The transition region of elastohydrodynamic lubrication

A semi-analytic approach is presented for the elastohydrodynamic lubrication problem of two cylinders in line contact. The model takes account of the effects of elastic deformation and piezo-viscosity in the transition region (the area of parameter space where the pressure spike emerges and develops). Following Poritsky, pressure and displacement are expressed as Chebyshev series and Fejér’s method is used to deal with the sharp crease in the film shape that is a feature of piezoviscous contacts. It is shown that the film thickness depends solely upon two non-dimensional parameters and can be accurately represented by an equation of the form: H = a0g3a1g1 + a2g3a3, where the ai = 0, 1, 2, 3) are constant coefficients. Important features of this Chebyshev series method include accurate representations for the emerging pressure spike and the associated sharp crease in the film shape together with film thickness predictions which smoothly link those areas of parameter space on either side of the transition region.