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A comprehensive comparative investigation of frictional force models for dynamics of rotor-bearing systems

考虑不同摩擦力模型的转子−轴承系统振动特性研究

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Abstract

Vibrations of a rotor-bearing system (RBS) can be affected by the frictional forces between the components of the inherent bearings. Thus, an in-depth investigation of the influences of the frictional moments of the bearings on the vibrations of the RBS can be helpful for understanding the vibration mechanisms in the rotating machinery. In this study, an improved dynamic model of a RBS considering different frictional force models is presented. A comparative investigation on the influences of the empirical and analytical frictional force models on the vibration characteristics of the RBS is proposed. The empirical frictional force models include Palmgren’s and SKF’s models. The analytical frictional force model considers the rolling friction caused by the radial elastic material hysteresis, slipping friction between the ball and races, viscosity friction caused by the lubricating oil, and contact friction between the ball and cage. The influences of the external load and rotational speed on the vibrations of the RBS are analyzed. The comparative results show that the analytical frictional force model can give a more reasonable method for formulating the effects of the friction forces in the bearings on the vibrations of the RBS. The results also demonstrate that the friction forces in the bearings can significantly affect the vibrations of the RBSs.

摘要

轴承各部件之间的摩擦力直接影响转子−轴承系统的振动特性. 因此, 深入研究轴承摩擦力对转子系统振动的影响将有助于解释转子系统的振动机理. 本文提出了一种考虑不同摩擦力模型的改进转子−轴承系统动力学模型. 研究了经验摩擦力模型和解析摩擦力模型对转子−轴承系统振动特性的影响规律. 经验摩擦力模型包括 Palmgren 模型和 SKF 模型. 分析摩擦力模型考虑了径向弹性材料迟滞引起的滚动摩擦、球与滚道之间的滑动摩擦、 润滑油引起的粘性摩擦、 球与保持架之间的接触摩擦. 分析了外载荷和转速对系统振动特性的影响规律. 结果表明, 本文所建立的分析摩擦力模型可以为研究轴承摩擦力对转子−轴承系统振动特性的影响规律提供一种更合理的方法; 轴承内的摩擦力对转子− 轴承系统的振动特性有显著的影响.

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References

  1. LIU J, SHAO Y. Overview of dynamic modelling and analysis of rolling element bearings with localized and distributed faults [J]. Nonlinear Dynamics, 2018, 93(4): 1765–1798. DOI: https://doi.org/10.1007/s11071-018-4314-y.

    Article  Google Scholar 

  2. LIU J, TANG C, WU H, XU Z, WANG L. An analytical calculation method of the load distribution and stiffness of an angular contact ball bearing [J]. Mechanism and Machine Theory, 2019, 142: 103597. DOI: https://doi.org/10.1016/j.mechmachtheory.2019.103597.

    Article  Google Scholar 

  3. PALMGREN A. Ball and roller bearing engineering [M]. 3rd ed. Burbank, Philadelphia: SKF Industries, 1959.

    Google Scholar 

  4. DENG S R, LI X L, WANG J G, TENG H F. Frictional torque characteristic of angular contact ball bearings [J]. Journal of Mechanical Engineering, 2011, 47(5): 114–120.

    Article  Google Scholar 

  5. KAKUTA K. Generating mechanism of friction torque in a ball bearing 2 [J]. Mechanism, 1965, 3: 645–648.

    Google Scholar 

  6. SNARE B. Rolling resistance in lightly loaded bearings [J]. The Ball Bearing Journal, 1968, 152: 3–8.

    Google Scholar 

  7. SNARE B. Rolling resistance in lightly loaded bearings [J]. The Ball Bearing Journal, 1968, 153: 19–24.

    Google Scholar 

  8. SNARE B. Rolling resistance in lightly loaded bearings [J]. The Ball Bearing Journal, 1968, 154: 3–14.

    Google Scholar 

  9. TODD M J, STEVENS K T. Frictional torque of angular contact ball bearings with different conformities [R]. Risley, Technical Report ESA-CR(P)-1221, 1978.

  10. GENTLE R, PASDARI M. Measurement of cage and pocket friction in a ball bearing for use in a simulation program [J]. ASLE Transactions, 1985, 28(4): 536–541. DOI: https://doi.org/10.1080/05698198508981652.

    Article  Google Scholar 

  11. TRIPPETT R. Ball and needle bearing friction correlations under radial load conditions [J]. SAE Tech, 1985, Paper No. 851512. DOI: https://doi.org/10.4271/851512.

