Investigating the Parameterization of Dugoff Tire Model Using Experimental Tire-Ice Data

Tire modeling plays an important role in the development of an Active Vehicle Safety System. As part of a larger project that aims at developing an integrated chassis control system, this study investigates the performance of a 19” all-season tire on ice for a sport utility vehicle. A design of experiment has been formulated to quantify the effect of operational parameters, specifically: wheel slip, normal load, and inflation pressure on the tire tractive performance. The experimental work was conducted on the Terramechanics Rig in the Advanced Vehicle Dynamics Laboratory at Virginia Tech. The paper investigates an approach for the parameterization of the Dugoff tire model based on the experimental data collected. Compared to other models, this model is attractive in terms of its simplicity, low number of parameters, and easy implementation for real-time applications. The relations correlating tire forces with slip ratios were identified by applying zero-phase filtering techniques to the raw test data. Next, an optimization procedure was utilized to extract parameters for the Dugoff tire model from the tire-on-ice drawbar pull coefficient versus slip ratio at certain levels of normal load and inflation tire pressure. CITATION: He, R., Jimenez, E., Savitski, D., Sandu, C. et al., "Investigating the Parameterization of Dugoff Tire Model Using Experimental Tire-Ice Data," SAE Int. J. Passeng. Cars Mech. Syst. 10(1):2017, doi:10.4271/2016-01-8039. Published 09/27/2016 Copyright © 2016 SAE International doi:10.4271/2016-01-8039 saepcmech.saejournals.org 83 © SA E I nt rn tio na l these models. The tire testing machine drum is probably the most common indoor testing machine utilized by the tire industry. Shimizu coated the machine drum in ice so that the variation of the lateral friction coefficient with the slip angle and of the longitudinal friction coefficient with the slip ratio could be tested [8]. Using the same testing facility, Shimizu also explored the effect of various ice textures on the friction coefficient versus slip ratio relation [9]. The influence of operational parameters such as normal load, inflation pressure, toe angle, tread depth, and camber angle on the normalized drawbar pull (named the drawbar pull coefficient) was studied by Bhoopalam via indoor testing of a 16” SRTT tire on ice on the Terramechanics Rig at the Advanced Vehicle Dynamics Laboratory (AVDL) at Virginia Tech [10]. Outdoor tests using the same tire mounted on a truck were also performed to investigate the traction force on ice [11, 12]; it has been noted in this study that a direct benchmarking between the indoor and the outdoor tests results was not possible due to multiple reasons, among which: impossibility to control some of the operational parameters in the outdoor tests, while they were controlled in the indoor tests (e.g., ice temperature and normal load); accurate control of the slip ratio (indoor tests have been performed for very precise slip ratios); vehicle speed (indoor tests can only be performed at low speed). For the parameterization of a tire model it is important to characterize the dynamic performance of the physical tire first. The complexity of the parameterization process, the associated cost, as well as time needed, increase with the number of tire model parameters. The parameterization processes of three popular tire models: Dugoff tire model, Magic Formula tire model, and FTire model, are briefly discussed here. Dugoff tire model, with a low number of parameters and acceptable accuracy of predicting longitudinal and later forces, is quite popular for applications involving vehicle control system design [5, 6, 7]. The parameters of Dugoff tire model have physical meanings, and the parameterization could be completed by referring to typical physical values [5] or by using regression techniques to extract longitudinal stiffness and corner stiffness from the tire testing data. Furthermore, the Dugoff tire model is relatively computationally inexpensive, making it a great candidate for real-time simulations or hardware/ software in-the-loop simulations. The Magic Formula tire model [13] has more parameters than the Dugoff tire model, and its parameters don’t have physical meanings. Optimization of the tire testing data is needed for the parameterization of the Magic Formula. The main optimization method applied to parameterize the Magic Formula, developed by TNO, uses an optimization technique to fit the Magic Formula parameters using the Matlab toolbox [14]. This method requires starting values of the parameters at the beginning of the optimization. Proper starting values of parameters are not easily accessible for combined a slip condition, for example [14, 15]. Therefore, for this case, the global minimum might not be reached, and, as a consequence, suitable parameters of the Magic Tire model may not necessarily be obtained using this method. An alternative optimization method based on genetic algorithms could avoid the unfavorable scenario resulted from improper starting values for combined slip condition, as this method doesn’t need any starting values to launch the optimization [14]. Compared with the aforementioned two tire models, FTire has a large number of tire design, physical, and modal parameters. Because of this fact, the parameterization process is more complex, including: cleat tests, modal tests, simulations of a Finite Element (FE) model, and optimization techniques. Furthermore, tire design data sheets and simple measurements [16] are also used. Three packages, FTire/calc, FTire/fit, and FTire/estimate, assist users in parameterizing the FTire after the modal test and cleat test are done for an initial and partial parameterization [17]. FTire/calc performs simulations of FE model to partially validate the initial parameterization and to provide a first FTire input file to FTire/fit. FTire/fit tunes the parameters of FTire and does the optimization to minimize the least-squares distance of cleat test measurements and the simulation result of the FTire model on a cleat. Finally, FTire/estimate utilizes the well-validated tire data file and extrapolation techniques to tweak the modal and stiffness parameters of FTire. As part of the project Innovative Engineering of Ground Vehicles with Integrated Active Chassis Systems (“Project EVE”), funded by the European Union Horizon 2020 Framework Program [18], this study conducted testing of a 235/55R-19 all-season tire on ice at Virginia Tech for various combinations of tire pressure, normal load, and slip ratio. The relationship between the drawbar pull coefficient and the slip ratio was extracted from the testing data; the results were further used to study the influence of the design of experiment parameters on the traction efforts of studied tire on ice. By applying a genetic algorithm (GA), the drawbar pull coefficient vs. slip ratio relations obtained from the tire-on-ice testing data are then used to parameterize a Dugoff model for the 19” all-season tire. This tire has been selected since it is the tire selected to be used in the EVE projects. The Dugoff model has been selected due to its relatively small number of parameters required and due to its suitability for real-time simulations. The tire model is intended to be used next for real-time tire inflation pressure control, one of the sub-system control strategies of the integrated chassis control for ground vehicles with off-road ability being developed under the Project EVE. The paper has the following structure. Section 2 summarizes the key aspects of the indoor tire-ice testing at AVDL used to collect tire-ice data in this study. Next, observations regarding the testing and the presentation of the processed testing data are included in Section 3. Analysis of the testing data has been done in Section 4, discussing aspects of the effects of the inflation pressure and of the normal load on the traction performance of the tire on ice. Section 5 contains the description of the Dugoff tire model and its parameterization method. The paper ends with conclusions on the work conducted, presented in Section 6. He et al / SAE Int. J. Passeng. Cars Mech. Syst. / Volume 10, Issue 1 (April 2017) 84 © SA E I nt rna t o l