Abstract The paper investigates the in-plane vibration property of static and rotating tires with the proposed tire model. The tire model is based on the linear ring model, and a mathematical approach is proposed to handle the tire contact problem. With this improvement, the tire model allows for directly calculating the eigenmodes of a loaded tire by solving its eigenvalue problem. A group of simulations is carried out using this improved ring model. For a static (not rotating) tire, the eigenfrequency and corresponding mode shape are investigated under both unloaded and loaded conditions. For a rotating tire, the effect of rotational speed on the eigenfrequencies of unloaded and loaded tires are modeled, and the results are observed using co-rotating and non-rotating reference frames. The main original contribution of this work is an evaluation of the quantitative relationship between unloaded and loaded conditions using modal assurance criterion (MAC) or improved modal assurance criterion (IMAC) analyses on both static and rotating tires. For a static tire, the eigenmodes can be classified into rigid ring modes and flexible ring modes, according to their mode shape and MAC evaluation results. For a rotating tire, the eigenfrequency and mode shape could vary with increasing rotational speed and behave differently in non-rotating and co-rotating reference frames. In a non-rotating frame, the IMAC value percentages for a loaded tire vary with increasing rotational speed, especially in the frequency veering ranges. In a co-rotating frame, the IMAC value variations for loaded modes are weaker than those seen in a non-rotating frame.

中文翻译：

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基于改进环模型的轮胎面内振动特性研究

摘要 本文利用所提出的轮胎模型研究了静态和旋转轮胎的面内振动特性。轮胎模型基于线性环模型，提出了一种数学方法来处理轮胎接触问题。通过这种改进，轮胎模型允许通过解决其特征值问题直接计算加载轮胎的特征模态。使用这种改进的环模型进行了一组模拟。对于静态（非旋转）轮胎，在空载和加载条件下研究特征频率和相应的振型。对于旋转轮胎，模拟了转速对空载和加载轮胎的特征频率的影响，并使用同向和非旋转参考系观察结果。这项工作的主要原始贡献是使用模态保证准则 (MAC) 或改进的模态保证准则 (IMAC) 对静态和旋转轮胎的分析来评估卸载和加载条件之间的定量关系。对于静态轮胎，根据模态形状和 MAC 评估结果，本征模态可分为刚性环模态和柔性环模态。对于旋转轮胎，特征频率和振型会随着转速的增加而变化，并且在非旋转和同向旋转参考系中表现不同。在非旋转坐标系中，负载轮胎的 IMAC 值百分比随着转速的增加而变化，尤其是在频率转向范围内。在同向旋转的框架中，