An Integrated Mathematical Model for Manufacturing Rotating Cutters with Constant Helical Angle

摘要

The paper presents an integrated mathematical model for producing a rotating cutter with constant helical angle. The principles of differential geometry and kinematics facilitate the development of correlative models of cutting-edge and helical groove. Based on the envelope condition, approaches for solving the inverse problems that related to the manufacturing models are also presented. The velocities of the cutter in the radial and axial directions are then derived based on the given rotating speed and gouging avoidance of grooves. A ball-end cutter with constant pitch helical grooves is selected for design and manufacture to illustrate the effectiveness of the proposed systematic design method by using 2-axis NC machine setup. The results of numerical experiment indicate that the proposed approaches are feasible and reliable.