Prediction of cutting forces along Pythagorean-hodograph curves

This paper proposes a new approach to predicting cutting forces in milling operations. The approach attempts to find the analytic relationship between cutting forces and the tangential direction of the tool path when a tool moves along an analytical curve, i.e., a Pythagorean-hodograph curve that describes a group of analytic curves with special properties, in a milling operation. In conventional methods for the prediction of cutting forces in milling operations, cutting forces are estimated by considering such cutting parameters as feed rate, depth of cut, and tool geometry. However, the change in the moving direction of the cutter, which has a major effect on cutting forces, is often neglected by previous researchers. This work aims to establish the theoretical basis to show how cutting forces along a curve can be predicted. Two case studies are used to illustrate the proposed cutting force prediction strategy.