Hot Wheels

When people talk about Hyperloop, friction-less locomotion such as magnetic levitation or air bearings is what comes to a person’s mind apart from the name Elon Musk of course. Even though the Hyperloop will run on friction-less systems at high speeds but it still needs some system to function at low speeds. As magnets and air bearings have very little effect at low speeds thus wheels are a viable and currently the only option. Wheels will be used for the initial run i.e. until the speed required to levitate successfully is achieved. And if the levitation is active like ARXPAX, still wheels will be viable so as to conserve energy at lower speeds. Also, wheels may be required to balance certain moments generated. Now imagine a scenario where the pod is travelling at a very high speed and the levitation fails due to unforeseen circumstances. In this event, the wheels must thermally survive the heat generated due to the friction from the aluminum sub track.

Keeping this scenario in mind, we have performed thermal simulations on the wheels to analyze the maximum temperature developed. To maximize safety in our design, we have assumed that the wheels are used for the entire track length at the speed of 150m/s.

Now the simulation can be performed using multiple methods. One method is to:

1. Make a CAD file of track along with the wheel

2. Provide frictional contacts between the track and the wheel

3. Apply the pod’s weight to get the proper normal force

4. Input the required rpm/velocity

5. Run the simulation as transient structural along with temperature degree of freedom(an extra ANSYS command snippet is required) of course for a shorter length of the track

The above method will give accurate results and ANSYS will calculate the heat flux etc. but it is computational expensive.

An alternative and easier method that we used is to:

1. Make a CAD file of the wheel only

2. Analytically calculate the heat flux for two rubbing surfaces (rotating and planar in our case) over the entire track length

3. Apply the calculated heat flux value over the entire circumference of the wheel. Even though the wheel will have a line contact always but at very high rpm we can assume that every ‘line’ on the circumference of the wheel will be at the same temperature/heat flux which basically becomes the entire circumference(surface) of the wheel

4. Apply convection on the required regions and run the simulation as Transient thermal

Transient simulation makes more sense because the pod will not reach a steady state as it is constantly in contact with the track. Also, with transient thermal simulation, data for the temperature of the wheel for the entire track duration can be obtained.

The material used for the wheel is Aluminum 6061. A separate layer of polyurea is added on to the circumference of the aluminum. The thickness of the extra layer is 2cm. This layer is required to prevent the rubbing of Aluminum wheel and Aluminum sub track surface.

Setup Bonded contacts were defined between the aluminum and polyurea surface. Tetrahedron mesh was generated and further refinement was performed using ‘body sizing’ option. An initial temperature was set to the model. This value was obtained from the CFD simulation. Please refer aerodynamics blog to check out our shape iterations and results. Convection was applied on all the faces and heat flux calculated from the analytical equations was applied on the circumference. The model was solved for 5 s and the heat flux was activated for all the 5 sec mimicking the worst case situation.

The maximum temperature plot for 5 sec is shown below. We observe that at the end of 5 seconds polyurea reaches a max temperature of 434.56 ̊C. This shows that the wheel can withstand thermally in the event of failure of levitation wheels because ployurea becomes soft only at temperatures above 600 ̊C. We also observe that the conductivity of aluminium is 8000 times the conductivity of polyurea. Due to such vast difference in thermal conductivity, the aluminium doesn’t receive any heat during the 5 second run and the temperature remains at approx 35 ̊C. From the fig 4 we also observe that 2cm of poly urea is not required and the thickness can be reduced to save material costs.

Transient thermal simulations was performed on a aluminium wheel with polyurea on the outer surface. The wheel was assumed to be in contact with the track and translating at 150m/s for the entire track length(worst case scenario). Heat flux generated on the wheel due to friction was calculated analytically and applied on the surface of the wheel. Maximum temperature obtained was 434.56 ̊C which is well below the softening temperature of polyurea. The thickness of the polyurea can also be optimized to save the material costs. Now it’s time to check the stress distribution on the wheel due to high centrifugal forces.

![endif]--![endif]--