人字齿轮功率二分支传动系统模态跃迁现象
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摘要
模态跃迁会导致人字齿轮功率二分支传动系统的动力学特性剧烈变化,因此,在该类系统的动态设计过程中,必须对模态跃迁现象进行分析。建立了人字齿轮功率二分支传动系统扭转振动模型和扭转自由振动微分方程,通过分析计算系统扭转振动固有频率和模态振型,将人字齿轮功率二分支传动系统扭转振动模式归纳为耦合振动模式和分支齿轮振动模式两类模态振型。在此基础上,研究了人字齿轮功率二分支传动系统扭转振动的模态跃迁现象,确定了系统扭转振动固有频率轨迹发生模态跃迁现象的准则:对于耦合振动模式和分支齿轮振动模式,不同类型模态振型之间不会发生模态跃迁,同类型的模态振型之间将会发生模态跃迁。最后,通过实例计算验证了所提出模态跃迁准则的准确性。
The mode transition will bring about the dramatical changes of the dynamics characteristics of the herringbone gear power-split transmission system,so the mode transition phenomenon must be analyzed in the process of the transmission system dynamic design. The torsional vibration model and the free torsional vibration differential equations of the herringbone gear power-split transmission system are established,and the torsional vibration models are classified to two kinds of the coupled vibration mode and the branch gear vibration model by calculating the torsional vibration natural frequency and vibration mode. On this basis,the mode transition phenomenon of the transmission system is studied,and the criterion of mode transition phenomenon is determined,the mode transition phenomenon is not going to happen between two different types of modal vibration mode,and will happen between the same types. Finally,the accuracy of the proposed mode transition criterion is verified by an example.
The mode transition will bring about the dramatical changes of the dynamics characteristics of the herringbone gear power-split transmission system,so the mode transition phenomenon must be analyzed in the process of the transmission system dynamic design. The torsional vibration model and the free torsional vibration differential equations of the herringbone gear power-split transmission system are established,and the torsional vibration models are classified to two kinds of the coupled vibration mode and the branch gear vibration model by calculating the torsional vibration natural frequency and vibration mode. On this basis,the mode transition phenomenon of the transmission system is studied,and the criterion of mode transition phenomenon is determined,the mode transition phenomenon is not going to happen between two different types of modal vibration mode,and will happen between the same types. Finally,the accuracy of the proposed mode transition criterion is verified by an example.
引文
[1]WU X H,PARKER R G.Modal properties of planetary gears with an elastic continuum ring gear[J].Journal of Applied Mechanics,2008,75(3):1014-1026.
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[3]WU X H,PARKER R G.Vibration of rings on a general elastic foundation[J].Journal of Sound and Vibration,2006,295(1/2):194-213.
[4]KIRACOFE D R,PARKER R G.Structured Vibration Modes of General Compound Planetary Gear Systems[J].Journal of Vibration and Acoustics20071291511-526.General Compound Planetary Gear Systems and Acoustics,2007,129(1):511-526.
[5]GUO Y C,PARKER R G.Purely rotational model and vibration modes of compound planetary gears[J].Mechanism and Machine Theory,2010,45(3):365-377.
[6]GUO Y,PARKER R G.Sensitivity of general compound planetary gear natural frequencies and vibration modes to model parameters[J].Journal of Vibration and Acoustics,2010,132(1):1006-1019.
[7]LIN J,PARKER R G.Sensitivity of planetary gear natural frequencies and vibration modes to model parameters[J].Journal of Sound and Vibration,1999,228(1):109-128.
[8]LIN J,PARKER R G.Structured vibration characteristics of planetary gears with unequally spaced planets[J].Journal of Sound and Vibration,2000,233(5):921-928.
[9]LIN J,PARKER R G.Natural frequency veering in planetary gears[J].Mechanics of Structures and Machines,2001,29(4):411-429.
[10]KAHRAMAN A.Natural modes of planetary gear trains[J].Journal of Sound and Vibration,1994,173(1):125-130.
[11]KAHRAMAN A.Planetary gear train dynamics[J].Journal of Mechanical Design,1994,116(3):713-720.
