Abstract
This paper proposes a brush-type tire model with a new mathematical representation. The presented model can be seen as a generic model that describes the distributed viscoelastic force and Coulomb-like friction force, which are balancing each other at each point, in the contact patch. The model is described as a partial differential algebraic inclusion (PDAI), which involves the set-valuedness to represent the static friction. A numerical integration algorithm for this PDAI is derived through the implicit Euler discretization along both space and time. Some numerical comparisons with Magic Formula and a LuGre-based tire model are presented. The results show that, with appropriate choice of parameters, the proposed model is capable of producing steady-state characteristics similar to those of Magic Formula. It is also shown that the proposed model realizes a proper static friction state, which is not realized with a LuGre-based tire model.
Highlights
Tire-road interaction plays a crucial role in the dynamic behaviors of wheeled machinery, such as automobiles and wheeled mobile robots
In the kinetic friction state, the force is determined by the relative velocity, while in the static friction state, the relative velocity maintains zero as long as the friction force is below the maximum static friction force. at is, the causality between the relative velocity and the friction force is reversed between the two states
One strength of the proposed approach is that it realizes the static friction state, which is not realized by LuGre-based tire models
Summary
Tire-road interaction plays a crucial role in the dynamic behaviors of wheeled machinery, such as automobiles and wheeled mobile robots. One strength of the proposed approach is that it realizes the static friction state, which is not realized by LuGre-based tire models Another notable point may be that it does not involve singularity at the zero velocity [14], which should be properly handled in the application of Pacejka’s Magic Formula [15, 16]. Many of the brush-type tire models are based on the LuGre friction model (3) In their approach, the input velocity v is the velocity of the rigid wheel (or of the deformed carcass centerline, as will be discussed below) relative to the road and the output f corresponds to the distributed tangential force per length
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