Parametric vibration stabilityof locomotivegear transmission system with tooth surface friction
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摘要: 针对机车齿轮传动系统的参数振动问题, 建立了考虑齿面摩擦时机车齿轮传动系统的动力学模型, 基于势能原理获得了齿轮时变啮合刚度, 并利用傅里叶级数展开, 利用多尺度法进行求解, 获得了系统参数振动稳定的边界条件。最后开展实例分析, 研究了齿面摩擦因数对机车齿轮传动系统参数振动稳定性的影响。分析结果表明: 不计齿面摩擦时, 当机车速度约为119.02/j km·h-1 (j是谐波项) 时, 系统会产生参数共振, 摩擦因数越大, 对应的参数共振速度越大; 在参数共振速度附近存在系统振动不稳定区域, 当系统阻尼系数和摩擦因数均为0, 谐波项分别为1、2、3、4时, 相对于参数共振速度的波动值分别为9.16、1.46、0.53、0.55 km·h-1, 系统振动不稳定; 当阻尼系数为0时, 在对应谐波项下, 与摩擦因数为0时相比, 齿面摩擦因数分别为0.1、0.2时, 系统振动不稳定区域内相对于参数共振速度的波动值分别增加了约4.88%、9.54%;当阻尼系数为0.01时, 随着摩擦因数的增大, 在系统振动不稳定区域内相对于参数共振速度的波动值不一定增加; 摩擦因数越大, 系统稳定所需的阻尼系数越小。Abstract: Aiming at solving the problem of parametric vibration of locomotive gear transmission system, the dynamic model of gear transmission system was established considering tooth surface friction.In the model, the time-varying mesh stiffness was obtained based on the potential energy method, fitted by using the technique of Fourier series, and solved by using the method of multiple scales to gain the boundary condition of parametric stable vibration.Finally, a case study was carried out for studying the influence of tooth surface friction on the parametric vibration stability.Analysis result indicates that when the resonance speed is about 119.02/j km·h-1 (j is harmonic term), the prametric vibration will happen under the condition that friction coefficint is 0.The greater the friction coefficient is, the bigger the resonance speed at corresponding harmonic term is.Meanwhile, there exist an unstable vibration region in the vicinity of resonance speed.Under the condition that the damping coefficient and the friction coefficient are 0, when the harmonic terms are 1, 2, 3, 4, respectively, the corresponding fluctuation ranges relative to resonance speeds are about 9.16, 1.46, 0.53, 0.55km·h-1, respectively, so the system is unstable.Under the condition that the damping coefficient is 0, when the friction coefficients are 0.1and 0.2, respectively, compared to the result that the friction coefficient is 0, the fluctuation ranges relative to resonance speeds increase by about4.88%, 9.54%, respectively, with the corresponding harmonic term in unstable vibration regions.But when the damping coefficient is 0.01and the system is unstable, with the increase of friction coefficient, the fluctuation range relative to resonance speeds does not necessarily increase.Furthermore, the larger the friction coefficient is, the smaller the damping coefficient required by the stability of system is.5tabs, 13figs, 30refs.
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Figure 3. Dynamic model of torsional vibration for locomotive gear transmission system
Figure 9. Curves of parametric vibration stability in plane between stiffness ratio and speed
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