Computational Approach to Improve Bearings by Residual Stresses Based on Their Required Bearing Fatigue Life

Computational Approach to Improve Bearings by Residual Stresses Based on Their Required Bearing Fatigue Life

F. Pape O. Maiss | B. Denkena G. Poll 

Institute for Machine Design and Tribology, Leibniz Universitaet Hannover, Germany

Institute of Production Engineering and Machine Tools, Leibniz Universitaet Hannover, Germany

| |
| | Citation



In drive systems and component technology a high reliability is very important for machines. Machine element dimensions are calculated for reliability. The properties for these elements are based on conventional manufacturing techniques. Very high stresses are applied on bearings in their operating time. To improve the endurance life, residual stresses can be induced into the subsurface zone. In contrast to a conventional grinding process, the mechanical surface modification process deep rolling is able to induce very high compressive residual stresses. A computational approach was developed to establish an appropriate residual stress depth profile matching the applied loads. Thus, the costs of manufacturing can be chosen in accordance to the required properties. The method to determine the residual stresses is based on an iterative reverse calculation of an existing bearing fatigue life model of Ioannides et al. The model originates from the approach of Lundberg and Palmgren (1947) including a stress fatigue limit tu. For the term ti, the fatigue criterion of Dang-Van is applied. The equation accounts for the maximum orthogonal shear stress and the local hydrostatic pressure phyd, corrected for residual and hoop stress. The inputs into the computational model are the stresses on the surface, which are simulated based on the load and geometry of the contact between roller and bearing surface. As an output the required residual stress profile underneath the bearings raceway is given to achieve a bearing fatigue life as required for the given application. In order to verify the model, the bearing fatigue life was experimentally determined for a given residual stress profile by experiments.


bearing fatigue life, inverse computational model, residual stresses


[1] Karas, F., Werkstoffanstrengung beim druck achsenparalleler Walzen nach den gebräuchlichen Festigkeitshypothesen. Forschung auf dem Gebiet des Ingenieurwesens, 11(6), pp. 334–339, 1940.

[2] Föppl, L., Der Spannungszustand und die Anstrengung des Werkstoffes bei der Berührung zweier Körper. Forschung auf dem Gebiet des Ingenieurwesens, 7(5), p. 209, 1936.

[3] Voskamp, A., Microstructural changes during rolling contact fatigue metal fatigue in the subsurface region of deep groove ball bearing inner rings, Technische Universität Delft, Thesis, 1996.

[4] Hacke, B., Radnai, B. & Hinkelmann, K., Berücksichtigung von Betriebszuständen, Sonderereignissen und Überlasten bei der Berechnung der Wälzlager-Lebensdauer in Windenergieanlagen und Großgetrieben. Abschlussbericht FVA Forschungsheft Nr. 967, AiF-Nr. 15227 N, 2011.

[5] Neubauer, T., Betriebsund Lebensdauerverhalten hartgedrehter und festgewalzter Zylinderrollenlager, Leibniz Universität Hannover, IMKT. Doctoral Thesis, 2015.

[6] Denkena, B., Poll, G., Maiß, O., Pape, F. & Neubauer, T., Enhanced boundary zone rolling contact fatigue strength through hybrid machining by hard turn-rolling. Bearing World Journal, Volume 1, Proceedings of the 1st Bearing World Conference 12–13 April 2016, Hanover/Germany, ISBN 978-3-8163-0705-1, pp. 87–102, 2016.

[7] Weibull, W., A Statistical Theory of the Strength of Materials. Generalstabens litografiska anstalts förlag, 1939. (Ingeniörsvetenskapsakademiens handlingar)

[8] Lundberg, G. & Palmgren, A., Dynamic Capacity of Rolling Bearings. Generalstabens Litografiska Anstalts Förl, 1947 (Acta polytechnica. Mechanical engineering series).

[9] Ioannides, E. & Harris, T.A., A new fatigue life model for rolling bearings. Journal of Tribology, 107(3), pp. 367–377, 1985.

[10] Ioannides, E., Bergling, G. & Gabelli, A., An analytical formulation for the life of rolling bearings. In: Acta Polytechnica Scandinavica, Mechanical Engineering Series No. 137, 1999.

[11] Dang Van, K., Griveau, B. & Message, O., On a new mulitiaxial fatigue criterion: theory and application. In: M.W. Brown & K.J. Miller (eds), Mechanical Engineering Publications, London, pp. 479–496, 1989.

[12] Pape, F., Neubauer, T., Maiss, O., Denkena, B. & Poll, G., Influence of manufacturing processes and related residual stresses on bearing fatigue life, TFC Tribology Frontiers Conference, STLE, 14. November 2016.

[13] Denkena, B. Grove, T. & Maiß, O., Influence of  the  cutting  edge  radius  on  surface integrity in hard turning of roller bearing inner rings. Production Engineering, 9(3), pp. 299–305, 2015.

[14] Denkena, B., Grove, T. & Maiß, O., Influence of hard turned roller bearings surface on surface integrity after deep rolling. Proceedia CIRP, 45, pp. 359–362, 2016.