A Geometric Multigrid Solver for the Piston–Cylinder Interface of Axial Piston Machines

Abstract

A geometric multigrid scheme for the solution of the Reynolds equation in the piston–cylinder interface of an axial piston machine is presented in this article. The application of this numerical method represents a significant advancement in the fluid power research community, where the solution of the fluid flow in the piston–cylinder interface has thus far been obtained using standard iterative schemes. An efficient numerical solver for the piston–cylinder interface Reynolds equation is necessary to couple the solution of the nonisothermal fluid film flow with the solid boundaries’ surface elastic deformations as part of a larger simulation procedure. The piston–cylinder interface is in fact one of the most complex tribological pairs of an axial piston machine. It operates in an elastohydrodynamic regime under oscillating load conditions, where the additional influences of heat transfer and solid boundaries’ thermal strains cannot be neglected. To consider all of the described physical phenomena and investigate the piston–cylinder interface lubricating behavior, the authors developed a fully coupled fluid–structure and thermal simulation model. The geometric multigrid method discussed in this article represents the core of this model, allowing for a fast and accurate solution of the piston–cylinder fluid film flow. The improvements linked to the introduction of this method are presented together with fluid–structure numerical results.