An Analysis of Contact Interaction of the Cylinder Roller with the Bearing Races Using the Finite Element Method

In order to clarify the relationships used to describe contact interaction in a cylindrical bearing, a large series of numerical experiments was performed for a roller of finite length compressed by elastic plates imitating bearing rings. Based on the analysis of the results of numerical experiments, a load-displacement relationship is obtained that takes into account the influence of the diameter, length of the roller, and thickness of the plates. Verification of the developed relationship against the known experimental results demonstrated its accuracy. The proposed formula is compared with similar dependencies obtained by other authors. Using the correction factor, the developed formula is refined taking into account the influence of the curvature of the raceways.

References

[1] Harris T.A. Rolling bearing analysis. USA, CRC Press, 2006. 760 p.

[2] Palmgren A. Ball and roller bearing engineering. Philadelphia, S.H. Burbank and company Inc., 1959. 50 p.

[3] Hoeprich M.R., Zantopulos H. Line contact deformation – a cylinder between two flat plates. Journal of Tribology, 1981, vol. 103, is. 1, pp. 21–25, doi: 10.1115/1.3251609

[4] Houpert L. An engineering approach to Hertzian contact elasticity — part I. Journal of Tribology, 2001, vol. 123, is. 3, pp. 582–588, doi: 10.1115/1.1308043

[5] Lundberg G., Sjövall H. Stress and deformation in elastic contacts, Pub. 4. Gothenburg, Institute of Theory of Elasticity and Strength of Materials, Chalmers Inst. Tech., 1958. 47 p.

[6] Houpert L. An enhanced study of the load-displacement relationships for rolling element bearings. Journal of Tribology, 2014, vol. 136, is. 1, no. 011105, doi: 10.1115/1.4025602

[7] Degtyarev S.A., Kutakov M.N., Popov V.V. Consideration of contact interactions when mo-delling stiffness characteristics of roll bearings. Vestnik Moskovskogo aviatsionnogo instituta, 2015, vol. 22, no. 2, pp. 137–141 (in Russ.).

[8] Antoine J.-F., Visa C., Sauvey C., Abba G. Approximate analytical model for Hertzian ellip¬tical contact problems. Journal of Tribology, 2006, vol. 128, is. 3, pp. 660–664, doi: 10.1115/1.2197850

[9] Luk’yanova A.N. Modelirovaniye kontaktnoy zadachi s pomoshch’yu pro-grammy ANSYS [Modeling a contact problem using ANSYS]. Samara, Samara Polytech publ., 2010. 52 p.

[10] Luk’yanova A.N. Modelirovaniye kontaktnogo vzaimodeystviya detaley [Modeling of contact interaction of parts]. Samara, Samara Polytech publ., 2012. 87 p.

[11] Basov K.A. ANSYS v primerakh i zadachakh [ANSYS in examples and tasks]. Moscow, Komp’yuter Press publ., 2002. 224 p.

[12] Chigarev A.V., Kravchuk A.S., Smalyuk A.F. ANSYS dlya inzhenerov [ANSYS for engineers]. Moscow, Mashinostroyeniye-1 publ., 2004. 512 p.

[13] Goryainov V.B., Pavlov I.V., Tsvetkova G.M. Matematicheskaya statistika [Mathematical statistics]. Moscow, Bauman Press, 2002. 424 p.

[14] Freedman D.A. Statistical models: theory and practice. Cambridge, Cambridge University Press, 2005. 414 p.

[15] Revinskaya O.G. Osnovy programmirovaniya v MatLab [The basics of programming in MatLab]. Sankt-Petersburg, BHV-Peterburg publ., 2016. 208 p.