An isogeometric analysis approach for solving the Reynolds equation in textured piston ring – cylinder liner contacts. Issue 9 (20th April 2020) - Liu, Wei; Huang, Zhengdong; Liu, Yunhua
Abstract : Purpose: The purpose of this study is to propose an isogeometric analysis (IGA) approach for solving the Reynolds equation in textured piston ring cylinder liner (PRCL) contacts. Design/methodology/approach: The texture region is accurately and conveniently expressed by non-uniform rational B-splines (NURBS) besides hydrodynamic pressure and the oil film density ratio is represented in this mathematical form. A quadratic programming method combined with a Lagrange multiplier method is developed to address the cavitation issue. Findings: The comparison with the results solved by an analytical method has verified the effectiveness of the proposed approach. In the study of the PRCL contact with two-dimensional circular dimple textures, the solution of the IGA approach shows high smoothness and accuracy, and it well satisfies the complementarity condition in the case of cavitation presence. Originality/value: This paper proposes an IGA approach for solving the Reynolds equation in textured PRCL contacts. Its novelty is reflected in three aspects. First, NURBS functions are simultaneously used to express the solution domain, texture shape, hydrodynamic pressure and oil density ratio. Second, the streamline upwind/Petrov–Galerkin method is adopted to create a weak form for the Reynolds equation that takes the oil density ratio as a first-order unknown variable. Third, a quadratic programming approach is developed to impose the complementarity conditions between the hydrodynamic pressure and the oil density ratio.