基于摩擦的空间齿轮系统振动特性分析与试验研究
摘要
齿轮传动机构是空间机械结构的关键部件,属于故障多发件,故障多为润滑失效,其失效比例占总故障的60%。由于真空环境中缺少传导热的有效介质,导致齿轮运转过程中齿面因摩擦、冲击产生的热量不易散失,齿轮较高的温升,导致齿面油膜损伤和润滑失效。齿轮系统一旦出现故障将直接威胁到传动机构甚至整个航天器系统的安全。因此有必要对齿轮系统进行故障诊断和寿命预测。齿轮的润滑失效形式主要与摩擦有关,因此,本文从摩擦角度出发,研究摩擦与振动的关系,通过振动信号的变化判断齿轮的使用寿命。开展齿轮寿命周期过程中摩擦与振动信息耦合、故障监测和诊断、寿命评价等的研究,建立轮齿摩擦副摩擦系数与故障诊断、寿命评价间的联系,将对空间齿轮系统摩擦磨损机理和振动故障研究具有重要的意义,也将对空间齿轮系统状态监测和寿命预测具有重要的应用价值。
本文从弹流润滑理论着手,分析了摩擦系数同油膜比厚的变化关系,指出摩擦系数可以作为油膜厚度评定的指标。考虑齿轮摩擦和振动的相关性,将摩擦系数引入到齿轮系统的动力学方程中,建立了两自由度的齿轮啮合动力学方程,分区段讨论了变摩擦系数对齿轮径向力的影响。利用ABAQUS对该齿轮机构在不同摩擦系数下进行了动力学分析,通过对提取的运动学参量(角速度)和动力学参量(角加速度、摩擦力、径向力)的时域和频域特征分析,提出振动信号的均方幅值RMS指标可以有效识别摩擦系数的变化,具有相对较好的灵敏性,并给出了径向力的均方幅值RMS和频率幅值随摩擦系数变化的函数关系。
搭建振动测试试验平台,分别对干摩擦和脂润滑条件下齿轮径向力进行RMS和频谱分析。与仿真结果比较,数据吻合,满足分析要求,证明了采用RMS指标建立振动与摩擦系数间关系的可行性。提出了采用振动信号RMS指标作为真空条件下齿轮运行寿命的评价指标,依据齿轮运行的时间—RMS曲线,可以初步预测齿轮的寿命。
Gear transmission agencies are important parts of airspace structures, there areabout 60 percents of faults happened in gears. In vacuum, the energy which caused byfriction or impact couldn’t loss, lacking of effective heat conduction medium. With thetemperature increasing in gear tooth surfaces, oil film of teeth will be damanged orlubrication failure. Once faults happened in gear system, Which will affect thetransmission agencies, what’s worse, will threat the whole airspace system. Lubricationfailure or wear usually is taken as the criteria standand to evaluate the life. So it isnecessary to do some researches in the relationships between wear and vibration, faultsmonitoring and diagnosis, evaluation about life. Friction is the main factor which causethe lubrication failure. To build the relationships between gear friction and faultsdiagnosis, it is great for researching in the theory of friction and wear, vibrationcharacters, as well as very useful to promote the application of faults monitoring andevaluation life in gear system.
In this article, we can get some information between friction coeficient from EHLtheory. Under the analysis the empirical formulation, we can get the relationship betweenfriction coefficient and the thickness of oil film. Friction coefficient is an good indicatorto infer the thicken of oil film. Consider of the correlation between the friction andvibration, adding friction coefficient into the dynamic equation. To establish the twodegrees of freedom dynamic equations of gear meshing, and analysis the changes ofradial force under varying friction coefficients. Dynamics simulation and analysis useABAQUS under different friction coefficients. By extracting the kinematicsparameters(angular velocity) and mechanical dynamical parameters (angularacceleration,friction,the radial force) from this gear system and analysis them in timedomain and frequency domain , get that the amplitude RMS and frequency amplitude caneffectively indentify the friction coefficient.
To build the vibration test platform on dry friction and grease lubricationconditions, and analysis the RMS and frequency of signal from vibration test, frequencyamplitude is fluctuating by accidental factors from interior or exterior, and RMS is wellagreement with the simulation results.Analysis RMS in the vibration signal which fromthe vacuum whole life test of gear box, get gear running time-RMS curve, which isagreement with the wear-time curve. Propose the method in predition and evaluationgearing life, and development of life evaluation criteria.
