Film thickness prediction in elastohydrodynamically lubricated elliptical contacts

Abstract

This paper analyses the minimum and central film thickness evolution of elastohydrodynamically lubricated contacts, from circular to wide elliptical contacts. It is shown that already for moderate ellipticity, the minimum film thickness is found on the centre-line of the contact, rather than in the side lobes as for the circular contact. In such cases, the film thickness can be accurately predicted from an equivalent line contact, defined as the line contact with the same Hertzian pressure, radius of curvature, and speed and oil parameters. In this paper, a formula is presented to predict the central film thickness in elliptical contacts using prediction formulas for the line and circular contacts as limiting cases, and the results of numerical calculations to fit the film thickness variation with ellipticity. The formula gives an accurate prediction of the central film thickness over the entire ellipticity regime.

Film Thickness in Slender Elliptic Contacts: Part I - Numerical Studies of Central Film Thickness

“…Following the pioneer work of Hamrock and Dowson [5] in 1977, many more analytical film thickness formulas for point and elliptic contacts were derived [10][11][12][21][22][23][24][25]. A comprehensive overview is given by Marian et al [26] and Van Leeuwen [27], which also provides a comparison to experimental data.…”

“…is used [25]. H refers to the maximum Hertzian pressure in Pa. For comparison, as defined by Moes [10] from eq.…”

“…The final form of the film thickness equation is analogous to Nijenbanning et al [11]. It is a weighting of the contributions of different lubrication regimes and reads: (25) as the transition parameters between the isoviscous-rigid and isoviscous-elastic ( 00 ) and between the isoviscous and piezoviscous regimes ( ). The coefficients for weighting are based on simulations in between the lubrication regimes.…”

Revisiting film thickness in slender elasto-hydrodynamically lubricated contacts

“…The problem of film prediction in wide elliptic contacts was revisited, see reference [19], and a new accurate central film thickness prediction approach was developed based on the circular contacts, the fundamental physical trends observed in numerical computations for wide elliptic contacts, and the equivalent line contact asymptotic solution. The resulting formula is more accurate, but not as simple as the Dowson, Higginson, and Hamrock power law curve-fits.…”

“…In this special issue article, the problem of narrow elliptic contacts is considered. The objective is the same as in reference [19]: first to review fundamental trends and next to develop an accurate film thickness formula for practical use in engineering. This formula should then reflect the actual physical behaviour of the problem such that it can be accurately used over a large range of operating conditions.…”