Tire vertical damping

[silente]

Hi!

I have searched the forum to find an answer to my question, but didn't find much if you exclude a nice picture from DaveW which was anyway related to another discussion.

My question is somehow connected to a quarter car modeling, with both sprung and unsprung masses, suspension and tire stiffness and suspension and tire damping.

Normally we claim that tire damping is so small compared to dampers that it can be neglected. But does anybody know how small/big is it?

Ok, i know this is a spread question; this value could depend on a lot of things, see tire pressure, construction, maybe compound... I am not looking for a precise number, just something more precise than what i found till now, i.e. any values ranging from 0.3 to 6 kN/m/s.

Thanks!

[sectionate]

Surely you want to know what your tyre construction, along with the optimal pressure, is to determine what its damping ratio would be?

I don't think this is something that can be determined by a 'finger in the air' as a tyre wall height of 50mm will have a vastly different stiffness/damping ratio that one of 100mm high.

[silente]

yes, right, but at least somebody who have some knowledge about this topic could will to share some values using some particular tires as an example...

What i mean is, does anybody know how big vertical damping a certain tire (at a certain pressure and with a certain vertical stiffness, for example) is?
I know each tire can be a different story, but at least it could give a feel about the magnitude of this parameter.

[Ciro Pabón]

For the benefit of the forum, here is a picture of the quarter car model: the gray square at the top represents the car, the one at the bottom the suspension. The squiggly lines are springs and the little withe squares are the dampers.

k1 and k2 are the spring coefficients of tyres and springs and c1 and c2 are the damping coefficients of tyres and dampers. m1 is the mass of the suspension, including tyres and m2 is the mass of the rest of the car.



I'm sorry for the fuzziness, the picture was really small: most quarter car models, as silente mentions, do not include a damping coefficient for tyres.

That is, c1 doesn't appear: the tyre is simplified to a spring with no damping at all and the bottom square has only a spring below it, no withe square appears.

The spring coefficient, k, represents how large is the force you have to exert for every meter the tyre or spring moves. That's why its units are Newtons per meter.

On the other hand c represents how large is the force exerted by the damper for every meter per second of velocity of the object damped. That's why its units are Newtons per meter per second.

Well, what I have from HDM 3 Watanatada model is damping coefficient for tyres of c1 = 6 N*s/m.

This paper tries to estimate good parameters for three models and uses 7 Ns/m (page 259) but gives no reason for it.

http://papers.uth.gr/files/JVC_Natsiavas.pdf

The part that could be interesting for you is that the paper estimates how good are those parameters when compared with "reality" (actually, Mathlab).

Of course this is a small value, as you mention, compared with c2 = 1425 Ns/m

(that means that the damping coefficient of dampers is 200 times larger than the one for tyres: no wonder most models do not take it in account).

On the other hand the spring coefficiente is k1 = 200 kN/m for tyres and k2 = 15 kN/m for dampers.

(roughly speaking this means tyres are 30 times more resistant to vertical deflection than springs).

[silente]

Hi Ciro,

thanks for your post.

Unfortunately your document bring even more uncertainty into my picture, since the figures that the guy is using are much smaller than the one i had found (and they were already pretty different one from the other!).

Anyway 7N/m/s seems very low to me, at least compared to the numbers i have found before. The lowest ones were something like 100 times bigger than that!!

[DaveW]

Tyre damping tends to be application dependent. Tyres for "sprint" vehicles are slightly better damped than tyres for "endurance" vehicles (which have almost no damping, particularly at the rear axle).

See here for a transfer function of typical race tyres (F-- front, R-- rear). These were extracted from a GP2 test on Pirelli tyres. The crosses and associated legends show the results of a model fitted to the measurements of the form [Ks + i(Cs*w + Cc)] (i = sqrt(-1), w = angular frequency). It shows that damping is mainly hysteretic (Cc). That is not convenient for a time domain simulation, so here is an alternative form covering a slightly different frequency range. The parameter units are N/mm & N/mm/sec.

Hope this helps...

[silente]

Hi Dave,

thanks a lot for your contribution.

I really hoped that you could jump in!

One thing is not clear to me: why in the second picture Cc is always = 0? This case is covering a part of the frequency range that was already shown in the first picture, but the shown values are pretty different.

