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

The paper presents the theoretical basis for modelling the contact conditio ns and elastohydrodynamic lubrication (EHL) of worm gears, the results of w hich are presented in Part 2. The asymmetric elongated contact that typifie s 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 considerat ions require a non-Newtonian, thermal analysis, and the appropriate form of a novel Reynolds equation is developed that can incorporate any form of th e non-Newtonian relationship between shear stress and strain rate. A form t hat incorporates both limiting shear stress and Eyring shear thinning is ut ilized in which the two effects can be included both singly or together.