In this study, a solution technique based on a discrete time approach is presented to the stability problem for the variable spindle speed face-milling process. The process dynamics are described by a set of differential-difference equations with time varying periodic coefficients and time delay. A finite difference scheme is used to discretize the system and model it as a linear time varying (LTV) system with multiple time delays. By considering all the states over one period of speed variation, the infinite dimensional periodic time-varying discrete system is converted to a finite dimensional time-varying discrete system. The eigenvalues of the state transition matrix of this finite dimensional system are then used to propose criteria for exponential stability. Predicted stability boundaries are compared with lobes generated by numerical time-domain simulations and experiments performed on an industrial grade variable speed face-milling testbed.
Chatter Stability Analysis of the Variable Speed Face-Milling Process
Contributed by the Manufacturing Engineering Division for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received July 1999; revised June 2000. Associate Editor: K. Ehmann.
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Sastry, , S., Kapoor, , S. G., DeVor, and , R. E., and Dullerud , G. E. (June 1, 2000). "Chatter Stability Analysis of the Variable Speed Face-Milling Process ." ASME. J. Manuf. Sci. Eng. November 2001; 123(4): 753–756. https://doi.org/10.1115/1.1373649
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