基于中心流形理论的多维耦合摆振系统稳定性分析

doi:10.3901/JME.2023.04.155

机械工程学报 ›› 2023, Vol. 59 ›› Issue (4): 155-162.doi: 10.3901/JME.2023.04.155

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基于中心流形理论的多维耦合摆振系统稳定性分析

魏恒, 卢剑伟, 叶盛勇, 石磊

合肥工业大学汽车与交通工程学院合肥 230009

收稿日期:2022-07-30 修回日期:2022-10-26 出版日期:2023-02-20 发布日期:2023-04-24
通讯作者: 卢剑伟(通信作者),男,1975年出生,博士,教授,博士研究生导师。主要研究方向为机械系统动力学、振动噪声控制、可靠性设计等。E-mail:jwlu75@163.com
作者简介:魏恒,男,1995年出生,博士研究生。主要研究方向为车辆系统动力学与控制。E-mail:weih9520@163.com
基金资助:
国家自然科学基金(51875150)和航空科学基金(2018ZEP4006)资助项目。

Stability Analysis of Multi-dimensional Coupled Shimmy System Based on Center Manifold Theory

WEI Heng, LU Jianwei, YE Shengyong, SHI Lei

School of Automotive and Transportation Engineering, Hefei University of Technology, Hefei 230009

Received:2022-07-30 Revised:2022-10-26 Online:2023-02-20 Published:2023-04-24

摘要/Abstract

摘要： 由于轮胎侧向力对垂向载荷的变化较为敏感，从而使得汽车簧载质量的运动对摆振的影响不容忽视。在汽车垂向运动和侧向运动之间的动力学耦合机制分析的基础上，建立多维耦合的独立悬架汽车摆振系统动力学模型。由系统微分方程组的雅克比矩阵，考察摆振系统特征值随车速的变化情况，并应用中心流形理论得到了系统的二维中心流形。此外，通过中心流形的稳定性参数，讨论系统极限环的稳定性。最后，采用数值算例对稳定性分析结果进行了验证，并考察系统参数对摆振幅值的影响，结果表明，汽车的轻量化和簧载质量质心到其侧倾轴距离的减小均有利于抑制汽车摆振，从而提高汽车行驶稳定性和安全性。

关键词: 汽车摆振, 动力学耦合, 独立悬架, 中心流形, 稳定性

Abstract: Since the tire lateral force is sensitive to the change of the vertical load, the influence of the motion of the sprung mass on vehicle shimmy cannot be ignored. Therefore, based on the analysis of dynamic coupling mechanism of the vertical and lateral motion of the vehicle, a dynamic model of vehicle shimmy system with independent suspension considering multi-dimensional coupling is established. According to the Jacobian matrix of the system differential equations, the eigenvalues of the shimmy system with the change of the vehicle speed are investigated. Then, the two-dimensional center manifold of the shimmy system is obtained on basis of the center manifold theory. Moreover, the stability of the limit cycle of the system is discussed by calculating the stability parameters of the central manifold. Finally, numerical examples are used to verify the results of stability analysis, and the influence of the system parameters on the shimmy amplitude is investigated. The results show that the lightweight of the vehicle and the reduction of the distance from the mass center of the sprung mass to its roll axis are beneficial to attenuate vehicle shimmy, thus improving the stability and safety of the vehicle.

Key words: vehicle shimmy, dynamic coupling, independent suspension, center manifold, stability

中图分类号:

O323
U461

魏恒, 卢剑伟, 叶盛勇, 石磊. 基于中心流形理论的多维耦合摆振系统稳定性分析[J]. 机械工程学报, 2023, 59(4): 155-162.

WEI Heng, LU Jianwei, YE Shengyong, SHI Lei. Stability Analysis of Multi-dimensional Coupled Shimmy System Based on Center Manifold Theory[J]. Journal of Mechanical Engineering, 2023, 59(4): 155-162.

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基于中心流形理论的多维耦合摆振系统稳定性分析

Stability Analysis of Multi-dimensional Coupled Shimmy System Based on Center Manifold Theory

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