关键词: 成形磨削, 成形砂轮, 渐开线齿轮, 磨削误差, 拓扑修形, 优化

Abstract: Since the contact lines between grinding wheel and gear are dynamically changing for form grinding with additional radial motion of topologically modified gear, the calculated wheel profile based on any cross-section of gear will cause a larger grinding error. For reducing grinding error, a method to optimize the profile of grinding wheel is proposed. Firstly, the mathematical models to solve the profile of grinding wheel with additional radial parabolic trajectory is established based on the space engagement theory. Secondly, multiple equidistant plane is used to intercept the gear and to obtain a number of cross-sections for solving the wheel profiles represented with points corresponding to the cross-sections of gear; then a cloud of points is formed by projecting the wheel profiles to a plane, the fitting points of each interval obtained by dividing the cloud into equal intervals is solved based on the least square method, and connecting all the fitting points to form an optimal wheel profile. Given a formula of deviation between actual tooth profile and ideal profile, a mathematical model of gear tooth profile is established based on the meshing condition between wheel and gear to verify the grinding effect of grinding wheel. As an example of axial modified gear, wheel profile both the un-optimized and optimized are calculated, and the results show that the method can be used in the profile calculation of form grinding wheel and effectively reduce the grinding errors of topologically modified gear.

Key words: Form grinding, Grinding error, Grinding wheel, Involute gear, Optimization, Topologically modified