**Finite Element Analysis of
Case-Hardened Roller Bearings**

Jan Pettersson

**Akademisk avhandling**

som för avläggande av teknisk doktorsexamen vid Linköpings Tekniska Högskola kommer att försvaras offentligt i sal C3, C-huset, Universitetet i Linköping, fredagen den 6 november 1998 kl. 10.15. Fakultetsopponent är professor Roland Fortunier, Ecole des Mines Saint-Étienne, Frankrike.

**ABSTRACT**

This thesis deals with the material modelling of case-hardened bearing steel, with special reference to hardened roller bearing components. The result of a case-hardening process is a hardened component with substantially improved material properties within a restricted region beneath the heat-treated surface. In most cases, the dominant material phase in the hardening area is martensite. This material improvement is decreasing with increasing distance below the surface. Thus, a type of gradient material is obtained. The case depth is strongly related to the carbon profile created by an initial carburizing process.

A rate-independent nonlinear isotropic hardening model is implemented where the material characteristics are functions of the carbon content. The model is verified by comparing results from finite element analysis with static high-load test on case-hardened single rollers having different case depths. A good correlation is found. A study is made on a roller bearing including case-hardened rollers and raceways. The focus is set on the relation between the case depths and the load-carrying response.

The strength differential effect (SDE), i.e. different mechanical behaviour in tension and compression, is observed in martensite containing a high carbon content. To examine the effect of the SDE on the load response of the roller, the material model is extended to cover this phenomenon. The obtained results show that the SDE has no influence on the response for the particular loading situation studied.

The heat-treatment process can introduce residual stresses of significant magnitude in the roller. The residual state interacts with the stresses present during operation. To compare the load response of a case-hardened roller containing an initial residual stress state with a stress-free roller, the quench process is simulated. A nonlinear isotropic and a linear kinematic material model are used separately to derive the stress field. The response of the roller on subsequent loading is greatly influenced by the type of model used.

Shakedown is a phenomenon that can occur in structures subjected to a pulsating or cyclic load above the yield limit. The shakedown limit is an important factor defined as the maximum load level at which plastic deformation ceases. To examine the relation between the shakedown limit and the case depth, the cyclic stress state experienced by a case-hardened raceway is analysed. Two material models, a linear and a nonlinear kinematic hardening model are used and compared. The analysis show that the shakedown limits are unaffected by both the case depths and material model used.

Division of Solid Mechanics

Department of Mechanical Engineering

Linköpings universitet, S-581 83 Linköping, Sweden

ISBN 91-7219-313-1 ISSN 0345-7524