Meshing theory of toroidal surface enveloping cylindrical worm drive with arc-toothed worm

This paper aims to establish a rich and complete meshing theory of the toroidal surface enveloping cylindrical worm drive with arc-toothed worm and obtain the meshing performance of the proposed worm drive. The arc-toothed worm is machined by a disc-shaped grinding wheel whose formulae of the installation position parameters are determined according to differential geometry. The characteristic of the contact line on the worm helicoid during cutting engagement is analyzed by establishing the Frenet frame. Then the relative motion model and some important results of the worm pair are acquired using the meshing theory of gearing. Based on this, the locus features of the knot of meshing are analyzed in different coordinate systems. In addition, the meshing points which determine the conjugated zone and instantaneous contact lines are classified according to their different positions on the tooth surface of the worm gear. Utilizing the methods of eliminating and geometric construction, the nonlinear equations are solved. Finally, a numerical example is implemented and the result shows the proposed worm drive has favorable meshing performance.