包含齿根裂纹的风电行星齿轮动力学特性分析
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摘要
将轮齿简化为悬臂梁模型,推导单一轮齿的刚度计算方法。建立裂纹模型,计算包含太阳轮齿根裂纹故障时系统的时变啮合刚度。将得到的时变啮合刚度代入系统平移-扭转耦合动力学模型,以研究太阳轮齿根裂纹对系统响应的影响。仿真计算结果表明,太阳轮齿根裂纹会引起太阳轮-行星轮啮合刚度下降;随着裂纹的增长,太阳轮扭转振动会出现愈加明显的冲击现象;太阳轮平移振动无明显的冲击现象;裂纹的增长不会明显改变振动响应的频率成分;太阳轮轴心轨迹对太阳轮齿根裂纹敏感。
A modified cantilever beam model is used to represent the gear tooth and derive the analytical equations of the stiffness. The crack model is established and the time-varying mesh stiffness of wind turbine epicyclic gear set with a tooth crack in the sun gear is derived. Then the time-varying mesh stiffness is incorporated into the dynamic model of wind turbine epicyclic gear set for investigating the effect of the tooth crack in the sun gear. The simulation result showed that the mesh stiffness of the sun-planetary gear pair decresses due to the tooth root crack in the sun. The impact of the torsional vibration of the sun gear increases significantly and the translational vibration of the sun gear and its corresponding spectrum change insignificantly with the growth of the crack. The trajectory of the sun gear center is sensitive to the tooth crack of sun gear.
A modified cantilever beam model is used to represent the gear tooth and derive the analytical equations of the stiffness. The crack model is established and the time-varying mesh stiffness of wind turbine epicyclic gear set with a tooth crack in the sun gear is derived. Then the time-varying mesh stiffness is incorporated into the dynamic model of wind turbine epicyclic gear set for investigating the effect of the tooth crack in the sun gear. The simulation result showed that the mesh stiffness of the sun-planetary gear pair decresses due to the tooth root crack in the sun. The impact of the torsional vibration of the sun gear increases significantly and the translational vibration of the sun gear and its corresponding spectrum change insignificantly with the growth of the crack. The trajectory of the sun gear center is sensitive to the tooth crack of sun gear.
引文
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[8]万志国,訾艳阳,曹宏瑞,等.时变啮合刚度算法修正与齿根裂纹动力学建模[J].机械工程学报,2013,49(11):153—160.[8] Wan Zhiguo,Zi Yanyang,Cao Hongrui,et al. Time-varying mesh stiffness algorithm correction and toothcrack dynamic modeling[J]. Journal of MechanicalEngineering,2013,49(11):153—160.
[9] Ma Hui,Pang Xu,Feng Ranjiao,et al. Improved time-varying mesh stiffness model of cracked spurgears[J]. Engineering Failure Analysis,2015,55:271—287.
[10] Ma Hui,Pang Xu,Zeng Jin,et al. Effects of gear crackpropagation paths on vibration responses of theperforated gear system[J]. Mechanical Systems&SignalProcessing,2015,62-63:113—128.
[11] Ma Hui,Zeng Jin,Feng Ranjiao,et al. Review ondynamics of cracked gear systems[J]. EngineeringFailure Analysis,2015,55:224—245.
[12] Liang Xihui, Zuo M J, Pandey M. Analyticallyevaluating the influence of crack on the mesh stiffness ofa planetary gear set[J]. Mechanism&Machine Theory,2014,76(6):20—38.
[13] Chen Zaigang, Shao Yimin. Dynamic simulation ofplanetary gear with tooth root crack in ring gear[J].Engineering Failure Analysis,2013,31(9):8—18.
[14] Chen Zaigang,Zhu Zhifang,Shao Yimin. Fault featureanalysis of planetary gear system with tooth root crackand flexible ring gear rim[J]. Engineering FailureAnalysis,2015,49:92—103.
[15]陈长征,张磊,刘杰,等.考虑齿侧间隙的风力机齿轮箱行星传动系统非线性动力响应分析[J].太阳能学报,2016,37(6):1587—1593.[15] Chen Changzheng,Zhang Lei,Liu Jie,et al. Nonlineardynamic response analysis of planetary set of windturbine gearbox considering backlash[J]. Acta EnergiaeSolaris Sinica,2016,37(6):1587—1593.
[16]李润方.齿轮系统动力学[M].北京:科学出版社,1997.[16] Li Runfang. Gear system dynamics[M]. Beijing:Science Press,1997.
[17]张建宇,刘鑫博,张飞斌.裂纹齿轮啮合刚度的劣化特性[J].振动、测试与诊断,2014,34(6):1124—1128.[17] Zhang Jianyu,Liu Xinbo,Zhang Feibin. Degradationcharacteristics of meshing stiffness of spur gears withroot crack[J]. Journal of Vibration Measurement&Diagnosis,2014,34(6):1124—1128.
