In this article, a nonlinear dynamic model with five degrees-of-freedom for a four-wheel-drive vehicle driveline connected by a cardan joint, including dynamic intersection angle, nonconstant velocity, and additional moment caused by the cardan joint, is established by using the Lagrange method to analyze the driveline coupling vibration in both torsional and lateral directions. High-order Runge–Kutta algorithm is applied to solve the differential equations and to calculate transient responses of the driveline rotors under acceleration condition. The color maps and second-order vibration of the driveline are acquired by frequency spectrum analysis and order tracking analysis, respectively. The second-order vibration and noise of the driveline and vehicle interior caused by the cardan joint is validated by vehicle experimental results and reduced effectively by decreasing intersection angle of the cardan joint under the operational condition. Moreover, application of a flexible coupling instead of the cardan joint significantly reduces the second-order vibration but simultaneously generates low-level third-order vibration.

中文翻译：

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万向节传动系统的二阶扭转和横向振动的非线性数值和实验研究

在本文中，建立了通过万向节连接的四轮驱动车辆动力传动系统的具有五个自由度的非线性动力学模型，包括动态交叉角，非恒定速度和由万向节引起的附加力矩。使用拉格朗日方法来分析传动系统在扭转和横向方向上的耦合振动。应用高阶Runge–Kutta算法求解微分方程，并计算加速条件下动力传动系统转子的瞬态响应。通过频谱分析和顺序跟踪分析分别获取传动系统的颜色图和二次振动。通过车辆试验结果验证了万向节引起的动力传动系统和车辆内部的二次振动和噪声，并通过在工作条件下减小万向节的交叉角度有效地降低了该振动。此外，使用挠性联轴器代替万向节可显着降低二阶振动，但同时会产生低级的三阶振动。