I have previously discussed how commonly used empirical tire models are essentially complex curve fits; an optimization process is employed to tune the parameters of the model such that which overlays the tire test data.
This is a solid approach as it typically results in a model that can be shown to accurately represent the test conditions, while also being fast to solve and easy to use. The only issue is that while the resulting model can be solved at any load case, its accuracy can only be relied upon for load cases within the tire’s tested range. This means that the usable operating range of an empirical model is dependent upon the testing conditions. Therefore, when establishing a tire modeling process, it is important to include some rationale to determine what range of conditions a given tire should be tested to.
Assuming the tire model is a standard, non-temperature sensitive handling model being tested on flat sandpaper, then there are usually only six test inputs to worry about. I think of these in high and low impact groups, with load, slip angle and slip ratio having the highest impact on the tire’s handling performance, while pressure, camber and forward velocity have less impact.
Now let’s go through each of those starting with the load. All road car tires have a load rating, and this is a good reference point to determine the loading conditions required for the testing. Typically 65% of this load rating is a good nominal load for testing purposes, then the tire can be tested up to two times the nominal load for the highest load condition and down to around 0.2 or 0.4 for the lowest load condition. Also, the maximum load over a tire is dependent on the tire itself. A very high-grip performance or race car tire can facilitate cornering at higher g-forces, meaning there is more lateral weight transfer, meaning the tire is exposed to a higher vertical load, and should be tested as such.
Then there is the slip angle and slip ratio. In this context it really depends on how the resulting tire model is to be used. If it’s only meant for everyday driving scenarios with on-center type of behavior, then there’s no need to test the tire to high slip conditions. In this case, a +/-10° slip angle and a +/-10-15% slip ratio would more than suffice. If the model is intended to be used to simulate more extreme maneuvers, then the tire must be tested at more extreme slip conditions. These could be around a +/-25° slip angle and a +/-20-30% slip ratio; though testing at these conditions should be minimized to avoid heat build-up in the tire as well as the wear that it causes.
After this we must consider the low-impact inputs. Some empirical models such as the Magic Formula 6.0 support pressure interpolation. This means we can test the tire at three inflation pressures and interpolate to any pressure between them. However it’s advisable to test the tire at (or at least close to) the correct running pressure. Here it must be considered that the running pressure is not the same as the inflation pressure of the tires on the vehicle. Pressure should also be checked when the tire is cold. As a vehicle is driven, the tires warm up and pressure increases, if only slightly. So for running pressure, if you have a TPMS then this should be used. Otherwise a rule of thumb is to assume the running pressure to be about 0.2 bar above the inflation pressure. This can be the middle pressure value used in testing and then further testing should be done at about 0.5 bar above and below this pressure to facilitate pressure interpolation in the model.
Next we must consider camber. This again depends on the vehicle and the suspension kinematics. If the vehicle is known, then the maximum obtainable camber on a flat road can be measured, and this should then be increased by a small amount to account for a non-flat road. Fortunately, camber has less influence than the load and slip conditions, so it’s less critical. The maximum tested cambers in the range of +/-6° would typically work for a road car, probably more for a race car.
Finally there is forward velocity. This generally has the least impact on performance, only really coming into play when estimating the rolling radius, which increases with speed due to centrifugal force causing the tire to swell. However this effect is usually only important for race cars with a high downforce. As with camber, the forward velocity is dependent on the vehicle. For a road car, measurements between 20mph and 60mph will usually suffice. For a race car it will be higher and will depend on the type of racing.
I’ve seen many enthusiastic engineers go headfirst into the modeling process, forgetting the age-old mantra of ‘garbage in is garbage out’. If there’s something fundamentally wrong with the data, then no matter what you do, there will be something fundamentally wrong with the model.
