Machine Tool Vibrations and Cutting Dynamics

Machine Tool Vibrations and Cutting Dynamics

Brandon C. Gegg l Albert C.J. Luo C. Steve Suh Machine Tool Vibrations and Cutting Dynamics

Brandon C. Gegg Dynacon Inc. Winches and Handling Systems 831 Industrial Blvd Bryan, TX 77803, USA bgegg@dynacon.com C. Steve Suh Department of Mechanical Engineering Texas A&M University College Station, TX, USA ssuh@tamu.edu Albert C.J. Luo Department of Mechanical and Industrial Engineering Southern Illinois University Edwardsville, IL, USA aluo@siue.ed ISBN 978-1-4419-9800-2 e-isbn 978-1-4419-9801-9 DOI 10.1007/978-1-4419-9801-9 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011928682 # Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface Machining dynamics is a very old topic on manufacturing processes with consideration of cutting interruption, intermittency, and the coupled interaction between the tool- and work-piece for a better understanding of the underlying physics dictating material removal. In this book, cutting is treated as a nonsmooth system composed of three continuous dynamical subsystems. The corresponding boundaries are (1) the tool- and work-piece contact/impact boundary, (2) the onset/disappearance of cutting boundary, (3) the chip/tool friction boundary, and (4) the chip vanishing boundary. The complex motions in cutting dynamics are mainly caused by discontinuities, including chip and tool-piece seizure and complex stick slip motion. Through the application of discontinuous system theory, a comprehensive understanding of the grazing phenomena induced by the frictional-velocity boundary and the loss of contact between the tool- and work-piece are discussed. Significant insights are to control machine-tool vibration and to develop chatter-free machine-tool concept. The coupling, interaction, and evolution of different cutting states to mitigate machining instability and to enable better machine-tool design are addressed in this book. The monograph presents a sound foundation upon which engineering professionals, practicing and in-training alike, could explore with rigor to make advance in manufacturing, machine-tool design, and machining chatter control. Research professionals in the general areas of nonlinear dynamics and nonlinear control would also find the volume informative in qualitative and quantitative terms as to how semistable interrupted periodic motions lead to unstable motions. The research and endeavor needed for the creation of Machine Tool Vibrations and Cutting Dynamics necessarily put a burden on family life. Without the unwavering support of our families, the completion of the book would not have been possible. Our sincere gratitude also goes to our editor at Springer Science, Steven Elliot, for his professionalism and encouragement, and to the institutions we are associated with for the collegiate support. Brandon C. Gegg C. Steve Suh Albert C.J. Luo v

Contents 1 Introduction... 1 1.1 Machining Problems... 2 1.2 Discontinuous Systems... 6 1.3 Book Layout... 9 References...... 10 2 Discontinuous System Theory... 15 2.1 Domain Accessibility... 15 2.2 Discontinuous Dynamical Systems... 16 2.3 Flow Passability to Boundary... 18 2.4 Tangential Flows to Boundary... 26 2.5 Switching Bifurcations of Passable Flows... 34 2.6 Switching Bifurcations of Nonpassable Flows... 45 References...... 56 3 Friction-Induced Oscillators... 57 3.1 Constant Velocity Boundary... 57 3.1.1 Grazing Phenomena... 60 3.1.2 Sliding Motion... 66 3.2 Time-Varying Velocity Boundary... 76 3.2.1 Analytical Conditions... 78 3.2.2 Generic Mappings and Force Product Criteria... 89 3.2.3 Numerical Simulations... 95 3.3 Concluding Remarks... 98 References...... 98 4 Cutting Dynamics Mechanism... 101 4.1 Machine-Tool Dynamics... 101 4.2 Domains and Boundaries... 111 4.3 Motion Passability... 117 References...... 121 vii

viii Contents 5 Complex Cutting Motions... 123 5.1 Switching Planes and Mappings... 123 5.2 Local Mapping Structures... 130 5.3 Periodic Interrupted Cutting Motions... 133 5.4 Cutting Motions and Chip Adhesion... 137 5.5 Concluding Remarks... 164 References...... 165 Erratum... E1 Appendix... 167 A.1 Basic Solution... 167 A.2 Stability and Bifurcation... 169 A.3 Machine-Tool Systems... 170 A.4 Closed-Form Solutions... 173 Index... 177