高速圆柱滚子轴承保持架运行稳定性分析
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摘要
基于滚动轴承动力学理论,建立了高速圆柱滚子轴承的非线性动力学微分方程组,采用预估-校正的GSTIFF(Gear stiff)变步长积分算法对其进行求解,使用盒维数评价保持架质心轨迹的混乱程度,研究了保持架间隙比、轴承转速、轴承径向载荷、轴承径向游隙以及滚子个数等因素对保持架运行稳定性的影响。研究结果表明:盒维数能够发现相似保持架心轨迹之间的差别,并对保持架稳定性进行量化描述;较大的保持架间隙比不利于保持架的稳定运行,存在最佳间隙比使保持架质心轨迹涡动效果最好,保持架运行最稳定;内圈转速较低时,保持架质心不发生涡动,质心轨迹非常混乱,保持架运行不稳定;随着转速、滚子个数的增加,保持架运行稳定性增加;随着径向载荷、径向游隙的增加,保持架运行稳定性先增大后减小。
Based on the dynamics theory of rolling bearings, nonlinear dynamic differential equations for a high-speed cylindrical roller bearing were established and solved with the prediction-correction GSTIFF(Gear stiff) integration algorithm with variable steps. The box dimension was used to evaluate disorder level of cage mass center trajectory. Effects of cage clearance ratio, bearing rotating speed, bearing radial load, bearing radial clearance and roller number on cage operational stability were investigated. The results showed that the box dimension can be used to find the difference between similar cage mass center trajectories and quantitatively describe cage operational stability; larger cage clearance ratio is not helpful for cage stable operation, and there is an optimal clearance ratio to make cage mass center trajectories' whirl effect be the best and cage operation be the most stable; when inner ring rotating speed is lower, cage mass center doesn't whirl and cage mass center trajectory is very disorder, cage operation is unstable; with increase in rotating speed and roller number, cage operational stability increases; with increase in radial load and radial internal clearance, cage operational stability increases firstly and then decreases.
Based on the dynamics theory of rolling bearings, nonlinear dynamic differential equations for a high-speed cylindrical roller bearing were established and solved with the prediction-correction GSTIFF(Gear stiff) integration algorithm with variable steps. The box dimension was used to evaluate disorder level of cage mass center trajectory. Effects of cage clearance ratio, bearing rotating speed, bearing radial load, bearing radial clearance and roller number on cage operational stability were investigated. The results showed that the box dimension can be used to find the difference between similar cage mass center trajectories and quantitatively describe cage operational stability; larger cage clearance ratio is not helpful for cage stable operation, and there is an optimal clearance ratio to make cage mass center trajectories' whirl effect be the best and cage operation be the most stable; when inner ring rotating speed is lower, cage mass center doesn't whirl and cage mass center trajectory is very disorder, cage operation is unstable; with increase in rotating speed and roller number, cage operational stability increases; with increase in radial load and radial internal clearance, cage operational stability increases firstly and then decreases.
引文
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[17] 李曙光,张梅军,陈江海.基于小波包和分形盒维数的滚动轴承故障诊断[J].机械,2010,37(8):21-23.LI Shuguang,ZHANG Meijun,CHEN Jianghai.Application of wavelet packet and fractal box-counting dimension in fault diagnosis of rolling bearing[J].Machinery,2010,37(8):21-23.
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[19] CAO Y P,YING Y L,LI J C,et al.Study on roller bearing fault diagnosis approach based on improved generalized fractal box-counting dimension and adaptive gray relation algorithm[J].Advances in Mechanical Engineering,2016,8(10):132-143.
[20] YANG Haisheng,CHENG Guoding,DENG Si'er,et al.Analysis of the roller-race contact deformation of cylindrical roller bearing using a improved slice method[C]//2011 International Conference on Mechatronic Science,Electric Engineering and Computer.Jilin:MEC,2011.
[21] ZHANG W H,DENG S E,CHEN G D,et al.Study on the impact of roller convexity excursion of high-speed cylindrical roller bearing on roller's dynamic characteristics[J].Mechanism & Machine Theory,2016,103:21-39.
[22] 王东升,汤鸿霄,栾兆坤.分形理论及其研究方法[J].环境科学学报,2001,1(增刊1):10-16.WANG Dongsheng,TANG Hongxiao,LUAN Zhaokun.A brief introduction to the fractal theory and methodology[J].Acta Science Circumstantiae,2001,1(Sup1):10-16.
[23] ERIC J O,JAMES C R.A simple example concerning the upper Box-Counting Dimension of a Cartesian prod uct[J].Real Analysis Exchange,2015,40(2):449-454.
[2] GHAISAS N,WASSGREN C R,SADEGHI F.Cage Instabilities in Cylindrical Roller Bearings[J].Journal of Tribology,2004,126(4):681-689.
[3] GUPTA P K.Advanced dynamics of rolling elements[M].Berlin:Springer-Verlag,1984.
