Accurate tyre models are important to ensure valid and reliable simulation of vehicle behaviour. To this purpose, the Magic Formula (MF) became the de facto standard for vehicle dynamics simulations, despite requiring many empirically derived coefficients. This paper shows how the accuracy of a simple physical-based brush-type tyre model can be enhanced to simulate tyre behaviour that closely matches MF results. To do so, the real, highly complex rubber friction characteristics are incorporated into the brush model. The friction characteristics were obtained from friction measurements with a tread rubber block. The developed model is validated against experimental tyre data obtained on a flat-track test rig and the corresponding MF model. Results show that the inclusion of friction characteristics allow accurate simulation of longitudinal and lateral slip conditions over a wide range of normal loads with the simple brush model. At extreme loading scenarios, the simulation accuracy deteriorates because of the significant influence of highly nonlinear deformation behaviour of the tyre that is not accounted for in the brush model formulation.

准确的轮胎模型对于确保有效和可靠地模拟车辆行为非常重要。为此，魔术公式 (MF) 成为车辆动力学模拟的事实标准，尽管需要许多经验导出的系数。本文展示了如何提高简单的基于物理的刷式轮胎模型的准确性，以模拟与 MF 结果非常匹配的轮胎行为。为此，将真实的、高度复杂的橡胶摩擦特性纳入刷模型。摩擦特性是通过使用胎面橡胶块的摩擦测量获得的。所开发的模型已根据在平轨试验台上获得的实验轮胎数据和相应的 MF 模型进行验证。结果表明，包含摩擦特性允许使用简单的刷子模型在大范围的正常载荷下准确模拟纵向和横向滑动条件。在极端负载情况下，由于轮胎的高度非线性变形行为的显着影响，而在刷模型公式中没有考虑到，模拟精度会下降。