Roller-bearing energy model experimental verification for aircraft engines supporting nodes modeling. Part 1. Roller-bearing loading by radial force and lateral moment on the special test bench, preventing the rings bending

Dynamics, strength of machines, instruments and equipment


Sorokin F. D.1*, Zhang H. 1**, Popov V. V.1***, Ivannikov V. V.2****

1. Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia
2. Scientific and technical centre of rotor dynamic «Alfa-Tranzit», 1, Leningradskaya str., Khimky, Moscow region, 141400, Russia



A wide range of scientific contributions discloses various aspects of roller-bearings parts behavior and interaction [1-15]. De Mul [9] developed relatively simple but at the same time quite efficient model where each rolling element was discretized with a set of thin slices and the nonlinear static equations were constructed afterwards. The paper [10] significantly advances the de Mul’s ideas. It revealed that the use of energy conservation approach instead of equilibrium equations derivation was much more convenient. Once the deformation energy of the roller is constructed, the forces acting onto the rolling element (along with the corresponding tangent operators) are easily restored from the potential as the first order (or the second order for the tangent operators case) derivatives.

To verify the energy model of the roller bearing, a full-scale experiment was performed on the universal Zwick/Roell Z100 test machine. Roller bearing of the 12309KM type, fixed in a special device that secured the outer ring, was loaded by a radial force and bend moment through a rigid bar. Deformations of the parts, used for the bearing fastening and loading, were preliminary estimated by calculation using the FEM. The experimental data was processed by the of least squares method to approximate it by analytical relationships. Comparison of the experimental data with the numerical results obtained from the previously developed energy model revealed their good agreement. From the study, we can conclude that the energy model of the roller-bearing is rather accurate.


the roller-bearing energy model, test equipment, least squares method


  1. Houpert L. An enhanced study of the load-displacement relationships for rolling element bearings, Journal of Tribology, 2014, vol. 136, no. 1, pp. 011105 - 011116.

  2. Houpert L. A uniform analytical approach for ball and roller bearings calculations, Journal of Tribology, 1997, vol. 119, no. 4, pp. 851 - 858.

  3. Guo Y., Parker R.D. Stiffness matrix calculation of rolling element bearings using a finite element/contact mechanics model, Mechanism & Machine Theory, 2012, vol. 51, no. 5, pp. 32 - 45.

  4. Cavallaro G., Ne´lias D., Bon F. Analysis of high-speed inter-shaft cylindrical roller bearing with flexible rings, Tribology Transactions, 2005, vol. 48, no. 2, pp. 154 - 164.

  5. Antoine J.F., Visa C., Sauvey C. Approximate analytical model for Hertzian elliptical contact problems, Journal of Tribology, 2016, vol. 128, no. 3, pp. 660 - 664.

  6. Leblanc A., Nelias D., Defaye C. Nonlinear dynamic analysis of cylindrical roller bearing with flexible rings, Journal of Sound & Vibration, 2009, vol. 325, no. 1, pp. 145 - 160.

  7. Houpert L. An engineering approach to Hertzian contact elasticity part I, Journal of Tribology, 2001, vol. 123, no. 3, pp. 582 - 588.

  8. Houpert L. An engineering approach to Hertzian contact elasticity part II, Journal of Tribology, 2001, vol. 123, no. 3, pp. 589 - 594.

  9. De Mul J.M., Vree J.M., Maas D.A. Equilibrium and associated load distribution in ball and roller bearings loaded in five degrees of freedom while neglecting friction -Part II: Application to roller bearings and experimental verification, Journal of Tribology, 1989, vol. 111, no. 1, pp. 142 - 148.

  10. Sorokin F.D., Chzhan Kh., Ivanikov V.V. Izvestiya vysshikh uchebnykh zavedenii. Mashinostroenie, 2018, no. 3, C. 14 - 23.

  11. Zubko A.I., Dontsov S.N. Trudy MAI, 2014, no. 74, available at:

  12. Khaustov A.I., Shashkin I.N., Mal'gichev V.A., Nevzorov A.M. Trudy MAI, 2012, no. 50, available at:

  13. Ermilov Yu.I., Ravikovich Yu.A., Klimenko A.V., Kholobtsev D.P. Trudy MAI, 2010, no 39, available at:

  14. Degtyarev S.A., Kutakov M.N., Leont'ev M.K., Popov V.V., Romashin Yu.S. Vestnik moskovskogo aviatsionnogo instituta, 2015, vol. 22, no. 2, pp. 137 - 141.

  15. Tong V.C., Hong S.W. Characteristics of tapered roller bearing subjected to combined radial and moment loads, IJPEMGT, 2014, vol. 1, no. 4, pp. 323 - 328.

  16. Beizel'man R.D., Tsypkin B.V., Perel' L.Ya. Podshipniki kacheniya. Spravochnik (Roller-bearings. Directory), Moscow, Mashinostroenie, 1975, 572 p.

  17. Chermenskii O.N., Fedotov N.N. Podshipniki kacheniya: Spravochnik-katalog (Roller-bearings. Directory and Catalogue), Moscow, Mashinostroenie, 2003, 576 p.

  18. Perel' L.Ya. Podshipniki kacheniya: Raschet, proektirovanie i obsluzhivanie opor. Spravochnik (Roll-bearings: Supports calculation, design and maintenance: a Handbook), Moscow, Mashinostroenie, 1983, 543 p.

  19. Chigarev A.V., Kravchuk A.S., Smalyuk A.F. ANSYS dlya inzhenerov (ANSYS for engineers), Moscow, Mashinostroenie-1, 2004, 512 p.

  20. Baraz V.R. Korrelyatsionno-regressionnyi analiz svyazi pokazatelei kommercheskoi deyatel'nosti s ispol'zovaniem programmy Excel (Correlation and regression analysis of of business activities indicators with Excel), Ekaterinburg, GOU VPO “UGTU–UPI”, 2005, 102 p.

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