Optimization on Motion Errors of Ultra-Precision Machine Tools Based on Multi-Body System and Monte Carlo Simulation

Abstract

Numerical optimization method is increasingly applied into the design of machine tools so as to improve their performance. This paper employs Monte Carlo optimization method to predict and reduce the errors of ultra-precision machine tools in term of motion errors between cutting tool and workpiece closely associated with machine processing of ultra-precision machine tools. Using a quite different origin position of location coordinate system from traditional in that every ideal frame on current body is coincided with the reference actual one on the adjacent body, the motion errors are expressed in homogeneous matrix defined with adjacent bodies’ residuals in multi-body system analysis. This expression clearly shows that the final position errors are decided by the motion accuracy of the guideline, and gesture errors are affected by accuracy of the spindle assembly. With geometric errors extracted from the matrix, a new optimization method of error allocation is presented to maximize the machine precision by reasonable distribution of tolerances key parts. Using variables intimately related to motion errors and under constrained by cost, optimization model is established, then it is solved with Monte Carlo simulation method to compute top ten key factors contributed to errors and obtain distribution probabilities of both position error and gesture error. Case study formulated is reported to illustrate the method proposed and to evaluate its effectiveness.