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Journal of Mechanical Science and Technology

, Volume 32, Issue 11, pp 5241–5250 | Cite as

Shakedown analysis of a wind turbine gear considering strain-hardening and the initial residual stress

  • Haifeng He
  • Huaiju Liu
  • Caichao Zhu
  • Longhua Yuan
Article
  • 5 Downloads

Abstract

Under some heavy-duty conditions, the shakedown state may occur on gears such as those used in a megawatt wind turbine gearbox. The plastic deformation and the residual stress formed within the shakedown process further influence the contact behavior and the service life of the gear. The initial residual stress caused by the heat treatment of the case-hardening gear, together with the strain-hardening constitutive behavior of the material, have a combined effect on the shakedown state. A two-dimensional elastic-plastic contact numerical model was developed for a case-hardened wind turbine gear to study effects of the initial residual stress and the strain-hardening properties. Plastic strain and residual stress are calculated at each loading cycle without the consideration of the tooth friction. The initial yield limit and the hardening modulus of the material were obtained through a tension test on a universal tensile test machine. The initial residual stress distribution was measured with the X ray diffraction method and then embedded in the finite element model. The results show that strain-hardening behavior can significantly improve the shakedown performance, and the larger the hardening modulus is, the less the maximum plastic strain is at the final shakedown state. Initial residual compressive stress is helpful to improve the shakedown performance, while initial residual tensile stress has negative influence on the shakedown performance. As the normal load increases, the influence of the initial residual stress on the shakedown state becomes weakened.

