Aplicação de técnicas de otimização para o cálculo da pressão de contato em superfícies rugosas

Abstract

Contact is a phenomenon that occurs in various mechanical components such as gears, rolling bearings, wheel-rail systems, for which contact fatigue is considered one of the leading causes of failure. For this reason, analyzing the pressures and stresses in the materials in contact is of great importance as it aids in predicting and evaluating surface-related failures. In real situations, contact pressures and stresses are often challenging to obtain and depend on several factors, such as load, material properties, contact area, and surface characteristics. All mechanical component surfaces are microscopically rough, regardless of the manufacturing process employed. Surface roughness affects contact characteristics such as the local pressure distribution, subsurface stresses, real contact area and, consequently, the contact strength. Such factors directly affect characteristics such as adhesion, friction, load capacity, wear and fatigue of components. Thus, a major challenge lies in determining the interface’s pressure and contact stress distributions. Within this context is inserted the present research, which objective is to propose, apply and evaluate computational methods to efficiently calculate the pressure distribution in the contact between rough surfaces. The formulation of the contact problem, considered elastic, uses the linear complementarity problem (LCP) approach, obtaining its solution by different optimization techniques: Lemke’s method, quadratic programming, solving quadratic programming by non-negative least squares and the Gubori package. In the simulations carried out in one-dimensional domain contact cases, there are no significant differences among the methods used, either in terms of computational time or in the values of pressures and contact region. For the two-dimensional domain cases, the Lemke method, with a modification proposed here, presents advantages in terms of computational time to obtain the solution when applied to smooth and virtual surfaces; however, the method of solving the quadratic programming by non-negative least squares proved to be the fastest one among the tested methods when applied to real rough surfaces. The results achieved in the simulations, both for the contact where the domain is one-dimensional or two-dimensional, are low computational cost and consistent with observations of usual real cases, such as: regions of maximum pressures, null pressures in regions without contact, influence of roughness on the values of pressures and contact regions.