Curvature interference characteristic analysis of offset involute cylindrical worm drive

Abstract

The theory of calculating the curvature interference limit line of the offset involute cylindrical worm drive based on the singular point condition on the enveloping surface is established. The tooth surface equations and the meshing function of the worm drive are derived. Based on the singular point condition that the normal vector of the enveloping surface is zero, the equation of the curvature interference limit line is obtained. By employing the resultant elimination method and the geometric construction, the existence of the solutions of the curvature interference limit line is determined, and the reasonable initial values for the iteration program are afforded. The numerical outcomes show that there is one meaningful curvature interference limit line on each flank of single tooth of the worm gear, which usually does not enter the worm gear tooth surface. Both flanks of the worm gear are all settled in the side of the limit line, the curvature interference does not happen on the worm gear tooth surface. The undercutting of the cutting engagement process generally does not happen. The results also reveal that the curvature interference limit line is closer to the addendum and heel of the face worm gear on the i flank, which has the greatest potential venture inflict the undercutting.