Model
Goals
The Hohenheim Tyre Model is based on an entirely physical approach. This conduces to both development goals of a broad range of validity and of a small number of physical parameters. These parameters shall be primarily determined on the institute owned test stands with high accuracy. To increase the model availability, their determination shall also be possible via road tests and with manufacturer's data, if necessary. Since the model does not use the slip as an input, it is numerically robust and is distinguished with short computational time.
Structure and Integration
The Hohenheim Tyre Model is constructed as a spoke model with an adaptive footprint, figure 1. Force elements in radial, tangential and axial direction are each assigned to a characteristic force transmission process of agricultural tyres. The force transmission between the tyre and the road surface is modelled via a stick-slip approach. A detailled description of the model structure can be found in various publications by Witzel and Bürger.
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| Figure 1: Structure of the Hohenheim Tyre Model with specification of the parameters needed | ||
The forces transmitted by the tyre are calculated based on the deflection processes of the tyre. For this purpose, the model needs 6 inputs as following:
- Longitudinal and lateral velocity of the wheel hub
- Distance between wheel hub and road surface
- Camber angle
- Angular velocities around the lateral and vertical axes
The tyre modell is built up in MATLAB/Simulink and can be integrated into arbitrary multi-body software via a co-simulation interface, figure 2. During a co-simulation, inputs and outputs of the tyre model are exchanged in between the two simulation partners at a constant step size.
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| Figure 2: Integration of the tyre model via MATLAB/Simulink | ||
Parameterisation
The parameters used can be determined from different sources. The most accurate results though are achieved by test stand measurements due to the high reproducability and a wide adjustable range, Table 1.
Table 1: Model parameters and their sources
| Model parameter | Data source |
|---|---|
| constructive tyre radius | manufacturer |
| dynamic rolling radius | flatbelt test stand |
| radial runout | |
| radial spring and damper coefficients | |
| interradial spring coefficients | |
| tangential spring and damper coefficients | single wheel tester |
| axial spring and damper coefficients | |
| additional spring and damper coefficients |
Validation
The validation of the Hohenheim Tyre Model is carried out on the test stands of the Institute of Agricultural Engineering in two steps.
Validation on a single tyre
The simulated force transmission behaviour in vertical direction and the reproduction of the radial runout is compared to measurements on the flatbelt test stand. The force transmission characteristics in longitudinal and lateral direction, the behaviour during combined slip conditions and during obstacle passes is validated with measurements on the single wheel tester.
Validation on a total vehicle
The last validation step is defined by a comparison of force courses determined during road tests with an instrumented test tractor and the simulated courses of a multi-body model of this tractor in co-simulation with the Hohenheim Tyre Model.