Static Analysis of Rolling Bearing Using Finite Element Analysis

Abstract

In this study the static analysis of an angular contact ball bearing using Finite Element Method is investigated. The main goal is to find the most important influencing parameters for radial stiffness of the bearing under an axial load. All the results are based on one specific angular contact ball bearing with the radius of ball around 22 mm and the inner and outer groove radii around 11mm.

The factors which mostly influence the radial reaction force from the housing to the outer ring are analyzed. The most important parameter which affects the reaction force is the curvature of the ball and the raceway of inner and outer ring. An increase of the ball diameter by 1.3% leads to the increase of reaction force by 27%. A decrease of ball diameter by 1.3% results in the decrease of reaction force by 9.3%.

With respect to the Finite Element formulation, the next important parameters are the mesh density and normal contact stiffness factor FKN if Augmented Lagrange is used. The mesh density affects the contact stiffness and the whole reaction force mostly in contact region. After the program finds a suitable contact area the mesh density affects the reaction force only a little. For example if the number of nodes increases by approx.

6 times, the final reaction force increases only 13.8%. For the penetration further investigation shows that the reaction force has little sensitivity to it. For example, when the penetration increases from 0 (Pure Lagrange method) to 0.0056 mm (Pure Penalty method) which is relative large in bearing analysis, the final reaction force decreases by only 1%.

The second goal of this study is to simplify this angular contact ball bearing using beam element between the inner and outer ring to reduce the number of nodes and shorten the calculation time. For this specific ball bearing, it is possible to use a “beam star" structure with 12 beams and the radius of each circular beam is 4.5mm. Although it has an equivalent stiffness as the bearing with ball, for some other kind of bearing and the angular contact ball bearing with different geometry size, further investigation should be carried out.