tire spring rate VS wheel rate

[Brian Evans]

Is there a way to use a known tire spring rate to predict an appropriate wheel rate, presuming that all the variables that go along with wheel rates are known? Basically thinking about how the tire rate and the wheel rate are in series and how to apportion the two rates optimally.

Thanks

[Drew Price]

I think you are grasping what is going on, but might be thinking about it from the wrong direction? My thinking is based around selecting a front and rear natural frequency, and then working out what wheel rate combined with tire spring rate will give that frequency. So it's kind of about the proportion of the two rates, but if you pick the frequency, and you know the tire spring rate, then the wheel rate from the linkage falls out.

Best,
Drew

[Charlie]

I think I see what you are saying, but I don't think you can successfully predict the wheel rate with the tire rate alone. It might help you get to a range though (you don't want your wheel rate so stiff that the tire is doing all the suspension work).

However, I can't put any numbers to it (as far as X times the tire rate)

[exFSAE]

I'd start by picking wheel rates (based on whatever your favorite method is.. be it limiting pitch, front and rear natural frequencies, whatever), and if you know the tire rate the spring rate should define itself.

Since the effective springrate at the wheel, and the tire rate, work in series I would think it would be good to have the tire rate significantly higher than the pure spring rate. That way you can make small spring or bar changes that affect balance noticeably, rather than having to make massive changes to make up for an overly compliant tire.

Likewise, I'd think small changes in tire pressure from buildup would have a smaller effect on your TLLTD changing. I could be wrong though I haven't actually run the numbers.

[murpia]

Originally posted by exFSAE:
... I would think it would be good to have the tire rate significantly higher than the pure spring rate. That way you can make small spring or bar changes that affect balance noticeably, rather than having to make massive changes to make up for an overly compliant tire.
Is there much choice available in tyre rate? I would have thought teams were stuck with what's available and have to make the springs work for the tyres and the rest of the chassis package rather than the other way round?

Regards, Ian

[Drew Price]

Originally posted by murpia:

Is there much choice available in tyre rate? I would have thought teams were stuck with what's available and have to make the springs work for the tyres and the rest of the chassis package rather than the other way round?

Regards, Ian



Air pressure in the tire can change it a bit, and that will vary with which tire, but since tire spring rate has a lot to do with sidewall construction you are pretty stuck with what you get. Just something you have to take into account.

Pat Clarke commented in one of his columns a few months ago that very few teams (even at Formula Student) build a rig to test tire spring rate v. inflation pressure, leading the conclusion that it's at least worth looking into. The teams that know the numbers are very unlikely to share them since it is a pretty simple thing to check that easily sets your program apart.

....And may or may not be a significant factor... Although if you think in terms of something like an air shock for bikes, a fairly small ratio change in air pressure has a pretty big effect on spring rate. The recommended pressure range for the Goodyears at least (I don't actually know what it is for the Hoosiers) is a pretty wide range.

Best,
Drew

[exFSAE]

Originally posted by murpia:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by exFSAE:
... I would think it would be good to have the tire rate significantly higher than the pure spring rate. That way you can make small spring or bar changes that affect balance noticeably, rather than having to make massive changes to make up for an overly compliant tire.
Is there much choice available in tyre rate? I would have thought teams were stuck with what's available and have to make the springs work for the tyres and the rest of the chassis package rather than the other way round?

Regards, Ian </div></BLOCKQUOTE>

Can make tire rate whatever you want with air pressure. Makes a big difference.

[Drew Price]

Originally posted by exFSAE:

Can make tire rate whatever you want with air pressure. Makes a big difference.


....within some set of values.

I believe the primary effect present with adjusting inflation pressure has to do with normal load distribution in, and shape of, the contact patches. Don't forget to take that into account when messing with tire pressures (that and surface temp, rolling resistance, lateral stiffness [dependent on wheel width as well...etc.])

Changing wheel rates is what the ride springs are for. Tire pressure should be optimized for other things than summed wheel rate in my oppinion, the contact patches are much more important, and sacrificing load distribution at the tire to change wheel rate by 3% is dumb, and can ruin the tires in a hurry (if you have drivers who can take full advantage of them anyways). See first sentence of this paragraph.

