An analytical method to calculate cutter-workpiece engagement based on arc-surface intersection method

The cutter-workpiece engagement (CWE) determination is an essential step in cutting force prediction, and it varies at each cutter location point. However, the calculation of CWE remains a challenge as a result of the complexity of freeform surface and tool movement in five-axis milling. An analytical method based on arc-surface intersection is presented in this paper. Based on the information of tool movement, feasible contact arc is obtained by splitting the cutter rotary surface into two parts. Tool swept surface of each tool path is constructed to avoid updating the in-process workpiece which is a time-consuming step in CWE extraction. And then, a torus patch approximation approach is adopted to speed up intersection calculation. All steps of the proposed method are realized by C++ program without activating any commercial software, which means this algorithm can be integrated into the cutting force model easily. Finally, experiments and application cases are carried out to illustrate the validity and effectiveness of the proposed method, and the comparison result shows that the computational efficiency has been improved about 40% in this paper.