[12]王世宇.基于相位调谐的直齿行星齿轮传动动力学理论与实验研究[D].天津:天津大学,2005:72-90.
[13]赵永强.舰船用大功率两级串联混合行星传动系统动力学研究[D].哈尔滨:哈尔滨工业大学,2010:71-77.
[14]AL-SHYYAB A,KAHRAMAN A.Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method:period-one motions[J].Journal of Sound and Vibration,2005,284(1):151-172.
[15]KUBUR M,KAHRAMAN A.Dynamic Analysis of a MultiShaft Helical Gear Transmission by Finite Elements:Model and Experiment[J].Journal of Vibration and Acoustics,2004,126(3):398-406.
[16]郭家舜.功率分流传动系统非线性动力学特性及其分析方法研究[D].西安:西北工业大学,2013:29-32.
[17]王琳杰.弹性辐板人字齿轮传动系统的减振设计研究[D].西安:西北工业大学,2014:42.
[18]杨通强.斜齿行星传动动力学研究[D].天津:天津大学,2004:39-46.
[19]FOX R L,KAPOOR M P.Rates of change of eigenvalues and eigenvectors[J].AIAA Journal,2015,6(12):2426-2429.
[2]KAHRAMAN A.Free torsional vibration characteristics of compound planetary gear sets[J].Mechanism and Machine Theory,2001,36(8):953-971.
[3]WU X H,PARKER R G.Vibration of rings on a general elastic foundation[J].Journal of Sound and Vibration,2006,295(1/2):194-213.
[4]KIRACOFE D R,PARKER R G.Structured Vibration Modes of General Compound Planetary Gear Systems[J].Journal of Vibration and Acoustics20071291511-526.General Compound Planetary Gear Systems and Acoustics,2007,129(1):511-526.
[5]GUO Y C,PARKER R G.Purely rotational model and vibration modes of compound planetary gears[J].Mechanism and Machine Theory,2010,45(3):365-377.
[6]GUO Y,PARKER R G.Sensitivity of general compound planetary gear natural frequencies and vibration modes to model parameters[J].Journal of Vibration and Acoustics,2010,132(1):1006-1019.
[7]LIN J,PARKER R G.Sensitivity of planetary gear natural frequencies and vibration modes to model parameters[J].Journal of Sound and Vibration,1999,228(1):109-128.
[8]LIN J,PARKER R G.Structured vibration characteristics of planetary gears with unequally spaced planets[J].Journal of Sound and Vibration,2000,233(5):921-928.
[9]LIN J,PARKER R G.Natural frequency veering in planetary gears[J].Mechanics of Structures and Machines,2001,29(4):411-429.
[10]KAHRAMAN A.Natural modes of planetary gear trains[J].Journal of Sound and Vibration,1994,173(1):125-130.
[11]KAHRAMAN A.Planetary gear train dynamics[J].Journal of Mechanical Design,1994,116(3):713-720.
[12]王世宇.基于相位调谐的直齿行星齿轮传动动力学理论与实验研究[D].天津:天津大学,2005:72-90.
[13]赵永强.舰船用大功率两级串联混合行星传动系统动力学研究[D].哈尔滨:哈尔滨工业大学,2010:71-77.
[14]AL-SHYYAB A,KAHRAMAN A.Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method:period-one motions[J].Journal of Sound and Vibration,2005,284(1):151-172.
[15]KUBUR M,KAHRAMAN A.Dynamic Analysis of a MultiShaft Helical Gear Transmission by Finite Elements:Model and Experiment[J].Journal of Vibration and Acoustics,2004,126(3):398-406.
[16]郭家舜.功率分流传动系统非线性动力学特性及其分析方法研究[D].西安:西北工业大学,2013:29-32.
[17]王琳杰.弹性辐板人字齿轮传动系统的减振设计研究[D].西安:西北工业大学,2014:42.
[18]杨通强.斜齿行星传动动力学研究[D].天津:天津大学,2004:39-46.
[19]FOX R L,KAPOOR M P.Rates of change of eigenvalues and eigenvectors[J].AIAA Journal,2015,6(12):2426-2429.
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