Abstract
In the research on rolling bearing misalignment, the influence of bearing misalignment on the vibration characteristics of the rotor system is rarely considered, especially for the dynamic bearing misalignment. Based on the limitations of the existing research, a five-degree of freedom (5-DOF) nonlinear force model considering bearing misalignment is proposed firstly. The model comprehensively considers the parallel and angular misalignment, static and dynamic misalignment, inner ring and outer ring misalignment. Secondly, the effects of misalignment on the dynamic contact characteristics of bearing and the vibration characteristics of the rotor system are analyzed. Then, based on the dynamic response, the evaluation indexes of bearing misalignment are given. Finally, the similarities and differences between parallel and angular misalignment, static and dynamic misalignment are compared. The results show that the bearing misalignment increases the resonance speed of the rotor, and the amplitude jum** phenomenon appears in the resonance region, showing the characteristics of hardening-type nonlinearity. In terms of frequency characteristics, dynamic parallel misalignment and dynamic angular misalignment increase the amplitude of frequency components fr and 2fr, respectively. The research can be used as a theoretical basis and valuable reference for fault identification of the rotor-bearing system.
摘要
在滚动轴承不对中问题的研究中, 以往的研究中很少考虑轴承不对中对转子系统振动特性的影响。基于现有研究的局限性, 首先, 给出了一种考虑轴承不对中的5 自由度非线性力模型, 该模型综合考虑了轴承的**行和角不对中、静态与动态不对中、内圈与外圈不对中等多种情况。其次, 将该模型应用在转子有限元模型中, 分析了不对中对轴承动态接触特性和转子系统振动特性的影响。然后, 给出了衡量轴承不对中程度的评价指标。最后, 对比分析了**行和角不对中、静态与动态不对中的异同点。结果表明, 轴承不对中提高了转子的共振转速, 在共振区出现了幅值跳跃现象, 表现出硬式非线性特征。从频率特征上来看, 滚动轴承动态**行不对中和动态角不对中分别导致转子旋转频率成分fr和2fr的幅值增大。动态不对中导致轴承的承载区随着轴承内圈的旋转而时刻变化。该研究可为转子-轴承系统的故障识别提供理论依据和有价值的参考。
References
HINTON W R. An investigation into the causes of ball bearing failures in types P2 and P3 engine-driven generators [J]. Wear, 1970, 16(1–2): 3–42. DOI: https://doi.org/10.1016/0043-1648(70)90261-9.
SALAM I, TAUQIR A, UL HAQ A, et al. An air crash due to fatigue failure of a ball bearing [J]. Engineering Failure Analysis, 1998, 5(4): 261–269. DOI: https://doi.org/10.1016/S1350-6307(98)00024-7.
XU Rui, SHEN **an-shao, FAN Qiang, et al. Failure analysis on aero-engine spindle ball bearings [J]. Bearing, 2012(6): 20–24. DOI: https://doi.org/10.19533/j.issn1000-3762.2012.06.009. (in Chinese)
CHEN Cong-hui. The common failures of aero-engine mechanical system [M]. Bei**g: China Aviation Publishing & Media, 2013. (in Chinese)
CRAWFORD T S. The experimental determination of ball bearing cage stress [J]. Wear, 1970, 16(1–2): 43–52. DOI: https://doi.org/10.1016/0043-1648(70)90262-0.
ISO 15243: 2017. Rolling bearings-damage and failures-terms, characteristics and causes [R]. Geneva: International Organization for Standardization, 2017.
HARRIS T A, KOTZALAS M N. Advanced concepts of bearing technology: Rolling bearing analysis [M]. Fifth edition. Boca Raton: CRC Press, 2006. DOI: https://doi.org/10.1201/9781420006582.
LIOULIOS A N, ANTONIADIS I A. Effect of rotational speed fluctuations on the dynamic behaviour of rolling element bearings with radial clearances [J]. International Journal of Mechanical Sciences, 2006, 48(8): 809–829. DOI: https://doi.org/10.1016/j.ijmecsci.2006.03.006.
