Thin film lubrication problems frequently involve the use of lubricants with non-Newtonian characteristics, and a relatively simple viscosity model that can describe several non-Newtonian fluids is the Herschel–Bulkley relation. This relation can model solid-like properties of a lubricant at low shear stress using a yield stress, while at higher shear stress values shear-thinning or thickening can be included. In literature, this viscosity model has been combined with various governing equations to solve the non-Newtonian thin film problem, resulting in models that range from full 3D CFD simulations, to 1D Reynolds equation based methods. However, something that all of these approaches have in common is that they are either computationally expensive, can only be used for 1D geometries, or use non-exact, regularised versions of the Herschel–Bulkley model for reasons of numerical stability. This paper therefore introduces a method for solving a thin film problem with a non-regularised Herschel–Bulkley lubricant using the 2D generalised Reynolds equation, and this approach is shown to be fast without compromising on accuracy. The increased speed will allow the model to be used more efficiently in complex simulations or design optimisation scenarios.

A journal bearing test bench is used to find the transition speed between the hydrodynamic and mixed lubrication regimes for a modified magnetorheological (MR) fluid. It is shown that the transition speed of the bearing can be reduced by applying a local magnetic field near minimum film when it is lubricated with the MR fluid, and that this will only marginally increase friction. The lubricating performance of the MR fluid is compared to that of a reference oil, and all experimental results are compared with a Finite Element model based on the Reynolds equation.