[2] Kahraman A. Load sharing characteristics of planetarytransmissions[J]. Mechanism and Machine Theory,1994,29(8):1151—1165.
[3]徐向阳,朱才朝,刘怀举,等.柔性销轴式风电齿轮箱行星传动均载研究[J].机械工程学报,2014,50(11):43—49.[3] Xu Xiangyang,Zhu Caichao,Liu Huaiju,et al. Loadsharing research of planetary gear transmission system ofwind turbine gearbox with flexible pins[J]. Journal ofMechanical Engineering,2014,50(11):43—49.
[4] Wang Jianhong, Qin Datong, Ding Yi. Dynamicbehavior of wind turbine by a mixed flexible-rigid multi-body model[J]. Journal of System Design andDynamics,2009,3(3):403—419.
[5]周志刚,秦大同,杨军,等.变载荷下风力发电机行星齿轮传动系统齿轮-轴承耦合动力学特性[J].重庆大学学报:自然科学版,2012,35(12):7—14.[5] Zhou Zhigang,Qin Datong,Yang Jun,et al. Gear-bearing coupling dynamics characteristics of windturbine planetary gear transmission system undervariable load[J]. Journal of Chongqing University:Natural Science Edition,2012,35(12):7—14.
[6]秦大同,田苗苗,杨军.变风载下风力发电机齿轮传动系统动力学特性研究[J].太阳能学报,2012,33(2):190—196.[6] Qin Datong, Tian Miaomiao, Yang Jun. Study ondynamic characteristics of gear transmission system ofwind generator under varying wind load[J]. ActaEnergiae Solaris Sinica,2012,34(2):186—194.
[7]秦大同,李超,唐飞熊.变风载下变速风力发电机传动系统动力学特性研究[J].太阳能学报,2013,34(2):186—195.[7] Qin Datong,Li Chao,Tang Feixiong. Study on dynamiccharacteristics of gear transmission system of variablespeed wind generator under varying wind load[J]. ActaEnergiae Solaris Sinica,2012,34(2):186—194.
[8]万志国,訾艳阳,曹宏瑞,等.时变啮合刚度算法修正与齿根裂纹动力学建模[J].机械工程学报,2013,49(11):153—160.[8] Wan Zhiguo,Zi Yanyang,Cao Hongrui,et al. Time-varying mesh stiffness algorithm correction and toothcrack dynamic modeling[J]. Journal of MechanicalEngineering,2013,49(11):153—160.
[9] Ma Hui,Pang Xu,Feng Ranjiao,et al. Improved time-varying mesh stiffness model of cracked spurgears[J]. Engineering Failure Analysis,2015,55:271—287.
[10] Ma Hui,Pang Xu,Zeng Jin,et al. Effects of gear crackpropagation paths on vibration responses of theperforated gear system[J]. Mechanical Systems&SignalProcessing,2015,62-63:113—128.
[11] Ma Hui,Zeng Jin,Feng Ranjiao,et al. Review ondynamics of cracked gear systems[J]. EngineeringFailure Analysis,2015,55:224—245.
[12] Liang Xihui, Zuo M J, Pandey M. Analyticallyevaluating the influence of crack on the mesh stiffness ofa planetary gear set[J]. Mechanism&Machine Theory,2014,76(6):20—38.
[13] Chen Zaigang, Shao Yimin. Dynamic simulation ofplanetary gear with tooth root crack in ring gear[J].Engineering Failure Analysis,2013,31(9):8—18.
[14] Chen Zaigang,Zhu Zhifang,Shao Yimin. Fault featureanalysis of planetary gear system with tooth root crackand flexible ring gear rim[J]. Engineering FailureAnalysis,2015,49:92—103.
[15]陈长征,张磊,刘杰,等.考虑齿侧间隙的风力机齿轮箱行星传动系统非线性动力响应分析[J].太阳能学报,2016,37(6):1587—1593.[15] Chen Changzheng,Zhang Lei,Liu Jie,et al. Nonlineardynamic response analysis of planetary set of windturbine gearbox considering backlash[J]. Acta EnergiaeSolaris Sinica,2016,37(6):1587—1593.
[16]李润方.齿轮系统动力学[M].北京:科学出版社,1997.[16] Li Runfang. Gear system dynamics[M]. Beijing:Science Press,1997.
[17]张建宇,刘鑫博,张飞斌.裂纹齿轮啮合刚度的劣化特性[J].振动、测试与诊断,2014,34(6):1124—1128.[17] Zhang Jianyu,Liu Xinbo,Zhang Feibin. Degradationcharacteristics of meshing stiffness of spur gears withroot crack[J]. Journal of Vibration Measurement&Diagnosis,2014,34(6):1124—1128.
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