基于非线性Drive-shaft模型的车辆传动系统冲击响应

建立了包含线性与非线性项的车辆传动系统非线性Drive-shaft模型, 应用具有耗散项的拉格朗日方程将非线性Drive-shaft模型转换为当量化的两质量模型, 通过将两端扭转角等效到同一端获得了传动系统的冲击响应方程, 应用Routh-Hurwitz准则分析了冲击响应方程的稳定性, 获得了稳定性参数区间。仿真结果表明: 将非线性阻尼分别设置为0和线性阻尼的1/10、-1/10时, 冲击响应首个峰值的绝对值分别为0.153 9、0.101 4、0.371 6, 当非线性阻尼为线性阻尼的1/10时, 冲击响应的首个峰值的绝对值最小, 这说明正的非线性阻尼有利于冲击响应的衰减; 将非线性刚度分别设置为0和线性刚度的1/10、-1/10时, 获得的冲击响应首个峰值的绝对值分别为0.153 9、0.178 8、0.115 9, 当非线性刚度为线性刚度的-1/10时, 冲击响应的首个峰值的绝对值最小, 这说明负的三次方非线性刚度有利于冲击响应的衰减; 在固定非线性刚度为线性刚度的-1/10的基础上, 将代表非线性阻尼的系数分别设置为0.1、0、-0.1, 获得的冲击响应首个峰值的绝对值分别为0.078 4、0.114 2、0.231 6。可见, 当代表非线性阻尼的系数设置为0.1时, 冲击响应的首个峰值的绝对值最小, 这表明在传动系统线性刚度及线性阻尼的基础上, 设计负的非线性刚度及正的非线性阻尼可以提升传动系统抵抗冲击的性能。

Shock response of vehicle powertrain based on nonlinear drive-shaft model

The nonlinear drive-shaft model of the vehicle powertrain that consists of linear and nonlinear terms was established. Based on the Lagrange equation with dissipative terms, the quantized two-mass model was obtained from the nonlinear drive-shaft model. The shock response equation was obtained by the equivalent torsion angle from two ends of the powertrain to one end. The stability of the shock response equation, as well as the stable region of the parameters, were obtained by using the Routh-Hurwitz criterion. Simulation result shows that when the values of the nonlinear damping are set as 0, 1/10, and-1/10 of the linear damping, the absolute values of the first peak of shock response are 0.153 9, 0.101 4, and 0.371 6, respectively. When the value of the nonlinear damping is 1/10 of the linear damping, the absolute value of the first peak is the smallest, which indicates that the positive nonlinear damping is beneficial to the shock response. When the values of nonlinear stiffness are set as 0, 1/10, and-1/10 of the linear stiffness, the absolute values of the first peak of the shock response are 0.153 9, 0.178 8, and 0.115 9, respectively. When the value of nonlinear stiffness is-1/10 of the linear stiffness, the absolute value of the first peak is the smallest, which indicates that the negative cubic nonlinear stiffness is beneficial to shock response. When the value of nonlinear stiffness is fixed at-1/10 of linear stiffness and the coefficients that represent the nonlinear damping are set as 0.1, 0, and-0.1, respectively, the absolute values of the first peak are obtained as 0.078 4, 0.114 2, and 0.231 6, respectively. When the coefficient representing the nonlinear damping is set as 0.1, the absolute value of the first peak of the shock response is the smallest, which indicates that, on the basis of the linear stiffness and damping of the powertrain system, the shock resistance of the powertrain can be improved by introducing negative nonlinear cubic stiffness and positive nonlinear damping to the linear powertrain.