A generalized meshing analysis method and its application to toroidal surface enveloping conical worm drive

A generalized method for the meshing analysis of conical worm drive is proposed, whose mathematical model is more general and whose application scope is expanded. A universal mathematical model, which can be conveniently applied to left-handed and right-handed conical worm pairs and their tooth flanks on different sides, is established by introducing the helical spin coefficient and tooth side coefficient of the conical worm. The pressure angle at the reference point, which is a key parameter for calculating the curvature parameters and lubrication angle, is determined based on the unit normal vector of the worm helical surface and is no longer determined by the tooth profile angle in the worm shaft section. The above improvement breaks away from the limitation of the classic meshing analysis method based on the reference-point-based meshing theory and thus expands its application scope. The toroidal surface enveloping conical worm drive is taken as an instance to illustrate the proposed method and the numerical example studies are conducted. The approaches to determine the reference point, the normal unit vector, and the curvature parameters at the reference point are all demonstrated in detail. The numerical results all manifest that the method presented in the current work is correct and practicable.

Meshing limit line of the conical surface enveloping conical worm pair

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.

Influence of grinding wheel parameters on the meshing performance of toroidal surface enveloping conical worm drive

A new type of toroidal surface enveloping conical worm gearing is proposed in our recent work (Chongfei and Yaping, 2019b). According to its forming principle, the geometrical shape of the generating surface has an important influence on the geometry characteristic of the enveloping worm pair. To explore the reasonable principles for selecting the geometrical parameters of the grinding wheel, some numerical study examples are performed. In this process, the methods for the tooth crest width are developed. Simple strategies for estimating the risk of the worm tooth surface being located in the invalid area and the risk of the curvature interference on the tooth surface are proposed. The numerical result shows that increasing the radius of the toroidal-generating surface and the nominal pressure angle of the grinding wheel are beneficial to improve the engagement behavior of the conical worm pair, but the tooth crest sharpening of the conical worm may happen if they are too large. For the nominal radius of the grinding wheel, it has a negligible effect on the meshing characteristics of this worm set. In addition, the selection principle of the parameters is also suggested.