First-order friction models with bristle dynamics: lumped and distributed formulations

2026-02-10

AI Summary

This work addresses the limitations of existing rate-dependent friction models, which are often empirical, lack physical interpretability, and fail to satisfy mathematical properties essential for control and estimation. By leveraging fundamental physical principles and inverting the dynamics of bristle elements, the authors propose a physically grounded first-order dynamic friction modeling framework that guarantees stability and passivity. The framework not only recovers lumped-parameter models akin to LuGre but also, for the first time, yields a distributed-parameter hyperbolic partial differential equation (PDE) model directly linked to bristle dynamics, suitable for rolling contact scenarios. Experimental validation demonstrates that the proposed model reproduces key behaviors of the LuGre model while revealing critical differences, thereby exhibiting superior physical consistency and modeling efficacy.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Intelligent Robots: Behavior Learning & Control

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

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.

Problem

• friction modeling
• bristle dynamics
• rate-dependent friction
• physical interpretability
• rolling contact

Innovation

• bristle dynamics
• first-order friction models
• distributed friction model
• hyperbolic PDE
• passivity analysis