波动负载对齿轮系统振动特性及边频调制影响研究
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摘要
齿轮传动系统在工作时常承受复杂多变的外部波动载荷,导致轮齿啮合特性和系统振动响应频率特征复杂。基于时变啮合刚度的能量法合成模型,建立考虑系统扭振和横振响应影响的时变啮合刚度动态修正模型。建立单级齿轮传动系统的弯扭耦合模型,用Newmark法求解系统的振动响应。利用啮合刚度动态修正模型和齿轮系统弯扭耦合模型,通过数值算例分析波动负载对啮合刚度和系统振动响应的影响。结果表明,在波动负载作用下,啮合刚度和系统振动响应均存在明显的以波动负载频率为调制频率的边频调制现象,且被调制的中心谐波频率越高,调制现象越明显;外部波动负载的幅值越大,啮合刚度和系统振动响应的调制现象越明显,且当波动负载幅值较小时,表现为窄带调频和调幅的叠加,啮合频率两侧仅各有一条明显的边频谱线。
Gear transmission is often subjected to complex fluctuating external torques,which usually results in complex characteristics of gear meshing and complicated frequency feature of dynamic response.Based on the potential energy method model of time-varying mesh stiffness,a modified model of time-varying mesh stiffness is proposed,which takes the influence of the torsional and translational vibration into account.The translational-torsional coupling model of a one-stage gear set is developed,and the dynamic vibration response is computed by the Newmark method.Numerical simulations are implemented to investigate the influence of the fluctuating external torque on the dynamic response and modulation sidebands.The results indicate that distinct sidebands appear in both the spectra of the mesh stiffness and the dynamic response when the effect of the fluctuating external torque is considered,and the modulation frequency of those sidebands is no other than the frequency of the fluctuating external torque.What's more,the higher the central frequency is,the more obvious the modulation phenomenon is.The results also show that more obvious and richer sidebands appear with a larger fluctuating external torque.Meanwhile,a superposition of narrow-band frequency modulation and amplitude modulation is discovered,resulting in only one significant sideband on either side of the mesh frequency.
Gear transmission is often subjected to complex fluctuating external torques,which usually results in complex characteristics of gear meshing and complicated frequency feature of dynamic response.Based on the potential energy method model of time-varying mesh stiffness,a modified model of time-varying mesh stiffness is proposed,which takes the influence of the torsional and translational vibration into account.The translational-torsional coupling model of a one-stage gear set is developed,and the dynamic vibration response is computed by the Newmark method.Numerical simulations are implemented to investigate the influence of the fluctuating external torque on the dynamic response and modulation sidebands.The results indicate that distinct sidebands appear in both the spectra of the mesh stiffness and the dynamic response when the effect of the fluctuating external torque is considered,and the modulation frequency of those sidebands is no other than the frequency of the fluctuating external torque.What's more,the higher the central frequency is,the more obvious the modulation phenomenon is.The results also show that more obvious and richer sidebands appear with a larger fluctuating external torque.Meanwhile,a superposition of narrow-band frequency modulation and amplitude modulation is discovered,resulting in only one significant sideband on either side of the mesh frequency.
引文
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[14] Cai Y.Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon(a new stiffness function of helical involute tooth pair)[J].Journal of Mechanical Design,1995,117(3):460-469.
[2] Chaari F,Baccar W,Abbes M S,et al.Effect of spalling or tooth breakage on gearmesh stiffness and dynamic response of a one-stage spur gear transmission[J].European Journal of Mechanics-A/Solids,2008,27(4):691-705.
[3] Saxena A,Parey A,Chouksey M.Time varying mesh stiffness calculation of spur gear pair considering sliding friction and spalling defects[J].Engineering Failure Analysis,2016,70:200-211.
[4] Jia S,Howard I.Comparison of localised spalling and crack damage from dynamic modelling of spur gear vibrations[J].Mechanical Systems and Signal Processing,2006,20(2):332-349.
[5]Ma H,Song R,Pang X,et al.Time-varying mesh stiffness calculation of cracked spur gears[J].Engineering Failure Analysis,2014,44(6):179-194.
[6] Ma H,Li Z,Feng M,et al.Time-varying mesh stiffness calculation of spur gears with spalling defect[J].Engineering Failure Analysis,2016,66:166-176.
[7] Ma H,Zeng J,Feng R,et al.Review on dynamics of cracked gear systems[J].Engineering Failure Analysis,2015,55:224-245.
[8]李永焯,丁康,何国林,等.齿轮系统振动响应信号调制边频带产生机理[J].机械工程学报,2018,54(5):105-112.Li Yongzhuo,Ding Kang,He Guolin,et al.Modulation sidebands of the vibration signal of gearbox[J].Journal of Mechanical Engineering,2018,54(5):105-112.
[9] Sika G,Velex P.Instability analysis in oscillators with velocity-modulated time-varying stiffness—Applications to gears submitted to engine speed fluctuations[J].Journal of Sound and Vibration,2008,318(1):166-175.
[10] Qiu X,Han Q,Chu F.Analytical investigation on unstable vibrations of single-mesh gear systems with velocity-modulated time-varying stiffness[J].Journal of Sound and Vibration,2014,333(20):5130-5140.
[11] Kim W,Hong H Y,Chung J.Dynamic analysis for a pair of spur gears with translational motion due to bearing deformation[J].Journal of Sound and Vibration,2010,329(21):4409-4421.
[12] Liang X,Zuo M J,Patel T H.Evaluating the timevarying mesh stiffness of a planetary gear set using the potential energy method[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2014,228(3):535-547.
[13] Bartelmus W.Mathematical modelling and computer simulations as an aid to gearbox diagnostics[J].Mechanical Systems and Signal Processing,2001,15(5):855-871.
[14] Cai Y.Simulation on the rotational vibration of helical gears in consideration of the tooth separation phenomenon(a new stiffness function of helical involute tooth pair)[J].Journal of Mechanical Design,1995,117(3):460-469.