本文从弹流润滑理论着手,分析了摩擦系数同油膜比厚的变化关系,指出摩擦系数可以作为油膜厚度评定的指标。考虑齿轮摩擦和振动的相关性,将摩擦系数引入到齿轮系统的动力学方程中,建立了两自由度的齿轮啮合动力学方程,分区段讨论了变摩擦系数对齿轮径向力的影响。利用ABAQUS对该齿轮机构在不同摩擦系数下进行了动力学分析,通过对提取的运动学参量(角速度)和动力学参量(角加速度、摩擦力、径向力)的时域和频域特征分析,提出振动信号的均方幅值RMS指标可以有效识别摩擦系数的变化,具有相对较好的灵敏性,并给出了径向力的均方幅值RMS和频率幅值随摩擦系数变化的函数关系。
搭建振动测试试验平台,分别对干摩擦和脂润滑条件下齿轮径向力进行RMS和频谱分析。与仿真结果比较,数据吻合,满足分析要求,证明了采用RMS指标建立振动与摩擦系数间关系的可行性。提出了采用振动信号RMS指标作为真空条件下齿轮运行寿命的评价指标,依据齿轮运行的时间—RMS曲线,可以初步预测齿轮的寿命。
Gear transmission agencies are important parts of airspace structures, there areabout 60 percents of faults happened in gears. In vacuum, the energy which caused byfriction or impact couldn’t loss, lacking of effective heat conduction medium. With thetemperature increasing in gear tooth surfaces, oil film of teeth will be damanged orlubrication failure. Once faults happened in gear system, Which will affect thetransmission agencies, what’s worse, will threat the whole airspace system. Lubricationfailure or wear usually is taken as the criteria standand to evaluate the life. So it isnecessary to do some researches in the relationships between wear and vibration, faultsmonitoring and diagnosis, evaluation about life. Friction is the main factor which causethe lubrication failure. To build the relationships between gear friction and faultsdiagnosis, it is great for researching in the theory of friction and wear, vibrationcharacters, as well as very useful to promote the application of faults monitoring andevaluation life in gear system.
In this article, we can get some information between friction coeficient from EHLtheory. Under the analysis the empirical formulation, we can get the relationship betweenfriction coefficient and the thickness of oil film. Friction coefficient is an good indicatorto infer the thicken of oil film. Consider of the correlation between the friction andvibration, adding friction coefficient into the dynamic equation. To establish the twodegrees of freedom dynamic equations of gear meshing, and analysis the changes ofradial force under varying friction coefficients. Dynamics simulation and analysis useABAQUS under different friction coefficients. By extracting the kinematicsparameters(angular velocity) and mechanical dynamical parameters (angularacceleration,friction,the radial force) from this gear system and analysis them in timedomain and frequency domain , get that the amplitude RMS and frequency amplitude caneffectively indentify the friction coefficient.
To build the vibration test platform on dry friction and grease lubricationconditions, and analysis the RMS and frequency of signal from vibration test, frequencyamplitude is fluctuating by accidental factors from interior or exterior, and RMS is wellagreement with the simulation results.Analysis RMS in the vibration signal which fromthe vacuum whole life test of gear box, get gear running time-RMS curve, which isagreement with the wear-time curve. Propose the method in predition and evaluationgearing life, and development of life evaluation criteria.
引文
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[2] P.Bajpai, A.Kahraman, N.E. Anderson. Asurface wear prediction methodologyfor helical gear pairs[J]. ASME Tribology, 2004, 126 (3):597~605
[3] H.M.Broscoe.Why Space Tribology [J]. Tribology International,2000,(23):67~74
[4]梁斌,许文福等.地球静止轨道在轨服务技术研究现状与发展趋势[J].宇航学报,2011,01(31):1~13
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[6]陈磊,梁波,田林涛.真空环境中轴承油润滑失效原因分析[J].轴承.2002,(8):31~32
[7]龙慧,张光辉,罗文军.旋转齿轮瞬时接触应力和温度的分析模拟[J].机械工程学报, 2004,40(8):24~29.
[8]李桂华,费业泰.温度变化对圆柱齿轮齿形的影响[J].机械设计.2005,(2)22~23,
[9]卢立新.齿轮几何参数对齿轮传动弹流润滑性能的影响[J].机械传动,1998,(4):24~27.
