A New Analytical Path-Reshaping Model and Solution Algorithm for Contour Error Pre-Compensation in Multi-Axis Computer Numerical Control Machining

Abstract

Reduction of contour error is crucial for multi-axis computer numerical control (CNC) machining to produce products with required geometric and dimensional accuracy. Although various contour error pre-compensation methods have been developed, few studies are dedicated to five-axis machines when compared with three-axis ones. In this paper, a new contour error pre-compensation method that integrates analytical prediction of contour error, optimal path-reshaping model, and decoupling solution algorithm is proposed for five-axis machining. First, by analyzing the dynamic responses of servo drive to the typical step and ramp signals, linear expression of servo tracking error with respect to the sequence of discrete axis positions is yielded for the prediction of contour error ahead of servo loops. Then, using the Taylor-series expansion and the pseudo-inverse matrix of the Jacobian function, a least-square optimization-based path-reshaping model that implies the satisfaction condition of zero contour error is analytically built. Thus, the complicated nonlinear contour error pre-compensation problem is converted into a simple quadratic programming problem. Concerning the effects of tool orientation reshaping on tool-tip contouring accuracy, a simple yet effective synchronous compensation strategy is subsequently proposed, through which both tool tip and tool orientation contour errors are reduced to near-zero without any iteration. To address the neighbor-dependence of the contour error compensation in adjacent cutter locations, a progressive solution algorithm with linear computational complexity is also briefly presented. Both numerical simulations and laboratorial experiments are conducted to validate the effectiveness of the proposed method.