A finite element development for ball bearing nonlinear stiffness modelization

Abstract

A formulation and algorithmic treatment of a three-dimensional bearing stiffness is presented. This stiffness formulation is based on the non-linear equilibrium balance of forces and moments on the rolling elements, in a ball bearing, exerted by the inner and the outer races including contact forces. Newton-Raphson Method is used to solve the resulting non linear equation system. A non-linear two nodes finite element linking up a node of the inner race to another node of the outer race is developed. The tangent stiffness matrix of this element is deduced from the Jacobean of the convergent equilibrium. A numerical study is presented showing the influence of some parameters variation and the coupling between all stiffness terms.