Influence of geometric parameters on variation of motion during rolling process of involute spline

During the rolling process of involute spline with circular dedendum, the center distance between workpiece and spline rolling die gradually varies, and the tooth profile of workpiece is gradually formed. There is a notable variation of the angular velocity of workpiece or the transmission ratio between initial and late rolling stages. There is an interruption of motion between two forming stages in theory due to different curve meshing at different forming stage. The difference of transmission ratio at the interruption is defined as Δ. The difference Δ is independent on the motion parameters of spline rolling die, such as angular velocity and feed-in speed, but is dependent on the geometric parameters of workpiece and rolling die. The study indicated that teeth (Z_w) of spline/workpiece, pressure angle (α) of reference circle, addendum coefficient (ha∗) of spline/workpiece, dedendum coefficient (hf∗) of spline/workpiece and teeth (Z_d) of rolling die have an influence on the difference Δ , but only hf∗ and α present highly significant influence on difference Δ , and the other parameters have little influence.