一阶摩擦模型与绒毛动力学：集中与分布式公式
First-order friction models with bristle dynamics: lumped and distributed formulations
AI总结：
本文提出了一种基于物理原理的一阶摩擦模型，通过反向摩擦特性近似绒毛动力学，并推导出与LuGre模型相似的公式，同时提出分布式版本用于滚动接触摩擦建模。
摘要：
动态模型，特别是速率依赖型模型，在捕捉摩擦过程的关键现象学特征方面已被证明是有效的，同时具有重要的数学性质，有助于设计控制和估计算法。然而，许多速率依赖型公式基于经验考虑，而物理推导可能提供更大的可解释性。在此背景下，从基本物理原理出发，本文引入了一种新的第一阶动态摩擦模型，通过反向摩擦特性来近似绒毛元件的动力学。在所开发的模型中，通过简单的流变学方程为绒毛元件推导出一种特定的公式，其形式与LuGre模型非常相似。该模型在稳定性与被动性方面进行了严格分析——这些性质支持观测器和控制器的合成。此外，还提出了一种分布式版本，以超几何偏微分方程（PDE）形式提出，这使能够建模滚动接触现象中常见的摩擦过程。通过经典实验评估所提出描述的摩擦学行为，并与LuGre模型预测的响应进行验证，揭示了显著的相似性和关键差异。
英文摘要：
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.
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