Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 21 Jul 2020

In-Plane Bending and Shear Deformation of Belt Contributions on Tire Cornering Stiffness Characteristics

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Page Range: 276 – 297
DOI: 10.2346/tire.20.190213
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ABSTRACT

In radial tires, belt structure plays a role of minimizing the lateral deflection of carcass, which has a significant influence on the cornering and wear properties of a tire. The deflection of carcass affects the magnitude of tread block deformation when the tire is under the slip angle. As a result, it can change the cornering stiffness characteristics of the tire, especially when the vertical load is high.

During tire development, a tire design engineer tries to find the optimal belt ply angle that satisfies the various performance requirements simultaneously, but it is not an easy task because the effect of belt angle change is different depending on the size of the tire. There have been many attempts to construct a mathematical model that represents the structural properties of the belt package, including the string-based model and the beam on elastic foundation model. But, in many cases, only the in-plane bending of belt is considered and the shear deformation is not taken into consideration.

In this study, the effect of belt angle change on belt stiffness is analyzed using a mathematical model based on the Timoshenko beam theory. This model can account for the in-plane bending and shear deformation of the belt structure at the same time. The results of the analysis show how the contribution of bending and shear is changed depending on a tire design parameter, herein the belt cord angle. The effect of belt ply angle change on cornering stiffness is investigated by means of the brush model including belt flexibility. The prediction by the brush model is compared with the measurement using a Flat-trac machine, and the validity of the model is discussed.

Keywords: tire; cornering stiffness; belt stiffness; analytical model; Timoshenko beam theory
FIG. 1 —
FIG. 1 —

Structure of a radial tire.

FIG. 2 —
FIG. 2 —

Configuration of the belt package.

FIG. 3 —
FIG. 3 —

Change of in-plane modulus of belt with respect to cord angle.

FIG. 4 —
FIG. 4 —

Beam on elastic foundation model.

FIG. 5 —
FIG. 5 —

Coefficients for belt deflection w(x).

FIG. 6 —
FIG. 6 —

Belt lateral deflections for225/55R17 size tire.

FIG. 7 —
FIG. 7 —

Belt lateral deflections for different cord angles.

FIG. 8 —
FIG. 8 —

Belt lateral deflections for different sidewall stiffness parameters.

FIG. 9 —
FIG. 9 —

Belt lateral deflections for different belt widths.

FIG. 10 —
FIG. 10 —

Belt lateral deflections for different steel cord modulus.

FIG. 11 —
FIG. 11 —

Contact length and contact width in contact patch.

FIG. 12 —
FIG. 12 —

Mathematical representations for belt lateral deflection (left) and sidewall rotation (right).

FIG. 13 —
FIG. 13 —

Contact patch geometry of advanced brush model.

FIG. 14 —
FIG. 14 —

Cantilever beam shear deformation.

FIG. 15 —
FIG. 15 —

Comparison of cornering stiffness curve for 225/55R17 size tires.

FIG. 16 —
FIG. 16 —

Comparison of cornering stiffness at 6000 N load.

FIG. 17 —
FIG. 17 —

Comparison of load sensitivity of cornering stiffness.

FIG. 18 —
FIG. 18 —

Effect of shear deformation to the cornering stiffness load sensitivity.

Contributor Notes

Research Department, Hankook Tire & Technology Co., Ltd., 50 Yuseong-daero 935beon-gil, Daejeon, 34127, Korea

1 Corresponding author. Email: gibingil@hankooktech.com
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