Estimation of the Maximum Tire-Road Friction Coefficient

[+] Author and Article Information
Steffen Müller

Postdoc at the Department of Mechanical Engineering, University of California, Berkeley, California 94720 Since June 1st 2001: BMW AG, 80788 Münchene-mail: steffen.mc.mueller@bmw.de

Michael Uchanski

Department of Mechanical Engineering, University of California, Berkeley, California 94720e-mail: mikeu@vehicle.me.berkeley.edu

Karl Hedrick

Department of Mechanical Engineering, University of California, Berkeley, California 94720

J. Dyn. Sys., Meas., Control 125(4), 607-617 (Jan 29, 2004) (11 pages) doi:10.1115/1.1636773 History: Received January 16, 2002; Revised June 30, 2003; Online January 29, 2004
Copyright © 2003 by ASME
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μmax and slope k of regression lines for slip curves during braking. Dark stars come from dry road slip curves, and light diamonds come from soapy road slip curves. Left: Data points with μ ranging from 0 to −0.2 are used to calculate slope of regression lines. Right: Data points with μ ranging between 0 and −0.4 are used to calculate regression line.
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A sampling of tire-road friction estimation research. Complete reference information for these papers in bibliography.
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Normalized longitudinal force, μ, versus longitudinal slip, computed using “Magic Formula”
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Left: Measured μ versus slip data for 18 separate braking maneuvers on dry road and 10 separate braking maneuvers on wet and soapy road. Right: Same raw data as left graph, but the μ axis is divided into bins and one data point per bin is generated for each surface by averaging all of the slip values in that bin.
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Illustration of “Secant Effect:” Both slip curves calculated from the “brush model,” and both have the same longitudinal stiffness. Yet, the regression lines using data with μ between 0 and 0.4 have different slopes.
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Comparison between measured and estimated traction force. The wheel is on the verge of locking at time=3.5 seconds.
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Measured (solid) and estimated (circles) slip curves during braking. Left: Dry road. Right: Soapy road.
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Regression line slope for the measured and estimated slip curves from Fig. 8, plotted against the friction coefficient (kμcut versus μcut)
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μmax versus k0.4 for braking on dry (dark stars) and soapy (light diamonds) road surfaces using k0.4 of observed slip curves
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Slopes of the linear part of dry-road slip curves taken from the literature
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Measured μ versus slip data at several time instants during a hard braking maneuver (circles) and their least squares slip curves using tire model of Eq. 5 (solid line). μmax taken from the fitted slip curve tends to depend on the most extreme μ value attained.



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