Experimental and Theoretical Study of Distributed Delay in Machining

Abstract In this work, an experimental and theoretical studies are given for the well-known process damping effect arisen in turning processes. This effect generally pushes the stability chart (lobes) to higher depth of cuts in low spindle speed domain and causes difficulties to predict the stability of stationary cutting (equilibrium of the process). The orthogonal cutting model presented and investigated here contains distributed delays due to the cutting force distribution on the rake face. The paper presents measurement set up to create and to track the oscillating cutting force for the identification of the model parameters. An extended model also investigated that explains the experimental observations.

[1]  M. E. Merchant Mechanics of the Metal Cutting Process. I. Orthogonal Cutting and a Type 2 Chip , 1945 .

[2]  Emily Stone,et al.  Investigations of Process Damping Forces in Metal Cutting , 2005, ArXiv.

[3]  Yusuf Altintas,et al.  Analytical Prediction of Stability Lobes in Milling , 1995 .

[4]  Tamás Kalmár-Nagy,et al.  Subcritical Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations , 2001 .

[5]  B. Mann,et al.  Stability of Interrupted Cutting by Temporal Finite Element Analysis , 2003 .

[6]  Yusuf Altintas,et al.  Multi frequency solution of chatter stability for low immersion milling , 2004 .

[7]  Gábor Stépán,et al.  Semi‐discretization method for delayed systems , 2002 .

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

[9]  Jon Rigelsford,et al.  Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design , 2004 .

[10]  R. E. Wilson,et al.  Estimates of the bistable region in metal cutting , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[11]  R. L. Kegg,et al.  Cutting Dynamics in Machine Tool Chatter: Contribution to Machine-Tool Chatter Research—3 , 1965 .

[12]  Yusuf Altintas,et al.  Identification of dynamic cutting force coefficients and chatter stability with process damping , 2008 .

[13]  Gábor Stépán,et al.  State Dependent Regenerative Delay in Milling Processes , 2005 .

[14]  Francis C. Moon,et al.  Dynamics and chaos in manufacturing processes , 1998 .

[15]  Gábor Stépán,et al.  Criticality of Hopf bifurcation in state-dependent delay model of turning processes , 2008 .

[16]  Yusuf Altintas,et al.  Analytical Prediction of Chatter Stability in Milling—Part I: General Formulation , 1998 .

[17]  Paul Albrecht,et al.  Dynamics of the Metal-Cutting Process , 1965 .

[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]  Gbor Stpn Modelling nonlinear regenerative effects in metal cutting , 2001 .

[20]  T. Insperger,et al.  Analysis of the Influence of Mill Helix Angle on Chatter Stability , 2006 .

[21]  C. Andrew,et al.  Machining Forces: Some Effects of Tool Vibration: , 1965 .

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