Energy and environment are of major concern in internal combustion engine component design. The piston ring-cylinder liner (PRCL) contact plays an essential part in design and is highlighted in this study. In fact, the rings ensure the sealing property, reducing the environmental impact by avoiding lubricant contamination (blow-by) and lubricant consumption. Unfortunately, when sealing, the rings generate between 11 to 24% of the friction losses in an internal combustion engine , thus reducing the energy efficiency of the engine.
The cylinder liner surface features a special micro-geometry, a classical one is the cross-hatching pattern, obtained by honing. This texturing acts as a micro-bearing, oil reservoir and debris trap. Understanding the influence of texture parameters as groove depth and width or angle, will allow tribological improvements of the PRCL contact.
The 2D transient Reynolds equation has to be solved for this kind of surface. The statistical method using the Patir and Cheng  flow factors is widely used. This approach lumps the different components of the surface (grooves and plateaux) and does not consider the roughness directionality. Methods decoupling both components, like the homogenization method  are also used. Another alternative is to use a deterministic model on measured surfaces, but this is a “hugely” expensive approach. Multigrid methods  are used to drastically reduce the calculational cost.
The aim of the current study is to facilitate the understanding of measured surface calculations. Hence, analytical surfaces are used. They allow a flexible handling of the cross-hatching parameters. The plateaux are perfectly smooth and the grooves are sinusoidally shaped. The top ring is modelled using a parabolic profile. Periodic boundary conditions are used in the orthoradial direction and zero pressure conditions (Dirichlet) in the axial direction.
To investigate the effect of different parameters, various imposed film thicknesses are applied and the mean load carrying capacity (LCC) over time is calculated. When representing the LCC corresponding to each parameter compared to the smooth LCC, as a function of the logarithm of the minimum film thickness, the curves are quite linear for small values of the film thickness and then for larger values they converge to 1.