[10]李桂华,费业泰.温度变化对啮合齿轮侧隙的影响[J].合肥工业大学学报,.2004(10):1147~1150.
[11] J. Yi, P. D. Quinonez. Gear Surface Temperature Monitoring. Proc. I MechanicalPartⅠ[J]. Engineering Tribology, 2005,219:99~105.
[12]谢友柏,张金玉.时频分析方法在冲击故障早期诊断中的应用研究[J].振动工程学报,200013(2):25~32.
[13] Iida H,Tamura A,Yamada Y.Vibrational characteristics of friction between gearteeth[C].Bull JSME 1985,28:1512~1519.
[14] Borner J, Houser D R.Friction and bending moments on gear noise excitations[J].SAE Transmission,1996,105:1669~1676.
[15] Velex P, Cahouet V.Experimental and numerical investigations on the influenceoftooth friction in spur and helical gear dynamics[J].Journal of MechanicalDesign,2000,122:515~522.
[16] M. Vaishya, R. Singh. Analysis of periodiallly varying gear mesh system withcoulomb friction using floquet theory [J]. Journal of sound and vibration,2001,2(43):525~545.
[17] Gang liu, Robert G. parker. tooth wear effects on spur gear dynamics impact oftooth friction and its bending effect on gear dynamics[J].vibration, 2009,10(3)987~1002.
[18] F.K. Choy V. Polyshchuk.anslysis the effects of surfaces pitting and wear on thevibration of gear transmission system [J].Tribology International, 1996, 3 (29):77~83.
[19]李秀莲等.齿面摩擦下非对称齿轮接触疲劳强度的计算[J].南京理工大学学报（自然科学版）,2011,1(35):76~79.
[20]孙海月等.直齿圆柱齿轮传动系统振动的动力学模型[J].机械工程学报,200025( 8)
[21]李润方,王建军.齿轮系统动力学—振动、冲击、噪声[M].科学出版社,1997:1~9,154~188.
[22]徐辅仁.滑动摩擦及轴承间隙导致齿轮机构的齿轮振动[J].机电设备，2003,5.
[23]韩致信,石文瑞,彭国义等.齿轮系统振动加剧齿轮磨损毁坏的机理分析[J].机械传动,2006,2:47~49.
[24]王泽贵.钢质渐开线直齿在不同润滑介质下滚滑磨合磨损的试验研究[J].润滑与密封,2006,11
[25] T.H. Loutas, G. Sotiriades.condition monitoring of a single-stage gearbox withartificially induced gear cracks utilizing on-line vibration and acoustic emissionmeasurements [J]. applied Acoustics ,2009, 1148~1159
[26] Wang W.Y.Identification of gear mesh signal by kurtosis maximization and itsapplication to CH46 helicopter gear-box data[C].Proceedings of the 11th IEEE SignalProcessing on Statistical Signal Processing, 2001:369~372.
[27] Deuszkiewicz P,Radkowski S.On-line condition monitoring of a power transmissionunit of a rail vehicle[J].Mechanical SystemSignal Processing,2003,17(6):1321~1334
[28]张桂才,史铁林,杨叔子.基于高阶统计量的机械故障特征提取方法研究[J].华中理工大学学报,1998,27(3):6~8.
[29] Kuang J H,Lin A D.The effect of tooth wear on the vibration spectrum of a spurgearpair[J].ASME Journal of Vibration and Acoustics,2001,123(2):311~317.
[30]丁康,朱小勇,陈亚华.齿轮箱典型故障振动特征与诊断策略[J].振动与冲击,2001,30(3):7~12.
[31]陈庆虎,李柱表面粗糙度提取的小波频谱法[J].机械工程学报,1999,35(3)
[32] M. Vaishya, R. Singh.Sliding friction included non-linearity and parametric effectsin gear dynamics [J].Journal of Sound and Vibration,2001,284(4):671~694.
[33] Song He, Rajendra Singh.Dynamic interactions between sliding friction and tiprelief in spur gears[C]. Proceedings of the ASME 2007 international design engineeringtechnical conferences &compters and information in engineering conference, 2007:1~9
[34] C. Yuksel, A. Kahraman. Dynamic tooth loads of planetary gear sets having toothprofile wear [J]. Mechanism and Machine Theory, 2004,(39):695~715
[35] Siyan Wu,Ming J.Zuo.Experimental studies on the effects in gear tooth stiffness andlubricant film thickness in a spur geared system[J].Triobogy International42(2009)340~352
[36] Shengxiang Jia, Ian Howard.Comparison of localized spalling and crack damagefrom dynamic modeling of spur gear vibrations [J]. Mechanical Systems and SingalProcessing. 2006(20):332~349
[37] Matej GaMatej Ga?perin, Dani Juri?ic.Model-based prognostics of gear health usingstochastic dunamical models [J].Mechanical Systems and Signal Processing. 2011,25:537~548.
