Dynamic Acceptance Test for Machine Tools Based on a Nonlinear Stochastic Model

Abstract

A nonlinear two-degree-of-freedom mathematical model of a general machine tool is considered for describing the responses in translational and rotational modes under the action of the actual randomly fluctuating metal cutting forces in a Gaussian, wide band form. The response process is determined by the Fokker-Planck technique for the simplified case and also by the statistical linearization method for the general case to establish accuracy of the results obtained. Based on the variances of the response derived and the system constants, a dynamic stiffness coefficient Kd is proposed for defining the degree of acceptance of a given machine tool under actual cutting conditions. Numerical results for specific examples are provided for purpose of illustration.