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首页> 外文期刊>International Journal of Solids and Structures >Green's functions for a loaded rolling tyre
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Green's functions for a loaded rolling tyre

机译：格林的功能适用于装载的滚动轮胎

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摘要

A new formulation to determine the unit impulse response (Green's) functions of a loaded rotating tyre in the vehicle-fixed (Eulerian) reference frame for tyre/road noise predictions is presented. The proposed formulation makes use of the set of eigenfrequencies and eigenmodes for the statically loaded tyre obtained from a finite element (FE) model of the tyre. A closed-form expression for the Green's functions of a rotating tyre in the Eulerian reference system as a function of the eigenfrequencies and eigenmodes of the statically loaded tyre is found. Non-linear effects during loading are accounted for in the FE model, while the frequency shift due to the rotational velocity is included in the calculation of the Green's functions. In the literature on tyre/road noise these functions are generally used to determine the tyre response during tyre/road contact calculations. The presented formulation opens the possibility to solve the contact problem directly in the Eulerian reference frame and to include local tyre softening due to non-linear effects while keeping the computational advantage of describing the tyre dynamics as a set of impulse response functions. The advantage of obtaining the Green's functions in the Eulerian reference system is that only the Green's functions corresponding to the potential contact zone need to be determined, which significantly reduces the computational cost of solving the tyre/road contact and since the mesh is fixed in space, a finer mesh can be used for the potential contact zone, improving the accuracy of the contact force calculations. Although these effects might be less pronounced if a more accurate tyre model is used, it is found that using the Green's functions of the loaded tyre in a contact force calculation leads to smaller forces than in the unloaded case, lower frequencies are present in the response and they decrease faster as the rotational velocity increases.
机译：提出了一种新的公式，用于确定在车辆固定的（欧拉）参考系中加载的旋转轮胎的单位冲激响应（格林）函数，以预测轮胎/道路噪声。拟议的公式利用从轮胎的有限元（FE）模型获得的静态负载轮胎的特征频率和特征模态集。在欧拉参考系统中，旋转轮胎的格林函数与静态载荷轮胎的本征频率和本征模的函数的闭合形式被发现。有限元模型考虑了加载过程中的非线性影响，而格林函数的计算中包括了由于转速引起的频移。在关于轮胎/道路噪声的文献中，这些功能通常用于确定轮胎/道路接触计算期间的轮胎响应。提出的公式为直接解决欧拉参考系中的接触问题提供了可能性，并且由于非线性效应而包括了局部轮胎软化，同时保留了将轮胎动力学描述为一组脉冲响应函数的计算优势。在欧拉参考系统中获得格林函数的优势在于，仅需要确定与潜在接触区域相对应的格林函数，这大大降低了解决轮胎/道路接触的计算成本，并且由于网格固定在空间中，更细的网格可以用于潜在的接触区域，从而提高了接触力计算的准确性。尽管如果使用更精确的轮胎模型，这些影响可能不太明显，但是发现在接触力计算中使用加载轮胎的格林函数会产生比未加载情况下更小的力，但响应中存在较低的频率随着转速的增加，它们的减小速度更快。

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