Squishy Tyres

This is a short post covering the process of creating a deformable tyre model for CFD simulations, as mentioned in the last post. 

Tyres are made from rubber which is obviously quite flexible, but any tyre modelled as a simple 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 an intersection and thus non-zero contact area, which was exactly what I did for the original EV23 CFD setup. Using this method, we found three things:

• 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

• It was impossible to set up suspension positions for cornering cases realistically without having a significant ground intersection for the outboard tyres, and the sidewall shape was wildly incorrect for the amount of vertical and lateral load experienced.

Experimental testing

We therefore decided to model the tyre shape as accurately as possible, expecting this to naturally improve tyre wake correlation (which it did). The method was to first make some minor adjustments to the tyre's size and shape in CAD, and then throw it into FEA. 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. 

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, inflated to 10 psi, and a known mass bolted to the wheel centre at cambers of both 0.0 and 2.0 degrees. The chosen force was 700 N, being a little higher than the static per-corner load of the car with a driver seated. Unfortunately the tyre was too large to fit in the 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 both at the midpoint on the lower sidewall, and for the overall vertical displacement of the wheel.

Simulation

Splitting up the tyre model into the tread and sidewall 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 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. 

Under static loading, the deformed tyre had a much more realistic size and curvature, which led me to believe that whoever made the old model had based it on an uninflated tyre for some reason. 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, simply to avoid coincident surfaces), and the size of the plinth between the ground and tyre (to reduce mesh issues at the sharp intersection angle) could be reduced down to a 0.5mm height. 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 upper wake that ended up being critical for achieving correlation at the rear of the two rake planes.

Along the way, FEA tyre pressure was reduced from the correct 10psi to 8.5psi to target a more accurate, flatter tyre tread. With the exception of the final image, all other images show the 10psi version with a notably rounded appearance to the tread. This change made negligible difference to sidewall shape.

When it came to adding lateral load, we just had to trust that our calibrated model would behave realistically given we had no tyre testing machines or practical methods to measure experimental values in such a scenario. Based on 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 below. It's certainly a lot more accurate than what we had. 

The deformed mesh models were exported to CAD and converted back to a smooth solid body, with the interior space sealed and filled so no voids were imported into CFD. I've retrospectively added an image of the EV24 skidpan scenario CFD-CAD model at the end of this post to show the deformed tyres in use.