The refined strength calculation and optimization of the inner geometry of cylindrical bearing units

Authors

DOI:

https://doi.org/10.15587/1729-4061.2020.204013

Keywords:

closed bearing unit, crown, roller, multi-contact problem, finite element method, mathematical model

Abstract

Closed bearing units for railway rolling stock shall operate over 800,000 km or during 8 years of operating life (and, in the near future, 1 million km and 10 years) without any maintenance. In order to achieve such high operational indicators, it is necessary, already at the design stage of closed bearing units, to ensure almost absence of wear during the entire specified operating life.

This paper reports the results of the optimal design of the elements in the internal geometry of closed bearings based on refined mathematical models using an example of the cylindrical axlebox bearing unit "DUPLEX" for 1520 gauge rolling stock. The chosen principal mathematical model was a geometrically nonlinear contact problem from the theory of elasticity, which was solved using a finite element method.

An original non-linear finite-element model of the multi-contact problem has been developed, taking into consideration the contact deformations "rail‒wheel", the deformation of a wheel-set axis, the deformation of the axlebox and bearing rings during contact with all rollers. The model makes it possible to clarify the distribution of loads in the circumferential direction and, accordingly, the maximum load on a roller. The same model could be used, among other things, to analyze the wear of a wheel flange and the effect of gap difference on the bearing wear.

A mathematical model and an objective function have been constructed to optimize the profile of a roller ("crown", the generatrix of the lateral surface of rotation) considering the accumulation of damage as a result of the "irregular" loading the roller surface points due to contacts with both the outer and inner rings.

The shapes of the roller's face and the ring's operating flange have been optimized that are in contact in the axial direction, which has helped establish that the "anthropologically shaped" convex face of the roller and the concave flange of the ring are optimal. To simplify the structure technologically, a variant with a conical surface of the flange with the optimal "camber" value has been accepted instead of the concave flange of the ring

Author Biographies

Anatoliy Girshfeld, PJSC «U.P.E.C.» Marshal Batitskiy str., 4, Kharkiv, Ukraine, 61038

President

Eduard Simson, National Technical University «Kharkiv Polytechnic Institute» Kyrpychova str., 2, Kharkiv, Ukraine, 61002

Doctor of Technical Sciences, Professor, Laureate of the National Award in the Field of Science and Technology, Honored Scientist of Ukraine

