A study of the stress field generated by the contact between a sphere and a flat plate for a simplified model of deep-groove ball bearing

Abstract

Bearings are mechanical elements capable of transferring motion between two or more parts in a machine. When an external load is applied, the rolling elements and their rings tend to initiate a cyclical movement between themselves. Hence, they are linked by a variable type of contact, thus creating high surface stresses. As these elements are subjected to millions of cycles within their lifespan, these cyclical stresses may create cracks and cause failure by rolling contact fatigue (RCF). Due to the importance of this subject, it is vital to study the stress field caused by contact between the rolling parts in a bearing. This paper offers two approaches on the cyclical stresses in a deep-groove ball bearing: an analytical approach, using Hertz’s theory for contact stresses; and a numerical simulation, using the Finite Element Method (FEM) with the software Inventor and Nastran In-CAD. The results of both approaches were compared, and stress behavior was analyzed as the depth of the inner ring was increased. It was concluded that the surface stresses are greatly superior than the strength of the materials used in the bearings, and that the area influenced by these stresses are small when compared to the dimensions of the whole.

Keywords

• hertz contact stress
• fem model
• deep-groove ball bearing
• surface contact