多事件激励的滚动轴承动力学建模
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摘要
针对径向载荷作用下滚动轴承表面局部缺陷引起的振动问题,为了更加准确地揭示振动响应的机理,将滚动体经过缺陷的接触过程进一步细化为多事件,建立了内圈表面存在局部缺陷的滚动轴承2自由度动力学模型。将滚动体从进入缺陷到离开缺陷的过程细化为进入事件、冲击事件、离开事件和载荷补偿事件,根据相应事件构造合适的激励力函数;考虑缺陷和轴承变刚度振动引起的时变位移对动力学响应特性的影响,基于赫兹接触理论,建立局部缺陷轴承的动力学模型。利用四阶变步长的龙格-库塔法对动力学方程进行求解,得到了振动响应信号;同时研究了缺陷尺寸和转速对轴承系统振动加速度幅值的影响规律。通过故障轴承实验,验证了模型的正确性和可靠性。
A 2-DOF dynamic model for rolling bearings was built to reveal their vibration response mechanism more correctly due to their inner race surface existing localized defects under action of radial loads. The process of rolling elements entering defective area until leaving was described as four events including entry event,impact one,exit one and load compensation one. Appropriate excitation force functions were constructed according to the corresponding events.Considering the effects of time-varying displacements due to defects and bearing's stiffness-varying vibrations on bearing's dynamic characteristics, based on Hertz contact theory, the dynamic model for a bearing with local defects was established. The fourth-order Runge-Kutta method with varying steps was used to solve the dynamic equation and obtain the model's vibration response signals. The effect laws of defect size and rotating speed on bearing system 's vibration acceleration amplitude were investigated. The validity and feasibility of the dynamic model were verified using faulty bearings' tests.
A 2-DOF dynamic model for rolling bearings was built to reveal their vibration response mechanism more correctly due to their inner race surface existing localized defects under action of radial loads. The process of rolling elements entering defective area until leaving was described as four events including entry event,impact one,exit one and load compensation one. Appropriate excitation force functions were constructed according to the corresponding events.Considering the effects of time-varying displacements due to defects and bearing's stiffness-varying vibrations on bearing's dynamic characteristics, based on Hertz contact theory, the dynamic model for a bearing with local defects was established. The fourth-order Runge-Kutta method with varying steps was used to solve the dynamic equation and obtain the model's vibration response signals. The effect laws of defect size and rotating speed on bearing system 's vibration acceleration amplitude were investigated. The validity and feasibility of the dynamic model were verified using faulty bearings' tests.
引文
[1]WALTERS C T.The dynamics of ball bearings[J].Journal of Tribology,1970,93(1):1-10.
[2]SUNNERSJO C S.Varying compliance vibrations of rolling bearings[J].Journal of Sound and Vibration,1978,58(3):363-373.
[3]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.
[4]PATEL V N,TANDON N,PANDEY R K.A dynamic model for vibration studies of deep groove ball bearings considering single and multiple defects in races[J].Journal of Tribology,2010,132(10):041101-1-10.
[5]杨将新,曹冲锋,曹衍龙,等.内圈局部损伤滚动轴承系统动态特性建模及仿真[J].浙江大学学报(工学版),2007,41(4):551-555.YANG Jiangxin,CAO Chongfeng,CAO Yanlong,et al.Model for dynamic characteristics produced by inner race local defect in ball bearing system and its simulation[J].Journal of Zhejiang University(Engineering Science),2007,41(4):551-555.
[6]RAFSANJANI A,ABBASION S,FARSHIDIANFAR A,et al.Nonlinear dynamic modeling of surface defects in rolling element bearing systems[J].Journal of Sound and Vibration,2009,319(3/4/5):1150-1174.
[7]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,QIN Xiaomeng,et al.Dynamic modeling on localized defect of cylindrical roller bearing based on non-Hertz line contact characteristics systems[J].Journal of Mechanical Engineering,2014,50(1):91-97.
[8]SHAO Y,LIU J,YE J.A new method to model a localized surface defect in a cylindrical roller-bearing dynamic simulation[J].Proceedings of the Institution of Mechanical Engineers,Part J:Journal of Engineering Tribology,2013,228(2):140-159.
[9]NAKHAEINEJAD M,BRYANT M D.Dynamic modeling of rolling element bearings with surface contact defects using bond graphs[J].ASME Journal of Tribology,2011,133(1):011102-1-12.
[10]张根源,周泓,常宗瑜.存在点缺陷的深沟球轴承的动力学响应[J].浙江大学学报(工学版),2009,43(8):1497-1500.ZHANG Genyuan,ZHOU Hong,CHANG Zongyu.Dynamic response of deep groove ball bearing with point defects[J].Journal of Zhejiang University(Engineering Science),2009,43(8):1497-1500.
[11]SAWALHI N,RANDALL R B.Simulating gear and bearing interactions in the presence of faults:Part I.The combined gear bearing dynamic model and the simulation of localised bearing faults[J].Mechanical Systems and Signal Processing,2008,22(22):1924-1951.