All this assumes you also have reasonably light unsprung masses, if the unsprung is super heavy, that might throw the whole thing out the window and messing with tire pressure might be the only way you can dial out wheel studder or tramp, but at that point I think you have bigger fish to fry.

Best,
Drew

[Jersey Tom]

You might be surprised... that's all I'll say http://fsae.com/groupee_common/emoticons/icon_smile.gif

But in FSAE on a smooth track, yea, tire pressure isn't as huge a deal.

But you might be surprised at the best operating pressure for some of these tires, as well.

[Drew Price]

We ran about 10-11psi hot on our D2692's last year, largely due to the 6.5" wide wheels we used - things balloon like crazy. A third of the tire was off the track otherwise.

I will second about the smooth track surface. I have been thinking over a whole gamut of ways to stiffen up the roll rate since we don't really have to cope with track surface upsets at MIS. Unless we get to run on the banking again.

The difference in rate from 10 - 14 psi I'll agree could be significant, but I think you're sacrificing so much more at that point than just sprung rate that it should not be treated as a variable unless you discover you need that adjustabality. Until then it's basically a fixed parameter, just so long as you know what it's fixed at!

Best,
Drew

[exFSAE]

Why stiffen the roll rate? Beyond a point, it doesn't gain you anything. Tires become the limiting factor in vehicle response.

[bahous]

Originally posted by exFSAE:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by murpia:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by exFSAE:
... I would think it would be good to have the tire rate significantly higher than the pure spring rate. That way you can make small spring or bar changes that affect balance noticeably, rather than having to make massive changes to make up for an overly compliant tire.
Is there much choice available in tyre rate? I would have thought teams were stuck with what's available and have to make the springs work for the tyres and the rest of the chassis package rather than the other way round?

Regards, Ian </div></BLOCKQUOTE>

Can make tire rate whatever you want with air pressure. Makes a big difference. </div></BLOCKQUOTE>

what tire rates do you guys have? for my calculations, i'm using 750lb/in for a D2692

[Drew Price]

Right, the recent thread about higher roll centers and long swing arm lengths got me thinking about increasing the frequency of the response and having the tires provide a larger part of the compliance, like older F1 methodology in order to liven up steering response, and to sacrifice a little less in accel and braking due to camber change, to have less track-change-induced-scrub, and to be able to run less / no bar.

I subscribe to the 'less is more' idea as far as ARB's go, and like them as a fine tuning tool, but am looking into using faster instantaneous kinematic load transfer.

Some of the downsides being having to cope with greater jacking forces, having to pay more attention to inertial moments, and reduced tractive capacity over rough surfaces, but that's back to 'we know the surface we are going to compete on.' (And it's darn smooth).

Nothing super extreme mind you, it's just where the mental excersizes have taken me in the last month or so, since this will be my last year to do this learning stuff directly. After that I'll have to do what Tom is doing to keep trying out new ideas to get a grip of how they work.

I have more work to do to make sure I won't be lifting wheels though, or making it too slidey to be driven by 20 year old engineering students who drive Toyotas. Could be a good time to implement a spool though, I'm not as sold as I used to be on a solid rear axle.

This probably belongs in another thread somewhere, so apologies.

Best,
Drew

[exFSAE]

Just bear in mind, steering response and chassis response are related, but different.

I could take an F1 car, and put minivan tires on it... would be sprung to all hell and the chassis would react quickly relative to the tires.. but the steering and yaw response of the car would be junk on dishrag tires.

Or you could take a minivan and bolt F1 tires on it, in which case the tires would react very quickly to small steering inputs and would be too much tire for the suspension, with lazy and nonlinear chassis response.

Gotta have the right amount of both.

Point being, you can go with higher springrates and roll centers and make some of your load transfer as quick as you please... but if the yaw response of the tire is your limiting factor you won't gain anything.

Going with what Tom said earlier it's probably a good idea to do test a few pressure points for the tires. Maybe do a skid pad test with your 11 psi all around as nominal.. one at +2 psi all around, and one at -2 psi all around. See if you can figure out where the peak grip is.

From there you can try + or - 1 psi front and rear and see what the difference is in balance and response (which is closer to the whole tire rate thing).

[murpia]

How much do the tyres warm up through a skidpan / sprint / endurance...

