Meshing limit line of the conical surface enveloping conical worm pair

Abstract

In this study, the calculating principle of the meshing limit line of the conical surface enveloping conical worm pair is put forward systematically. The tooth face equations, the meshing function and the meshing limit function of a conical worm pair are all acquired. Investigating the meshing limit line is come down to solving an equivalent unary nonlinear equation, which is determined from its original equations with four variables by means of the elimination technique. Based on this, the meshing limit line characteristics are deeply researched after resolving preceding equation correctly. The numerical results declare that there may be two meshing limit lines on each helicoid of one tooth of an enveloping conical worm although not all of them have physical significance. All the significative meshing limit lines usually do not get into the worm helicoid and have no influence on its normal work. Therefore, the active length of the worm depends on the tooth face boundary of the conical worm wheel theoretically. Besides, when the center distance of the worm pair is less, the transmission ratio is larger and the number of thread of the worm is more, the meshing limit line may be closer to the little end of the conical worm e helicoid.