Written by: David Briant – Project Engineer
There are many benefits of creating multibody simulations of vehicles, in particular when looking at the suspension design. Many characteristics are investigated when designing suspension; camber, toe, caster, mechanical trail, Ackerman and installation ratio to name a few. Using multibody kinematic models can be entirely suitable when investigating this area, and do not necessarily need tyre models to gain useful and valid results.
However, when you need to gain full vehicle motions and forces it becomes very difficult to predict without some type of tyre model. This can be as simple or as complex as the problem requires, but interaction with the road is fundamentally what vehicles require to be able to move; getting the right tyre model and the tyre model right is important.
The type of contact the tyre has with the road is very important, with two classes of model; single point and multi-point models. The distinction between the two is how many road surface points are read by the contact model and how the effective contact point is calculated.
In addition, the road model type has a very big influence on the contact model chosen; if the road surface is of high fidelity, with higher frequency oscillations or larger steps, then a multiple point contact model or a single point with windowing function is required. If the surface is smooth with only low frequency oscillations then a single point contact model can be used. The type of investigation also drives the tyre type used, with higher fidelity or higher frequencies requiring the multiple points of contact; real time, smooth kinematic or static tests can use single point which yields computational effort and simplicity benefits.
Single contact point
Simpler models use a single point contact model which measures the height and calculates the normal at a single point position on the road surface. An example of this type of model is the Pacejka model. These models can be modified to yield a more representative result by using a windowing function that averages multiple points on the road and calculates a normal that is then used by the tyre model. The benefits of using this type of model is the simplicity and thus speed at which the model can be simulated. The example of the Pacejka model works primarily on one axis, using the road normal and contact point to then gain hub forces. This type of model has difficulty when interacting with high frequency road oscillations and fast amplitude changes. Without a windowing function it is less representative of a tyre that spreads the contact over a larger area, damping out vertical changes.
Below is an example of the VeSyMA – Suspensions application of a single point Pacejka tyre model performing a double lane change. In this instance, the road is perfectly smooth, therefore there is no need for a multiple point contact model.
Multiple contact point
Multiple point contact models are more representative of a real contact patch, as they measure a number of road points and define a relationship between them and the tyre surface model. This allows for more realistic contact patch deflection and allows higher fidelity when interacting with vertical changes in the road surface. The downside is that this type of tyre model can become highly computationally intensive.
The animation below shows an example of a multiple point contact model, using FTire, which has many contact points and has an individual carcass model and handles both high frequency, high fidelity experiments and handling experiments. This example is of a full vehicle model, using the FTire integration in the VeSyMA – Suspensions Library.
In the simpler single point models there is a choice of whether or not to include transients; these are a category of effects that include time dependent elements such as simplified tyre characteristics, tyre deflection characteristics or non-linear slip calculations. These are compared to ideal calculations that do not include these effects, and use simpler non-transient/linear effects.
Simple Linear Model
It is worth considering one of the simpler models if the vertical and lateral effects are not of interest. For drive cycle investigations, where the ride and handling dynamics are not of interest and the tyres are only intended to propel the vehicle forwards, these tyres are more efficient. These tyres do not have a maximum force, and use the ideal slip values to create a tractive force proportional to normal force. These tyres do not provide realistic limit force characteristics, assuming that the force applied does not exceed the maximum permissible force set in the tyre model.
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