Rapid calculation of the pressures and clearances in rough, rolling-sliding elastohydrodynamically lubricated contacts. Part 1: Low-amplitude, sinusoidal roughness

Abstract

Surface roughness in elastohydrodynamically lubricated (EHL) contacts may have a significant effect on component life and there is a need to be able to assess its effects quickly. This article describes a rapid calculation method, which provides accurate results where the amplitude of the roughness is relatively low and which gives good indications of the likely behaviour for higher amplitudes. In the first part, the effect of low-amplitude, sinusoidal roughness is examined, and it is shown that the behaviour can, for any wavelength and roughness orientation, be characterized by three complex quantities. Calculation of two of these is straightforward; the third requires curve fitting to the results obtained using a perturbation analysis. Details of the process are given. The second part of the article discusses how these results can be used to predict the behaviour of any rough surface under rolling-sliding EHL conditions.

Micropitting Modelling in Rolling–Sliding Contacts: Application to Rolling Bearings

“…In order to properly consider sliding, a non-Newtonian scheme is required; therefore, in the present article the scheme developed by Hooke (27) and Hooke, et al (28) and described in detail in Morales-Espejel, et al (21) is followed. As described in these references, in the center of an EHL contact, variations of the microgeometry with small amplitude will produce products of fluctuations (pressures and clearances) and products of derivatives in the Reynolds equation that can be neglected; thus, the Reynolds equation can be written as,…”

“…Hooke, et al (28) suggested an exponential decay with respect to the inlet (x = x + a) location. Because the waves propagate with the average speed of the lubricant, effectively they will have a wavenumber in x such that ω x ≈ ω x (u 2 /ū).…”

“…Substituting these equations and the associated changes in density into the linearized Reynolds Eq. [2] and collecting the first-order terms, Hooke, et al (28) obtained…”

“…To calculate the amplitude of the complementary waves h c and p c , Hooke, et al (28) suggested an interpolation scheme based on perturbation solutions. Morales-Espejel, et al (21) suggested a modified approach for non-Newtonian fluids based on the Newtonian numerical results from Venner and Lubrecht (31); the second approach is followed here.…”

Prediction of Shallow Indentation Effects in a Rolling-Sliding EHL Contact Based on Amplitude Attenuation Theory

“…The part of the model used in this study was published by Hooke [35][36][37] and other part by Lubrecht and Venner [29]. Inside an EHL contact a harmonic wave of amplitude and phase expressed by complex number A i is change to A d .…”