Dynamic models, particularly rate-dependent models, have proven effective in capturing the key phenomenological features of frictional processes, whilst also possessing important mathematical properties that facilitate the design of control and estimation algorithms. However, many rate-dependent formulations are built on empirical considerations, whereas physical derivations may offer greater interpretability. In this context, starting from fundamental physical principles, this paper introduces a novel class of first-order dynamic friction models that approximate the dynamics of a bristle element by inverting the friction characteristic. Amongst the developed models, a specific formulation closely resembling the LuGre model is derived using a simple rheological equation for the bristle element. This model is rigorously analyzed in terms of stability and passivity -- important properties that support the synthesis of observers and controllers. Furthermore, a distributed version, formulated as a hyperbolic partial differential equation (PDE), is presented, which enables the modeling of frictional processes commonly encountered in rolling contact phenomena. The tribological behavior of the proposed description is evaluated through classical experiments and validated against the response predicted by the LuGre model, revealing both notable similarities and key differences.

翻译：动态模型，特别是速率相关模型，已被证明能有效捕捉摩擦过程的关键现象学特征，同时具备重要的数学性质，有助于控制与估计算法的设计。然而，许多速率相关模型基于经验考量建立，而物理推导可能提供更好的可解释性。在此背景下，本文从基本物理原理出发，引入了一类新颖的一阶动态摩擦模型，该类模型通过反转摩擦特性来近似鬃毛单元的动力学。在所发展的模型中，通过为鬃毛单元建立简单的流变方程，推导出了一个与LuGre模型高度相似的具体表述。该模型在稳定性和无源性方面得到了严格分析——这些重要性质支持观测器和控制器的综合设计。此外，本文还提出了一个分布式版本，其表述为双曲型偏微分方程，能够对滚动接触现象中常见的摩擦过程进行建模。通过经典实验评估了所提描述的摩擦学行为，并与LuGre模型预测的响应进行了对比验证，揭示了显著的相似性与关键差异。