A Nonlinear Torsional Dynamic Model of Multi-Mesh Gear Trains Having Flexible Shafts
A Nonlinear Torsional Dynamic Model of Multi-Mesh Gear Trains Having Flexible Shafts
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发表时间：
2007
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通讯作者：
Ahmad Al-Shhyab;A. Kahraman
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作者：
Ahmad Al-Shhyab;A. Kahraman
建立了一种非线性时变动力学模型，用于研究典型多啮合齿轮系的扭转动力学行为。物理系统由M个轴（2 ≥ M）组成，这些轴通过1 − M个齿轮对相互耦合。离散动力学模型包括齿轮侧隙间隙、齿轮啮合刚度波动和轴的扭转柔度。此外，齿轮齿的修改和典型的制造误差包括在齿轮啮合的周期性时变位移函数的形式。一个多项谐波平衡制定结合离散傅立叶变换和参数连续技术，以获得稳态周期n运动。直接数值积分的结果被用来证明谐波平衡预测的准确性。关键系统参数的影响也进行了研究。
A non-linear time-varying dynamic model is developed to study torsional dynamic behavior of a typical multi-mesh gear train. The physical system consists of M shafts ( 2 ≥ M ) coupled to each other by 1 − M gear pairs. The discrete dynamic model includes the gear backlash clearance, gear mesh stiffness fluctuations, and torsional flexibilities of the shafts. In addition, the gear tooth modifications and typical manufacturing errors are included in the form of periodically time-varying displacement functions applied at gear meshes. A multi-term Harmonic Balance formulation is used in conjunction with discrete Fourier Transforms and a Parametric Continuation technique to obtain the steady-state period-n motions. Direct numerical integration results are used to demonstrate the accuracy of the harmonic balance predictions. Effects of key system parameters are also studied.