Object-oriented Modeling of Wheels and Tires in Dymola/Modelica

Description

A fairly large number of new tire models with varying degrees of complexity and application domains were developed during the 80s and 90s of the last century. Of importance among them are the semi-empirical tire models. These models are based on physical considerations, as embraced by the theory of multi-body dynamics, yet enhance these with empirical formulas representing friction and slipping characteristics.

Semi-empirical tire models offer a good trade-off between model accuracy and complexity. Consequently, they are suited for the simulation of entire vehicles and can be used for analysing properties of vehicle dynamics. Two models that have found wide-spread dissipation and acceptance are TMeasy by G. Rill [3,7] and the magic-formula model by H.B. Pacejka [6].

These and other models are however rather flat and unstructured. One may find several hundreds of equations on a single hierarchy level. Consequently, these models are difficult to understand. Maintaining these models and adaptating them to particular situations is painful and error prone. The computation of geometrical properties and especially the determination of the contact point are often imprecise.

A recent paper by Zimmer and Otter [10] builds on the aforementioned models and demonstrates how wheel and tire models of varying degrees of complexity can be integrated within the object-oriented framework of Modelica [4] and its multi-body systems library [5]. However, the object-orientation in these models limits itself mostly to their external interfaces. The models themselves continue to be mostly flat. They feature many equations within a single model file.

Tasks to be tackled

Goal of this MS thesis research is the creation of tire models in Modelica with a truly object-oriented, hierarchical composition. To this end, the existing models will have to be decomposed into suitable sub-components (bodies, geometry, contact point, contact physics, etc.). Individual components will be of different character: geometric, empirical, and physical. The design of the interfaces constitutes therefore a central facet of the research effort. The physical aspects of the models shall be described by means of bond graphs [1,2]. The so constructed wheel and tire models shall be integrated into the multi-bond graph library [8,9].

The focus of this research effort thus concerns itself less with modeling new tire properties, and more with an improved organization of existing knowledge concerning models that have been developed in the past by other researchers. This effort is of particular value, as it shall enable a considerably improved understandability and maintainability of the resulting models. Of course, it is perfectly acceptable that the new models be simultaneously upgraded by incorporating recently published results on tire model dynamics into them, especially as they concern the accurate representation of tire dynamics for motorbikes.

References

  1. Cellier, F.E. (1991), Continuous System Modeling, Springer-Verlag, New York.

  2. Cellier, F.E. and A. Nebot (2005), The Modelica Bond Graph Library, Proc. 4th International Modelica Conference, Hamburg, Deutschland, Vol.1, pp. 57-65.

  3. Hirschberg, W., G. Rill, and H. Weinfurter (2007), Tire Model TMeasy, Vehicle System Dynamics, 45(S1), pp. 101-119.

  4. Modelica Association (2005), Modelica 3.0 Language Specification.

  5. Otter, M., H. Elmqvist, and S.E. Mattsson (2003), The New Modelica MultiBody Library, Proc. 3rd International Modelica Conference, Linköping, Sweden, pp. 311-330.

  6. Pacejka, H.B. (2005), Tire and Vehicle Dynamics, 2nd Edition, SAE International, Warrendale, PA.

  7. Rill, G. (2007), Simulation von Kraftfahrzeugen, Nachdruck, Vieweg-Verlag, Regensburg, Germany.

  8. Zimmer, D. (2006), A Modelica Library for MultiBond Graphs and its Application in 3D-Mechanics, Dept. für Computational Science, ETH Zürich, Zürich, Schweiz.

  9. Zimmer, D. and F.E. Cellier (2006), The Modelica Multi-bond Graph Library, Proc. 5th International Modelica Conference, Vienna, Austria, Vol.2, pp.559-568.

  10. Zimmer, D. and M. Otter (2008), Real-Time Models for Wheels and Tires in an Object-Oriented Modelling Framework, Vehicle System Dynamics, to appear.
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Last modified: September 7, 2008 -- © François Cellier