Shape Parameterization Comparison for Full-film Lubrication Texture Design

Minimizing energy loss and improving system load capacity and compactness are important objectives for fluid power applications. Recent studies have revealed that a micro-textured surface can reduce friction in full-film lubrication, and an asymmetric textured surface can further improve the performance by reducing friction and increasing normal force simultaneously. As an extension of these previous discoveries, we explore how enhanced texture design can maximize these objectives together. We design the surface texture using a set of distinct parameterizations, ranging from simple to complex (including very general geometries), to improve friction and normal force properties beyond what is possible for limited texture geometries. Here we use a rotational visco-rheometer configuration with a fixed bottom disc, a periodic textured surface, and a rotating top flat disc. The Reynolds equation is formulated in a cylindrical coordinate system and solved using a pseudo-spectral method to model Newtonian fluid flow within the gap between discs. Model assumptions include incompressibility, steady flow, constant viscosity, and a small gap height to texture radius ratio. Multiobjective optimization problems are solved using the epsilon-constraint method with an interior-point algorithm. The trade-off between competing objectives is quantified, revealing important insights. Arbitrary continuous texture geometries are represented using two dimensional cubic spline interpolation. Shifting to more general texture geometries resulted in significant simultaneous improvement in both performance metrics for full-film lubrication texture design. An important qualitative result is that textures resembling a helical blade tend to improve performance for rotating contacts in fluid power systems.