Prediction of cutting force in ball-end milling of sculptured surface using improved Z-map

Abstract

This paper presents an approach for prediction of cutting forces in three-axis ball-end milling of a sculptured surface along an arbitrary tool path. The idea of differentiation is adopted to deal with the problems of varying feed direction, varying cutter engagement, and the consequent varying cutting forces in sculptured surface machining. Based on the differential idea, the whole process of sculptured surface milling is discretized at intervals of feed per tooth, and each segmented process is considered as a small steady-state cutting. For the discrete cuttings, mathematical models of feed turning angle and feed inclination angle are proposed according to the position of start/end points. By using an improved Z-map method, the detailed algorithms of determining the cutter–workpiece interface and the instantaneous in-cut edge segment for sculptured surface machining are suggested. A new integrative chip thickness model which involves the effects of feed turning angle, feed inclination angle, and cutter engagement is also presented. In validation experiment, two practical examples of a sculptured surface three-axis ball-end milling with arbitrary tool path are operated. Comparisons of the predicted cutting forces with the measurements show the effectiveness of the proposed approach.