Abstract: The method to use Hertz Formula to caculate the contact stress of toroidal wormwheel is put forward. To divide contact lines into countless mini sections, on each of which, Hernz Formular is used. By using integral calculus along the contact line, the relationship between the strength of worwheel surface and force against it is found out. Based on the configuration characteristics of worm pair and space engagement theory, the formulars of contact stress at wormwheel surface are calculated, each of which includes characteristic and geometry parameters of wormwheel, so that maths relationship with contact stress is clearly stated. To understand the rule, improve worm pair working conditions and increase its life, a scientific basis is provided. Meanwhile according to the specialty of project design, the formulars are simplified. Practical formulars for calculaating and checking fatigue strength and working life of wormwheel are set up. The relavant coefficients resulted from various calculation has made it special to calculate carrying capacity and working life of totoidal worm pair. The application of the educed formulars is successful to calculate the carrying capacity of the wormwheel compared with column worm pair.

Key words: Fatigue strength, Toroidal worm