Non-linear elasto-dynamic model of faulty rolling elements bearing

In this paper an elasto-dynamic model of a defective sphere bearing is presented. This two-dimensional model can simulate local faults on the bearing races and rolling elements, and it is based on the non-linear Hertzian contact deformation of the rolling elements. In the model the outer race is supposed to be fixed, and the rolling elements are supposed to roll without slipping. These assumptions yield a total of z + 4 Degrees of Freedom (DOF), where z is the number of rolling ele-ments: three DOF come from the inner race (two displacements and one rotation), one DOF from the cage (rotation) and one DOF from each rolling element (i.e., z radial displacements). Each contact between the spheres and the races is modelled by a non-linear spring (Hertz contact theory) and a damper proportional to the spring stiffness (Palmgren). The model uses a kinematic approach to calculate the trajectory of the rolling elements when passing over the defect. This trajectory is introduced into the equations of motion for the calculation of the rolling elements deformations; subsequently, the internal bearing forces are calculated. The model inputs are the bearing and defect geometry, the materials characteristics and the radial load. The model outputs the overall force transmitted to the outer race, which accurately reproduces the typical behaviour exhibited by a faulty bearing both in time and frequency domain