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Research Papers

Identification of Tire Model Parameters Through Full Vehicle Experimental Tests

[+] Author and Article Information
Francesco Braghin

Department of Mechanical Engineering, Politecnico di Milano, Via La Masa 1, 20156 Milano, Italyfrancesco.braghin@polimi.it

Federico Cheli

Department of Mechanical Engineering, Politecnico di Milano, Via La Masa 1, 20156 Milano, Italyfederico.cheli@polimi.it

Edoardo Sabbioni

Department of Mechanical Engineering, Politecnico di Milano, Via La Masa 1, 20156 Milano, Italyedoardo.sabbioni@polimi.it

The lack of experimental data prevents to extend the identification procedure to the combined slip MF coefficients.

At present, the vehicle lateral velocity (and thus the sideslip angle) is measured through optical sensors, which are very expensive and however unsuitable for ordinary passenger car applications.

During the tests, peak values for the longitudinal forces lower than 600 N were observed, confirming the hypothesis of negligible combined slip effects.

Note that front and rear tire force plots have a different time scale since measures were not performed during the same test (see Sec. 3, Fig. 6, and Table 3). Similar considerations can be done for Fig. 1.

J. Dyn. Sys., Meas., Control 133(3), 031006 (Mar 24, 2011) (11 pages) doi:10.1115/1.4003093 History: Received April 17, 2009; Revised July 27, 2010; Published March 24, 2011; Online March 24, 2011

Individual tire model parameters are traditionally derived from expensive component indoor laboratory tests as a result of an identification procedure minimizing the error with respect to force and slip measurements. These parameters are then transferred to vehicle models used at a design stage to simulate the vehicle handling behavior. A methodology aimed at identifying the Magic Formula-Tyre (MF-Tyre) model coefficients of each individual tire for pure cornering conditions based only on the measurements carried out on board vehicle (vehicle sideslip angle, yaw rate, lateral acceleration, speed and steer angle) during standard handling maneuvers (step-steers) is instead presented in this paper. The resulting tire model thus includes vertical load dependency and implicitly compensates for suspension geometry and compliance (i.e., scaling factors are included into the identified MF coefficients). The global number of tests (indoor and outdoor) needed for characterizing a tire for handling simulation purposes can thus be reduced. The proposed methodology is made in three subsequent steps. During the first phase, the average MF coefficients of the tires of an axle and the relaxation lengths are identified through an extended Kalman filter. Then the vertical loads and the slip angles at each tire are estimated. The results of these two steps are used as inputs to the last phase, where, the MF-Tyre model coefficients for each individual tire are identified through a constrained minimization approach. Results of the identification procedure have been compared with experimental data collected on a sport vehicle equipped with different tires for the front and the rear axles and instrumented with dynamometric hubs for tire contact forces measurement. Thus, a direct matching between the measured and the estimated contact forces could be performed, showing a successful tire model identification. As a further verification of the obtained results, the identified tire model has also been compared with laboratory tests on the same tire. A good agreement has been observed for the rear tire where suspension compliance is negligible, while front tire data are comparable only after including a suspension compliance compensation term into the identification procedure.

Copyright © 2011 by American Society of Mechanical Engineers
Topics: Vehicles , Tires , Force , Stress
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References

Figures

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Figure 1

Identification methodology

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Figure 2

Single-track vehicle model

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Figure 3

EKF identification procedure

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Figure 4

Tire slip angles

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Figure 5

Influence of the shape factors E and C on the nondimensional MF characteristics

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Figure 6

Step-steer maneuver, V=100 km/h, δ=40 deg. Comparison of driver inputs (vehicle speed and steer angle, on the left) and vehicle response (sideslip angle, yaw rate, and lateral acceleration, on the right) during three test repetitions.

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Figure 7

4DOF vehicle model

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Figure 8

Front/rear tire cornering force versus tire slip angle, Fz=6000N

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Figure 9

Step-steer: V=100 km/h, δ=40 deg. Time histories of the sideslip angle, the yaw rate, and the lateral acceleration.

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Figure 10

Step-steer: V=100 km/h, δ=40 deg. Time histories of the front and rear slip angles.

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Figure 11

Step-steer: V=100 km/h, δ=40 deg. Time histories of the front and rear right vertical loads.

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Figure 12

Step-steer: V=100 km/h, δ=40 deg. Time histories of the front and rear right lateral forces.

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Figure 13

Step-steer: V=100 km/h, δ=60 deg. Time histories of the sideslip angle, the yaw rate and the lateral acceleration.

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Figure 14

Step-steer: V=100 km/h, δ=60 deg. Time histories of the front and rear right lateral forces.

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Figure 15

Front tire cornering force versus tire slip angle, Fz=2350, 3825, 5100, 6375 N: comparison between identified and measured cornering force

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Figure 16

Rear tire cornering force versus tire slip angle, Fz=3090, 4635, 6180, 7725 N: comparison between identified and measured cornering force

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Figure 17

Front tire cornering force versus tire slip angle, Fz=2350, 3825, 5100, 6375 N: comparison between identified and measured cornering force after including suspension compliance

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