration of the output signal in both the time and frequency domains when the system undergoes bifurcated or chaotic motion so as to restore the output response to periodic. These features together provide unprecedented advantages for the control of nonlinear, nonstationary system response.

This book presents a sound foundation which engineering professionals, practicing and in training alike, can rigorously explore to realize important progress in micro-manufacturing, precision machine-tool design, and chatter control. Viable solution strategies can be formulated drawing from the foundation to control cutting instability at high speed and to develop chatter-free machine-tool concepts. Research professionals in the general areas of nonlinear dynamics and nonlinear control will also find the volume informative in qualitative and quantitative terms on how discontinuity and chaos can be adequately mitigated.

The discourse of Control of Cutting Vibration and Machining Instability is organized into eleven chapters. The first chapter examines the coupled tool–workpiece interaction for a better understanding of the instability and chatter in turning operation. The second chapter is a brief review of the mathematical basics along with the common notations relevant to the derivation of the wavelet-based nonlinear time-frequency control law in Chapter 7. The third chapter reviews the essences of active noise control and the filtered-x LMS algorithm that are incorporated in the time-frequency control as features for system identification and error reduction. The notion of time-frequency analysis is discussed in the fourth chapter. This chapter presents several analysis tools important for the proper characterization of nonlinear system responses. It also lays the fundamentals needed to comprehend wavelet filter banks and the underlying concept of time-frequency resolution that are treated in the chapter that follows, Chapter 5.

The philosophical basis on which the nonlinear time-frequency control is based is elaborated in greater detail in Chapter 6. Chapter 7 presents the time-frequency control theory along with all the salient physical features that render chaos control feasible. The feasibility is demonstrated in applications in Chapters 8 through 11 using examples from high-speed manufacturing and friction-induced discontinuity. The last chapter, Chapter 11, explores an alternative solution to mitigating chaos using the time-frequency control. The implication for exploring synchronization of chaos to achieve suppressing self-sustained chaotic machining chatter is emphasized.

Two working MATLAB® m-files by which all the results and figures in Chapters 10 and 11 are generated are listed in the Appendix. The one for the friction-induced instability control in Chapter 10 has an extensive finite element coding section in it that utilizes several user-defined MATLAB® functions in Simulink® for the calculation of the beam vibration. We hope the examples will encourage the gaining of practical experience in implementing the wavelet-based nonlinear time-frequency control methodology. Readers who are reasonably familiar with the MATLAB® language and Simulink simulation tool should find the examples extensive, complete, and easy to follow.

Since it was first conceived years ago, many talented individuals have come along and helped evolve the core ideas of time-frequency control. Among them are Baozhong Yang, who explored instantaneous frequency as the tool of preference for characterizing nonlinear systems, and Achala Dassanayake, to whom we owe the comprehensive understanding of what machining instability and chatter really are.

C. Steve Suh and Meng-Kun Liu

Texas A&M University, College Station, USA

February 2013

1

Cutting Dynamics and Machining Instability

Material removal – as the most significant operation in manufacturing industry – is facing the ever-increasing challenge of increasing proficiency at the micro and nano scale levels of high-speed manufacturing. Fabrication of submicron size three-dimensional features and freeform surfaces demands unprecedented performance in accuracy, precision, and productivity. Meeting the requirements for significantly improved quality and efficiency, however, are contingent upon the optimal design of the machine-tools on which machining is performed. Modern day precision machine-tool configurations are in general an integration of several essential components including process measurement and control, power and drive, tooling and fixture, and the structural frame that provides stiffness and stability. As dynamic instability is inherently prominent and particularly damaging in high-speed precision cutting, design for dynamics is favored for the design of precision machine tool systems [1]. This approach employs computer-based analysis and design tools to optimize the dynamic performance of machine-tool design at the system level. It is largely driven by a critical piece of information – the vibration of the machine-tool. Due to the large set of parameters that affect cutting vibrations, such as regenerative effects, tool nonlinearity, cutting intermittency, discontinuous frictional excitation, and environmental noise, among many others, the effectiveness of the approach commands that the dynamics of machining be completely established throughout the entire process.

This book explores the fundamentals of cutting dynamics to the formulation and development of an innovative control methodology. The coupling, interaction, and evolution of different cutting states are studied so as to identify the underlying critical parameters that can be controlled to negate machining instability and enable better machine-tool design for precision micro and nano manufacturing.

The main features that contribute to the robust control of cutting instability are: (1) comprehension of the underlying dynamics of cutting and interruptions in cutting motions, (2) operation of the machine-tool system over a broad range of operating conditions with minimal vibration, such as high-speed operation to achieve a high-quality finish of the machined surface, (3) an increased rate of production to maximize profit and minimize operating and maintenance costs, (4) concentration on the apparent discontinuities that allows the nature of the complex machine-tool system motions to be fully established. The application of simultaneous time-frequency nonlinear control to mitigate complex intermittent cutting is both novel and unique. The impact on the area of material removal processes is in the mitigation of cutting instability and chaotic chattering motion induced by frictional and tool nonlinearity, and (5) development of concepts for cutting instability control and machine-tool design applicable to high-speed cutting processes.