Contact and elastohydrodynamic analysis of worm gears Part 1: Theoretical formulation

Abstract

The paper presents the theoretical basis for modelling the contact conditions and elastohydrodynamic lubrication (EHL) of worm gears, the results of which are presented in Part 2. The asymmetric elongated contact that typifies worm gears is non-Hertzian and is treated using a novel three-dimensional elastic contact simulation technique. The kinematic conditions at the EHL contact are such that the surfaces have a slide-roll ratio equal to almost 2, and the sliding direction varies over the contact area. These considerations require a non-Newtonian, thermal analysis, and the appropriate form of a novel Reynolds equation is developed that can incorporate any form of the non-Newtonian relationship between shear stress and strain rate. A form that incorporates both limiting shear stress and Eyring shear thinning is utilized in which the two effects can be included both singly or together.