[12]SAWALHI N,RANDALL R B.Simulating gear and bearing interactions in the presence of faults:Part II.Simulation of the vibrations produced by extended bearing faults[J].Mechanical Systems and Signal Processing,2008,22(8):1952-1966.
[13]张建军,王仲生,芦玉华,等.基于非线性动力学的滚动轴承故障工程建模与分析[J].振动与冲击,2010,29(11):30-34.ZHANG Jianjun,WANG Zhongsheng,LU Yuhua,et al.Nonlinear dynamic modeling for localized defects in a rolling element bearing[J].Journal of Vibration and Shock,2010,29(11):30-34.
[14]MOAZENAHMADI A,PETERSEN C D,HOWARD C Q.A nonlinear dynamic model of the vibration response of defective rolling element bearings[C]//Acoustics.Bangkok,2013.
[15]CUI L,ZHANG Y,ZHANG F,et al.Vibration response mechanism of faulty outer race rolling element bearings for quantitative analysis[J].Journal of Sound and Vibration,2015,364(3):67-76.
[16]赵联春.球轴承振动的研究[D].杭州:浙江大学,2003.
[17]剡昌锋,苑浩,王鑫,等.点接触弹流润滑条件下的深沟球轴承表面局部缺陷动力学建模[J].振动与冲击,2016,35(14):61-70.YAN Changfeng,YUAN Hao,WANG Xin,et al.Dynamics modeling on local defect of deep groove ball bearing under point contact elasto-hydrodynamic lubrication condition[J].Journal of Vibration and Shock,2016,35(14):61-70.
[18]CAO H,LI Y,NIU L,et al.A general method for the dynamic modeling of ball bearing-rotor systems[J].Journal of Manufacturing Science and Engineering,2015,137(2):021016-1-11.
[19]NIU L,CAO H,HE Z,et al.A systematic study of ball passing frequencies based on dynamic modeling of rolling ball bearings with localized surface defects[J].Journal of Sound and Vibration,2015,357:207-232.
[20]NIU L,CAO H,XIONG X.Dynamic modeling and vibration response simulations of angular contact ball bearings with ball defects considering the three-dimensional motion of balls[J].Tribology International,2017,209:26-39.
[21]MCFADDEN P D,SMITH J D.Model for the vibration produced by single point defect in a rolling element bearing[J].Journal of Sound and Vibration,1984,96(1):69-82.
[22]EPPS I K.An investigation into vibrations excited by discrete faults in rolling element bearings[D].Christchurch:University of Canterbury,Upper Riccarton,1991.
[23]TANDON N,CHOUDHURY A.An analytical model for the prediction of the vibration response of rolling element bearings due to a localized defect[J].Journal of Sound and Vibration,1997,205(3):275-292.
[24]CHOUDHURY A,TANDON N.Vibration response of rolling element bearings in a rotor bearing system to a local defect under radial load[J].Journal of Tribology,2006,128(2):252-261.
[25]SINGH S,KOPKE U G,HOWARD C Q,et al.Analyses of contact forces and vibration response for a defective rolling element bearing using an explicit dynamics finite element model[J].Journal of Sound and Vibration,2014,333(21):5356-5377.
[26]KHANAM S,TANDON N,DUTT J K.Force analysis due to local defect in rolling bearings for fault diagnosis[M]//Proceedings of the 9th IFTo MM International Conference on Rotor Dynamics.Springer International Publishing,2015:577-586.
[27]KHANAM S,TANDON N,DUTT J K.Multi-event excitation force model for inner race defect in a rolling element bearing[J].Journal of Tribology,2016,138(1):011106-1-15.
[28]FAN Zhiqi.Vibration-based condition monitoring in planetary gearbox via using an internal sensor[D].Sydney:The University of New South Wales,2015.
[2]SUNNERSJO C S.Varying compliance vibrations of rolling bearings[J].Journal of Sound and Vibration,1978,58(3):363-373.
[3]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.
[4]PATEL V N,TANDON N,PANDEY R K.A dynamic model for vibration studies of deep groove ball bearings considering single and multiple defects in races[J].Journal of Tribology,2010,132(10):041101-1-10.
[5]杨将新,曹冲锋,曹衍龙,等.内圈局部损伤滚动轴承系统动态特性建模及仿真[J].浙江大学学报(工学版),2007,41(4):551-555.YANG Jiangxin,CAO Chongfeng,CAO Yanlong,et al.Model for dynamic characteristics produced by inner race local defect in ball bearing system and its simulation[J].Journal of Zhejiang University(Engineering Science),2007,41(4):551-555.
[6]RAFSANJANI A,ABBASION S,FARSHIDIANFAR A,et al.Nonlinear dynamic modeling of surface defects in rolling element bearing systems[J].Journal of Sound and Vibration,2009,319(3/4/5):1150-1174.
[7]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,QIN Xiaomeng,et al.Dynamic modeling on localized defect of cylindrical roller bearing based on non-Hertz line contact characteristics systems[J].Journal of Mechanical Engineering,2014,50(1):91-97.
