Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 27 Sept 2021

Theoretical Tire Model for Wear Progress of Tires with Tread Pattern Considering Two-Dimensional Contact Patch

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Page Range: 337 – 369
DOI: 10.2346/tire.21.20010
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ABSTRACT

A new theoretical tire model for the wear progress of tires with tread block pattern is developed considering a two-dimensional contact patch. In the model, the wear energy is calculated from the shear force and pressure distribution in a two-dimensional contact patch that are changed with not only shear forces in a contact patch but also with the wear and irregular wear of tires. The fore–aft shear force in a contact patch consists of six mechanisms related to slip ratio, camber, contact between a tire and a road, barrel deformation of a loaded block, rolling resistance, and a rolling tire with rounded crown shape, whereas the lateral shear force consists of three mechanisms related to slip angle/camber, contact of a tire with rounded crown shape, and barrel deformation of a loaded block. The heel and toe irregular wear and the progress of irregular wear under pure slip condition qualitatively agree with the conventional knowledge of tire engineers. The expected wear energy is introduced to predict the wear progress under combined slip condition in the wear course. Using the vehicle dynamics to predict the tire force history, a histogram of external forces is obtained by transforming from it. Calculating wear energies by changing slip angle and slip ratio, the relation between external forces and the wear energy is expressed as the response surface. Multiplying the wear energy by the histogram, the expected wear energy distribution in a block is calculated. Assuming that the worn depth is proportional to the expected wear energy, the wear progress is predicted.

Keywords: tire; wear progress; irregular wear; heel and toe; force and moment; theoretical tire model
FIG. 1 —
FIG. 1 —

Model of contact area of a tire with rectangular block pattern under external forces.

FIG. 2 —
FIG. 2 —

Conceptual figure of the cross section of a worn tire.

FIG. 3 —
FIG. 3 —

Conceptual figure of contact shape and pressure distribution of theoretical tire wear model.

FIG. 4 —
FIG. 4 —

Conceptual figure of shear force distribution of theoretical tire wear model.

FIG. 5 —
FIG. 5 —

Basic steps of wear progress simulation.

FIG. 6 —
FIG. 6 —

Flowchart of theoretical wear model under combined slip condition.

FIG. 7 —
FIG. 7 —

Wear progress of a tire with rib pattern under pure slip condition (slip angle = 2°, slip ratio = 0).

FIG. 8 —
FIG. 8 —

Wear energy distribution of a new tire with rib pattern under pure slip condition (slip angle = 2°, slip ratio = 0).

FIG. 9 —
FIG. 9 —

Wear progress of a tire with rib pattern under braking condition (slip angle = 0°, slip ratio = 0.03).

FIG. 10 —
FIG. 10 —

Wear energy distribution of a new tire with rib pattern under braking condition (slip angle = 0°, slip ratio = 0.03).

FIG. 11 —
FIG. 11 —

Wear progress of a tire with rib pattern under driving condition (slip angle = 0°, slip ratio = −0.03).

FIG. 12 —
FIG. 12 —

Wear energy distribution of a new tire with rib pattern under driving condition (slip angle = 0°, slip ratio = −0.03).

FIG. 13 —
FIG. 13 —

Wear energy distribution of a new tire with block pattern under zero slip angle and zero slip ratio.

FIG. 14 —
FIG. 14 —

Wear progress in the block 1 of a tire with block pattern in the longitudinal direction (slip angle = 0°, slip ratio = 0).

FIG. 15 —
FIG. 15 —

Wear energy distribution in blocks 1 and 5 of a new tire with block pattern under pure slip condition (slip angle = 2°, slip ratio = 0).

FIG. 16 —
FIG. 16 —

Wear energy component in block 1 of a new tire with block pattern under pure slip condition (slip angle = 2°, slip ratio = 0).

FIG. 17 —
FIG. 17 —

Shear force distribution in the block 1 of a new tire with block pattern under pure slip condition (slip angle = 2°, slip ratio = 0).

FIG. 18 —
FIG. 18 —

Wear energy distribution in blocks 1 and 3 of a new tire with block pattern under braking condition (slip angle = 0°, slip ratio = 0.03).

FIG. 19 —
FIG. 19 —

Wear energy component in block 1 of a new tire with block pattern under braking condition (slip angle = 0°, slip ratio = 0.03).

FIG. 20 —
FIG. 20 —

Wear energy distribution in blocks 1 and 3 of a new tire with block pattern under driving condition (slip angle = 0°, slip ratio = –0.03).

FIG. 21 —
FIG. 21 —

Wear course.

FIG. 22 —
FIG. 22 —

External force histogram.

FIG. 23 —
FIG. 23 —

Response surface of wear energy of a new tire with rib pattern equipped on front left wheel.

FIG. 24 —
FIG. 24 —

Expected wear energy of a new tire with rib pattern equipped on front left wheel.

FIG. 25 —
FIG. 25 —

Change of tread thickness of a tire with rib pattern equipped on front left wheel.

FIG. A1 —
FIG. A1 —

Model for a tread rubber block under vertical compression.

FIG. A2 —
FIG. A2 —

Contact pressure distribution for a rib and a block under vertical compression.

FIG. A3 —
FIG. A3 —

Shear stress distribution for a rib and blocks with different sizes under vertical compression.

Contributor Notes

1 Corresponding author. Email. gt13298@g.kogakuin.jp

Department of Mechanical Science and Engineering, Kogakuin University, 678-18 Ogawa, Akiruno-Shi, Tokyo, 197-0821, Japan

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