CNC grinding machining of topologically modified helical gear

In this paper, first, a modified tooth surface was represented by a sum of two vector functions that determined the theoretical tooth surface and the deviation surface, which was fitted by B-spline based on the tooth surface grid established by a profile and a longitudinal deviation curve. Next, according to the motion relationship between the grinding wheel and the gear in the grinding process of helical gear, the wheel is formulated as B-spline curves using a curve fitting technique by deducing the meshing equations. Then, a model of five-axis Free-Form CNC grinding machine was established and the kinematic relationships among the axes were derived based on the equivalence of wheel position vector. Moreover, an error correction model based on a sensitivity analysis was put forward, and each axis of the grinding machine was formulated as a six-order polynomial, and then a sensitivity analysis of disturbed polynomial coefficients on the topographic flank errors was carried out by estimating the wheel contact status. Finally, by using the minimum squared error as the objective function, kinematic parameters of the machine tool are obtained via the PSO optimization. The results show that the five-axis CNC grinding machining, which is based on the back calculation of grinding wheel section with modified tooth surface, decreases the grinding error effectively.