  12. CHIU Y, MYERS M. A rotational approach for determining permissible speed for needle roller bearings [J]. SAE Tech, 1998, Paper No. 982030. DOI: https://doi.org/10.4271/982030.

  13. SKF. General catalog 4000 [R]. Gothenburg, Sweden: Svenska Kullargerfabriken, 2004.

    Google Scholar 

  14. IQBAL S, BENDER F A, CROES J, PLUYMERS B, DESMET W. Frictional power loss in solid-grease-lubricated needle roller bearing [J]. Lubrication Science, 2013, 25(5): 351–367. DOI: https://doi.org/10.1002/ls.1195.

    Article  Google Scholar 

  15. LIU J, YAN Z, SHAO Y. An investigation for the friction torque of a needle roller bearing with the roundness error [J]. Mechanism and Machine Theory, 2018, 121: 259–272. DOI: https://doi.org/10.1016/j.mechmachtheory.2017.10.028.

    Article  Google Scholar 

  16. LIU J, LI X, DING S, PANG R. A time-varying friction moment calculation method of an angular contact ball bearing with the waviness error [J]. Mechanism and Machine Theory, 2020, 148: 103799. DOI: https://doi.org/10.1016/j.mechmachtheory.2020.103799.

    Article  Google Scholar 

  17. TONG V C, HONG S W. Study on the running torque of angular contact ball bearings subjected to angular misalignment [J]. Journal of Engineering Tribology, 2018, 232(7): 890–909. DOI: https://doi.org/10.1177/1350650117732921.

    Google Scholar 

  18. HAN Q, DING Z, QIN Z, WANG T, XU X, CHU F. A triboelectric rolling ball bearing with self-powering and self-sensing capabilities [J]. Nano Energy, 2020, 67: 104277. DOI: https://doi.org/10.1016/j.nanoen.2019.104277.

    Article  Google Scholar 

  19. HAN Q, DING Z, XU X, WANG T, CHU F. Stator current model for detecting rolling bearing faults in induction motors using magnetic equivalent circuits [J]. Mechanical Systems and Signal Processing, 2019, 131: 554575. DOI: https://doi.org/10.1016/j.ymssp.2019.06.010.

    Google Scholar 

  20. XU T, YANG L, WU Y. Friction torque study on double-row tapered roller bearing [C]// 2019 IEEE International Instrumentation and Measurement Technology Conference (I2MTC). Auckland, New Zealand: IEEE, 2019: 18974243.

    Google Scholar 

  21. KWAK W, LEE J, LEE Y B. Theoretical and experimental approach to ball bearing frictional characteristics compared with cryogenic friction model and dry friction model [J]. Mechanical Systems and Signal Processing, 2019, 124: 424–438. DOI: https://doi.org/10.1016/j.ymssp.2019.01.056.

    Article  Google Scholar 

  22. BABU C K, TANDON N, PANDEY R K. Vibration modeling of a rigid rotor supported on the lubricated angular contact ball bearings considering six degrees of freedom and waviness on balls and races [J]. Journal of Vibration and Acoustics, 2012, 134(1): 011006. DOI: https://doi.org/10.1115/1.4005140.

    Article  Google Scholar 

  23. BABU C K, TANDON N, PANDEY R K. Nonlinear vibration analysis of an elastic rotor supported on angular contact ball bearings considering 6 DOF and waviness on balls and races [J]. ASME Journal of Vibration and Acoustics, 2014, 136: 044503. DOI: https://doi.org/10.1115/1.4027712.

    Article  Google Scholar 

  24. LIU J, SHAO Y M, MING J Z. The effects of the shape of localized defect in ball bearings on the vibration waveform [J]. Journal of Multi-body Dynamics, 2013, 227(3): 261–274. DOI: https://doi.org/10.1177/1464419313486102.

    Google Scholar 

  25. LIU J, SHAO Y M, ZHU W D. A new model for the relationship between vibration characteristics caused by the time-varying contact stiffness of a deep groove ball bearing and defect sizes [J]. ASME Journal of Tribology, 2015, 137(3): 031101. DOI: 1.4029461.

    Article  Google Scholar 

  26. CAO H, NIU L, XI S, CHEN X. Mechanical model development of rolling bearing-rotor systems: A review [J]. Mechanical Systems and Signal Processing, 2018, 102: 37–58. DOI: https://doi.org/10.1016/j.ymssp.2017.09.023.

    Article  Google Scholar 

  27. CAO H, LI Y, CHEN X. A new dynamic model of ball-bearing rotor systems based on rigid body element [J]. Journal of Manufacturing Science and Engineering, 2016, 138(7): 071007. DOI: https://doi.org/10.1115/1.4032582.

