A general mathematical model for two-parameter generating machining of involute cylindrical gears

Abstract

• A general mathematical model for two-parameter generating machining of involute gears is developed. • A general discrete assisted model for two-parameter generating machining is proposed. • The instant contact line is derived by implicated information during discrete enveloping. • The engaged cutting edge segments can be distinguished when multiple-cutting edge are adopted. Instead of the common analytical model for involute gears machining, a general mathematical model for two-parameter generating machining is developed in this study with adopting discrete enveloping to increase its robustness and generality for machined profile calculation and instant contact analysis. The geometric parameters and motion relationships are integrated according to the cross-axis gear meshing at first, and the enveloping theory for two-parameter generating process is analyzed briefly with involving middle gear rack. By transforming the multiple cutting edges relative to the gear blank according to the generating motions, a numerical algorithm is proposed to distinguish the external enveloping profile on the shaft section, then the derivation of instant contact points via the implied time sequences of profile points is introduced. Finally, the coordinate transformations for the spatial trajectory of instant contact points identifying and the engaged cutting edge segments distinguishing are investigated. At last, a non- involute profile skiving is performed to verify the generality and the robustness of proposed method, and several typically generating machining operations for cylindrical involute gear are simulated numerically to proof the accuracy of the proposed model by finding the deviations from the standard involute curves and the geometries of the instant contact points.