Reconsideration of Hamrock-Dowson Formula for Elliptic Contact Elastohydrodynamic Lubrication

Hamrock-Dowson formula is commonly used to calculate the central film thickness of elliptical contact EHL. It is found that when the Hertz pressure at the contact center is maintained as a constant and the ellipticity ratio k_e is larger than a critical value, the central film thickness obtained would decrease instead of rise, which is contrary to its physical essence. Numerical calculation on isothermal elliptic contact elastohydrodynamic lubrication was carried out using finite element method and a new comprehensive geometric parameter was proposed to characterize the elliptic contact. Based on the numerical results, a modified side leakage factor and a modified central film thickness formula were obtained under a large range of speeds and loads. The modified formula was in agreement with the numerical results, and the relation between film thickness and elliptic ratio was given correctly.