考虑冲击力的球轴承外圈剥落缺陷双冲击现象动力学建模
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摘要
轴承故障动力学建模是探究剥落激发的双冲击现象与剥落区大小间内在联系的理论基础。基于Hertz接触理论,以外圈滚道表面存在剥落的球轴承为研究对象;对滚动体与剥落区接触的全过程进行内在分析,获得由剥落产生的时变位移激励函数,给出了包含剥落区长度与滚动体直径间比值的冲击力求解公式,并将之引入动力学模型中,建立了考虑冲击力的球轴承外圈剥落双冲击现象动力学模型。运用Runge-Kutta数值积分法求解动力学方程,通过仿真信号与混合陶瓷球轴承外圈故障实测信号对比。结果表明,所建立的考虑冲击力的动力学模型能够有效地预测球轴承故障信号双冲击时间间隔和轴承故障特征频率。
The dynamic modeling for a bearing is a theoretical foundation for investigating the interrelation of the dual-impulse behavior induced by a spall on the inner or outer race with the size of the spalling area. A certain bearing with a spall on its outer race was chosen to be the studied object and the overall passing process of the rolling elements across the outer race spall area was deeply analyzed. On this basis, the time-varying deflection excitation function produced by the outer race spall was obtained, and then the formula including the ratio of ball diameter to spall length for calculating the impact force of the rolling elements striking the spall edge was developed. As a result, a novel dynamic model of the ball bearing with a localized spall on its outer race was proposed based on the Hertzian contact theory, which considers the time-varying displacement mechanism and the impact force excitation due to the outer race spall. The solution to the dynamic equations was carried out using the Runge-Kutta numerical integration method. The comparison of the simulated results and the experimental results of the hybrid ceramic ball bearing with an outer race spall shows good effectiveness of the proposed dynamic model which incorporates impact forces in predicting the dual-impulse time interval and the characteristic defect frequency.
The dynamic modeling for a bearing is a theoretical foundation for investigating the interrelation of the dual-impulse behavior induced by a spall on the inner or outer race with the size of the spalling area. A certain bearing with a spall on its outer race was chosen to be the studied object and the overall passing process of the rolling elements across the outer race spall area was deeply analyzed. On this basis, the time-varying deflection excitation function produced by the outer race spall was obtained, and then the formula including the ratio of ball diameter to spall length for calculating the impact force of the rolling elements striking the spall edge was developed. As a result, a novel dynamic model of the ball bearing with a localized spall on its outer race was proposed based on the Hertzian contact theory, which considers the time-varying displacement mechanism and the impact force excitation due to the outer race spall. The solution to the dynamic equations was carried out using the Runge-Kutta numerical integration method. The comparison of the simulated results and the experimental results of the hybrid ceramic ball bearing with an outer race spall shows good effectiveness of the proposed dynamic model which incorporates impact forces in predicting the dual-impulse time interval and the characteristic defect frequency.
引文
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[3]SAWALHI N,RANDALL R B,ENDO H.The enhancement of fault detection and diagnosis in rolling element bearings using minimum entropy deconvolution combined with spectral kurtosis[J].Mechanical Systems and Signal Processing,2007,21(6):2616-2633.
[4]刘静,邵毅敏,秦晓猛,等.基于非理想Hertz线接触特性的圆柱滚子轴承局部故障动力学建模[J].机械工程学报,2014,50(1):91-97.LIU Jing,SHAO Yimin,QING Xiaomeng,et al.Dynamic modeling on localized defect of cylindrical roller bearing based on non-Hertz line contact characteristics[J].Journal of Mechanical Engineering,2014,50(1):91-97.
[5]徐东,徐永成,陈循,等.单表面故障的滚动轴承系统非线性动力学研究[J].机械工程学报,2010,46(21):61-68.XU Dong,XU Yongcheng,CHEN Xun,et al.Research on nonlinear dynamics of a single surface defect in rolling element bearing systems[J].Journal of Mechanical Engineering,2010,46(21):61-68.
[6]刘倩楠,郭瑜,伍星.滚动轴承外圈剥落故障双冲击特征机理建模[J].振动工程学报,2017,30(4):670-678.LIU Qiannan,GUO Yu,WU Xing.Mechanism modeling of the double-impulses phenomenon of a spall defect on a rolling element bearing outer race[J].Journal of Vibration Engineering,2017,30(4):670-678.
[7]SOPANEN J,MIKKOLA A.Dynamic model of a deep-groove ball bearing including localized and distributed defects.Part1:theory[J].Proceedings of the Institution of Mechanical Engineers,Part K:Journal of Multi-body Dynamics,2003,217(3):201-211.
