A numerical approach to solve an inverse problem in lubrication theory

In this paper we consider a numerical approach to reach the equilibrium position of a journal bearing with radial loading. The system consists of an external cylinder surrounding a rotating shaft. The problem is modelled by the hydrodynamic Reynolds equation with a cavitation model of Elrod–Adams. Both equations are coupled to Newton’s second law which describes the position of the shaft. The problem is considered as an inverse problem where the coefficient of the equation is unknown. The numerical approach to solve the inverse problem is based on a trust-region algorithm along with the finite element method. The Heaviside function in the Elrod–Adams equation is approximated by a third order Hermite polynomial. The trust-region algorithm for solving the inverse problem showed another way of solution, different from the ones that exist at this moment.