Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 01 Jun 2009

Experimental Validation of the Brush Tire Model5

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Page Range: 122 – 137
DOI: 10.2346/1.3130985
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Abstract

The paper contains an experimental validation of the physically based brush-tire model toward the tire behavior in a number of different realistic conditions. Results of measurements performed with summer, winter, and studded tires on different road foundations such as wet and dry asphalt, basalt, snow, and ice are presented. The purpose behind the validation is to study the possibilities of using the brush model to estimate the friction coefficient from measurements or estimates of the longitudinal tire forces and tire slip. The sensitivity of the included tire parameters toward various factors that may change during normal run of the vehicle is also investigated.

Keywords: tire characteristics; brush model; vehicle measurements; braking; tire stiffness; road friction estimation; slip; force
Copyright: The Tire Society
FIG. 1.
FIG. 1.

The test truck BV12 in Arjeplog.

FIG. 2.
FIG. 2.

The longitudinal deformation of the rubber layer between the tire carcass and the road, according to the brush model. The carcass moves with the slip velocity, vx-ωRe, relative the road. The contact zone moves with the wheel-travel velocity, vx.

FIG. 3.
FIG. 3.

Measurement data from Hällered showing results from the winter tire on wet asphalt with a vertical load of 4 kN. To the left: adaptation of the brush model. The normalized brake force is shown as a function of the slip, λ. To the right: recorded signals showing the test sequences in the measurement file.

FIG. 4.
FIG. 4.

Measurements of the winter tire at Hällered together with a brush model adaptation at the vertical load 4 kN. To the left: on wet asphalt. To the right: on basalt. Note that scaling on the axes differs between the figures.

FIG. 5.
FIG. 5.

Adaptation of the brush model toward measurements data from Arjeplog for the winter tire with the vertical load 4 kN. To the left: on snow. To the right: on ice. Note that scaling on the axes differs between the figures.

FIG. 6.
FIG. 6.

Adaptation of the brush model toward measurement data from Hällered using the summer tire with a vertical load of 4 kN. To the left: on wet asphalt. To the right: on dry asphalt. Note that scaling on the axes differs between the figures.

FIG. 7.
FIG. 7.

Adaptation of the brush model toward measurement data from Arjeplog using the summer tire with a vertical load of 4 kN. To the left: on snow. To the right: on ice. Note that scaling on the axes differs between the figures.

FIG. 8.
FIG. 8.

Adaptation of the brush model toward measurements data from Arjeplog with studded tire and with the vertical load 4 kN. To the left: on snow. To the right: on ice. Note that scaling on the axes differs between the figures.

FIG. 9.
FIG. 9.

Footprints of the studded tire on ice during brake application. The brake torque is applied as a ramp, and the increasing grooves are a result of the increasing tire force. The wheel is rolling from the left to the right.

FIG. 10.
FIG. 10.

Diagram showing the measurement results from Table 1 and the relation between the braking stiffness and the friction coefficient.

FIG. 11.
FIG. 11.

Diagrams showing the load dependence in the previously presented measurements (see Table 1). To the left: the normalized braking stiffness, C0x. To the right: the effective rolling radius, Re, of the winter tire.

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