A Novel Formula for Instantaneous Coefficients of Sliding Friction in Gearing

Gear tooth friction directly influences power losses and temperature rise as well as system dynamic behavior. Recently it attracted many attentions as friction is considered one of the main sources of power losses in geared systems, such as in automotive transmissions. Coefficient of friction has been found not a constant but varies with different contact conditions, which partly makes the measurement of friction a difficult and expensive process. Therefore an analytical model that is capable of predicting it accurately becomes very much demanded. A few empirical formulae based on experimental data and analytical models based on lubrication theory are found in the literature. However, they are either not suitable for a general gear contact or too complex to adapt in gearing. In this paper, a new coefficient of sliding friction based on a thermal Elastohydrodynamic Lubrication (EHL) model is developed by a multiple linear regression analysis. This formula retains reasonable accuracy from sophisticated EHL analyses, eliminates the complexity and computational time in EHL modeling, but also overcomes major shortcomings of many existing empirical formulae. Parametric studies are performed based on the new formula to highlight how coefficient of friction varies as a function of dependent variables.