WANG Li-qin, CUI Li, ZHENG De-zhi, et al. Nonlinear dynamics behaviors of a rotor roller bearing system with radial clearances and waviness considered [J]. Chinese Journal of Aeronautics, 2008, 21(1): 86–96. DOI: https://doi.org/10.1016/S1000-9361(08)60012-6.
WANG Hai-fei, GONG Jun-jie, CHEN Guo. Characteristics analysis of aero-engine whole vibration response with rolling bearing radial clearance [J]. Journal of Mechanical Science and Technology, 2017, 31(5): 2129–2141. DOI: https://doi.org/10.1007/s12206-017-0409-5.
WANG Kai, YANG Hong-juan, WU Han, et al. Theoretical model and experimental study of the influence of bearing inner clearance on bearing vibration [J]. Engineering Failure Analysis, 2022, 137: 106247. DOI: https://doi.org/10.1016/j.engfailanal.2022.106247.
LU Zhen-yong, ZHONG Shun, CHEN Hui-zheng, et al. Nonlinear response analysis for a dual-rotor system supported by ball bearing [J]. International Journal of Nonlinear Mechanics, 2021, 128: 103627. DOI: https://doi.org/10.1016/j.ijnonlinmec.2020.103627.
CHENG Hong-chuan, ZHANG Yi-min, LU Wen-jia, et al. Mechanical characteristics and nonlinear dynamic response analysis of rotor-bearing-coupling system [J]. Applied Mathematical Modelling, 2021, 93: 708–727. DOI: https://doi.org/10.1016/j.apm.2020.12.041.
GAO Peng, HOU Lei, YANG Rui, et al. Local defect modelling and nonlinear dynamic analysis for the inter-shaft bearing in a dual-rotor system [J]. Applied Mathematical Modelling, 2019, 68: 29–47. DOI: https://doi.org/10.1016/j.apm.2018.11.014.
YANG Rui, JIN Yu-lin, HOU Lei, et al. Study for ball bearing outer race characteristic defect frequency based on nonlinear dynamics analysis [J]. Nonlinear Dynamics, 2017, 90(2): 781–796. DOI: https://doi.org/10.1007/s11071-017-3692-x.
YANG Yang, OUYANG Hua-jiang, YANG Yi-ren, et al. Vibration analysis of a dual-rotor-bearing-double casing system with pedestal looseness and multi-stage turbine blade-casing rub [J]. Mechanical Systems and Signal Processing, 2020, 143: 106845. DOI: https://doi.org/10.1016/j.ymssp.2020.106845.
JIN Yu-lin, LIU Zhi-wen, YANG Yang, et al. Nonlinear vibrations of a dual-rotor-bearing-coupling misalignment system with blade-casing rubbing [J]. Journal of Sound and Vibration, 2021, 497: 115948. DOI: https://doi.org/10.1016/j.jsv.2021.115948.
XIE Wen-zhen, LIU Chao, WANG Nan-fei, et al. Numerical and experimental analysis of rubbing-misalignment mixed fault in a dual-rotor system [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2021, 235(17): 3179–3198. DOI: https://doi.org/10.1177/0954406220968581.
PRABITH K, PRAVEEN KRISHNA I R. Response and stability analysis of a two-spool aero-engine rotor system undergoing multi-disk rub-impact [J]. International Journal of Mechanical Sciences, 2022, 213: 106861. DOI: https://doi.org/10.1016/j.ijmecsci.2021.106861.
LIU **g-ze, FEI Qing-guo, WU Shao-qing, et al. Nonlinear vibration response of a complex aeroengine under the rubbing fault [J]. Nonlinear Dynamics, 2021, 106(3): 1869–1890. DOI: https://doi.org/10.1007/s11071-021-06717-4.
LUO Yue-gang, WANG Peng-fei, JIA Hai-feng, et al. Dynamic characteristics analysis of a seal-rotor system with rub-impact fault [J]. Journal of Computational and Nonlinear Dynamics, 2021, 16(8): 081003. DOI: https://doi.org/10.1115/1.4051185.
LEE Y S, LEE C W. Modelling and vibration analysis of misaligned rotor-ball bearing systems [J]. Journal of Sound and Vibration, 1999, 224(1): 17–32. DOI: https://doi.org/10.1006/jsvi.1997.1301.
