人字齿轮分扭传动系统动力学建模与动态分析
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摘要
以某航空发动机人字齿分扭传动减速器为研究对象,基于有限单元节点法建立考虑轴、齿轮转子陀螺效应、轴承支撑、系统阻尼及齿轮啮合作用的人字齿分扭传动系统动力学模型,计算人字齿时变啮合刚度,根据实测齿面计算出静态传递误差。根据建立的系统动力学方程,按振动理论方法计算得到轮系典型模态,经试验测试验证了计算模态的正确性;利用NewMark法对系统的时域及频域响应进行仿真计算,计算得到的系统时域响应收敛且存在调制现象,频域分析中存在啮合频率的次频、倍频与轴频。计算结果均与试验结果基本相符。研究工作为航空齿轮传动动态性能分析提供了有参考价值的方法。
Taking an aero-engine gearbox with split torque transmission system and double helical gears as research object.Based on the finite element node method,the model of a split torque transmission system with considering the effects of the supporting shafts and bearings,gyroscopic effect of rotor,is constructed.The time-varying meshing stiffness of double helical gear is calculated by finite element method,and the static transmission error is calculated according to the measured tooth surface.According to the established system dynamics equation,the typical modal of gear train is calculated according to the vibration theory method,and the correctness of the calculated modal is verified by the test.The time-domain and frequency-domain response is simulated with NewMark method,the time-domain response of the system is convergent and the modulation phenomenon appeared.In the frequency-domain analysis,several high and low order components of mesh frequency,shaft frequency exist.The calculated results are basically consistent with the experimental results.The study work provides a valuable reference method for the dynamic performance analysis of aeronautical gear transmission.
Taking an aero-engine gearbox with split torque transmission system and double helical gears as research object.Based on the finite element node method,the model of a split torque transmission system with considering the effects of the supporting shafts and bearings,gyroscopic effect of rotor,is constructed.The time-varying meshing stiffness of double helical gear is calculated by finite element method,and the static transmission error is calculated according to the measured tooth surface.According to the established system dynamics equation,the typical modal of gear train is calculated according to the vibration theory method,and the correctness of the calculated modal is verified by the test.The time-domain and frequency-domain response is simulated with NewMark method,the time-domain response of the system is convergent and the modulation phenomenon appeared.In the frequency-domain analysis,several high and low order components of mesh frequency,shaft frequency exist.The calculated results are basically consistent with the experimental results.The study work provides a valuable reference method for the dynamic performance analysis of aeronautical gear transmission.
引文
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[3]陈思雨,唐进元.间隙对含摩擦和时变刚度的齿轮系统动力学相应的影响[J].机械工程学报,2009,45(8):119-124.
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[12]吴新跃,朱石坚.人字齿轮传动的振动理论分析模型[J].海军工程大学学报,2001,13(5):13-19.
[13]吴新跃,邓福顺.人字齿轮振动模型的解算方[J].海军工程大学学报,2001,13(6):32-36.
[14]ERITENEL T,PARKER R G.Three-dimensional nonlinear vibration of gear pairs[J].Journal of Sound and Vibration,2012,331(15):3628-3648.
[15]ERITENEL T,PARKER R G.Nonlinear vibration of gears with tooth surface modifications[J].Journal of Vibration and Acoustics,2013,135(5):051005.
[16]WEI J,BAI P,QIN D,et al.Study on vibration characteristics of fan shaft of geared turbofan engine with sudden imbalance caused by blade off[J].Journal of Vibration and Acoustics,2018,140(4):041010.
[17]MA H,SONG R,PANG X,et al.Fault feature analysis of a cracked gear coupled rotor system[J].Mathematical Problems in Engineering,2014,2014:832192.
[18]MA H,SONG R,PANG X,et al.Time-varying mesh stiffness calculation of cracked spur geas[J].Engineering Failure Analysis,2014(44):179-194.
[19]CHEN S Y,TANG J Y.Effects of staggering and pitch error on the dynamic response of a double-helical gear set[J].Journal of Vibration and Control,2015,23(11):1844-1856.
[20]CHEN S,TANG J,LI Y,et al.Rotordynamics analysis of a double-helical gear transmission system[J].Meccanica,2016,51(1):251-268.
[2]CHEN S,TANG J,HU Z.Comparisons of gear dynamic responses with rectangular mesh stiffness and its approximate form[J].Journal of Mechanical Science and Technology,2015,29(9):3563-3569.
[3]陈思雨,唐进元.间隙对含摩擦和时变刚度的齿轮系统动力学相应的影响[J].机械工程学报,2009,45(8):119-124.
[4]李润方,王建军.齿轮系统动力学[M].北京:科学出版社,1997:4-17.
[5]王建军,李润方.齿轮系统动力学的理论体系[J].中国机械工程,1998,9(12):55-58.
[6]JOHNSON D.Modes and frequencies of shafts coupled by straight spur gears[J].Journal of Mechanical Engineering Science,1962(4):241-250.
[7]WANG S.Analysis of nonlinear transient motion of a geared torsional[J].Journal of Manufacturing Science and Engineering,1974(96):51-59.
[8]王三民,沈允文,董海军.含摩擦和间隙直齿轮副的混沌与分叉研究[J].机械工程学报,2002,38(9):8-11.
[9]唐进元,陈思雨,钟掘.一种改进的齿轮非线性动力学模型[J].工程力学,2008,25(1):217-223.
[10]THOMAS J,HOUSER D R.A procedure for predicting the load distribution and transmission error characteristics of double helical gears[EB/OL].(1991)[2019-02-20].https://www.artec-machine.com/wp-content/docs/protected/procedure_for_predicting_load_distribution_&_gearbox_transmission_errors.pdf.
[11]王成.人字齿轮啮合特性与修形设计研究[D].西安:西北工业大学,2009:9-2.
[12]吴新跃,朱石坚.人字齿轮传动的振动理论分析模型[J].海军工程大学学报,2001,13(5):13-19.
[13]吴新跃,邓福顺.人字齿轮振动模型的解算方[J].海军工程大学学报,2001,13(6):32-36.
[14]ERITENEL T,PARKER R G.Three-dimensional nonlinear vibration of gear pairs[J].Journal of Sound and Vibration,2012,331(15):3628-3648.
[15]ERITENEL T,PARKER R G.Nonlinear vibration of gears with tooth surface modifications[J].Journal of Vibration and Acoustics,2013,135(5):051005.
[16]WEI J,BAI P,QIN D,et al.Study on vibration characteristics of fan shaft of geared turbofan engine with sudden imbalance caused by blade off[J].Journal of Vibration and Acoustics,2018,140(4):041010.
[17]MA H,SONG R,PANG X,et al.Fault feature analysis of a cracked gear coupled rotor system[J].Mathematical Problems in Engineering,2014,2014:832192.
[18]MA H,SONG R,PANG X,et al.Time-varying mesh stiffness calculation of cracked spur geas[J].Engineering Failure Analysis,2014(44):179-194.
[19]CHEN S Y,TANG J Y.Effects of staggering and pitch error on the dynamic response of a double-helical gear set[J].Journal of Vibration and Control,2015,23(11):1844-1856.
[20]CHEN S,TANG J,LI Y,et al.Rotordynamics analysis of a double-helical gear transmission system[J].Meccanica,2016,51(1):251-268.
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