Semilinear single-track vehicle models with distributed tyre friction dynamics

2026-01-01

Nonlinear dynamics

AI Summary

This study addresses the limitations of conventional single-track vehicle models in accurately capturing the coupled effects of frictional nonlinearity and transient tire deformation. To overcome this, a novel semi-linear single-track model is proposed, integrating distributed friction brush dynamics (FrBD) to embed transient friction effects from rolling contact into the full-vehicle dynamics as a semi-linear partial differential equation (PDE). This formulation yields an ODE–PDE coupled system that unifies classical friction models such as Dahl and LuGre within a single framework for the first time. The well-posedness and physical consistency of the system are rigorously established, accommodating both flexible and rigid tire carcass configurations. Simulations successfully reproduce micro-oscillations and complex transient lateral responses under aggressive steering maneuvers, demonstrating the model’s superior balance of physical fidelity, mathematical rigor, and computational tractability.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Planning, Routing, and Scheduling: Model-Based Reasoning

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
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

This paper introduces a novel family of single-track vehicle models that incorporate a distributed representation of transient tyre dynamics, whilst simultaneously accounting for nonlinear effects induced by friction. The core of the proposed framework is represented by the distributed Friction with Bristle Dynamics (FrBD) model, which unifies and extends classical formulations such as Dahl and LuGre by describing the rolling contact process as a spatially distributed system governed by semilinear partial differential equations (PDEs). This model is systematically integrated into a single-track vehicle framework, where the resulting semilinear ODE–PDE interconnection captures the interaction between lateral vehicle motion and tyre deformation. Two main variants are considered: one with rigid tyre carcass and another with flexible carcass, each admitting a compact state-space representation. Local and global well-posedness properties for the coupled system are established rigorously, highlighting the dissipative and physically consistent properties of the distributed FrBD model. A linearisation procedure is also presented, enabling spectral analysis and transfer function derivation, and potentially facilitating the synthesis of controllers and observers. Numerical simulations demonstrate the model’s capability to capture micro-shimmy oscillations and transient lateral responses to advanced steering manoeuvres. The proposed formulation advances the state-of-the-art in vehicle dynamics modelling by providing a physically grounded, mathematically rigorous, and computationally tractable approach to incorporating transient tyre behaviour in lateral vehicle dynamics, when accounting for the effect of limited friction.

Problem

• tyre friction dynamics
• vehicle lateral dynamics
• transient tyre behaviour
• micro-shimmy oscillations
• distributed friction model

Innovation

• distributed friction
• semilinear PDE
• single-track vehicle model
• transient tyre dynamics
• Friction with Bristle Dynamics (FrBD)