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Research Papers

# Estimation of Road Friction Coefficient Based on the Brush Model

[+] Author and Article Information
Osamu Nishihara

Graduate School of Informatics, Kyoto University, Yoshida-honmachi 36-1, Sakyo-ku, Kyoto 606-8501, Japannishihara@i.kyoto-u.ac.jp

Kurishige Masahiko

Advanced Technology R&D Center, Mitsubishi Electric Corporation, Tsukaguchi-honmachi 8-1-1, Amagasaki, Hyogo 661-8661, Japankurishige.masahiko@bp.mitsubishielectric.co.jp

J. Dyn. Sys., Meas., Control 133(4), 041006 (Apr 07, 2011) (9 pages) doi:10.1115/1.4003266 History: Received April 29, 2009; Revised August 12, 2010; Published April 07, 2011; Online April 07, 2011

## Abstract

Road friction coefficients are highly effective for advanced vehicle control technologies, although the estimation at four individual tires has not been practically used for ordinary vehicles. This study describes the essential relation between the tire forces and the aligning torque that can be rearranged as an estimation equation for the grip margin. The grip margin is readily convertible into the friction coefficient. The brush model is reanalyzed, beginning from the conventional simple physical model, and intrinsic expressions are derived. The grip margin, which is defined as the residual tire force normalized by the radius of friction circle, was estimated using three components of the tire forces and the aligning torque. A simple cubic equation is obtained as a grip margin equation for an isotropic brush model. Previous studies assumed an anisotropic brush model and obtained an imperfect quintic equation. In the present study, a new term is added to the algebraic equation, which was shown to be consistent with the isotropic model. The solutions to the equations are approximated by Chebyshev polynomials. The estimation methods are tested by numerical simulations using CarSim, which is a popular vehicle simulation software application. The estimated friction coefficients agree well with the values that are set during each run of the simulations, especially for the cases of smaller grip margins and lower friction conditions.

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## Figures

Figure 1

Friction circle and grip margin

Figure 2

Contact area of the brush model

Figure 3

Grip margin of the isotropic model

Figure 4

Sensitivities of the estimation function

Figure 5

Example of the grip margin for the anisotropic model

Figure 6

CarSim tire model: (a) lateral force (μ=0.87), (b) traction/braking force (μ=0.89), and (c) aligning torque (μ=0.89)

Figure 7

Road friction coefficients estimated by the isotropic brush model (●: front left wheel and ○: front right wheel): (a) μ=0.2, (b) μ=0.3, and (c) μ=0.5

Figure 8

Difference in estimated grip margin (●: front left wheel and ○: front right wheel)

Figure 9

Estimated and real μ ratios

Figure 10

Estimation function for the upper bound of η

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