Short-Time Acceptance Test for Machine Tools Based on the Random Nature of the Cutting Forces

Abstract

A short-time dynamic acceptance test for machine tools based on a single measurement of a coefficient of dynamic stiffness (Kd ) is proposed. A feature of this test is that it takes into account the random fluctuation of the cutting forces that will be experienced by the machine tool in actual operation. Kd is defined as the inverse of the standard deviation of the steady state translational dynamic response of the machine tool under these cutting forces and is a function of the static stiffness of the machine-tool-workpiece system, the damping in the machine, and the equivalent intensity coefficient of the random cutting forces. The analytical expression for the coefficient Kd is obtained from the stationary solution of the Fokker-Planck equation that describes the probabilistic response of the machine tool. The form of excitation considered in the final results is the equivalent “white-noise” spectral density of the ensemble of the cutting forces experienced by the particular machine over the range of feed rates and cutting speeds during operations such as roughing, finishing, etc.