Editorial Type:
Article Category: Research Article
 | 
Online Publication Date: 15 Oct 2024

Generation of SWIFT Models Virtually Using FE Analysis: Application to Cleat Simulations

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Page Range: 193 – 209
DOI: 10.2346/137595
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ABSTRACT

Parameterization methods for two “commercial tire models—short wavelength intermediate frequency tire (SWIFT) model and flexible ring tire model—are developed around existing testing protocols. As an example, cleat tests are used for estimating belt mass and stiffness and enveloping tests are used for estimating belt bending and contact stiffness parameters in the respective tire models. This is the only possible way when commercial tire models are parameterized and used mainly by vehicle original equipment manufacturer companies. At present, tire suppliers are stepping up to supply commercial tire models as a part of virtual tire submissions and are virtually simulating standard testing protocols. It is envisioned that with a proper fundamental understanding of commercial tire model parameters and their modeling approaches to capture the respective tire dynamics, we can develop simple finite element (FE) techniques to estimate respective tire model parameters, thereby avoiding the simulation of cleat and other dynamic tests by using FE. With that motivation, previous work has already shown the estimation of belt mass and bending properties from FE part separation technique [1]. In this work, with a fundamental understanding that the front cam and rear cam models in SWIFT are mathematically modeling the curvature of a loaded tire just outside of the footprint, we show that by fitting the tandem model to the loaded FE model deformed coordinates: length, height, order of cam, and distance between the cams can be estimated easily. This simple loaded FE model-fitting technique is combined with other computationally simple FE static stiffness, footprint, and modal analyses to estimate other SWIFT parameters. Finally, SWIFT models from the above-mentioned FE techniques are developed for several tire designs and validated against enveloping and dynamic in-plane cleat test data. The variations in enveloping and other ride metrics from simulations are inline with testing data.

Keywords: tire modeling; SWIFT; enveloping; finite element; virtual tire; vehicle ride; vehicle dynamics; cleat
FIG. 1 —
FIG. 1 —

Two core elements of SWIFT model: rigid ring model integrated with enveloping model [4].

FIG. 2 —
FIG. 2 —

(a) Enveloping model. (b) Connection of rigid ring enveloping model via residual springs representing tire tread [4, 5].

FIG. 3 —
FIG. 3 —

Fx and Fz cleat response dependence on components of tire (tread, belt, structure, footprint) and corresponding SWIFT core parameters.

FIG. 4 —
FIG. 4 —

Traditional and proposed methods for estimation of belt mass, sidewall spring stiffness, and enveloping model.

FIG. 5 —
FIG. 5 —

Notice dotted line at leading and trailing edges of contact zone (at the arrows) matches tire contour just outside of footprint [4].

FIG. 6 —
FIG. 6 —

FE nodal CAM fitting concept.

FIG. 7 —
FIG. 7 —

Fitting FE tread node co-ordinates (red and blue circles) to tandem model (orange and yellow dots).

FIG. 8 —
FIG. 8 —

Material modulus needed for respective tire analysis; stiffness equivalence of rolling tire under cleat to unloaded tire at higher strains [8].

FIG. 9 —
FIG. 9 —

Test – unloaded tire subjected to high strains is similar to FE – unloaded modal analysis using a material modulus at higher strains.

FIG. 10 —
FIG. 10 —

FE part separation method for estimation of belt mass, which corresponds to rigid ring element in SWIFT.

FIG. 11 —
FIG. 11 —

FTire is used for estimation of auxiliary modules in SWIFT.

FIG. 12 —
FIG. 12 —

Fitting to FTire data and estimated parameters are given at the top.

FIG. 13 —
FIG. 13 —

SWIFT parameters in .tir file and respective FE techniques used for estimation.

FIG. 14 —
FIG. 14 —

Simulated (top) and tested (bottom) vertical and longitudinal force for 245/40R20 tire rolling at 1 kph over a rectangular 10 mm × 20 mm cleat. A, baseline; C, soft tread; H, sidewall reinforced.

FIG. 15 —
FIG. 15 —

Enveloping metrics peak-peak of Fz and Fx and dip in Fz. Simulated (top) and tested (bottom).

FIG. 16 —
FIG. 16 —

Simulated (top) and tested (bottom) vertical and longitudinal force for 225/60R17 tire rolling at 1 kph over a semicircle cleat of radius 20 mm. A, baseline; D, soft tread and final approved spec.

FIG. 17 —
FIG. 17 —

Enveloping metrics peak-peak of Fz and Fx and dip in Fz. Simulated (top) and tested (bottom).

FIG. 18 —
FIG. 18 —

Simulated (top) and tested (bottom) vertical and longitudinal force for 245/40R20 tire rolling at 20 and 90 kph over rectangular 10 mm × 20 mm cleat. A, baseline; D, soft tread and final approved spec.

FIG. 19 —
FIG. 19 —

Simulated (top) and tested (bottom) vertical and longitudinal force for 225/60R17 tire rolling at 1 kph over a rectangular 10 mm × 50 mm cleat. A, baseline; D, soft tread and final approved spec.

FIG. 20 —
FIG. 20 —

Dynamic cleat metrics peak-peak of Fx at 20 kph and peak-peak of Fz at 90 kph. Simulated (top) and tested (bottom) for 245/40R20 size.

FIG. 21 —
FIG. 21 —

Dynamic cleat metrics peak-peak of Fx at 20 kph and peak-peak of Fz at 90 kph. Simulated (top) and tested (bottom) for 225/60R17 size.

Contributor Notes

1  Corresponding author. Hankook Tire & Technology America Technical Center, 3535 Forest Lake Drive, Uniontown, Ohio 44685, USA. Email: iramdasu.yaswanth@hankookn.com
2  Hankook Tire & Technology, R&D Division, 50, Yuseong-daero 935beon-gil, Yuseong-gu, Daejeon, 34127, Korea
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