A contact stress capacity model for cylindrical wormsets

Abstract

A contact stress capacity expression is derived for cylindrical worm sets by considering the worm as a helical rack mating with a helical gear. The concept of the equivalent spur gear for a helical gear defined by the instantaneous radius of curvature in the virtual plane of the helical gear is utilized in the contact stress capacity model formulation. All the basic design parameters of worm and gear are incorporated in the expression which explicitly shows the influence of the base and nominal helix angles on the contact stress. By considering the geometry of the worm and gear in engagement, active gear face width and active threaded length of the worm are defined and used to estimate load sharing among gear teeth. This allows the interaction of motion and forces in wormset meshes to be captured by a semi-empirical factor, an aspect not previously considered. The new model also accounts for multiple threaded worms which seem not to have been treated till now. The service load factor expression for cylindrical gears is modified for wormsets to take account of different worm thread profile designs and mesh friction. Four illustrative examples of contact stress computations are carried out using the new contact stress capacity model for wormset designs from different references. The contact stress estimates from the new model are compared with previous solution values. The estimated percentage variances between the previous and new model values are within the range of -4.5% to 0.3%. These variances indicate excellent to a very favorable comparison that should inspire some confidence in using the new model for preliminary design tasks of cylindrical wormsets.