Tire model

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A tire model is a special application of multi-body simulation (MBS) for investigating vehicle dynamics .

Motivation for tire models

Within the chassis, the tire plays an important role in terms of the vehicle's driving dynamics . Conceivable as a body ( multibody system ), via a complex joint ( joint ) is connected with the roadway. The tire thus represents the force-transmitting link between the vehicle and the road.

In the vehicle dynamics simulation, one is always dependent on a tire model, because due to the large number of influencing variables, it is not possible to record measurements at all operating points. The most important influencing variables are: slip angle , slip , wheel load , camber , driving speed, road surface. There are also others such as B. air pressure, tread depth, ....

Depending on the area of ​​application of the tire model (cars, agricultural and construction machinery, on / off-road), certain tire properties are of outstanding importance:

  • Stationary tire properties for car tires (e.g. lateral force / slip angle or circumferential force / slip behavior)
  • Unsteady tire properties (tire run-in behavior).
  • Suspension and damping properties of the tire. Filtering of uneven floors.
  • Vibration properties
  • Profile design of the tread in terms of traction or water displacement capacity of the tire.

This justifies the development of different tire models.

Classification of tire models

The tire models can be classified according to the following scheme:

  • Vehicle dynamics models (empirical approach)
    • Hohenheim tire model (physical approach)
    • Magic Formula Tire
    • TameTire (semi-physical approach)
    • TMeasy (semi-physical approach)
  • Comfort models (physical approach)
    • BRIT (Brush and Ring Tire)
    • CDTire (Comfort and Durability Tire)
    • Ctire (Comfort tire)
    • Dtire (Dynamical Nonlinear Spatial Tire Model)
    • FTire (Flexible Structure Tire Model)
    • RMOD-K (Comfort and Durability Tire)
    • SWIFT (Short Wavelength Intermediate Frequency Tire)

While in vehicle dynamics models the characteristic curves of tires are first measured on a test bench and then reproduced as precisely as possible in the model (empirical approach), the physical modeling (comfort model) is based on the knowledge of the exact physical mechanism of generation of the tire forces, which results in longer computing times. However, there are now even real-time physical tire models. Another difference is that driving dynamics models are suitable for simulating stationary and unsteady tire properties in the driving dynamics frequency range up to 20 Hz (modeling of low-frequency forces and deformations). In contrast, comfort models are able to display highly dynamic driving conditions of 80 Hz and more (e.g. vibrations on uneven surfaces). This also makes it possible to predict operating points that are not supported by measurement technology. Depending on the task at hand, the tire model that achieves the best compromise between computing time and performance must be selected.

Parameterization and verification of the tire models

A very important part of a tire model are the required parameters, because each model is only as precise as the parameters entered allow it. The parameterization of the tire model is therefore of great importance. The parameters are determined on tire test benches, which are also used to verify the model. A tire test stand can be designed as a drum or flat belt test stand. Mobile test stands are also used. Here, the measuring, loading and adjusting device is mounted on a truck or semi-trailer, the wheel to be measured runs underneath on the road surface.

With drum test stands, the tire rolls outside or inside (inside drum test stand) on a drum. It should be noted that the drum must be sufficiently large, otherwise its rounding will influence the measurement results too much. As a rule of thumb, a factor of 6 × tire radius applies. In flat belt test stands, the wheel rolls on a steel belt that slides on a lubricated surface so that the contact surface is not curved. Both the drum and the flat belt test stands are usually provided with a corundum-like surface that is similar to the road surface. The test stands require relatively high performance in order to dynamically generate the high forces to be measured. The vertical, longitudinal and lateral forces are measured, as well as moments around all three axes of the fixed wheel coordinate system. Dynamically measured forces can be used to determine the stiffness and damping of the tire. Longitudinal force and side force behavior are measured at different slip or slip angles. The parameters obtained are then used in the respective tire model. The test benches are also used to verify the tire models by carrying out further tests, the results of which serve as a reference for the tire model. A distinction is made between the stationary characteristics and the dynamic tire behavior. The deformation of the tires results in a delay in the build-up of force, which is particularly important in the case of large-volume and soft tires, for example agricultural tractor tires.

However, it must be taken into account that tire test stands, e.g. B. Drum test benches only approximate the conditions on the road. The results of tire test stands are therefore only suitable for validation to a limited extent. A certain exception here are 'physical' tire models such as FTire, CDTire and Rmod-K. These are able to simulate at least the geometry of the test benches and thus enable error correction, e.g. B. to make the measured tire reset torque. The boundary conditions of the measurement, which lead to excessive temperatures and wear, remain problematic.

literature

  • B. Ferhadbegović: Development and application of a transient tire model for the driving dynamics simulation of farm tractors. (= Research Report Agricultural Technology VDI-MEG. No. 475). Dissertation University of Stuttgart 2009. Shaker Verlag , Aachen 2009.
  • HB Pacejka: Tire and Vehicle Dynamics. Butterworth-Heinemann, Oxford, 2002, ISBN 0-08-097016-8 .
  • M. Gipser: FTire: a physically based, application-oriented tire model for all important vehicle dynamics issues. 4. Darmstadt tire colloquium, Darmstadt 2002, pp. 42-68.
  • W. Hirschberg, G. Rill, H. Weinfurter: Tire Model TMeasy. In: Vehicle System Dynamics. Vol. 45, Issue SUPPL. 1, 2007, pp. 101-119.

Web links

Individual evidence

  1. ^ University of Hohenheim: Model: Hohenheim tire model. Retrieved June 13, 2017 .
  2. ↑ Ferhadbegoviċ, B .: Development and application of an unsteady tire model for driving dynamics simulation of agricultural tractors (homepage of the University of Hohenheim)