Posted by: drracing | September 12, 2011

Rims compliance

Here we are! today i have finally found some time to write a post here after quite a long time…again.

At the moment i am on a train to go back to Turin after some days spent at home (in Rome) for my father’s birthday. I had a very beautiful time with my family this weekend and i am very happy about this! I also had the time to think a bit of my present. This is probably the reason why i have finally taken  some time to write here.

Today i would like to talk about a topic i never found to be dealt very much on the web.

Everybody who is used to work on racecars (designer or not) surely knows the problems connected with a lack of stiffness in crucial parts of the vehicle, such as supensions attachments, chassis, steering system, etc. But one thing i have never seen to be discussed much (at least in a quantitative way) is the stiffness of maybe one of the most important parts of a suspension system, at least because it is what actually keep in place the really most important part of the suspension and, probably, of the whole car: the tyre. I am talking about rims.

During the years i have spent on the racetracks, i have always found people claiming that they are using a certain rim because it is light and it is stiff as well. It is crystal clear that to have a very light rim is normally a very good thing: in this way, not only we can have a lower weight of the whole racecar, but we can also have less unsprung mass and less rotational inertia. But what is happening when it is going against rim stiffness? And how stiff a rim is/should be?

The only person who gave me an idea of the stiffness of an aluminium rim was Claude Rouelle in his fantastic seminar. He has probably done a lot of similar tests in his long career and with its company. At that time, that information was for me something completely new and when it told THAT value i was really surprised (i am not sure he would be happy to see me writing the number, so i won’t do it, but it is something you cannot ignore when studing how camber change in a corner, the same order of magnitude of the car roll angle, at least with single seaters suspension settings).

With that number in my mind, some months ago, since the company i work for had to buy some new rims for our cars, i proposed to choose them because of their weight (both lightness and consistance of the mass of the rim: i think it is a good thing when several rims of the same manufacture has more or less the same weight) but also taking a look to their stiffness. They were actually mad of aluminium, so it was really a good possibility to compare the numbers with what Claude said.

So, we decided to build a very simple device to measure rims stiffness: it was made of a car jack, a strain gauge and a wheel hub and upright firmly connected to a big (and heavy) jig. A dial gauge was then placed to read rim deflection on a point very close to where the load was applied. The procedure we used was to increase the load till we were reading 1 mm of deflection on the dial gauge. It was zeroed with already some preload acting on the rime to avoid mistakes in our readings.

What we saw from our experiments with different rims was quite interesting.

The first thing, maybe intuitive but anyway interesting, was that the wheel nut tightening torque plays a very important role on the wheel assembly stiffness. If you increase this torque (and, so, the clamping force) you reduce the overall compliance by reducing both the deformation of the hub assembly and of the connection zone between rim and hub. Of cours, you cannot go too high with this torque cause it could lead to other problems, but this is another story.

One thing we must say is that, with our experiment, we were measuring the overall wheel assembly stiffness. Also the device stiffness was probably playing its role in the game, but i think it was anyway quite high, high enough not to change our readings in a significant way. The experiment, in a few words, was anyway good to compare different rims, but it didn’t give a stiffness value for the rim only. I am anyway quite sure, looking to rims deformation and knowing how the hub is built, that the most of the compliance was coming from the rim.

And i was anyway surprised of the magnitude of the deformation we had for a certain load. You could really see the rim changing its shape during the test and re-taking it after the load was taken away. A fast calculation of the actual deformation told us very interesting things. One thing is completely clear is that this deformation is playing a really big role in the overall camber change of the wheel in a corner. Obviously the effect is bigger if car weight is bigger, but also with a F3-like (540kg) car it plays a very very important role.

As i could imagine, i actually found that Claude figures were right. Rims (or wheel assembly) deformation is not something you can ignore when you try to figure out how much camber your tire is experiencing in a corner, above all at high lateral accelerations, when the forces are bigger and the most of loads are carried over by the outside wheels.

With this results on your paper, it could be really interested to understand how a design change aimed to increase wheel assembly stiffness could improve your performance and how much weight it could add to your car (if you actually need to add weight doing it). Having an higher stiffness could let you leave the pit lane with less static camber, improving, for example your car braking potential by some extent.

One thing it must be considered also, for example when we are going to try to simulate how an higher stiffness could improve car performance, is that (somebody correct me if i am wrong) tyre data are normally collected measuring camber ignoring rims compliance. What i mean is that they probably fix a camber value on the machine, but then, because of cornering forces, also the test rims is experiencing some deflection. Maybe less of our aluminium rim, if it is made of steel. But some deflection must always be present. So, when we read x newtons of cornering force at y degress of camber, we are probably reading a force produced by the tire at a different camber than y degrees, because of the test rim deformation.

Some food for thought.

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