WANG Nan-fei, JIANG Dong-xiang. Vibration response characteristics of a dual-rotor with unbalance-misalignment coupling faults: Theoretical analysis and experimental study [J]. Mechanism and Machine Theory, 2018, 125: 207–219. DOI: https://doi.org/10.1016/j.mechmachtheory.2018.03.009.
LU Kuan, JIN Yu-lin, HUANG Pan-feng, et al. The applications of POD method in dual rotor-bearing systems with coupling misalignment [J]. Mechanical Systems and Signal Processing, 2021, 150: 107236. DOI: https://doi.org/10.1016/j.ymssp.2020.107236.
LIU **g. A comprehensive comparative investigation of frictional force models for dynamics of rotor-bearing systems [J]. Journal of Central South University, 2020, 27(6): 1770–1779. DOI: https://doi.org/10.1007/s11771-020-4406-y.
YI Jun, LIU Heng, WANG Feng-tao, et al. The resonance effect induced by the variable compliance vibration for an elastic rotor supported by roller bearings [J]. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics, 2014, 228(4): 380–387. DOI: https://doi.org/10.1177/1464419314540901.
GAO Peng, HOU Lei, CHEN Yu-shu. Dynamic load and thermal coupled analysis for the inter-shaft bearing in a dual-rotor system [J]. Meccanica, 2021, 56(11): 2691–2706. DOI: https://doi.org/10.1007/s11012-021-01410-7.
ZHANG Du-zhou, WU Deng-yun, HAN Qin-kai, et al. Nonlinear dynamic force transmissibility of a flywheel rotor supported by angular contact ball bearings [J]. Nonlinear Dynamics, 2021, 103(3): 2273–2286. DOI: https://doi.org/10.1007/s11071-021-06221-9.
GAO Tian, CAO Shu-qian, SUN Yong-tao. Nonlinear dynamic behavior of a flexible asymmetric aero-engine rotor system in maneuvering flight [J]. Chinese Journal of Aeronautics, 2020, 33(10): 2633–2648. DOI: https://doi.org/10.1016/j.cja.2020.04.001.
HOU Sheng-liang, HOU Lei, DUN Shi-wei, et al. Vibration characteristics of a dual-rotor system with non-concentricity [J]. Machines, 2021, 9(11): 251. DOI: https://doi.org/10.3390/machines9110251.
XU Teng-fei, YANG Li-hua, WU Wei, et al. Effect of angular misalignment of inner ring on the contact characteristics and stiffness coefficients of duplex angular contact ball bearings [J]. Mechanism and Machine Theory, 2021, 157: 104178. DOI: https://doi.org/10.1016/j.mechmachtheory.2020.104178.
ZHENG **g-yang, JI **-chen, YIN Shan, et al. Internal loads and contact pressure distributions on the main shaft bearing in a modern gearless wind turbine [J]. Tribology International, 2020, 141: 105960. DOI: https://doi.org/10.1016/j.triboint.2019.105960.
YANG Li-hua, XU Teng-fei, XU Hao-liang, et al. Mechanical behavior of double-row tapered roller bearing under combined external loads and angular misalignment [J]. International Journal of Mechanical Sciences, 2018, 142–143: 561–574. DOI: https://doi.org/10.1016/j.ijmecsci.2018.04.056.
YANG Zhong-chi, ZHANG Yu, ZHANG Ke, et al. Wear analysis of angular contact ball bearing in multiple-bearing spindle system subjected to uncertain initial angular misalignment [J]. Journal of Tribology, 2021, 143(9): 091703. DOI: https://doi.org/10.1115/1.4049258.
XU Hong-yang, WANG Peng-fei, MA Hui, et al. Analysis of axial and overturning ultimate load-bearing capacities of deep groove ball bearings under combined loads and arbitrary rotation speed [J]. Mechanism and Machine Theory, 2022, 169: 104665. DOI: https://doi.org/10.1016/j.mechmachtheory.2021.104665.
WEN Cheng-wei, MENG **ang-hui, LYU Bu-gao, et al. Influence of angular misalignment on the tribological performance of high-speed micro ball bearings considering full multibody interactions [J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2021, 235(6): 1168–1189. DOI: https://doi.org/10.1177/1350650120948292.
