In this paper, we discuss three improved brush models. The first one deals with the coupling between the slip and spin parameters and is valid for relatively high steering speed and small camber angles; the second one is more complex and considers the presence of a two-dimensional velocity field inside the contact patch due to large camber angles; the third one is more general and combines both the previous formulations. For the last two models, the investigation is conducted with respect to a rectangular contact patch, for which we show that three different regions can be identified, each of them corresponding to a different steady-state solution for the deflection of the bristle. Furthermore, from the transient analysis it emerges that each region can be in turn separated into an area in which steady-state conditions reign and another one in which the transient solution takes place. An asymptotic analysis is carried out for the three models and it is shown that the solutions are equivalent to the ones predicted by the standard brush theory for small values of the spin ratio and camber angle. Finally, a comparison is performed amongst the models to highlight the differences in the predicted tyre characteristics.

在本文中，我们讨论了三种改进的画笔模型。第一个处理滑移和旋转参数之间的耦合，并且对于较高的转向速度和较小的外倾角有效。第二个更复杂，并且考虑到由于较大的外倾角而在接触片内部存在二维速度场。第三个比较笼统，结合了以前的公式。对于最后两个模型，针对矩形接触面进行了研究，为此，我们显示可以识别出三个不同的区域，每个区域对应于鬃毛偏转的不同稳态解。此外，从瞬态分析中可以看出，每个区域可以依次分为一个区域，在该区域中处于稳态条件，另一个区域在其中发生瞬态解。对这三个模型进行了渐近分析，结果表明，对于较小的旋转比和外倾角值，这些解决方案与标准电刷理论所预测的解决方案等效。最后，在模型之间进行比较以突出预测轮胎特性的差异。