Modeling of a Motorbycicle in Dymola/Modelica

Description

In recent years, more and more detailed and partly animated models of vehicles are being used in practice. These models serve on the one hand to support the design of new vehicle types. Ever shorter development periods of new vehicle types (models) force the designers to replace tests that used to be performed in the past on prototypes of the new vehicles by simulation runs to be executed before a prototype is ever build. On the other hand, it has become customary to employ mathematical simulations of vehicles also for training purposes. For example, driving a vehicle on an icy road is being trained in Sweden on a computer by means of a detailed and realistic vehicle model.

Among the vehicle models, models of motorbycicles turn out to be particularly delicate. Whereas a four-wheeled vehicle remains stable on its own, the same does not hold true for a two-wheeled vehicle. For this reason, the stabilization of a motorbike, a control issue, requires special attention. The simulation has to account for the inclination of the motorbike in a curve as well as for the shift of the center of gravity of the driver. Such models are currently not yet being offered in the public libraries of Dymola/Modelica.

Tasks to be tackled

This MS thesis research deals with modeling and simulation of motorbycicles as controlled vehicles. Already developed Modelica [4] models of uncontrolled bycicles, made available as part of the multi-bond graph library [7,8], can be used as a starting point for this research effort. Much basic knowledge concerning the vehicle dynamics of bycicles [1,6] is applicable to motorbycicles as well.

The adaptation of the bycicle model for describing a motorbycicle requires first the addition of a simple motor model. Furthermore, it will be necessary to retrieve realistic data for one or two reference vehicles from the literature. Also the visualization of the vehicle needs to be adjusted. The new modules shall be implemented using bond graphs [2], and depending on their nature, they shall be incorporated in either the bond graph library [3] or the multi-bond graph library [7,8].

The vehicle itself shall now be analysed concerning its range of stability. This is done by means of eigenvalue analysis of a linearized motorbycicle model. The methodology to be used has already been developed for bycicles. It is appicable to motorbycicles as well.

To enable control of the vehicle, it is necessary to develop a simple model of a driver (cf. chapter 11 [5]). In particular, two primary aspects shall be taken into consideration: modeling of the side-wise shifting of weight of the driver in curves and modeling the forces experienced by the driver.

The vehicle controller thus has 3 primary actuator variables at its disposal: acceleration/deceleration, side-wise shifting of the driver's center of gravity, and force applied to the handle-bar. The most common sensors to be used by the controller include the angle of inclinationof the vehicle, the velocity, and the centrifugal force. It is recommended that additional literature relating to these issues be studied.

The controlled vehicle dynamics shall be simulated using simple standard maneuvers. For example, it may be useful to simulate maneuvering the motorbike through a 90o curve or along an S-shaped track with given radius and predefined velocity.

Should there be time for more advanced topics, it is possible to enhance the models by adding more details to them. For example, it may make sense to replace the simple motor model by a more complex (complete) description of motor dynamics. Also it may make sense to add a model of a realistic transmission and/or a model of the shock absorbers. Of particular interest are the influence of different tire models and vibrations on vehicle dynamics.


References

  1. Åström, K.J., R.E. Klein, and A. Lennartsson (2005), Bicycle Dynamics and Control: Adapted Bicycles for Education and Research, IEEE Control Systems Magazine, 25(4), pp. 26-47.

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

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

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

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

  6. Schwab, A.L., J.P. Meijaard, and J.M. Papadopoulos (2005), Benchmark Results on the Linearized Equations of Motion of an Uncontrolled Bicycle, KSME Intl. J. Mechanical Science and Technology, 19(1), pp. 292-304.

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

  8. 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.

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Last modified: September 7, 2008 -- © François Cellier