Editorial Type:
Article Category: Research Article
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Online Publication Date: 09 Aug 2021

Virtual Generation of Flexible Ring Tire Models Using Finite Element Analysis: Application to Dynamic Cleat Simulations

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Page Range: 288 – 315
DOI: 10.2346/tire.21.20025
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ABSTRACT

The main goal of this work is to investigate if finite element (FE) model techniques with special applications of material properties accurately estimate the parameters of flexible ring tire models. It is known that commercially available ring tire models are used as standard tools for simulating and predicting vehicle ride and durability, e.g., rigid ring MF-Swift [1] and flexible ring Flexible Structure Tire Model (FTire) [2–5]. Despite wide acceptance of these models, difficulty in model parameterization limits their application in the vehicle development process. For estimation of tire dynamic stiffnesses and inertial properties, rolling tire cleat test data are required for most ring models. Although this test method produces reliable models, the parameterization is not time and cost effective as it requires measurement and processing of cleat data at multiple speeds and loads and is prone to test rig dynamic compliance variations. This approach also limits the ability to evaluate tire performances during the virtual stages of tire design. The objective of this work is to develop virtual data using time and cost effective FE-based methods towards the estimation of flexible ring model parameters rather than relying on measured cleat data on physical tires. Commercial product ABAQUS is used for the FE simulations and FTire for tire flexible ring model simulations. Two FE modeling techniques are utilized in this work. Firstly, it is shown that the dynamic stiffness of a rolling tire can be estimated from a steady state eigensolution modal analysis of a static tire using material properties characterized for a rolling tire. Secondly, a method of separation of the sidewall from the tread band is developed for the estimation of mass and bending properties of the tread band. The estimated stiffnesses, inertias, and dimensions from the FE model results are converted into FTire model parameters. Finally, to validate the virtually generated FTire model, simulated dynamic cleat data response trends at multiple inflation pressures and velocities are compared with measurements. The virtual FE based techniques presented in this work can be applied to other ring based models as well.

Keywords: Virtual tire modeling; FTire; finite element; vehicle dynamics; cleat
FIG. 1 —
FIG. 1 —

Rigid modes of flexible ring model at static loaded condition [10].

FIG. 2 —
FIG. 2 —

Effect of rolling speed on measured vertical resonance at free spindle condition [12].

FIG. 3 —
FIG. 3 —

Modal softening technique used for parameterization of flexible ring.

FIG. 4 —
FIG. 4 —

Frequency response of flexible ring model with and without adjusted measured modal frequencies [12].

FIG. 5 —
FIG. 5 —

Four operating conditions of tire considered for material testing for FE simulations.

FIG. 6 —
FIG. 6 —

Material modulus and dependency at various strain amplitude and frequency testing, test data adopted from [16].

FIG. 7 —
FIG. 7 —

Material modulus and dependency at various sine on sine strain amplitude and frequency testing, test data adopted from [16].

FIG. 8 —
FIG. 8 —

Tire regions and corresponding flexible ring elements.

FIG. 9 —
FIG. 9 —

Representing stiffness of tire regions with flexible ring model elements.

FIG. 10 —
FIG. 10 —

Tension stiffness of tire tread belt region.

FIG. 11 —
FIG. 11 —

Contribution of model parameters to natural frequencies [20].

FIG. 12 —
FIG. 12 —

Estimation of flexible ring dimensions from dimensions of tire mold drawings.

FIG. 13 —
FIG. 13 —

(a) Cross section of deformed sidewall in footprint region with reduced tension at the bead, (b) sidewall radial tension acting on tread band [19].

FIG. 14 —
FIG. 14 —

FE part separation method for estimation of tread-belt region, which corresponds to flexible ring element.

FIG. 15 —
FIG. 15 —

Bending mode of separated FE tread belt part.

FIG. 16 —
FIG. 16 —

Estimation of KR, KT, by fitting to FE modal data at different inflation pressures.

FIG. 17 —
FIG. 17 —

Estimation of KR, KT, by fitting to FE modal data for different carcass rubber stiffness.

FIG. 18 —
FIG. 18 —

Description of commercial flexible ring model, FTire.

FIG. 19 —
FIG. 19 —

Simulated and experimental longitudinal force for tire rolling over trapezoidal 15 × 50 mm cleat at 32 psi, time domain (top), and frequency domain (bottom).

FIG. 20 —
FIG. 20 —

Simulated and experimental longitudinal force for tire rolling over trapezoidal 15 × 50 mm cleat at 38 psi, time domain (top), and frequency domain (bottom).

FIG. 21 —
FIG. 21 —

Simulated and experimental vertical force for tire rolling over trapezoidal 15 × 50 mm cleat at 32 psi, time domain (top), and frequency domain (bottom).

FIG. 22 —
FIG. 22 —

Simulated and experimental vertical force for tire rolling over trapezoidal 15 × 50 mm cleat at 38 psi, time domain (top), and frequency domain (bottom).

Contributor Notes

1 Hankook Tire & Technology America Technical Center, 3535 Forest Lake Dr., Uniontown, Ohio 44685, USA.
2 Corresponding author. Email: siramdasu.yaswanth@hankooktech.com
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