Come si possono simulare ruote in gomma e pneumatici?

The model of a wheel rolling over an arbitrary landscape is complex and requires a very accurate description of both surfaces in contact (the landscape and the wheel). Currently, WM3D up to version 4.0 represents the surface of CAD imported geometries with a faceted approximation, while newest versions 5.0 and 6.0, as well as WM4D, allow for collision detection on Nurbs surfaces. Therefore, when using older versions this can lead to problems in modeling surface to surface interactions:

As the point of contact between the two touching bodies changes from one facet to another, the application of the contact force can change abruptly and discontinuously. This change in the contact point is often severe enough to be interpreted as a collision and results in bodies that bounce apart from one another. The Kinetic Energy of the bodies involved is then adjusted to reflect the energy loss, as specified by the Coefficient of Restitution. This reduction in Kinetic Energy can have the effect of incorrectly slowing down the relative motion of the touching bodies. Setting the Coefficient of Restitution to 1 (to create perfectly elastic collisions that do not dissipate energy) does not solve the problem as the bouncing of the wheels is then amplified.

To eliminate the error introduced to your simulation through these erroneous collisions, you would need to replace the faceted approximation of both surfaces with analytic descriptions. WM3D up to v.4.0 is limited to faceted approximations for arbitrary surfaces. If You haven't a newer version 5.0 or 6.0, you can improve your model of wheels however, by replacing them with the spherical bodies which, if created with the WM3D geometry tool, are analytically defined. You will notice that cylinders created in the same way are faceted approximations and will not improve the performance of your model.

As far as modeling wheels and tires with WM3D spheres, you should be careful to acknowledge the effect on your simulation of those spheres being completely rigid. Real tires are very pliable and the result of their deformation can influence strongly the traction and behavior of the tire. WM3D tools cannot account for these influences without some special programming, nor can anyone in our price range account for them with a physics based, non-empirical approach.

Recently, the work carried out at Padua University in Italy with a team of prof. Vittore Cossalter has certified a powerful tire simulation for Working Model 2D and 3D. The consistency, efficiency and effectiveness of such a simulation (a complex assembly of analytical relations yet extremely fast to be solved by Working Model) has been immediately recognized by some Italian motorbikes Companies, like Cagiva, Ducati and Aprilia motorbikes, and effectively used in both racing and normal production vehicle analysis. A movie of one of such implementation is available here.

Additionally, a reduced version of the tyre model ready for testing is available here:

A new product, a Working Model Add-On for tyre simulations both on 2D and 3D models has been developed by prof. Vittore Cossalter and is now distribuited worldwide by Lista Studio with full instructions in English.

Please click here for more information on the add-on.

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Data ultimo aggiornamento: 2 settembre 2011

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