The pressure change due to warmup could undo much analysis / measurement work.

Regards, Ian

[ben]

Just to give you a reference on pressure rise. We tested the other week at Bruntingthorpe and went from 0.8 bar cold to 1 bar hot in 5km of running. Tread temps were low 50s (celsius) with 12C ambient and track.

BTW 0.8 to 1 bar is a 25% increase and the spring rate change is just under that due to the sidewall. Even at low pressure the sidewall isn't carrying the majority of the load (at least for our radials)

Ben

[Drew Price]

Originally posted by murpia:

The pressure change due to warmup could undo much analysis / measurement work.

Regards, Ian

Extremely valid point, and one more tally among many why testing is vital.

Without having measured it myself, I imagine that people controlling ride height to a few mm would need to take that into account as well.


Originally posted by ben:
....12C ambient and track.

.... Even at low pressure the sidewall isn't carrying the majority of the load (at least for our radials).

Ben

Lucky, we're probably not going to see track temps above 4C or 5C until April, had the old car out a few weekends ago in the morning when it was around 5C, and 20 minutes of sustained hard running probably only got the tires up to 20 or 22, so I won't be able to make notes on this till it warms up.

Now we're just praying they keep our testing lot plowed and not too covered in salt to do test some kinematic changes on the last vehicle.



That all being said...

I am going to stand by my initial feelings that the change to natural frequency and oscillation is very small, even with a 25% change in tire spring rate. For a linkage wheel rate of 150 lbs/in and a cold tire rate of 500 lbs/in, a 40% increase in tire rate to 700 lbs/in only yields a total rate increase of about 7%, from 115 lbs/in to 123 lbs/in:


1 / ((1 / 150) + (1 / 500)) = 115.38 lbs/in ------>

1 / ((1 / 150) + (1 / 700)) = 123.53 lbs/in


Stiffer initial tire spring rate yields less change, say with a 1000 in/lb tire going to 1400 lbs/in gives just under a 4% increase, from 130.5 lbs/in to 135.5 lbs/in:

1 / ((1 / 150) + (1 / 1 000)) = 130.43 lbs/in ----->

1 / ((1 / 150) + (1 / 1 400)) = 135.48 lbs/in



For reference, a 40% change in ride wheel rate in the initial situation, from 150 lbs/in to 210 lbs/in gives almost a 29% increase, from 115 lbs/in to 148 lbs/in.



1 / ((1 / 150) + (1 / 500)) = 115.38 lbs/in ----->


1 / ((1 / 210) + (1 / 500)) = 147.88 lbs/in



But, like I proposed above somewhere that same 40% increase in tire spring rate with a modest unsprung weight of 40 lbs gives a change in the unsprung mass' natural frequency of nearly [B]19%[B], from 3.5 to 4.2 Hz.


sqrt(500 / 40) = 3.53 Hz ---->

sqrt(700 / 40) = 4.18 Hz



That's enough of a change to put you well in or out of oscillation under braking with not much anti-dive, or if your engine guys are giving you enough squeeze to set up an oscillation on accel.



I am gonna keep treating it as essentially a parameter, just one that you should not rule out when diagnosing handling problems. For the purposes of analysis I know we're not at the level where it will play a significant role just yet, so it can be filed away for now.

Ben, would you say that the effect is more important on much heavier vehicles though?

Best,
Drew

[The Stigg]

Hi Drew,

maybe you should take a closer look to the problem from a different point of view!
It's more common to design a suspension (incl. springs and dampers) to get the best out of your tires and not the other way around!

Maybe the Wheelrate doesn't change that much, but what about the roll camber comming from the vertical tire deflection which is in deed a pain in the ass?
And what about the differencies in the torsion and bending behaviour of the tire carcass while changing pressure, camber, stiffness, etc.

From my experience I can tell you one thing!
Don't overstate the influence of suspension kinematics and don't understate the influence of the tire.

The trade off is that tires are damn complex.

Regards Andy

[exFSAE]

In terms of effect of tire pressure buildup I'd still be more interested in how that 0.2 bar (or whatever) increase changes roll stiffness distribution, rather than ride frequencies.

Rear will probably build more than the front, too. For example if you started at 11 psi all around at 75F ambient, and wound up at 160F front and 200F rear. How much does it build up, how much does that change springrate, how does that change roll distribution and balance.