ZHANG Yan-fei, FANG Bin, KONG Ling-fei, et al. Effect of the ring misalignment on the service characteristics of ball bearing and rotor system [J]. Mechanism and Machine Theory, 2020, 151: 103889. DOI: https://doi.org/10.1016/j.mechmachtheory.2020.103889.
WARDA B, CHUDZIK A. Effect of ring misalignment on the fatigue life of the radial cylindrical roller bearing [J]. International Journal of Mechanical Sciences, 2016, 111–112: 1–11. DOI: https://doi.org/10.1016/j.ijmecsci.2016.03.019.
YI Jun, PANG Bi-tao, LIU Heng, et al. Influence of misalignment on nonlinear dynamic characteristics for matched bearings-rotor system [J]. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multibody Dynamics, 2014, 228(2): 172–181. DOI: https://doi.org/10.1177/1464419313520143.
WANG Peng-fei, XU Hong-yang, MA Hui, et al. Effects of three types of bearing misalignments on dynamic characteristics of planetary gear set-rotor system [J]. Mechanical Systems and Signal Processing, 2022, 169: 108736. DOI: https://doi.org/10.1016/j.ymssp.2021.108736.
PARMAR V, SARAN V H, HARSHA S. Effect of dynamic misalignment on the vibration response, trajectory followed and defect-depth achieved by the rolling-elements in a double-row spherical rolling-element bearing [J]. Mechanism and Machine Theory, 2021, 162: 104366. DOI: https://doi.org/10.1016/j.mechmachtheory.2021.104366.
WEN Bao-gang, WANG Mei-ling, HAN Qing-kai, et al. Effect of ball bearing misalignment on dynamic characteristics of rotor system [J]. IOP Conference Series: Materials Science and Engineering, 2021, 1081(1): 012014. DOI: https://doi.org/10.1088/1757-899x/1081/1/012014.
MONMOUSSEAU P, FILLON M. Analysis of static and dynamic misaligned tilting-pad journal bearings [J]. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 1999, 213(4): 253–261. DOI: https://doi.org/10.1243/1350650991542640.
LI M. Nonlinear vibration of a multirotor system connected by a flexible coupling subjected to the holonomic constraint of dynamic angular misalignment [J]. Mathematical Problems in Engineering, 2012: 1–15. DOI: https://doi.org/10.1155/2012/243758.
WU Kun, LIU Zhi-wei, DING Qian. Vibration responses of rotating elastic coupling with dynamic spatial misalignment [J]. Mechanism and Machine Theory, 2020, 151: 103916. DOI: https://doi.org/10.1016/j.mechmachtheory.2020.103916.
LIEW H V, LIM T C. Analysis of time-varying rolling element bearing characteristics [J]. Journal of Sound and Vibration, 2005, 283(3–5): 1163–1179. DOI: https://doi.org/10.1016/j.jsv.2004.06.022.
ZHU Hai-min, CHEN Wei-fang, ZHU Ru-peng, et al. Dynamic analysis of a flexible rotor supported by ball bearings with dam** rings based on FEM and lumped mass theory [J]. Journal of Central South University, 2020, 27(12): 3684–3701. DOI: https://doi.org/10.1007/s11771-020-4510-z.
Author information
Authors and Affiliations
Corresponding author
Additional information
Contributors
WANG Peng-fei established the models and edited the draft of manuscript. YANG Yang, XU Hong-yang and MA Hui edited the manuscript. MA Hui, HAN Qing-kai, LUO Zhong and WEN Bang-chun developed the overarching research goals and provided technical guidance.
Foundation item
Project(20195208003) supported by the Basic Research, China
Conflict of interest
WANG Peng-fei, YANG Yang, XU Hong-yang, MA Hui, HAN Qing-kai, LUO Zhong and WEN Bang-chun declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Wang, Pf., Yang, Y., Xu, Hy. et al. Effect of static and dynamic misalignment of rolling bearing on nonlinear vibration characteristics of rotor system. J. Cent. South Univ. 30, 871–903 (2023). https://doi.org/10.1007/s11771-023-5268-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-023-5268-x