Adding Surroundings to Model: Car Axle on Tires

This example adds a simple tire model to the model presented in the CarAxle example. As the tires' stiffness and damping will influence vibrations, this results in a more accurate model. 

Figure 1: Car axle on tires.

With the addition of four more supports (six supports in total, marked by anchors), five constraints must be relaxed in order to avoid an overconstrained system during initialization. Figure 1 depicts the Car Axle on Tires model, indicating which supports have been relaxed. By default, the pinned supports mounted on tires (flexible supports with springs and dampers) are relaxed. In the CarAxle example, shaftRight was relaxed. In addition to this, two additional constraints must be relaxed due to the additional supports. In this scenario, the flexible supports, leftTire and rightTire, are relaxed by setting the parameter isRoot to false. It is worth noting that the pinnedRight support is now fixed axially, while the flexible support, the tire, is free axially.

Figure 2: Applied force and vertical deflections at the middle of the shaft.

The deflections under the applied force for both with tires and without tires are shown in Figure 2. The axle on tires shows higher deflections, as the tires also deflect when the force is applied. 

Figure 3: FFT of the shaft vibrations.

Studying the FFT shows that the resonance is at 14.5 Hz or 870 rpm; see Figure 3. This is lower than the shaft without tires (18 Hz), as the added wheels decrease the total stiffness.