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Parameterization Process of the Maxwell Model to Describe the Transient Force Behavior of a Tire
(2017)
The present technical article deals with the modeling of dynamic tire forces, which are relevant during interactions of safety relevant Advanced Driver Assistance Systems (ADAS). Special attention has been paid on simple but effective tire modeling of semi-physical type. In previous investigations, experimental validation showed that the well-known first-order Kelvin-Voigt model, described by a spring and damper element, describes good suitability around fixed operation points, but is limited for a wide working range. When aiming to run vehicle dynamics models within a frequency band of excitation up to 8 Hz, these models deliver remarkable deviations from measured tire characteristics. To overcome this limitation, a nonlinear Maxwell spring-damper element was introduced which is qualified to model the dynamic hardening of the elastomer materials of the tire. However, the advantage of a more realistic description of the transient behavior leads to a more complex parametrization process. Therefore, in the proposed article attention is paid to describe the identification process including defined maneuvers to parameterize the tire model, where the accuracy of the parameter strongly depends on the quality of the available input data from measurement. In order to study this important aspect of parameterization, the reference data from simulation of the full physical tire model FTire is applied like a “virtual measurement” of specified testing maneuvers. The procedure of simulation by means of the enhanced first order dynamics model is implemented by the semi-physical tire model TMeasy. Finally, the improvements of the extended model are discussed and an outlook for future work is given.
The present paper deals with the experimental validation of tyre dynamics approaches as it is widely applied in tyre models for vehicle dynamics and handling. Firstly it gives a brief derivation of two modelling principles regarding the deflection velocity in the considered direction of the tyre’s deformation. This is than followed by a brief description of the performed measurement procedure. From the measurements, a set of model parameters of the considered tyre, depending on different manoeuvre speeds and frequencies, is identified, where no particular fitting parameters for the tyre dynamics are needed. Based on these model parameters, the related dynamic simulations are carried out. The comparisons show that the applied first-order model describes the behaviour quite well within a certain operation range, whereas the second-order approach cannot deliver better results in spite of the longer computational time. However, for investigations within an enlarged frequency range of the steer input and at high slip angles, a more detailed model is recommended.