Milling stability analysis with simultaneously considering the structural mode coupling effect and regenerative effect

Abstract Machining stability analysis is important for chatter avoidance and machining efficiency improvement. To accurately predict the stability, the chatter mechanism must be recognized. Chatter is a kind of self-excited vibrations and the two most widely used theories explaining chatter in milling are the regenerative effect and the mode coupling effect. However, these two mechanisms are always separately considered in the previous stability researches, and none of them can explain the great difference between the stability prediction results with the classical model and the experimental results in many cases. This paper investigates the structural mode coupling effect in the regenerative milling stability analysis. Based on lots of experimental data, we found that these two mechanisms actually co-exist during the practical milling process, and the usually neglected structural mode coupling effect has a great effect on the stability lobe diagram in many practical milling cases. The theoretical prediction taking the cross coupled terms into account alters the stability boundary and such prediction is verified by the chatter experimental results.

[1]  F. Ismail,et al.  Machining chatter of end mills with unequal modes , 1990 .

[2]  T. Caughey,et al.  Classical Normal Modes in Damped Linear Dynamic Systems , 1960 .

[3]  J. Tlusty,et al.  Dynamics of High-Speed Milling , 1986 .

[4]  K. Foss COORDINATES WHICH UNCOUPLE THE EQUATIONS OF MOTION OF DAMPED LINEAR DYNAMIC SYSTEMS , 1956 .

[5]  T. Schmitz,et al.  Closed-form solutions for surface location error in milling , 2006 .

[6]  Han Ding,et al.  Numerical Integration Method for Prediction of Milling Stability , 2011 .

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

[8]  Hui Zhang,et al.  Chatter analysis of robotic machining process , 2006 .

[9]  Miklós Farkas,et al.  Periodic Motions , 1994 .

[10]  P. Lancaster On eigenvalues of matrices dependent on a parameter , 1964 .

[11]  Richard E. DeVor,et al.  The effect of runout on cutting geometry and forces in end milling , 1983 .

[12]  Yusuf Altintas,et al.  An Improved Time Domain Simulation for Dynamic Milling at Small Radial Immersions , 2003 .

[13]  Alessandro Gasparetto,et al.  A System Theory Approach to Mode Coupling Chatter in Machining , 1998 .

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

[15]  William Benjamin Stewart Ferry Virtual five-axis flank milling of jet engine impellers , 2008 .

[16]  A. Galip Ulsoy,et al.  Analysis of a System of Linear Delay Differential Equations , 2003 .

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

[18]  Tony L. Schmitz,et al.  Runout effects in milling: Surface finish, surface location error, and stability , 2007 .

[19]  Marian Wiercigroch,et al.  Sources of nonlinearities, chatter generation and suppression in metal cutting , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[20]  Alessandro Gasparetto,et al.  Eigenvalue Analysis of Mode-Coupling Chatter for Machine-Tool Stabilization , 2001 .

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

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

[23]  Jon R. Pratt,et al.  The Stability of Low Radial Immersion Milling , 2000 .

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

[25]  Gábor Stépán,et al.  On stability prediction for milling , 2005 .

[26]  Tony L. Schmitz,et al.  A Robust Semi-Analytical Method for Calculating the Response Sensitivity of a Time Delay System , 2008 .

[27]  A. Galip Ulsoy,et al.  Delay differential equations via the matrix Lambert W function and bifurcation analysis: application to machine tool chatter. , 2007, Mathematical biosciences and engineering : MBE.

[28]  Yusuf Altintas,et al.  Prediction of Milling Force Coefficients From Orthogonal Cutting Data , 1996 .

[29]  Tony L. Schmitz,et al.  Bivariate uncertainty analysis for impact testing , 2007 .

[30]  Gilles Dessein,et al.  Surface roughness variation of thin wall milling, related to modal interactions , 2008 .

[31]  John W. Sutherland,et al.  An Improved Method for Cutting Force and Surface Error Prediction in Flexible End Milling Systems , 1986 .

[32]  Han Ding,et al.  A full-discretization method for prediction of milling stability , 2010 .

[33]  G. Boothroyd,et al.  Fundamentals of machining and machine tools , 2006 .

[34]  L. Gaul,et al.  Effects of damping on mode‐coupling instability in friction induced oscillations , 2003 .

[35]  I. E. Minis,et al.  A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling , 1993 .

[36]  Balakumar Balachandran,et al.  Nonlinear dynamics of milling processes , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[37]  Gábor Stépán,et al.  Updated semi‐discretization method for periodic delay‐differential equations with discrete delay , 2004 .

[38]  Paolo Gallina,et al.  On the stabilizing and destabilizing effects of damping in wood cutting machines , 2003 .

[39]  Aitzol Iturrospe,et al.  State-space analysis of mode-coupling in orthogonal metal cutting under wave regeneration , 2007 .

[40]  S. Smith,et al.  Efficient simulation programs for chatter in milling , 1993 .

[41]  Yusuf Altintas,et al.  Chatter Stability in Turning and Milling with in Process Identified Process Damping , 2010 .

[42]  Eric A. Butcher,et al.  Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels , 2009 .

[43]  J. Tlusty,et al.  Basic Non-Linearity in Machining Chatter , 1981 .