Amplitude Reduction of Waviness in Transient EHL Line Contacts

The problem of surface waviness in ElastoHydrodynamic Lubrication is commonly considered as a first step towards understanding the lubrication of rough surfaces. Both problems are generally transient. The current paper investigates the deformation of sinusoidal waviness in the contact, more precisely it studies the amplitude reduction of one-sided waviness in a transient EHL line contact. The film thickness amplitude at X = 0 is called Ad (deformed amplitude). It is shown that for waviness amplitudes smaller than the film thickness Ai <Hc, the ratio Ad/Ai is independent of the undeformed amplitude Ai. In other words: for small amplitudes the deformed amplitude depends linearly on the initial amplitude Ai. Rather surprisingly, the same behaviour is found for Ai >Hc. The results show that qualitatively waviness with short wavelengths λ/b < 1 is hardly deformed, thus Ad ≃Ai. Long wavelengths on the contrary, disappear nearly completely: Ad ≪Ai thus Ad/Ai ≃ 0. However, quantitatively the amplitude reduction was found to depend also on the contact operating conditions. With a generalized coordinate ∇, instead of λ/b, the relative amplitude Ad/Ai can be described by a single function of ∇ for all operating conditions: Ad/Ai = F(∇),∀(M, L). A possible way of expressing ∇ is:∇ = λ/bM3/4/L1/2.