Mathematical modelling of power skiving for general profile based on numerical enveloping

Power skiving is an effective generating machining method for internal parts like gears with respect its high productivity. The general mathematic modelling for power skiving is the basis for cutting tools design, machining precision evaluation, and machining process optimization. Currently, mainly studies are focus on the involute gear machining with adopting the analytical enveloping equation. However, these analytical methods have failed to deal with overcutting for general profile skiving tasks. Moreover, little attention has been devoted to investigate the power skiving process with taking variable configuration parameters, which is significant to control the machined surface topography. Herein, we introduce a mathematic modelling method for power skiving with general profile based on the numerical discrete enveloping. Firstly, the basic mathematic model of power skiving is established, in which the center distance is formulated as polynomial of time. By transforming the power skiving into a forming machining of the swept volume of cutting edge, a numerical algorithm is designed to distinguish the machined transverse profile via the discrete enveloping ideology. Especially, the precise instant contact curve is extracted according to the feed motion speed inversely. Finally, simulations for involute gear and cycloid wheel are carried out to verify the effectiveness of this method and investigate the influence of variable radial motions on the machined slot surface topography. The results validate capability of this method on simulate the dynamic power skiving process for general desire profiles and evaluate the machined results.