Numerical simulation of a lubricated hertzian contact problem under imposed load

Abstract A lot of lubrication problems can be reduced to a contact between an elastic sphere and a rigid plane which leads to a Reynolds–Hertz nonlinear coupled model, where the cavitation phenomenon, the lubricant piezoviscosity and the balance between an imposed load on the device and the hydrodynamic load, must be taken into account. Last aspects add some difficulties: a new piezoviscous nonlinearity and a nonlocal constraint on the main unknown. In this paper, the proposed coupled problem is modelled, normalized and numerically solved. Thus, a numerical scheme which combines fixed point algorithms, the method of characteristics, duality techniques and finite element approximations is developed. Finally, when using a numerical flux conservation test, some computed results for real data are presented.