[38] T Bell, Y. Sun,H.Dong.表面工程系统接触力学.中国表面工程[J],2007,2(24):57~63.
[39] Isa Yesilyurt,Fengshou Gu .gear tooth stiffness reduction measurement using modalanalysis and its wear fault severity assessment of spur gears[J].NDT&Einternational,2003,36:357~372.
[40] A. V. Olver. Gear lubrication areview[J].Tribology international,1997,5(30):321~331
[41]沈伟,徐大伟等.对高速及中低速齿轮磨损后齿轮齿廓的研究[J].现代机械,2002,2:12~15.
[42]陈思雨,唐进元,谢耀东.齿轮传动系统的非线性冲击动力学行为分析[J].振动与冲击,2009,28（4）：70~75.
[43]徐辅仁.弹性变形及滑动摩擦对精密渐开线齿轮强迫振动的影响[J].航空精密制造技术,2004,40(3):42~46.
[44]曹一波,谢小鹏.齿轮全寿命过程轮齿形貌变化的试验研究[J].润滑和密封,2008,33(4):4~7
[45]宋红光,唐进元.直齿轮轮齿间摩擦系数的计算[J].设备设计与维修,2003,12.
[46] Jiangqun Yang, Yong Liu.Grease-lubricated tribological behaviour of nitrided layeron2Cr13 steel[J].Applied Surface Science,2010,1:1~9.
[47]韩致信,朱秋玲.考虑摩擦力时的齿轮系统动力学分析[J].机床与液压,2005,2.
[48]余辉.基于小波的空间典型活动件振动监测和诊断[D].哈尔滨工业大学硕士论文，2009,6.
[2] P.Bajpai, A.Kahraman, N.E. Anderson. Asurface wear prediction methodologyfor helical gear pairs[J]. ASME Tribology, 2004, 126 (3):597~605
[3] H.M.Broscoe.Why Space Tribology [J]. Tribology International,2000,(23):67~74
[4]梁斌,许文福等.地球静止轨道在轨服务技术研究现状与发展趋势[J].宇航学报,2011,01(31):1~13
[5]屈梁生,何正嘉.机械故障诊断学[M].上海科学技术出版社,1986
[6]陈磊,梁波,田林涛.真空环境中轴承油润滑失效原因分析[J].轴承.2002,(8):31~32
[7]龙慧,张光辉,罗文军.旋转齿轮瞬时接触应力和温度的分析模拟[J].机械工程学报, 2004,40(8):24~29.
[8]李桂华,费业泰.温度变化对圆柱齿轮齿形的影响[J].机械设计.2005,(2)22~23,
[9]卢立新.齿轮几何参数对齿轮传动弹流润滑性能的影响[J].机械传动,1998,(4):24~27.
[10]李桂华,费业泰.温度变化对啮合齿轮侧隙的影响[J].合肥工业大学学报,.2004(10):1147~1150.
[11] J. Yi, P. D. Quinonez. Gear Surface Temperature Monitoring. Proc. I MechanicalPartⅠ[J]. Engineering Tribology, 2005,219:99~105.
[12]谢友柏,张金玉.时频分析方法在冲击故障早期诊断中的应用研究[J].振动工程学报,200013(2):25~32.
[13] Iida H,Tamura A,Yamada Y.Vibrational characteristics of friction between gearteeth[C].Bull JSME 1985,28:1512~1519.
[14] Borner J, Houser D R.Friction and bending moments on gear noise excitations[J].SAE Transmission,1996,105:1669~1676.
[15] Velex P, Cahouet V.Experimental and numerical investigations on the influenceoftooth friction in spur and helical gear dynamics[J].Journal of MechanicalDesign,2000,122:515~522.
[16] M. Vaishya, R. Singh. Analysis of periodiallly varying gear mesh system withcoulomb friction using floquet theory [J]. Journal of sound and vibration,2001,2(43):525~545.
[17] Gang liu, Robert G. parker. tooth wear effects on spur gear dynamics impact oftooth friction and its bending effect on gear dynamics[J].vibration, 2009,10(3)987~1002.
