Enhancing Tire Model Parameterization for Rollover Simulation: A Validated Approach

C. Ludwig; F. Birnbaum; H. Abel; H. Olsson; G. Prokop

doi:10.2346/TST-24-010

Article Contents

ABSTRACT
Introduction
Methodology
Rollover Driving Tests
Tire Testing
Model Parameterization
Model Validation
Conclusion
Acknowledgments
Declaration
References

Editorial Type: research-article

Online Publication Date: 23 Sept 2025

Enhancing Tire Model Parameterization for Rollover Simulation: A Validated Approach

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Article Category: Research Article

Page Range: 227 – 251

DOI: 10.2346/TST-24-010

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ABSTRACT

This work addresses the challenge of modeling tire behavior for virtual vehicle development, particularly in untripped rollover scenarios where a vehicle rolls over solely due to the tire–road friction interface. Despite the existence of various models, limited attention has been given to tire testing methods that accurately represent rollover conditions. We propose a revised lateral tire testing method that uses data from rollover-critical driving tests to derive conditions for a flat-track test bench and that focuses on operational and thermal conditions. These data are used to parameterize empirical Magic Formula Tire 6.2 models, emphasizing the importance of accurate measurements for model parameterization. Component-level validation through comparison of measured and simulated tire reaction forces and moments demonstrates improved estimates of lateral forces, hence lateral friction coefficient, and overturning moments compared with models based on outdoor tire test data with limited operating conditions. At the full vehicle level, the proposed method significantly reduces the error in rollover key performance indicators based on wheel lift-off during Fishhook maneuvers. These findings are particularly relevant for battery electric sport utility vehicles with increased vehicle mass and wheel loads.

Keywords: rollover; tire testing; tire modeling; validation; lateral friction; test methods

FIG. 1

Methodological overview for parameterization and validation of empirical tire models for rollover simulations in this work.

FIG. 2

Coordinate transformation (left) and gyroscopic effects (right).

FIG. 3

Maximum tire operating conditions of outer tires on front axle on a battery electric sport utility vehicle in different lateral dynamics maneuvers [10].

FIG. 4

Tire testing with different test bench methods. (Left) State-of-the-art hybrid method (described in [7]). (Right) New proposed method, the rollover method (this study).

FIG. 5

Tire excitation of tire tests for model parameterization.

FIG. 6

Different tread surface temperatures resulting from lowrate and highrate slip angle test procedures on rollover method flat-track test bench by using tire A.

FIG. 7

Comparison of structural properties of tire A identified on separate flat-track test benches at 0° camber and 2.9 bar of inflation pressure.

FIG. 8

Comparison of steady-state characteristics of lateral force, overturning, and aligning moment of tire A identified on a test trailer and a flat-track test bench by using the SAVT lowrate procedure (2°/s) at 9 kN of wheel load and 0° camber angle.

FIG. 9

Comparison of lateral friction coefficients of tire A for test trailer data and flat-track data in the lowrate (2°/s) and the highrate (15°/s) procedures.

FIG. 10

Comparison of thermal conditioning of tire A for test trailer data and flat-track data in the lowrate (2°/s) and the highrate (15°/s) procedures.

FIG. 11

Datasets for tire model parameterization compared in this work.

FIG. 12

Scheme of the MFT model-fitting process.

FIG. 13

Fitting process of steady-state lateral force of the rollover method.

FIG. 14

Verification of dynamic lateral forces, overturning, and aligning moment of tire A at a high wheel load of 14 kN and camber angle of 8° by using the SAVT highrate (15°/s).

FIG. 15

Maximum lateral forces in sinus weave maneuver measured on the front axle of vehicle 1 by using tire A.

FIG. 16

Range of MAPE of the maximum lateral forces in rollover maneuvers.

FIG. 17

Time signals of measured and simulated lateral forces of front left tire in the steady-state and dynamic nonlinear driving condition of sinus weaves at 0.2 and 0.7 Hz.

FIG. 18

Range of MAE of lateral forces of outer tires in rollover maneuvers.

FIG. 19

Mean MAE of overturning and aligning moment of the outer tires in the sinus weave maneuver of tire A.

FIG. 20

NHTSA preramp maneuver model validation result with default vehicle parameterization and with 5% increase in CoG height for vehicle 1.

FIG. 21

Comparison of tire model datasets in full vehicle simulation environment in dynamic rollover stability assessment by using the Fishhook maneuver and vehicle 1.