Abstract:

In this paper,first,a modified tooth surface was represented by a sum of two vector functions that deter-mined the theoretical tooth surface and the deviation surface,which was fitted by B- spline based on the tooth sur-face grid established by a profile and a longitudinal deviation curve.Next,according to the motion relationship be-tween the grinding wheel and the gear in the grinding process of helical gear,the wheel is formulated as B- splinecurves using a curve fitting technique by deducing the meshing equations.Then,a model of five- axis Free- FormCNC grinding machine was established and the kinematic relationships among the axes were derived based on the e-quivalence of wheel position vector.Moreover,an error correction model based on a sensitivity analysis was put for-ward,and each axis of the grinding machine was formulated as a six- order polynomial,and then a sensitivity analy-sis of disturbed polynomial coefficients on the topographic flank errors was carried out by estimating the wheel con-tact status.Finally,by using the minimum squared error as the objective function,kinematic parameters of the ma-chine 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 grindingerror effectively.

Key words: helical gear, topological modification, five- axis CNC grinding, Free- Form machine tool, forming wheel