考虑面外振动的轮胎三维环模型

Three-dimensional REF model of tire including the out-of-plane vibration

提出了包含面外扭转和面外弯曲振动的三维环模型,并应用于卡车子午线轮胎振动模态分析。在综述轮胎环模型发展的基础上,考虑了大变形应变和非线性应变项、面内面外弯曲和面外扭转三维位移模式,修正文献中的轮胎初始应力和气压功表达式,利用Hamilton变分原理首次建立了三维轮胎环模型的动力学控制方程,并利用模态展开技术得到了三维环模型面内和面外振动固有频率的解析解。该解析解首次建立了轮胎物理参数和轮胎三维振动固有频率之间的解析表达式,为轮胎的动态设计提供了理论指导。为验证三维环模型的准确性,对比了环模型分析、有限元模型和实验模态分析的结果,发现三者之间吻合良好,这证明文中建立的轮胎三维环模型的可靠性和准确性,能抓住子午线轮胎振动的本质规律。

In this paper, a three-dimensional REF model of the tire including the out-of-plane torsional and bending vibration is given, and applied to the vibration modal analysis of the radial truck tire. Based on the review of the ring models of tire, a model is developed where the large deformation and the nonlinear terms are considered in the strain. The three-dimensional dis- placement model of the in-plane and out-of-plane bend and the out-of-plane torsion is given. Some errors in the derivation of the initial stress and the work of the internal pressure in some related references are revised. The dynamic equations of the three-di- mensional REF model are obtained for the first time by using Hamilton variation principle, and the mode expansion is used to get the analytical solution of the natural frequencies. The analytic equations of the tire physics parameters and the three-dimen- sional vibration natural frequencies are deduced, which can provide a theoretical base for the dynamic design of the tire. To ver- ify the accuracy of the model, the results of theoretical formula are proved to be in good agreement with the results of finite ele- ment model and the experimental data. By means of case analysis, the model has high reliability and accuracy and can fully de- scribe the essential characteristics of the vibration of radial tires.