Keywords

Gear contact Shakedown state Strain-hardening Initial residual stress 

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References

  1. [1]
    Y. Wen and J. Y. Tang, A solution considering elasticplastic deformation of asperities for contact between rough cylindrical surfaces, Industrial Lubrication and Tribology, 70 (2) (2018) 353–362, https://www.emeraldinsight.com/doi/abs/10.1108/ILT–09–2017–0269.CrossRefGoogle Scholar
  2. [2]
    A. W. Aditya and F. Sadeghi, Rolling contact fatigue of case carburized steels, International J. of Fatigue, 95 (2017) 264–281, https://www.sciencedirect.com/science/article/pii/S014 2112316303668.CrossRefGoogle Scholar
  3. [3]
    H. Haifeng, H. Liu, C. Zhu and Z. P. Wei, Sun study of rolling contact fatigue behavior of a wind turbine gear based on damage–coupled elastic–plastic model, International J. of Mechanical Sciences, 141 (2018) 512–519, https://www. sciencedirect.com/science/article/pii/S0020740318301127.CrossRefGoogle Scholar
  4. [4]
    A. F. Bower and K. L. Johnson, The influence of strain hardening on cumulative plastic deformation in rolling and sliding line contact, J. of the Mechanics & Physics of Solids, 37 (1989) 471–493, https://www.sciencedirect.com/science/article/pii/0022509689900252.CrossRefGoogle Scholar
  5. [5]
    A. Kapoor and K. L. Johnson, Effect of changes in contact geometry on shakedown of surfaces in rolling/sliding contact, International J. of Mechanical Sciences, 34 (1992) 223–239, https://www.sciencedirect.com/science/article/pii/002074039 290073P.CrossRefGoogle Scholar
  6. [6]
    A. Kapoor, G. E. Morales–Espejel and A. V. Olver, A shakedown analysis of simple spur gears, Tribology Transactions, 45 (2002) 103–109, https://www.tandfonline. com/doi/abs/10.1080/10402000208982527.CrossRefGoogle Scholar
  7. [7]
    R. S. P. Alan, H. F. Chen, M. Ciavarella and G. Specchia, Shakedown analyses for rolling and sliding contact problems, International J. of Solids & Structures, 43 (2006) 4201–4219, https://www.sciencedirect.com/science/article/pii/S0020768 305003070.CrossRefzbMATHGoogle Scholar
  8. [8]
    E. Conrado, S. Foletti, C. Gorla and I. V. Papadopoulos, Use of multiaxial fatigue criteria and shakedown theorems in thermo–elastic rolling–sliding contact problems, Wear, 270 (2011) 344–354, https://www.sciencedirect.com/science/article/abs/pii/S0043164810004187.CrossRefGoogle Scholar
  9. [9]
    B. D. Allison, Evolution of mechanical properties of M50 bearing steel due to rolling contact fatigue, University of Florida, Florida, United State (2013) 148, https://search. proquest.com/openview/8b0dda537c17a658793f827f029230 34/1?pq–origsite=gscholar&cbl=18750&diss=y.Google Scholar
  10. [10]
    P. N. Moulik, H. T. Y. Yang and S. Chandrasekar, Simulation of thermal stresses due to grinding, International J. of Mechanical Sciences, 43 (2001) 831–851, https://www. sciencedirect.com/science/article/pii/S0020740300000278.CrossRefzbMATHGoogle Scholar
  11. [11]
    Batista,Dias, Lebrun, Flour Le and Inglebert, Contact fatigue of automotive gears: evolution and effects of residual stresses introduced by surface treatments, Fatigue & Fracture of Engineering Materials & Structures, 23 (2000) 217–228, https://onlinelibrary.wiley.com/doi/abs/10.1046/j. 1460–2695.2000.00268.x.Google Scholar
  12. [12]
    Y. Q. Xu, T. Zhang and P. Xu, Analysis of the gear contact fatigue strength based on the compressive residual stress, Advanced Materials Research, 143–144 (2010) 1086–1090, https://www.scientific.net/AMR.143–144.1086.CrossRefGoogle Scholar
  13. [13]
    N. Ahmadi and A. Nayebi, Predicting the ratcheting strain of 304 stainless steel by considering yield surface distortion and using a viscoplastic model, J. of Mechanical Science and Technology, 29 (2015) 2857–2862, https://link.springer. com/article/10.1007/s12206–015–0614–z.CrossRefGoogle Scholar
  14. [14]
    H. P. Evans, M. F. Al–Mayali and K. J. Sharif, Assessment of the effects of residual stresses on fatigue life of real rough surfaces in lubricated contact, International Conference for Students on Applied Engineering, IEEE, Newcastle upon Tyne, UK (2016) 5, https://ieeexplore.ieee.org/abstract/document/7810173/.Google Scholar
  15. [15]
    N. K. Fukumasu, G. A. A. Machado, R. M. Souza and I. F. Machado, Stress analysis to improve pitting resistance in gear teeth, Procedia CIRP, 45 (2016) 255–258, https://www. sciencedirect.com/science/article/pii/S2212827116006442.CrossRefGoogle Scholar
  16. [16]
    A. Warhadpande, An elastic–plastic finite element model for rolling contact fatigue, Mechanical Engineering, Purdue University, Indiana, United States (2012) 208, http://appliedmechanics.asmedigitalcollection.asme.org/article.asp x?articleid=1407904.Google Scholar
  17. [17]
    Y. Shen, S. M. Moghadam, F. Sadeghi, K. Paulson and R. W. Trice, Effect of retained austenite–Compressive residual stresses on rolling contact fatigue life of carburized AISI 8620 steel, International J. of Fatigue, 75 (2015) 135–144, https://www.sciencedirect.com/science/article/pii/S0142112 315000547.CrossRefGoogle Scholar
  18. [18]
    H. Liu, C. Zhu, Z. Sun and C. Song, Starved lubrication of a spur gear pair, Tribology International, 94 (2016) 52–60, https://www.sciencedirect.com/science/article/pii/S0301679 X15003217.CrossRefGoogle Scholar
  19. [19]
    H. Liu, K. Mao, C. Zhu and X. Xu, Mixed lubricated line contact analysis for spur gears using a deterministic model, J. of Tribology, 134 (2012) 021501, http://tribology.asme digitalcollection.asme.org/article.aspx?articleid=1468923.CrossRefGoogle Scholar
  20. [20]
    K. L. Johnson, A graphical approach to shakedown in rolling contact, Springer Netherlands (1990) https://link. springer.com/chapter/10.1007/978–94–009–0779–9_26.CrossRefGoogle Scholar
  21. [21]
    H. Liu, H. Liu, P. Bocher, C. Zhu and P. Wei, Effects of the case hardening properties on the contact fatigue of a wind turbine gear pair, International J. of Mechanical Sciences, 141 (2018) 520–527, https://www.sciencedirect.com/science/article/pii/S0020740317333921.CrossRefGoogle Scholar
  22. [22]
    D. L. Mcdowell and G. J. Moyar, Effects of non–linear kinematic hardening on plastic deformation and residual stresses in rolling line contact, Wear, 144 (1991) 19–37, https://www.sciencedirect.com/science/article/pii/B9780444 887740500067.CrossRefGoogle Scholar
  23. [23]
    W. Reinhardt and R Adibi–Asl, Non–cyclic shakedownratcheting boundary determination: Analytical examples, Pressure Vessels and Piping Conference, ASME, Washington, USA (2010) 555–563, http://proceedings. asmedigitalcollection.asme.org/proceeding.aspx?articleid=1 618525.Google Scholar
  24. [24]
    J. E. Merwin and K. L. Johnson, An analysis of plastic deformation in rolling contact, Proceedings of the Institution of Mechanical Engineers, 1847–1982 (1–196) 177 (1963) 676–690, http://J.s.sagepub.com/doi/abs/10.1243/PIME_ PROC_ 1963_177_052_02.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Haifeng He
    • 1
  • Huaiju Liu
    • 1
  • Caichao Zhu
    • 1
  • Longhua Yuan
    • 2
  1. 1.State Key Laboratory of Mechanical TransmissionsChongqing UniversityChongqingChina
  2. 2.Chongqing Wangjiang Industrial Co.ChongqingChina

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