Manufacturing Principle and Meshing Limit Line of Toroidal Surface Enveloping Cylindrical Worm Drive with Arc-Toothed Worm

The main purpose of this article is to determine the processing parameters of the worm and establish the theory of the meshing limit line of toroidal surface enveloping cylindrical worm drive with the arc-toothed worm. Based on this condition that the instantaneous contact line is a planar curve during grinding the worm blank, it can be deduced that its torsion is equal to zero, then the formulae which determine the installing position of the grinding wheel are acquired. Following this, the equations of the tooth surfaces and the meshing limit function are all obtained. According to the geometric construction and elimination method, the meshing limit points are determined by iteratively solving the corresponding nonlinear equation in its solution domain. In addition, the result of the numerical case demonstrates that the worm helicoid is divided into two parts by the meshing limit line, which makes the working length of the worm cannot reach half of its total thread length. And by adjusting the design parameters of the worm pair and the processing parameters of the worm, the meshing limit line cannot be eliminated and its position on the surfaces of the worm and the worm gear has no notable change.