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Who developed the Magic Formula Tyre Model widely used for the analysis of tire behavior?

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Effective use of FE modeling

It’s said that nothing is certain except death and taxes. However, I’d like to add a third ‘certainty’: tire manufacturers will not tell you their rubber formulations. This thought has led me to a firmly held but not universally shared opinion on the finite element (FE) modeling of tires: that tire FE modeling is not worthwhile for anyone other than tire manufacturers. Let me explain my reasoning.

If you’re building an FE model of any structure, you need to know the properties of all the materials contained within it, along with how they are arranged and fixed together. This is fundamental to the FE approach. But if this information is so fundamental and tire manufacturers are not going to give it to you, then how do you proceed? There are a couple of workarounds but neither is pretty.

First, you could carefully dismantle a tire. This would involve dissecting it and separating out all the distinctive rubber types, along with the radials and fabric. These samples could then be lab-tested to measure their stiffness, tensile strength, etc, as well as other material properties. However, this process is fraught with problems and potential inaccuracies. For example, how do you maintain a highly consistent sample size and shape when dissecting a tire? Good samples could be extracted from the tread blocks and maybe the outer sidewall, but how do you extract good quality samples of the rubbers used deep within the construction? You could gather a collection of scraps and melt them together to form a better sample, but the melting and reforming process will change the properties of the very material you’re trying to measure.

However, as this process requires the physical tire to exist prior to modeling, why not simply test it on a rig and empirically model the results? The later being a long established process that gives highly accurate outputs.

An alternative FE approach could be to simply make your best engineering judgment and guess the materials’ properties. Though if you’re going to do that, you may as well save yourself the trouble of building an FE model at all. Instead of presuming the materials’ properties, just guess the tire’s final performance. The old mantra of ‘garbage in, garbage out’ comes to mind here, but it’s true; if the material properties are not accurately known then the FE modeling results cannot be relied upon.

Of course the problem can be solved by the tire manufacturers themselves, who know the exact rubber formulations they are using in each part of the construction. So they can easily go to the source and get large samples of each rubber formulation and cure them in such a way as to mimic the tire manufacturing process (not a simple task). Once complete, the nice large samples can be cut up, the material properties accurately measured and an FE model built from the data. That’s why FE modeling is used by tire manufacturers; however I’ve yet to see anyone else effectively use FE tire modeling in a commercially viable way.

The problem is made worse when you look at the time and cost involved. Gathering all the necessary data and building an FE model of a tire is a long and arduous process, whereas having a tire manufacturer build a small batch of prototype tires and testing them on a rig can be quicker than you may think. In a straight race between the ‘build and test’ approach and the ‘gather data and build an FE model’ approach, my money would be on build and test. Add to that the ability to put the physical tires on a vehicle and get a subjective assessment as well, and you’re on the winning team.

As ever I remain open-minded and if you have any feedback, or would like to enlighten me with some successful examples of the commercial deployment of tire FE models outside tire companies, then please contact me. You’ll find my details on my website below.

Gregory Smith is the director of Tyre CAE & Modeling Consultants, providing tire testing and modeling services to the OEM and motorsport industries. More information can be found at www.TyreCAE.com

 

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