非线性空气弹簧数学模型的研究

为了建立既贴切实际又便于计算的空气弹簧力数学模型,考虑到空气弹簧的非线性变刚度特性,对空气弹簧的刚度特性和力进行了理论分析。结果表明非线性恢复力是空气弹簧位移的三次多项式;同时,根据车型匹配的空气弹簧型号和数据表,运用MATLAB/Simulink软件进行了多项式和径向基函数曲线拟合,建立了非线性空气弹簧多项式模型并对其进行了验证,多项式拟合仿真结果与实际试验结果相符合,比较真实地反映了空气弹簧的非线性变刚度特性,而且多项式拟合残差值比径向基函数拟合残差值小,从而证明了非线性空气弹簧多项式模型的正确性,为后续悬架系统模型的建立及控制策略的研究打下坚实的基础。

Study on the mathematical model of non-linear air spring

In order to set up a mathematical model of air-spring force which is practical and easy to calculate,the air spring’s stiffness and force are analyzed theoretically in consideration of its non-linear variable stiffness. The results show that the non-linear restoring force is the cubic polynomial of the air spring’s displacement. Besides,according to the air spring’s type and data sheet compatible with the vehicle model,the curve fittings of polynomial and radial basis function are carried out by means of the MATLAB/Simulink software,in order to set up and verify the non-linear air-spring polynomial model. The simulation results of polynomial fitting are in accordance with the experimental results,which reflect the air spring’s non-linear variable stiffness characteristics,and the residual value of polynomial fitting is smaller than that of radial basis function fitting,which proves that the non-linear air-spring polynomial model is correct and lays a foundation for both the follow-up model of the suspension system and the study on the control strategy.