Department of Continuum Mechanics and Strength of Materials

References

  1. Harris, T. A., Kotzalas, M. N. (2006). Essential Concepts of Bearing Technology. CRC Press, 392. doi: https://doi.org/10.1201/9781420006599
  2. Brändlein, J., Eschmann, P., Hasbargen, L., Weigahd, K. (1999). Ball and Roller Bearings: Theory, Design and Application. Wiley, 642.
  3. Harnoy, A. (2002). Bearing Design in Machinery. Engineering Tribology and Lubrication. CRC Press, 664. doi: https://doi.org/10.1201/9780203909072
  4. Mason, M. A., Cartin, C. P., Shahidi, P., Fetty, M. W., Wilson, B. M. (2014). Hertzian Contact Stress Modeling in Railway Bearings for Assorted Load Conditions and Geometries. 2014 Joint Rail Conference. doi: https://doi.org/10.1115/jrc2014-3846
  5. Yang, K., Zhang, G., Wang, Y. W., Cai, S. (2019). Finite element analysis on contact stress of high-speed railway bearings. IOP Conference Series: Materials Science and Engineering, 504, 012073. doi: https://doi.org/10.1088/1757-899x/504/1/012073
  6. Gopalakrishnan, T., Murugesan, R. (2015). Contact analysis of roller bearing using finite element method. Vels Journal of Mechanical Engineering, 2 (2), 30–33. Available at: https://www.researchgate.net/publication/305768098_CONTACT_ANALYSIS_OF_ROLLER_BEARING_USING_FINITE_ELEMENT_METHOD
  7. Pandiyarajan, R., Starvin, M. S., Ganesh, K. C. (2012). Contact Stress Distribution of Large Diameter Ball Bearing Using Hertzian Elliptical Contact Theory. Procedia Engineering, 38, 264–269. Available at: https://cyberleninka.org/article/n/531103
  8. Shah, D. B., Patel, K. M., Trivedi, R. D. (2016). Analyzing Hertzian contact stress developed in a double row spherical roller bearing and its effect on fatigue life. Industrial Lubrication and Tribology, 68 (3), 361–368. doi: https://doi.org/10.1108/ilt-06-2015-0082
  9. Nabhan, A., Ghazaly, N. (2015). Contact Stress Distribution of Deep Groove Ball Bearing Using ABAQUS. Journal of the Egyptian Society of Tribology, 12 (1), 49–61. Available at: https://www.academia.edu/25070023/Contact_Stress_Distribution_of_Deep_Groove_Ball_Bearing_Using_ABAQUS
  10. Pușcașu, A. M., Lupescu, O., Bădănac, A. (2017). Analysis of cylindrical roller bearings design in order to optimize the classical process using FEM. MATEC Web of Conferences, 112, 06017. doi: https://doi.org/10.1051/matecconf/201711206017
  11. Li, S., Motooka, M. (2017). A finite element method used for contact analysis of rolling bearings. The 8th International Conference on Computational Methods (ICCM2017). Available at: https://www.sci-en-tech.com/ICCM2017/PDFs/2199-9211-1-PB.pdf
  12. Demirhan, N., Kanber, B. (2008). Stress and Displacement Distributions on Cylindrical Roller Bearing Rings Using FEM#. Mechanics Based Design of Structures and Machines, 36 (1), 86–102. doi: https://doi.org/10.1080/15397730701842537
  13. Hao, X., Gu, X., Zhou, X., Liao, X., Han, Q. (2018). Distribution characteristics of stress and displacement of rings of cylindrical roller bearing. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233 (12), 4348–4358. doi: https://doi.org/10.1177/0954406218820551
  14. Lin, F., Zhao, Y. X. (2008). Finite Element Analysis on the Fatigue Stresses of a Railway Vehicle Roller Bearing. Advanced Materials Research, 44-46, 935–941. doi: https://doi.org/10.4028/www.scientific.net/amr.44-46.935
  15. Chen, G., Wang, H. (2016). Contact stress and radial stiffness of a cylindrical roller bearing with corrected roller generator. Transactions of the Canadian Society for Mechanical Engineering, 40 (5), 725–738. doi: https://doi.org/10.1139/tcsme-2016-0059
  16. Tong, V.-C., Hong, S.-W. (2017). Modeling and analysis of double-row cylindrical roller bearings. Journal of Mechanical Science and Technology, 31 (7), 3379–3388. doi: https://doi.org/10.1007/s12206-017-0627-x
  17. Simson, E. A., Anatskiy, Yu. P., Ovcharenko, V. V., Trohman, M. V., Zenkevich, Yu. A. (2009). Optimizatsiya obrazuyushchey poverhnosti rolika podshipnika kacheniya. Vestnik Nats. tehn. un-ta "KhPI", 30, 8–11. Available at: http://library.kpi.kharkov.ua/files/Vestniki/2009_30.pdf
  18. Simson, E. A., Anatskiy, Yu. P., Ovcharenko, V. V., Trohman, M. V., Zenkevich, Yu. A. (2009). Optimizatsiya bortov kolets i tortsevoy poverhnosti rolika podshipnika kacheniya. Vestnik Nats. tehn. un-ta "KhPI", 42, 8–11. Available at: http://library.kpi.kharkov.ua/files/Vestniki/2009_42.pdf
  19. Wang, Z. W., Meng, L. Q., Hao, W. S., Zhang, E. (2010). Finite Element Method Analysis and Optimal Design of Roller Convexity of Tapered Roller Bearing. Advanced Materials Research, 139-141, 1079–1083. doi: https://doi.org/10.4028/www.scientific.net/amr.139-141.1079
  20. Hirshfeld, A. M., Anatskyi, Y. P., Simson, E. A., Ovcharenko, V. V. (2009). Pat. No. 44588. Method for designing optimal geometric parameters of contacting end surfaces of roller bearing. No. u200903804; declareted: 17.04.2009; published: 12.10.2009, Bul. No. 19.
  21. Ovcharenko, V. V., Simson, E. A., Hirshfeld, A. M., Anatskyi, Y. P. (2009). Pat. No. 44969. Method for designing optimal geometric parameters of generatrix of working surface of roller of roller bearing. No. u200903761; declareted: 17.04.2009; published: 26.10.2009, Bul. No. 20.
  22. Girshfel'd, A. M., Rukavishnikov, V. F., Semykin, S. I., Shcherbina, A. V. (2009). Pat. No. 2425767 RF. Buksoviy podshipnikoviy uzel. declareted: 14.12.2009; published: 10.08.2011.
  23. Girshfel'd, A. M., Simson, E. A., Ovcharenko, V. V. (2010). Pat. No. 98790 RF. Rolikoviy podshipnik.

Downloads

Published

2020-06-30

How to Cite

Girshfeld, A., & Simson, E. (2020). The refined strength calculation and optimization of the inner geometry of cylindrical bearing units. Eastern-European Journal of Enterprise Technologies, 3(7 (105), 66–78. https://doi.org/10.15587/1729-4061.2020.204013

Issue

Vol. 3 No. 7 (105) (2020): Applied mechanics

Section

Applied mechanics

License

Copyright (c) 2020 Anatoliy Girshfeld, Eduard Simson

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.