Explanation for low-speed stability increases in machining: Application of a continuous delay model

This paper investigates the analysis of delay integro-differential equations to explain the increased stability behavior commonly observed at low cutting speeds in machining processes. In the past, this improved stability has been attributed to the energy dissipation from the interference between the workpiece and the tool relief face. In this study, an alternative physical explanation is described. In contrast to the conventional approach, which uses a point force acting at the tool tip, the cutting forces are distributed over the tool-chip interface. This approximation results in a second order delayed integro-differential equation for the system that involves a short and a discrete delay. A method for determining the stability of the system for an exponential shape function is described, and temporal finite element analysis is used to chart the stability regions. Comparisons are then made between the stability charts that use the conventional point force and those that use the distributed force model for continuous and interrupted turning.Copyright © 2008 by ASME

[1]  Steven Y. Liang,et al.  Chatter stability of a slender cutting tool in turning with tool wear effect , 1998 .

[2]  E. B. Magrab,et al.  Improved Methods for the Prediction of Chatter in Turning, Part 2: Determination of Cutting Process Parameters , 1990 .

[3]  R. L. Kegg,et al.  An Explanation of Low-Speed Chatter Effects , 1969 .

[4]  D. W. Jordan,et al.  Nonlinear ordinary differential equations : an introduction to dynamical systems , 1999 .

[5]  G. Stépán.  Retarded dynamical systems : stability and characteristic functions , 1989 .

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

[7]  Krzysztof Jemielniak,et al.  Numerical simulation of non-linear chatter vibration in turning , 1989 .

[8]  N. K. Chandiramani,et al.  Dynamics of 2-dof regenerative chatter during turning , 2006 .

[9]  Yung C. Shin,et al.  A comprehensive chatter prediction model for face turning operation including tool wear effect , 2002 .

[10]  D. William Wu,et al.  Application of a comprehensive dynamic cutting force model to orthogonal wave-generating processes , 1988 .

[11]  Gábor Stépán,et al.  Lobes and Lenses in the Stability Chart of Interrupted Turning , 2006 .

[12]  Nathan H. Cook,et al.  Self-Excited Vibrations in Metal Cutting , 1959 .

[13]  Y. S. Tarng,et al.  An analytical model of chatter vibration in metal cutting , 1994 .

[14]  Y. S. Tarng,et al.  Modeling of the process damping force in chatter vibration , 1995 .