In the second picture we see only Cs contribution. In the first picture Cc was much bigger than Cs..I tire damping is then very freuqnecy dependant, just would like to understand how to interpret this pics and which values to use to approximate tire behavior...

Thanks!

[DaveW]

To explain the plots:

The contact patch load is just that - a measure of load corrected for the live mass that is also measured. The check for that is the load measured with nothing on the platforms. That is typically less than 2N/gn after correction.

The displacement is obtained by double integrating the difference between hub acceleration and the platform acceleration. The two accelerometer measurements are calibrated so that the difference is less that 0.001 gn/gn when the hub accelerometer is mounted on the bare rig over the whole frequency range.

You will note (see the vertical title) that the transfer has been double differentented and multiplied by 0.0001019 (= 1/9810) to convert the function to N/mm. This is the best we can do, accepting that the accelerometers are also sensitive to cross axis acceleration, and also that the vertical accleration of the hub acceleration is position sensitive (the hub acceleration will vary with location - we try to the take care of that by mounting the hub accelerometer between the rim supports at the bottom of the wheel & making sure that the sensitive axes is vertical).

What we measure is represented by the solid lines. We then try to make some sense of the measurements by fitting a simple model to the response functions. We have several models available, but the one that is easy to model theoretically is a simple spring and parallel viscous damper (damping force increases with frequency). But that ignores the fact that most of the damping in a tyre is hysteretic (damping force is independent of frequency) - see my first plot.

It is not easy to model hysteretic damping in the time domain, so a "fix" is required. The frequency domain used to identify the parameters listed in the first plot covers 4.5 to 10 Hz, a range the covers the heave and pitch modes of a typical race vehicle. If we suppress hysteretic parameter identification (indicated by Cc set to zero), then Cs will be over-estimated and the damping force will be too high at the pitch mode. The "fix" for what that is worth, is to change the frequency range to 6 - 10 Hz. For interest, a frequency range of 4.5 to 10 Hz would have yielded 0.791 for the front left tyre.

[Jersey Tom]

To make this even more fun... all the discussion so far has been on static (non-rolling) tires...

[DaveW]

Too true. Forgive me, JT, but your contribution to the discussion would be ....?

[Jersey Tom]

Just making the comment that we can jump down any number of rabbit holes here - but it's all ultimately on non-rolling tires. To me, first question to ask is.. how much is it worth sweating the fine details? What's their level of relevance to begin with?

[humble sabot]

Well the whole point of suspension is to control the erratic and sensitive action at the contact patch is it not? I think that it's been proven that in terms of relevance by orders of magnitude, the tyre's characteristics are to be noted, but not significant enough that you need a more precise tool in analyzing them than explained so far, which suggests that the effect of the tyres rotational momentum has even less effect, and is probably a half to a whole order of magnitude lower again. The spinning of a wheel is largely in plane with its motion through the suspension travel so gyroscopic effects aren't liable to have much influence.

[DaveW]

.. how much is it worth sweating the fine details? What's their level of relevance to begin with?

You sound like someone talking himself out of a job....

The short answer is you have a vehicle; you have compiled a mathematical model of the vehicle, & now you want to validate the model by comparing the two, say at a rig test. The tyres are simply identifiable elements of the vehicle.

Back to your comment: the same could be said about the rest of the vehicle, which is why most people check them for accuracy (dimensions & weights) every time they are rebuilt. That could be called sweating over the fine details, but the more successful teams are generally those that pay attention to such details.

[Lycoming]

.. how much is it worth sweating the fine details? What's their level of relevance to begin with?

You sound like someone talking himself out of a job....

I'm sure he has plenty of other rabbit holes from which to make a living out of.

[silente]

Thanks all for your posts.

JT, i agree with you the effect of tire damping is very small. But anyway, i was curious to understand how small it was. I am also aware of the rolling speed changing significantly the picture, but at least now i have a reference about the order of magnitude.

So Dawe, thanks a lot for your insight!
To summarise and check if i understood correctly, a good approximation of tire damping for these particular tires is about 0.75 N/mm/s, with a stiffness around 265 N/mm at the front and 300 N/mm at the rear.

With an ipotethic low profile tire, like the 18" used by GT and LMP cars, you said this value drop down dramatically. Do you have an order of magnitude for this kind of tires as well?

Thanks again!