Curvature interference characteristic of conical worm gear

The primary objective of this article is to establish the computing theory to investigate the curvature interference characteristic of the conical worm gear of a conical surface enveloping conical worm gearing. The tooth surface equations, the meshing function, the curvature interference limit function of the conical worm gearing and so on, are all derived strictly. An approach to compute the curvature interference limit line is proposed according to the elimination and geometric construction. This method can be utilized to judge the existence of the limit line and can also provide the reasonable guess value for the following iteration. The solution domain of the limit line should be roughly identical to that of the conjugated zone of the worm gearing. The numerical results show that there is one significative limit line on each flank of one tooth of the gear, which generally does not enter into the gear tooth surface. The two flanks of the worm gear are all located on the non-curvature-interference side of the limit line. Therefore, the undercutting of the gear seldom takes place. Nevertheless, the limit line on the concave tooth surface is nearer to its toe. The influences of main designing parameters on the curvature interference limit line are analyzed systematically, and the obtained results indicate that the toe and the dedendum of the worm gear concave tooth surface have the greatest potential hazard to be undercut.