Computational models of bearings operating under extreme conditions for performance characteristics estimation

• Grant number: 25/12004-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2025
• End date: June 30, 2026
• Field of knowledge: Engineering - Mechanical Engineering - Mechanics of Solids
• Principal Investigator: Thales Freitas Peixoto
• Grantee: Nicolas Maiochi
• Host Institution: Faculdade de Engenharia Mecânica (FEM). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 23/11872-0 - Computational models of bearings operating under extreme conditions for performance characteristics estimation, AP.R

Abstract

Since the Industrial Revolution (1760-1820), 2040 gigatonnes of carbon dioxide were emitted to the atmosphere, due to burning of fossil fuels, increasing in 1.09 °C the average global surface temperature above pre-industrial levels. Nearly 20% of the energy consumed worldwide is used to overcome friction and up to 40% of the lost energy can be saved employing new lubrication technologies. The lost energy due to viscous shear in mineral and synthetic oils used as a lubricant separating two surfaces in contact still is the biggest cause limiting the efficiency of mechanical systems. In this scenario, rotating machineries with applications in different industrial segments represent a class of machines with broad applications, comprising turbines, compressors, pumps and generators. Particularly in the energy sector, performance is of paramount importance and losses due to friction should be minimized to guarantee an optimal performance. The need to satisfactorily predict the operating conditions requires the correct estimate of the bearings equivalent dynamic coefficients, that must be evaluated in the equilibrium position of the rotating system. The root-finding problem arises in the modeling of all lubricated bearings, as it is necessary to estimate the pressure distribution of the bearing at its static equilibrium position or for small perturbations in displacement and/or velocity around that equilibrium position. It is mandatory, during the computation of the pressure field, to find the equilibrium position of the bearing. The problem can be formally defined as a root-finding problem, in which it is necessary to find the equilibrium position of the journal in the bearing, in order to balance the external static forces acting on the journal with the hydrodynamic forces resulting from the oil film supporting the journal. Therefore, during this scientific initiation research project, different methods and algorithms for solving systems of nonlinear equations will be studied, comparing the methods in terms of robustness (i.e., convergence to the system solution for different initial conditions), convergence rate (number of iterations), and computational time. The basic and widely used algorithm is the Newton method. In this method, the Jacobian matrix is estimated numerically using finite differences, which can significantly increase the computational time required to find the equilibrium position, since each perturbation requires solving the Reynolds equation based on the perturbed position. Modified Newton methods try to reduce the computing cost by reducing the number of function calls, proposing alternatives to estimate the Jacobian matrix. Another strategy consists of using optimization methods to find the solution of the equation systems, since the problems may be equivalent. A third class of methods uses homotopy, reducing the root-finding problem to solving a system of ordinary differential equations, which can be numerically integrated using basic explicit time marching integrators.