Theoretical and Experimental Studies of Chatter in Turning for Uniform and Stepped Workpieces

This paper presents a method for predicting regenerative chatter onset conditions for uniform and stepped workpieces. The lateral deflections of flexible workpieces are modeled using the Timoshenko beam theory and three-node beam finite elements. The modal summation method is employed in conjunction with an adaptive remeshing scheme to determine the varying natural frequencies and varying mode shapes of workpieces during a cutting process, and to reduce the system equations of motion in terms of nodal variables to coupled equations of motion in terms of the modal coordinates. Various simulations were conducted and presented in this paper for understanding the gyroscopic and cross-coupling effect, and effects of other system and cutting process parameters on chatter onset conditions. Six experiments were carried out on an engine lathe for three uniform and three stepped workpieces to verify the theoretical chatter onset conditions. Good agreement in chatter onset conditions was observed between the simulations and the experiments.

[1]  C. K. Chen,et al.  A stability analysis of turning a tailstock supported flexible work-piece , 2006 .

[2]  Mohamed A. Elbestawi,et al.  Model-Based Predictive Control of Workpiece Accuracy in Bar Turning , 1998 .

[3]  G. Stépán,et al.  State-dependent delay in regenerative turning processes , 2006 .

[4]  K. Bathe.  Finite Element Procedures , 1995 .

[5]  Erhan Budak,et al.  Analytical modeling of spindle-tool dynamics on machine tools using Timoshenko beam model and receptance coupling for the prediction of tool point FRF , 2006 .

[6]  Etsuo Marui,et al.  Chatter Vibration of Lathe Tools. Part 1: General Characteristics of Chatter Vibration , 1983 .

[7]  Keith E. Rouch,et al.  Use of finite element structural models in analyzing machine tool chatter , 2002 .

[8]  Martin Hosek,et al.  A new perspective and analysis for regenerative machine tool chatter , 1998 .

[9]  H. E. Merritt.  Theory of Self-Excited Machine-Tool Chatter: Contribution to Machine-Tool Chatter Research—1 , 1965 .

[10]  Yung C. Shin,et al.  A comprehensive dynamic cutting force model for chatter prediction in turning , 1999 .

[11]  Cha'o-Kuang Chen,et al.  A stability analysis of regenerative chatter in turning process without using tailstock , 2006 .

[12]  M. Schill.  A critical study of the ``radiation condition'' for longitudinal waves in a damped semi-infinite bar supported by an ambient medium , 1988 .

[13]  Ming Une Jen,et al.  The Dynamic Interaction of the Cutting Process, Workpiece, and Lathe’s Structure in Facing , 1996 .

[14]  S. Kato,et al.  On the Cause of Regenerative Chatter Due to Workpiece Deflection , 1974 .

[15]  Yung C. Shin,et al.  A new procedure to determine instantaneous cutting force coefficients for machining force prediction , 1997 .

[16]  A. Galip Ulsoy,et al.  THE DYNAMIC-RESPONSE OF A ROTATING SHAFT SUBJECT TO A MOVING LOAD , 1988 .

[18]  Gábor Stépán,et al.  Modelling nonlinear regenerative effects in metal cutting , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[19]  S. A. Tobias.  Machine-tool vibration , 1965 .

[20]  R. P. Han,et al.  Natural frequencies and normal modes of a spinning timoshenko beam with general boundary conditions , 1992 .

[21]  John S. Agapiou,et al.  Metal Cutting Theory and Practice , 1996 .

[22]  Yusuf Altintas,et al.  Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design , 2000 .

[23]  S. A. Tobias.  Vibration of machine tools , 1964 .

[24]  Chun Liu,et al.  An Analytical Model of Cutting Dynamics. Part 1: Model Building , 1985 .