Cavitation analysis using finite elements and the Uzawa algorithm

Abstract

For the best performance and longer duration of devices or elements that participate in a mechanical energy transport system, they require an adequate lubrication process in the areas exposed to friction: bearings, gears, cylinder-piston, etc. This process is very important for the optimal functioning of the system, since it reduces repair costs and unscheduled failures. One of the frequent problems of poor lubrication is generated by the Cavitation phenomenon, for this reason it is important to study its effects under operating conditions. In the present work, the formulation and numerical simulation of Cavitation in bearings is carried out, considering the variation of the viscosity of the lubricant in relation to the pressure and the distribution space. In other works carried out on this phenomenon, it is mentioned how complex it would be to develop a numerical process in a two-dimensional Cartesian system, due to the difficulties of non-linearity that exist in the formulation to obtain the explicit solution. Considering some results of [1. 2 and 3], the present study contributes with the explicit solution of the generated free border problem; For this, the Reynolds differential equation and the application of Barus's law for the viscous effect are reduced to a Poison-type partial derivative equation, which is transformed into an elliptic variational inequality of the first kind on a Soboley functional space. of order one. Then, a numerical resolution scheme is built on a two-dimensional computational domain, using the Galerkin method with finite elements and an improved Uzawa algorithm. Finally, the results that allow simulating the location of the Cavitation zone are presented.