Quater car model

[ankush_mechforum]

I am working on quarter car model project.. can anybody suggest the methods to find out Tyre stiffness and damping..

[DaveW]

I am working on quarter car model project..

I would ask why, and argue that a "bicycle" model would be more instructive (if that is the objective).

can anybody suggest the methods to find out Tyre stiffness and damping..

You could estimate values from measurements, with care, but be advised that estimated parameters will depend both on the technique you use and the ambient conditions.

Alternatively (at least for starters), you might want to search this forum for typical values.

[Greg Locock]

ankush might be running a wheelhop rig, in which case the damping of the tire is essentially zero and the radial stiffness measured on a stationary tire is misleading.

[bill shoe]

Greg, I know the dynamic stiffness of rubber things is typically higher than the static stiffness due to internal damping of the rubber material. So I'd guess the dynamic stiffness during wheel hop was higher than static stiffness as measured on a quasi-stationary tire. But you say the damping is essentially zero for the case of wheel hop. What am I missing? I'm pretty new to the world of dynamic vs static stiffness.

[Greg Locock]

There's two effects with tires - first the dynamic (ie higher frequency) response is different to static, secondly the 0 Hz stiffness of a rolling tire is different to that of a stationary tire. So you need to account for both the frequency /and/ the rolling effect.

If you mount a tire on a wheel and bounce it on the ground, it bounces several times.

If you bounce the wheel when it is mounted to the suspension of a car, it doesn't bounce several times. therefore most of the damping is in the suspension, not the tire. The classic example of this is an old car that loses a wheelweight, initially it vibrates a lot but the wheel doesn't rise off the ground, eventually the shock absorber blows out and the wheel will rise clear off the ground.

Bouncing the tire+wheel off the ground is probably as good a way of estimating k_radial and c_radial as you will easily get.

[Jersey Tom]

There's two effects with tires - first the dynamic (ie higher frequency) response is different to static, secondly the 0 Hz stiffness of a rolling tire is different to that of a stationary tire. So you need to account for both the frequency /and/ the rolling effect.

Both are pretty small, though.

Assuming this is for some school project or really basic study, you could probably estimate 35 lbf/in spring rate per 1 psi inflation pressure and you'll be in the ballpark. If you really want damping included too, I dunno, could go with 1% of that (and changing to lbf-s/in of course).

[Greg Locock]

"Both are pretty small,"

I haven't measured it for a long time, but I vaguely remember 30%.

[DaveW]

There's two effects with tires....

I was tempted to reply "at least", Greg, noting that tyre stiffness varies with changes to most variables.

I haven't measured it for a long time, but I vaguely remember 30%.

Several years ago, I conducted are series on tests on a range of "Champ" car slick tyres on behalf of a customer. Briefly, we mounted a tyre, on its rim, spindle coupled to a modified damper dyno superstructure, which was in turn mounted rigidly to the top a one of our 4-post rig actuators. I took the opportunity to carry out a few runs for my own benefit. All of these runs were carried out at the same inflation pressure and ambient temperature. Here are some results.

Run 331 was an attempt to estimate "steady state" tyre stiffness. It records one cycle of a sinusoidal input that took 20 seconds to complete. The rising rate is evident, but the average stiffness was 345 N/mm. Runs 326, 329 & 332 were collected at different mean loads, but at an applied frequency of 5 HZ. Estimated stiffness varied between 334, 395 and 408 N/mm, increasing with mean load (hence still a rising rate). I than argued that the last three runs could be considered as three mean positions with "dither". Taking the average value of whole cycles extracted from each run produced the yellow points. Connected together these gave a stiffness estimate of 289 N/mm, which was close to the value a tyre manufacturer would quote, some 37 percent lower than the 5 Hz local estimate. Perhaps that explains Greg's recollection.

I leave others to explain the measurements, but would observe that each time the tyres were loaded (by controlling position) the measured load fell with time. I attempted to control that by resting the tyre (with no applied load) for 15 minutes between runs, and then loading it at the start of each run, and waiting for 10 minutes before the recording the next run to allow the tyre to "settle".

A tyre is not a spring....

[Greg Locock]

Maybe the OP needs to explain what he is looking for.

[DaveW]

...you could probably estimate 35 lbf/in spring rate per 1 psi inflation pressure and you'll be in the ballpark. If you really want damping included too, I dunno, could go with 1% of that (and changing to lbf-s/in of course).

I would estimate that tyre stiffness varies by around 8 N/mm (46 lb/in) per 1 psi inflation pressure. That is an average across a wide range of tyres, but estimated as indicated below. It would be unwise to neglect construction stiffness, however. On rare occasions a tyre will increase vertical rate with reduction in inflation pressure. Surely that must be caused by construction.....

As you pointed out, tyre damping is small. It is also mainly hysteretic. Here is a sample taken from a arbitrary rig test. Personally, I would discount results below 3 Hz, because displacement is estimated from accelerometer data. One of the beauties of working the the frequency domain is that response functions can be integrated or differentiated with few issues, so here the results are presented as stiffness, scaled to N/mm. In each case, I have fitted a transfer function to the measurements, in the form Ks + i*(Cc + w*Cs). Arguably, the fitted data (shown as over-plotted crosses) is reasonable, but shows that Cc (hysteretic damping) accounts for most of the damping.

That is not very convenient if the objective is use the model in the time domain, so the compromise, shown here is to identify a viscous damping (only) model, fitted over a higher frequency range. The model would be expected to deviate increasingly from measurements at higher frequencies (above 10 Hz. in this case).

[Greg Locock]

Interesting. If you look at the dynamic response of rubber it varies a lot more than that. Of course we'd expect a pneumatic spring to be essentially of constant rate, which would mask some of the change with frequency. I'm amazed by the phase, actually I'm puzzled, where's wheelhop gone? In fact where are all the carcase modes?

[DaveW]

... I'm amazed by the phase, actually I'm puzzled, where's wheelhop gone? In fact where are all the carcase modes?

Why are you amazed?

Here is another example - actually two from the same rig test. The difference between the two was 2 psi inflation pressure (quite by chance confirming my earlier comment on pressure sensitivity, as it happens). There is a lot going on above the tyre, see here, for example. The hub mode occurred at just over 30 Hz, was quite well damped (around 60% of critical - this is a race car), but was masked by the presence of a couple of front wing modes. Not sure about carcase modes, but the input was pure heave, so some of those might not have been excited....

Note also that both this and my previous example were for front tyres (hence camber might affect damping estimates).