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

A short-time dynamic acceptance test for machine tools based on a single measurement of a coefficient of dynamic stiffness (K_d) 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. K_d 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 K_d 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.