Contact surfaces in planar motion exhibit a coupling between tangential and rotational friction forces. This paper proposes planar friction models grounded in the LuGre model and limit surface theory. First, distributed planar extended state models are proposed and the Elasto-Plastic model is extended for multi-dimensional friction. Subsequently, we derive a reduced planar friction model, coupled with a pre-calculated limit surface, that offers 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 ~80 times lower computational cost.

翻译：处于平面运动的接触表面会表现出切向摩擦力与旋转摩擦力之间的耦合。本文提出了基于LuGre模型与极限曲面理论的平面摩擦模型。首先，提出了分布式的平面扩展状态模型，并将弹塑性模型扩展至多维摩擦场景。随后，我们推导出一个与预计算极限曲面相结合的简化平面摩擦模型，该模型具有更低计算成本。讨论了通过椭球体近似极限曲面方法。通过多种仿真评估平面摩擦模型的特性，结果表明简化平面摩擦模型在实现与分布式模型相当性能的同时，计算成本降低约80倍。