For the purposes of FSAE it's almost academic, with regard to how much other crap you have to worry about first, but it's worth bearing in mind.

[Drew Price]

Andy,

You are absolutely correct, and I agree with you 100%.

What I was responding to was the initial question about how tire rate affects wheel rate, and their interaction with each other, not the purpose of tire pressure and tire spring rate as a contributor to the behavior of the suspension as a whole, so I feel silly about that now, I should have been more clear.

What my response about taking the tire rate parameters as fixed should have read was: "Take the tire rate parameters as fixed after you determine what pressures / alignment / camber settings etc. that you want to run. What I was getting at was that during the design stage it's usually safe to look at a reasonable range of values and work from those. It's just because most of us don't have the ability to do any more than assume what the load distribution in the contact patch is doing at different pressures, and how the stiffnesses in the carcass should be affected without some pretty thorough tests.

What pressures yield the best result is definitely a part of the testing regimen, just like damper settings and spring rates and alignment are variables during a test session. You just have some set range of values you can give those variables, but after you narrow down what they are, they're basically fixed again. You should be able to (within a pretty narrow range) know what you need to set all those various things to once there is some time on the car.

And a day doesn't go by that I don't remind myself and the new people on my team trying to learn about suspension systems that the 'tires are damn complicated.'

I think we can all agree that's a pretty big understatement. Carroll Smith didn't call the tire engineers the 'Wizards from Akron' for nothing....

Best,
Drew

[ben]

Originally posted by Drew Price:

I am gonna keep treating it as essentially a parameter, just one that you should not rule out when diagnosing handling problems. For the purposes of analysis I know we're not at the level where it will play a significant role just yet, so it can be filed away for now.

Ben, would you say that the effect is more important on much heavier vehicles though?

Best,
Drew

You mean the effect of changing air pressure in the tyre?

It's not so much the weight of the car as what percentage of the load is carried by the air vs. the sidewall. On a big GT car 10% change in air pressure will give you pretty much 10% change in spring rate, same as an FSAE tyre.

Ben

[Drew Price]

Thanks Ben, that is what I was wondering.

I did not know if the tires meant for much heavier cars would carry more load in the sidewalls or not, I guess I figured that a more substantial sidewall might be needed for more lateral stiffness, so more of that must come from the carcass / cord structure than I thought.

Lots of reading to do over break!

Best,
Drew

[ben]

Originally posted by Drew Price:
Thanks Ben, that is what I was wondering.

I did not know if the tires meant for much heavier cars would carry more load in the sidewalls or not, I guess I figured that a more substantial sidewall might be needed for more lateral stiffness, so more of that must come from the carcass / cord structure than I thought.

Lots of reading to do over break!

Best,
Drew

You're right on more lateral stiffness. But you can add that in the base of the sidewall. Most of the vertical deflection occurs in the upper sidewall so if you go with a stiff belt, soft case and stiff lower sidewall you can make the vertical stiffness proportionately softer, still have good cornering stiffness and high lateral stiffness.

Why are radials better than cross plies? De-coupled stiffness.

Ben

[Zac]

Ben,
Does a radial really offer you much of an advantage for FSAE applications? I've only worked with bias-belted tires so I'm just curious.

[BillCobb]

The tire data supplied by TTC has tire vertical and lateral rate information vs. slip, load and camber in it. Might wanna watch the temperatures while doing this calulation. I would set pressure to get grip, run springs to stay within range of wheel travel. Design geometry to minimized steer curvature changes within this range of travel without ever bottoming out. I'm not aware of any major jounce hits to be concerned about in the FSAE events. Tire vertical rate to suspension rate ought to fall in the 3/1 to 4/1 ratio maybe??? (Just a swag, but you get the idea). The tire processing code I posted a few months back has tire rate calculation in it as I recall. If not, patch it in. BTW: a static rate tester won't give you the same values as rolling tire data will (That's ancient history, FYI).

[ben]

Originally posted by Zac:
Ben,
Does a radial really offer you much of an advantage for FSAE applications? I've only worked with bias-belted tires so I'm just curious.