[8]HARRIS T,KOTZALAS M.Rolling bearing analysisEssential concepts of bearing technology[M].5th ed.New York:Taylor and Francis,2007.
[9]SASSI S,BADRI B,THOMAS M.A numerical model to predict damaged bearing vibrations[J].Journal of Vibration and Control,2007,13(11):1603-1628.
[10]PATIL M S,MATHEW J,RAJENDRAKUMAR P K,et al.A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing[J].International Journal of Mechanical Sciences,2010,52(9):1193-1201.
[11]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].Journal of Tribology,2015,137(3):031101.
[12]PATEL V N,PANDEY R K,TANDON N.A dynamic model for vibration studies of deep groove ball bearings considering single and multiple defects in races[J].Journal of Tribology,2010,132(4):041101.
[13]LIU J,SHAO Y M,LIM T C.Impulse vibration transmissibility characteristics in the presence of localized surface defects in deep groove ball bearing systems[J].Proceedings of the Institution of Mechanical Engineers,Part K:Journal of Multi-body Dynamics,2014,228(1):62-81.
[14]SUNNERSJC S.Varying compliance vibrations of rolling bearings[J].Journal of Sound and Vibration,1978,58(3):363-373.
[2]SAWALHI N,RANDALL R B.Vibration response of spalled rolling element bearings:Observations,simulations and signal processing techniques to track the spall size[J].Mechanical Systems and Signal Processing,2011,25(25):846-870.
[3]SAWALHI N,RANDALL R B,ENDO H.The enhancement of fault detection and diagnosis in rolling element bearings using minimum entropy deconvolution combined with spectral kurtosis[J].Mechanical Systems and Signal Processing,2007,21(6):2616-2633.
[4]刘静,邵毅敏,秦晓猛,等.基于非理想Hertz线接触特性的圆柱滚子轴承局部故障动力学建模[J].机械工程学报,2014,50(1):91-97.LIU Jing,SHAO Yimin,QING Xiaomeng,et al.Dynamic modeling on localized defect of cylindrical roller bearing based on non-Hertz line contact characteristics[J].Journal of Mechanical Engineering,2014,50(1):91-97.
[5]徐东,徐永成,陈循,等.单表面故障的滚动轴承系统非线性动力学研究[J].机械工程学报,2010,46(21):61-68.XU Dong,XU Yongcheng,CHEN Xun,et al.Research on nonlinear dynamics of a single surface defect in rolling element bearing systems[J].Journal of Mechanical Engineering,2010,46(21):61-68.
[6]刘倩楠,郭瑜,伍星.滚动轴承外圈剥落故障双冲击特征机理建模[J].振动工程学报,2017,30(4):670-678.LIU Qiannan,GUO Yu,WU Xing.Mechanism modeling of the double-impulses phenomenon of a spall defect on a rolling element bearing outer race[J].Journal of Vibration Engineering,2017,30(4):670-678.
[7]SOPANEN J,MIKKOLA A.Dynamic model of a deep-groove ball bearing including localized and distributed defects.Part1:theory[J].Proceedings of the Institution of Mechanical Engineers,Part K:Journal of Multi-body Dynamics,2003,217(3):201-211.
[8]HARRIS T,KOTZALAS M.Rolling bearing analysisEssential concepts of bearing technology[M].5th ed.New York:Taylor and Francis,2007.
[9]SASSI S,BADRI B,THOMAS M.A numerical model to predict damaged bearing vibrations[J].Journal of Vibration and Control,2007,13(11):1603-1628.
[10]PATIL M S,MATHEW J,RAJENDRAKUMAR P K,et al.A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing[J].International Journal of Mechanical Sciences,2010,52(9):1193-1201.
[11]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].Journal of Tribology,2015,137(3):031101.
[12]PATEL V N,PANDEY R K,TANDON N.A dynamic model for vibration studies of deep groove ball bearings considering single and multiple defects in races[J].Journal of Tribology,2010,132(4):041101.
[13]LIU J,SHAO Y M,LIM T C.Impulse vibration transmissibility characteristics in the presence of localized surface defects in deep groove ball bearing systems[J].Proceedings of the Institution of Mechanical Engineers,Part K:Journal of Multi-body Dynamics,2014,228(1):62-81.
[14]SUNNERSJC S.Varying compliance vibrations of rolling bearings[J].Journal of Sound and Vibration,1978,58(3):363-373.