During planar motion, contact surfaces exhibit a coupling between tangential and rotational friction forces. This article proposes planar friction models grounded in the LuGre model and limit surface theory. First, distributed planar extended state models are proposed, and the elastoplastic model is extended for multidimensional friction. Subsequently, we derive a reduced planar friction model coupled with a precalculated limit surface, which offers the reduced computational cost. The limit surface approximation through an ellipsoid is discussed. The properties of the planar friction models are assessed in various simulations, demonstrating that the reduced planar friction model achieves comparable performance to the distributed model while exhibiting $\sim\! 80$ times the lower computational cost.

中文翻译：

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使用 LuGre 动力学和极限曲面进行平面摩擦建模


在平面运动期间，接触表面表现出切向摩擦力和旋转摩擦力之间的耦合。本文提出了基于 LuGre 模型和极限表面理论的平面摩擦模型。首先，提出了分布式平面扩展状态模型，并将弹塑性模型扩展为多维摩擦。随后，我们推导了一个减少的平面摩擦模型与预先计算的极限表面相结合，从而降低了计算成本。讨论了通过椭球体的极限表面近似。平面摩擦模型的属性在各种模拟中进行了评估，表明减少的平面摩擦模型实现了与分布式模型相当的性能，同时表现出 $\sim\!计算成本降低 80 美元。