Just to give you a quick overview of our development last year. We did a test with two Unis in the UK with a pretty stiff radial, much like the Michelin I suspect. It was too stiff and very peaky.

After that we knocked a ply out of it to take the spring rate down and we're now in the 500lb/in territory Drew assumed in his earlier post. I also reduced the belt stiffness in an effort to broaden the peak.

This tyre was run by Birmingham at FSG and by a number of German teams supplied by Dunlop Germany. The photo in the FS silverstone thread of the Birmingham car head on showing the lateral deflection highlights that although we had the right vertical rate, the lateral stiffness was probably a little on the low side.

Last month I stiffened the lower sidewall of that construction to reduce the lateral deflection without stiffening the tread area.

We also tested a new compound on the old case, which was better and will be combining the two in January and trying one more compound to determine the final spec for 2009.

To answer your question - yes. I do think the ability to decouple the stiffness' within the tyre is useful, even for FSAE. The crucial thing for me is to have the tyre progressive enough to be drivable - and I think we've achieved that.

Plus not many decent race series outside of FSAE race crossply any more so the students I'm working with have a better idea of how your average GT or LMP race tyre behaves and that has value IMO.

Ben

[ben]

Originally posted by BillCobb:
The tire data supplied by TTC has tire vertical and lateral rate information vs. slip, load and camber in it. Might wanna watch the temperatures while doing this calulation. I would set pressure to get grip, run springs to stay within range of wheel travel. Design geometry to minimized steer curvature changes within this range of travel without ever bottoming out. I'm not aware of any major jounce hits to be concerned about in the FSAE events. Tire vertical rate to suspension rate ought to fall in the 3/1 to 4/1 ratio maybe??? (Just a swag, but you get the idea). The tire processing code I posted a few months back has tire rate calculation in it as I recall. If not, patch it in. BTW: a static rate tester won't give you the same values as rolling tire data will (That's ancient history, FYI).

Just a quick point Bill - for lateral rate would you just divide Mx by Fz to give a lateral offset to the centre of pressure in the contact area and then divide lateral force by this offset to give lateral stiffness?

Ben

[Zac]

I think that would work pretty well at low loads, but at higher loads the Mx signal goes through a sign change once the carcass camber effect comes in to play.

Also as a caution to any teams doing static springrate tests. Make sure that you test at a couple different orientations. The location of splices in the tire construction can have a pretty significant influence on your results.

[ben]

Originally posted by Zac:
I think that would work pretty well at low loads, but at higher loads the Mx signal goes through a sign change once the carcass camber effect comes in to play.

Also as a caution to any teams doing static springrate tests. Make sure that you test at a couple different orientations. The location of splices in the tire construction can have a pretty significant influence on your results.

That's what I was getting at - i was looking at some CALSPAN data the other day. Another one for Bill - are you just using that approach to lateral stiffness up until that point?

Spring rate-wise our procedure is to use an internal drum and do it as a dynamic rate, I tend not to look at static rates.

Ben

[BillCobb]

Vehicle simulations I was writing used the data right off the machine (converted to a B-spline form). Therefore the Mx tendencies were preserved, including the pneumatic scrub and the sign change characteristics. This produced the phenomena we called "snap thru" which is perceived as a 2 stage lateral response, especially at the back end of a fwd car (light rear loads (get it?). Note that the traditional tire models (Pacejka, etc) lost this trait because the model doesn't contain the patterns found in actual Mx data. Then there was the brand issue. I often felt that some tire manufacturers used this tire property to attain a specified 1 degree cornering coefficient requirement, even though the stiffness was off target. Since the vehicle operates off of stiffness, tires with higher cornering coefficients were often found to be ranked lower subjectively. The simulations showed why. There are some other transient properties that are tied to the Mx data, including the tractive force response of a fwd vehicle with a high torque motor on launch. The Mx is in effect, a dynamic scrub radius modifier. As I mentioned, some brands consistently roll this one "better" than others.

BTW, I thought this topic was a bout VERTICAL stiffness....

[exFSAE]

Originally posted by BillCobb:
BTW, I thought this topic was a bout VERTICAL stiffness....

And we thought Corvettes weren't towing vehicles...

Things happen. Just sayin.

[Zac]

To be fair those corvette tires have enough load capacity to be used on an earth mover.