Cutting force prediction considering tool path curvature and torsion based on screw theory

There are common features such as the tool path curvature and torsion, and cutter-orientation change in sculptured surface machining, which bring new challenges to the accurate prediction of cutting force. Aiming at the tool path curvature and torsion, and cutter-orientation change, a cutting force prediction method based on the screw theory is proposed in this paper. For the first time, the screw theory is used to describe the cutter spatial motion, which includes the feed motion considering the tool path curvature and torsion, and cutter-orientation change. Combining with Frenet frame, the analytical formula of the screw of cutting edge elements is derived through the homogeneous coordinate transformation. Then, the instantaneous uncut chip thickness (IUCT) of each cutting edge element is calculated by the vector projection method. And the cutting state of the cutting edge element is determined by its IUCT and position relative to the workpiece surface, which is updated by the cutter envelope surface along the machined tool path derived with the screw. To verify the effectiveness of the proposed cutting force prediction method, a milling experiment is conducted on a conical surface workpiece along a tool path with curvature and torsion characteristics, and changing cutter-orientations. Then, the effects of the tool path curvature and torsion, and cutter-orientation change on the cutting force are simulated and analyzed. The results show that the proposed cutting force model based on the screw theory has higher prediction accuracy for the sculpture surface machining with curving and torsional tool paths and changing cutter-orientations.