Analytical Prediction of the Critical Depth of Cut and Worst Spindle Speeds for Chatter in End Milling

The frequency response function (FRF) method has been well used to determine the worst spindle speeds and their critical limiting chip width for turning operation by finding the maximum negative real part of the FRF. In this study, a modified FRF concept is adapted for a 2 DOF milling system of planar isotropic dynamics to determine the worst spindle speeds and the critical limiting axial depth of cut in explicit, analytic formulas. Analogous to the formulation of worst spindle speeds, similar expression for the best spindle speeds is also obtained. The modified FRF is obtained by multiplying the original FRF of the structure with a complex scaling factor, corresponding to a scaling and a rotation of its original Nyquist plot. The scaling factor is determined analytically from the system characteristic equation with the radial cutting constant and radial immersion angle as the major system parameters. Through the presented method, it is also shown that the worst spindle speeds for a milling operation can be found without the prior knowledge of modal dynamics and stability lobe diagram. The proposed analytical expressions are confirmed by the existing stability models and experimentally verified.

[1]  Chia-Shang Liu,et al.  Analysis of chatter vibration in the end milling process , 1991 .

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

[3]  Jiří Tlustý,et al.  Manufacturing processes and equipment , 1999 .

[4]  Jon R. Pratt,et al.  Stability Prediction for Low Radial Immersion Milling , 2002 .

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

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

[7]  L. N. López de Lacalle,et al.  An automatic spindle speed selection strategy to obtain stability in high-speed milling , 2009 .

[8]  W. Book,et al.  Convolution Analysis of Milling Force Pulsation , 1994 .

[9]  Gábor Stépán,et al.  Multiple chatter frequencies in milling processes , 2003 .

[10]  Svetan Ratchev,et al.  Chatter modelling in micro-milling by considering process nonlinearities , 2012 .

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

[12]  Y. S. Tarng,et al.  The change of spindle speed for the avoidance of chatter in end milling , 1994 .

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

[14]  J. Tlusty,et al.  Stability Lobes in Milling , 1983 .

[15]  Junz Jiunn-jyh Wang,et al.  The Effect of Harmonic Force Components on Regenerative Stability in End Milling , 2003 .

[16]  Dirk Biermann,et al.  A general approach to simulating workpiece vibrations during five-axis milling of turbine blades , 2010 .

[17]  Yunn-Shiuan Liao,et al.  A new on-line spindle speed regulation strategy for chatter control , 1996 .

[18]  Zoltan Dombovari,et al.  Chatter stability of milling in frequency and discrete time domain , 2008 .

[19]  S. Smith,et al.  An Overview of Modeling and Simulation of the Milling Process , 1991 .

[20]  S. Smith,et al.  Stabilizing chatter by automatic spindle speed regulation , 1992 .

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