    Article  Google Scholar 

  28. HALMINEN O, ACEITUNO J F, ESCALONA J L, SOPANEN J, MIKKOLA A. A touchdown bearing with surface waviness: Friction loss analysis [J]. Mechanism and Machine Theory, 2017, 110: 73–84. DOI: https://doi.org/10.1016/j.mechmachtheory.2017.01.002

    Article  Google Scholar 

  29. LIU J, SHAO Y. Dynamic modeling for rigid rotor bearing systems with a localized defect considering additional deformations at the sharp edges [J]. Journal of Sound and Vibration, 2017, 398: 84–102. DOI: https://doi.org/10.1016/j.jsv.2017.03.007.

    Article  Google Scholar 

  30. LIU J. A dynamic modelling method of a rotor-roller bearing-housing system with a localized fault including the additional excitation zone [J]. Journal of Sound and Vibration, 2020, 469: 115144. DOI: https://doi.org/10.1016/j.jsv.2019.115144.

    Article  Google Scholar 

  31. NEISI N, HEIKKINEN J E, SOPANEN J. Influence of surface waviness in the heat generation and thermal expansion of the touchdown bearing [J]. European Journal of Mechanics-A/Solids, 2019, 74: 34–47. DOI: https://doi.org/10.1016/j.euromechsol.2018.10.014.

    Article  Google Scholar 

  32. XU L X, CHEN B K, LI C Y. Dynamic modelling and contact analysis of bearing-cycloid-pinwheel transmission mechanisms used in joint rotate vector reducers [J]. Mechanism and Machine Theory, 2019, 137: 432–458. DOI: https://doi.org/10.1016/j.mechmachtheory.2019.03.035.

    Article  Google Scholar 

  33. ZHENG D, CHEN W, XIAO G, ZHENG D. Effect of vibration on power loss of angular contact ball bearings [J]. Industrial Lubrication and Tribology, 2019, DOI: https://doi.org/10.1108/ILT-06-2019-0217.

  34. POPESCU A, HOUPERT L, OLARU D N. Four approaches for calcuting power losses in an angular contact ball bearing [J]. Mechanism and Machine Theory, 2020, 144: 103669. DOI: https://doi.org/10.1016/j.mechmachtheory.2019.103669.

    Article  Google Scholar 

  35. HAMMAMI M, MARTINS R, FERNANDES C, SEABRA J, ABBES M S, HADDAR M. Friction torque in rolling bearings lubricated with axle gear oils [J]. Tribology International, 2018, 119: 419–435. DOI: https://doi.org/10.1016/j.triboint.2017.11.018.

    Article  Google Scholar 

  36. ZHANG X, XU H, CHANG W, XI H, XING Y, PEI S Y, WANG F C. Torque variations of ball bearings based on dynamic model with geometrical imperfections and operating conditions [J]. Tribology International, 2019, 133: 193–205. DOI: https://doi.org/10.1016/j.triboint.2019.01.002.

    Article  Google Scholar 

  37. MAJDOUB F, SAUNIER L, SIDOROFF-COICAUD C, MEVEL B. Experimental and numerical roller skew in tapered roller bearings [J]. Tribology International, 2020, 145: 106142. DOI: https://doi.org/10.1016/j.triboint.2019.106142.

    Article  Google Scholar 

  38. HARRIS T A, KOTZALAS M N. Rolling bearing analysis-essential concepts of bearing technology [M]. 5th ed. New York: Taylor and Francis, 2007.

    Google Scholar 

  39. LYNAGH N, RAHNEJAT H, EBRAHIMI M, AINI R. A bearing induced vibration in precision high speed routing spindles [J]. International Journal of Machine Tools and Manufacture, 2000, 40: 561–577. DOI: https://doi.org/10.1016/S0890-6955(02)00049-4.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an, 710072, China

    Jing Liu  (刘静)

  2. Laboratory for Unmanned Underwater Vehicle, Northwestern Polytechnical University, Xi’an, 710072, China

    Jing Liu  (刘静)

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  1. Jing Liu  (刘静)
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Correspondence to Jing Liu  (刘静).

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Foundation item: Projects(51605051, 51975068) supported by the National Natural Science Foundation of China; Project(3102020HHZY030001) supported by the Fundamental Research Funds for the Central Universities, China

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Liu, J. A comprehensive comparative investigation of frictional force models for dynamics of rotor-bearing systems. J. Cent. South Univ. 27, 1770–1779 (2020). https://doi.org/10.1007/s11771-020-4406-y

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