[8]SHAO Y,LIU J,YE J.A new method to model a localized surface defect in a cylindrical roller-bearing dynamic simulation[J].Proceedings of the Institution of Mechanical Engineers,Part J:Journal of Engineering Tribology,2013,228(2):140-159.
[9]NAKHAEINEJAD M,BRYANT M D.Dynamic modeling of rolling element bearings with surface contact defects using bond graphs[J].ASME Journal of Tribology,2011,133(1):011102-1-12.
[10]张根源,周泓,常宗瑜.存在点缺陷的深沟球轴承的动力学响应[J].浙江大学学报(工学版),2009,43(8):1497-1500.ZHANG Genyuan,ZHOU Hong,CHANG Zongyu.Dynamic response of deep groove ball bearing with point defects[J].Journal of Zhejiang University(Engineering Science),2009,43(8):1497-1500.
[11]SAWALHI N,RANDALL R B.Simulating gear and bearing interactions in the presence of faults:Part I.The combined gear bearing dynamic model and the simulation of localised bearing faults[J].Mechanical Systems and Signal Processing,2008,22(22):1924-1951.
[12]SAWALHI N,RANDALL R B.Simulating gear and bearing interactions in the presence of faults:Part II.Simulation of the vibrations produced by extended bearing faults[J].Mechanical Systems and Signal Processing,2008,22(8):1952-1966.
[13]张建军,王仲生,芦玉华,等.基于非线性动力学的滚动轴承故障工程建模与分析[J].振动与冲击,2010,29(11):30-34.ZHANG Jianjun,WANG Zhongsheng,LU Yuhua,et al.Nonlinear dynamic modeling for localized defects in a rolling element bearing[J].Journal of Vibration and Shock,2010,29(11):30-34.
[14]MOAZENAHMADI A,PETERSEN C D,HOWARD C Q.A nonlinear dynamic model of the vibration response of defective rolling element bearings[C]//Acoustics.Bangkok,2013.
[15]CUI L,ZHANG Y,ZHANG F,et al.Vibration response mechanism of faulty outer race rolling element bearings for quantitative analysis[J].Journal of Sound and Vibration,2015,364(3):67-76.
[16]赵联春.球轴承振动的研究[D].杭州:浙江大学,2003.
[17]剡昌锋,苑浩,王鑫,等.点接触弹流润滑条件下的深沟球轴承表面局部缺陷动力学建模[J].振动与冲击,2016,35(14):61-70.YAN Changfeng,YUAN Hao,WANG Xin,et al.Dynamics modeling on local defect of deep groove ball bearing under point contact elasto-hydrodynamic lubrication condition[J].Journal of Vibration and Shock,2016,35(14):61-70.
[18]CAO H,LI Y,NIU L,et al.A general method for the dynamic modeling of ball bearing-rotor systems[J].Journal of Manufacturing Science and Engineering,2015,137(2):021016-1-11.
[19]NIU L,CAO H,HE Z,et al.A systematic study of ball passing frequencies based on dynamic modeling of rolling ball bearings with localized surface defects[J].Journal of Sound and Vibration,2015,357:207-232.
[20]NIU L,CAO H,XIONG X.Dynamic modeling and vibration response simulations of angular contact ball bearings with ball defects considering the three-dimensional motion of balls[J].Tribology International,2017,209:26-39.
[21]MCFADDEN P D,SMITH J D.Model for the vibration produced by single point defect in a rolling element bearing[J].Journal of Sound and Vibration,1984,96(1):69-82.
[22]EPPS I K.An investigation into vibrations excited by discrete faults in rolling element bearings[D].Christchurch:University of Canterbury,Upper Riccarton,1991.
[23]TANDON N,CHOUDHURY A.An analytical model for the prediction of the vibration response of rolling element bearings due to a localized defect[J].Journal of Sound and Vibration,1997,205(3):275-292.
[24]CHOUDHURY A,TANDON N.Vibration response of rolling element bearings in a rotor bearing system to a local defect under radial load[J].Journal of Tribology,2006,128(2):252-261.
[25]SINGH S,KOPKE U G,HOWARD C Q,et al.Analyses of contact forces and vibration response for a defective rolling element bearing using an explicit dynamics finite element model[J].Journal of Sound and Vibration,2014,333(21):5356-5377.
[26]KHANAM S,TANDON N,DUTT J K.Force analysis due to local defect in rolling bearings for fault diagnosis[M]//Proceedings of the 9th IFTo MM International Conference on Rotor Dynamics.Springer International Publishing,2015:577-586.
[27]KHANAM S,TANDON N,DUTT J K.Multi-event excitation force model for inner race defect in a rolling element bearing[J].Journal of Tribology,2016,138(1):011106-1-15.
[28]FAN Zhiqi.Vibration-based condition monitoring in planetary gearbox via using an internal sensor[D].Sydney:The University of New South Wales,2015.