[18] F.K. Choy V. Polyshchuk.anslysis the effects of surfaces pitting and wear on thevibration of gear transmission system [J].Tribology International, 1996, 3 (29):77~83.
[19]李秀莲等.齿面摩擦下非对称齿轮接触疲劳强度的计算[J].南京理工大学学报（自然科学版）,2011,1(35):76~79.
[20]孙海月等.直齿圆柱齿轮传动系统振动的动力学模型[J].机械工程学报,200025( 8)
[21]李润方,王建军.齿轮系统动力学—振动、冲击、噪声[M].科学出版社,1997:1~9,154~188.
[22]徐辅仁.滑动摩擦及轴承间隙导致齿轮机构的齿轮振动[J].机电设备，2003,5.
[23]韩致信,石文瑞,彭国义等.齿轮系统振动加剧齿轮磨损毁坏的机理分析[J].机械传动,2006,2:47~49.
[24]王泽贵.钢质渐开线直齿在不同润滑介质下滚滑磨合磨损的试验研究[J].润滑与密封,2006,11
[25] T.H. Loutas, G. Sotiriades.condition monitoring of a single-stage gearbox withartificially induced gear cracks utilizing on-line vibration and acoustic emissionmeasurements [J]. applied Acoustics ,2009, 1148~1159
[26] Wang W.Y.Identification of gear mesh signal by kurtosis maximization and itsapplication to CH46 helicopter gear-box data[C].Proceedings of the 11th IEEE SignalProcessing on Statistical Signal Processing, 2001:369~372.
[27] Deuszkiewicz P,Radkowski S.On-line condition monitoring of a power transmissionunit of a rail vehicle[J].Mechanical SystemSignal Processing,2003,17(6):1321~1334
[28]张桂才,史铁林,杨叔子.基于高阶统计量的机械故障特征提取方法研究[J].华中理工大学学报,1998,27(3):6~8.
[29] Kuang J H,Lin A D.The effect of tooth wear on the vibration spectrum of a spurgearpair[J].ASME Journal of Vibration and Acoustics,2001,123(2):311~317.
[30]丁康,朱小勇,陈亚华.齿轮箱典型故障振动特征与诊断策略[J].振动与冲击,2001,30(3):7~12.
[31]陈庆虎,李柱表面粗糙度提取的小波频谱法[J].机械工程学报,1999,35(3)
[32] M. Vaishya, R. Singh.Sliding friction included non-linearity and parametric effectsin gear dynamics [J].Journal of Sound and Vibration,2001,284(4):671~694.
[33] Song He, Rajendra Singh.Dynamic interactions between sliding friction and tiprelief in spur gears[C]. Proceedings of the ASME 2007 international design engineeringtechnical conferences &compters and information in engineering conference, 2007:1~9
[34] C. Yuksel, A. Kahraman. Dynamic tooth loads of planetary gear sets having toothprofile wear [J]. Mechanism and Machine Theory, 2004,(39):695~715
[35] Siyan Wu,Ming J.Zuo.Experimental studies on the effects in gear tooth stiffness andlubricant film thickness in a spur geared system[J].Triobogy International42(2009)340~352
[36] Shengxiang Jia, Ian Howard.Comparison of localized spalling and crack damagefrom dynamic modeling of spur gear vibrations [J]. Mechanical Systems and SingalProcessing. 2006(20):332~349
[37] Matej GaMatej Ga?perin, Dani Juri?ic.Model-based prognostics of gear health usingstochastic dunamical models [J].Mechanical Systems and Signal Processing. 2011,25:537~548.
[38] T Bell, Y. Sun,H.Dong.表面工程系统接触力学.中国表面工程[J],2007,2(24):57~63.
[39] Isa Yesilyurt,Fengshou Gu .gear tooth stiffness reduction measurement using modalanalysis and its wear fault severity assessment of spur gears[J].NDT&Einternational,2003,36:357~372.
[40] A. V. Olver. Gear lubrication areview[J].Tribology international,1997,5(30):321~331
[41]沈伟,徐大伟等.对高速及中低速齿轮磨损后齿轮齿廓的研究[J].现代机械,2002,2:12~15.
[42]陈思雨,唐进元,谢耀东.齿轮传动系统的非线性冲击动力学行为分析[J].振动与冲击,2009,28（4）：70~75.
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