Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 01 Apr 2019

A Double Interaction Brush Model for Snow Conditions

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Page Range: 118 – 140
DOI: 10.2346/tire.18.460404
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ABSTRACT

Commonly used tire models for vehicle-handling simulations are derived from the assumption of a flat and solid surface. Snow surfaces are nonsolid and may move under the tire. This results in inaccurate tire models and simulation results that are too far from the true phenomena.

This article describes a physically motivated tire model that takes the effect of snow shearing into account. The brush tire model approach is used to describe an additional interaction between the packed snow in tire tread pattern voids with the snow road surface. Fewer parameters and low complexity make it suitable for real-time applications.

The presented model is compared with test track tire measurements from a large set of different tires. Results suggest higher accuracy compared with conventional tire models. Moreover, the model is also proven to be capable of correctly predicting the self-aligning torque given the force characteristics.

Keywords: tire modeling; driving simulator; tire on snow; tire brush model
FIG. 1
FIG. 1

Measurements with the brush models' approximation for three different winter tires: (a) European tire, (b) Nordic tire, (c) studded tire.

FIG. 2
FIG. 2

Open-loop single-track model simulation of a double-lane-change maneuver illustrating the consequences of the difference in tire characteristics between the tire on snow measurements (blue) and the conventional brush model (red).

FIG. 3
FIG. 3

Snow surface on the test track. The tire imprints are left by a BV12 truck that weighs 9 tons. Snow hardness is between 80 and 85 CTI units based on the U.S. standard ASTM F-1805.

FIG. 4
FIG. 4

Measurement rig scheme. Top view.

FIG. 5
FIG. 5

Schematics of the double interaction brush model.

FIG. 6
FIG. 6

Double interaction brush model compared with the single interaction brush model: (a) European tire, (b) Nordic tire, (c) studded tire. The parameters for all displayed models are presented in the appendix, Table 2.

FIG. 7
FIG. 7

Difference between measurements and tire models. Nordic tire: (a) absolute error in large slip range; (b) absolute error in zoomed-in low-slip range.

FIG. 8
FIG. 8

Coefficients for the double interaction model. Reference tire.

FIG. 9
FIG. 9

Coefficients for the double interaction model: dotted, Nordic; dashed, studded; solid, European.

FIG. 10
FIG. 10

Proportions of the forces generated by two interaction pairs.

FIG. 11
FIG. 11

Self-aligning torque. Double interaction brush model compared with the single interaction brush model. Reference tire.

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