Squishy Tyres

This is a short post detailing the work we did to create a deformable tyre model for CFD simulations, as briefly discussed in the last post. The justification stemmed from the existing model not only being an unrealistic shape, but also simply the wrong size by a solid 5mm in both diameter and maximum width (don't worry, we've always designed suspension and chassis to the correct tyre size, it was just the model that was wrong). We could just scale the existing tyre to be he right size, but it was the catalyst for us to put in a bit more effort. Tyres are made from rubber which is obviously quite flexible, but any tyre modelled as a revolution in CAD is not going to reflect this behaviour; it will end up with an infinitely small contact "point" tangent to the ground. The common way of solving this for CFD is to offset the ground by 1 or 2 mm to force a significant intersection, which was exactly what I did for the original EV23 CFD setup. Our findings from that setup and the validation testing we did using it were twofold:

• The amount of intersection with the ground in CFD significantly changes tyre squirt behaviour (we tried values between 0.5 and 5 mm)

• The tyre squirt and lower wake prediction from the original CFD setup didn't match track data well, regardless of the ground intersection distance used

• Unrelated to the total pressure correlation, it was impossible to set up suspension positions for cornering cases realistically without having a 5-10 mm contact patch ground intersection for the heavily loaded outboard tyres. 

Experimental testing

We therefore decided to model the tyre shape as accurately as possible, expecting this to also improve general mid and upper tyre wake correlation (which it did). Making a CAD model of a deformed tyre would be both incredibly time consuming, and practically impossible to do accurately. The solution was to make some minor adjustments to the size and shape in CAD, including modelling accurate wall thicknesses and a simplified two-layer tread-carcass structure, and throw it into structural analysis (FEA) software. We first ran a few tests to check if we could get the tyre to deform at all like we expected using simplified constraints and materials, and to make sure we could easily export the deformed shape into CFD without any hiccups. Fixed constraints were applied to the tyre bead, a 10 psi pressure was applied to the interior surfaces of the tyre, and a "rough" (i.e. infinite friction) contact was applied between the tyre and a 2D "ground" plate that was used to apply displacements (Figure 1). Tests were initially carried out using a more representative frictional contact, but results were nearly identical and setting the contact to rough saved a fair bit of simulation time. To ensure the deformed shapes were realistic, a test was run on a real tyre to give us some target values. This consisted of two loaded deformation tests, in which the tyre was placed on a set of scales at the operating pressure of 10 psi with a known (balanced) mass bolted to the wheel centre at cambers of both 0.0 and 2.0 degrees. The chosen force was 700 N, being very close to the static load per corner of the car with a driver seated. Unfortunately the tyre was too large to fit in the available calibrated press equipment in the workshop, so loading the tyre with mass and monitoring camber with a digital inclinometer had to suffice. For both cambers, target deflections were measured using a dial gage at the midpoint on the lower sidewall, and for the overall vertical displacement of the wheel shell (Figure 2).  

Simulation

Splitting up the tyre model into the tread and carcass allowed us to set their material properties separately, but without modelling details such as a multi-later carcass or exact geometries near the bead, we were never going to get perfect results using realistic material values. Instead, various combinations of elastic and plastic material properties were tested to calibrate the results against the four data points (two deflection measurements for two cambers) until a combination was found that satisfied all four within an acceptable tolerance. An example of the simulated sidewall deflection under static load is shown in Figure 3. 

Under static loading, the deformed tyre had a much more realistic size and curvature, which led me to believe the old tyre model we had was modelled on an uninflated tyre. Figure 4 shows the deformed model under static loading at 1.2 degrees of camber (representative of the front wheels on the vehicle under normal and static conditions), where lateral sidewall deflection can be seen on both sides, but particularly the left side, towards which the contact patch is biased due to the camber. The most critical improvement over the original model was the size and shape of the contact patch, which meant ground intersection could be reduced to negligible levels (~0.05 mm), and the size of the "plinth" between the ground and tyre (to reduce mesh issues at the sharp intersection angle) could be greatly reduced down to a 0.5mm height. The plinth and surround mesh are shown in Figure 7. The increased and more accurate curvature of the sidewall also had some effects on the mid wake, by increasing flow attachment around the rear sides of the tyre and powering up the rotational structure in the wake that ended up being critical for achieving an acceptable correlation of downstream off-body total pressure. 

Without a real tyre test rig, we had no way of testing deflections under anything but static/vertical load cases; we just had to trust that our calibrated model would behave realistically in such circumstances (e.g. high lateral load and different steering angles). These tyres have a considerable amount of flex under high loading, as a result of the low operating pressures, soft and thin rubber construction, and tall sidewalls. Based on existing photo/video of the tyres from car-mounted cameras under high lateral acceleration, the shape and magnitude of the sidewall deformation produced by our model appears realistic, the result of which is shown in Figure 5. It's still important to note that the "rough" contact in the FEA setup becomes less valid for load cases closer to the grip limit. The real tyre experiences slip in both lateral and longitudinal acceleration, with the rubber both sliding and consistently gripping and losing grip on different parts of the road surface. The net result of this would be less deformation, but again with evidence from previous onboard videos I can't really notice much difference, so the effect can't be too extreme. It's certainly a lot more accurate than where we were. 

The expected forces in all 3 axis were plugged into the model for each load case of interest, and the deformed mesh models were exported to CAD and converted back to a smooth solid body, with the interior space capped and filled so no voids are imported into CFD (Figure 6). I've retrospectively added an image of the EV24 skidpan scenario CFD-CAD model in Figure 8 to show the deformed tyres in use.