Dynamic Modeling And Analysis Of Flexible Suspension System Based On Spectral Method

The suspension system was one of the important components in the vehicle chassis.Its main function was to transmit the force and torque between the wheels and the frame,reduced the impact of vibration and shock caused by road conditions on the frame and body.When the driving road conditions of the vehicle were harsh,the force and torque transmitted by the suspension system were relatively large.The wishbone beam of the suspension system not only experienced a wide range of rotational motion,but also was accompanied by a certain degree of elastic deformation motion,which were often coupled together in suspension system dynamics modeling.Suspension system was a typical flexible multi-body system,the elastic deformation of the flexible beam needed to be considered when the suspension system model was built.When the hypothetical mode method and the finite element method were used to deal with the elastic deformation of the flexible beam in the suspension system,it was necessary to solve the mode shape function of the flexible beam or mesh the flexible beam before fitting the elastic deformation of the flexible beam.In order to improve the solution accuracy of the dynamic model,the hypothetical modal method generally used mode shape function with more terms to fit the elastic deformation of the flexible beam and the finite element method divided more meshes.Both of which would increase the computational complexity of the dynamic model,resulted the problem of low computational efficiency.Therefore,in order to simplify the fitting processing of the elastic deformation of the flexible beam and improve the solution efficiency of the dynamic model of the suspension system,an efficient simulation solution method was proposed for flexible multi-body dynamics of suspension system based on spectral method in this thesis.In this method,the elastic deformation of the flexible beam were discretized by the spectral method and the flexible multi-body dynamic model of the suspension system was established according to the Lagrange equation method.The modal reduction method was used to reduce the order of the flexible multi-body dynamic model of the suspension system and the generalized α method was used to iteratively solve.The main research work of this thesis was as follows:（1）The basic principles and characteristics of spectral methods were briefly introduced.The principle of selecting basis functions in discretely solving partial differential equations by spectral method was combed.The general solution process of solving partial differential equations based on the spectral method was deduced.The fast convergence and high precision of the spectral method were verified by an example of solving second-order partial differential equations in the spectral method.（2）The coordinate system of suspension system was established based on floating frame method and suspension decoupling method was used to decoup suspension system into indepentdent machanism.Then the spectral method was used to discretize the elastic deformation displacement function of the three-dimensional flexible beam in the suspension system.Finally,the SM-DM was established by Lagrangian equation method and the theoretical feasibility of SM-DM was verified.（3）The commonly used model reduction method in flexible multi-body dynamic models and their advantages and disadvantages were introduced.It was determined that the modal reduction method was more suitable for the reduction of SM-DM from the aspect of high efficiency.Then,the modal frequency and the corresponding modal vector of the flexible beam were solved according to the mass matrix,stiffness matrix and modal solution formula of the flexible beam of the suspension system.The obtained modal frequencies were converted into dimensionless frequencies and compared with the dimensionless frequencies of flexible beams obtained based on ANSYS software.The results showed that: when the number of terms of the Chebyshev orthogonal polynomial of the discrete flexible beam reached 10×10,the calculation accuracy of the natural frequency of the flexible beam did not change within three decimal places.The feasibility of the modal reduction method was verified.Finally,the low-order modal frequency of the flexible beam wa truncated according to the modal reduction method and the corresponding modal transformation matrix was obtained.The SM-RDM was obtained through modal transformation matrix.（4）The SM-RDM were solved by generalized α method.The solution results of the suspension system were compared with the solution results of SM-DM and the solution results of FEM-DM.Taking the solution result of FEM-DM as the accurate value,the results showed that the relative error of displacement in the z17-axis direction of the frame was 2.77%and the relative error of the β₁₇ rotation angle displacement of the frame was 3.16%,the relative error of the displacement of the wheels 1 and 4 in the z-axis direction was 2.93% and2.74% respectively of the SM-RDM.When the number of terms of the selected Chebyshev orthogonal polynomial was 20 and the order of the selected modal reduction was 160,the relative error of the elastic deformation of the flexible beam was within 2.76%.The solution efficiency of SM-RDM was 22.07 times that of the FEM-DM.The calculation accuracy of the elastic deformation of the flexible beam of the SM-RDM was 0.779% lower than that of SM-DM,but the computational efficiency was 5.82 times that of the SM-DM.