Mathematical modeling and simulation of generation milling process to manufacture complex face gear surface through multi-axis machine kinematics

Abstract

Manufacturing of face gear is a complex process, due to its varying geometry, hence the application is not wide as conventional gear geometry. The developments in analytical tools and kinematics of the CNC machine tools motivate researchers to explore the manufacturing process and associated applications. This article presents an efficient method for the generation milling of spur face gear utilizing a nutating head multi-axis CNC machine tool where the tool swings about an arbitrary axis in an inclined plane. The mathematical model of the disk milling cutter and face gear geometry were derived from the shaper geometry by applying the theory of gearing, equation of meshing and coordinate transformation. The cutter location (CL) data was evaluated by aligning the tool orthogonal unit vector and the tooth surface normal vector at the contact point by calculating the appropriate transformation matrices. The evaluation of machine coordinates on a multi-axis CNC milling machine was analyzed with respect to the machine pivot point and the axes movement during generation milling for the face gear drive was studied on the nutating head machine. The NC data is derived from the CL data using the inverse kinematics and the machining simulation was carried out using suitable software. The tooth surface deviation of a maximum of 43.5 μm was observed between the simulated model and the theoretical model, which is well within the requirement of roughing. The generation milling process with the proposed machine configuration is concluded as a profound face gear manufacturing technique.