[4] GUPTA P K.Dynamics of rolling bearing:part I-II[J].Journal of Tribology,1979,101(3):311.
[5] GUPTA P K.Cage unbalance and wear in ball bearings[J].Wear,1991,147(1):93-104.
[6] MEEKS C R.The dynamics of ball separators in ball bearings—Part II:Results of optimization study[J].Tribology Transactions,1985,28(3):288-295.
[7] RIVERA M P.Bearing-cage frictional instability—A mechanical model[J].Tribology Transactions,1991,34(1):117-121.
[8] TADA S.Dynamic analysis of sound,vibration and motion of cage in high speed ball bearings[J].KOYO Engineering Journal,2001,160:31-38.
[9] TAKAFUMI Y,YASUYOSHI T,HISAO M,et al.Analysis of cage slip in cylindrical roller bearing considering Non-Newtonian behavior and temperature rise of lubricating oil[J].Japanese Journal of Tribology,2008,53(6):647-662.
[10] ZHANG W H,DENG S E,CHEN G D,et al.Influence of lubricant traction coefficient on cage's nonlinear dynamic behavior in high-speed cylindrical roller bearing[J].Journal of Tribology,2017,139(6):061502-1.
[11] 邓四二,顾金芳,崔永存,等.高速圆柱滚子轴承保持架动力学特性分析[J].航空动力学报,2014,29(1):207-215.DENG Si'er,GU Jinfang,CUI Yongcun,et al.Analysis on dynamic characteristics of cage in high-speed cylindrical roller bearing[J].Journal of Aerospace Power,2014,29(1):207-215.
[12] 刘秀海,邓四二,滕弘飞.高速圆柱滚子轴承保持架运动分析[J].航空发动机,2013,39(2):31-38.LIU Xiuhai,DENG Si'er,TENG Hongfei.Kinematics analysis of cages in high-speed cylindrical roller bearings[J].Aeroengine,2013,39(2):31-38.
[13] 姜维,靳国栋,潘钢锋.专用电机轴承保持架稳定性试验分析[J].轴承,2009(1):36-38.JIANG Wei,JIN Guodong,PAN Gangfeng.Experimental analysis on stability of cages in dedicated motor bearing[J].Bearing,2009(1):36-38.
[14] 黄迪山.微型轴承保持架质心轨迹检测与特性分析[J].中国机械工程,2012,23(15):19-24.HUANG Dishan.Detection and characteristic analysis for mass center orbit of bearing cage[J].China Mechanical Engineering,2012,23(15):19-24.
[15] 胡家信.分形分析引论[M].北京:科学出版社,2013.
[16] 谭晶,储著金,顾志鑫,等.基于盒维数的保持架质心轨迹稳定性分析[J].轴承,2014(5):37-40.TAN Jing,CHU Zhujin,GU Zhixin,et al.Analysis on stability of mass center trajectory for cages based on box dimension[J].Bearing,2014(5):37-40.
[17] 李曙光,张梅军,陈江海.基于小波包和分形盒维数的滚动轴承故障诊断[J].机械,2010,37(8):21-23.LI Shuguang,ZHANG Meijun,CHEN Jianghai.Application of wavelet packet and fractal box-counting dimension in fault diagnosis of rolling bearing[J].Machinery,2010,37(8):21-23.
[18] 郝研,王太勇,万剑,等.分形盒维数抗噪研究及其在故障诊断中的应用[J].仪器仪表学报,2011,32(3):540-545.HAO Yan,WANG Taiyong,WANG Jian,et al.Research on fractal box dimension anti-noise performance and its application in fault diagnosis[J].Chinese Journal of Scientific Instrument,2011,32(3):540-545.
[19] CAO Y P,YING Y L,LI J C,et al.Study on roller bearing fault diagnosis approach based on improved generalized fractal box-counting dimension and adaptive gray relation algorithm[J].Advances in Mechanical Engineering,2016,8(10):132-143.
[20] YANG Haisheng,CHENG Guoding,DENG Si'er,et al.Analysis of the roller-race contact deformation of cylindrical roller bearing using a improved slice method[C]//2011 International Conference on Mechatronic Science,Electric Engineering and Computer.Jilin:MEC,2011.
[21] ZHANG W H,DENG S E,CHEN G D,et al.Study on the impact of roller convexity excursion of high-speed cylindrical roller bearing on roller's dynamic characteristics[J].Mechanism & Machine Theory,2016,103:21-39.
[22] 王东升,汤鸿霄,栾兆坤.分形理论及其研究方法[J].环境科学学报,2001,1(增刊1):10-16.WANG Dongsheng,TANG Hongxiao,LUAN Zhaokun.A brief introduction to the fractal theory and methodology[J].Acta Science Circumstantiae,2001,1(Sup1):10-16.
[23] ERIC J O,JAMES C R.A simple example concerning the upper Box-Counting Dimension of a Cartesian prod uct[J].Real Analysis Exchange,2015,40(2):449-454.
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