Wheel loads problems(statically indeterminent?) and roll stiffness calculations

[Yunlong Xu]

Hi Guys. My question here originated from my experience in the FSUK event this year.

The night before the dynamic events, we suddenly realized that the two springs on the front suspensions are not as long as each other! (I know it’s ridiculous. ). When we put our car on four Sainsbury’s basics scales, we get a funny weight distribution of about: FR: 100kg, FL: 65kg, RR: 65kg, RL: 100kg. (yes we have a very chunky car…it’s not the driver’s fault). At first we thought this could be the problem with the scales so we borrowed the sets from someone else and did it again. Surprisingly we had pretty much the same result. This put us into some serious thinkings…

The first thing we realised was that when thinking about force and moment equilibrium only and not using symmetry, the wheel load in static is in fact statically-indeterminent?! (you have four forces to solve but only three equations). Which means the actual loads depend on the compatibility and hence we need to include deflections in the calculations. And therefore the load distribution on the four wheels relies on the structures of the car as well, which means theoretically the deflections of the upright, control arms, push rods and chassis, etc all have their influences on the load distribution!

Is that true? If so then how big the influences are on the load distribution? Surely we’ve already demonstrated what unequal spring rates can do in our tragic case, but what about other stuff like the push rods, or the chassis?

I tend to think that is true because when I think about the distribution of lateral load transfer during cornering, the roll stiffness of the front and rear axles are definitely very important variables!

This also leads to one extra question of mine: How do we actually calculate the roll stiffness? Do we first convert the spring, rocker and pushrod assembly to an equivalent vertical spring connecting the chassis and wheel by using the installation ratio and then calculate the roll stiffness from that? If so, is that true we don’t need to take into account of the tyre springs because the roll motion that we are talking about is just the roll of the sprung mass (chassis) relative to the suspension system?

Any comments

Cheers

Yunlong

[Rear Admiral]

your car may not be aligned correctly

[Philipp Bachmann]

Hi Yunlong,
unequal springlength on one axle doesn`t influece the springrates that much, but your static and also dynamic wheel loads. You already have scales to check every wheelrate? Then you have to adjust them by changig pushrod length or the pretension on your springs. In your example you have to shorten the front right pushrod, or setup the front left pushrod longer. But you also can change your front wheel rates by seting your rear pushrod lengths. (in the example: shorten the left pushrod)

After you have the same LR:LF ratio as RR:RF
(if not, your car is heavier on one side) you have to check your ride height on both sides. Is your car lower on the left you can lower both right pushrods and so on...

If your car isn´t setup properly your car handling is different in right and left corners! (my name for that is "tweak" :-D)

And again, your spring rates are not that wrong, but your "pretension" of your springs

[jrickert]

Design the car to be as close to symmetric (left to right) weight distribution as possible. Standard practice is to Adjust your suspension with the car on scales so that your cross weights are equal.

[exFSAE]

I don't even think they run that much cross weight in NASCAR...

For one, measure your actual spring rates on an Instron or something similar. You may be surprised, with 4 springs marked "200 lb/in" how much variation there is (which will majorly effect static corner loads).

Likewise, manufacturing reality will affect your installation ratios which will further change your true wheel rates. You can measure your true installation ratio by removing the springs from the dampers, propping the chassis up, and comparing wheel movement to shock deflection.

Beyond that, you may want to take an alternate approach to analyzing the state of the car, and corner loads. What if you defined the chassis orientation as a function of heave displacement, pitch angle, and roll angle? Those 3 variables should simultaneously define your "corner spring" displacement (and loads). Then you're just writing out a system of equations relating that to your force and moment balance for Fz, Mx, and My.

[Yunlong Xu]

Thanks for the reply guys, but I don't think our car has got a cross weight problem. Maybe I didn't express it clearly, but the static weight distribution of our car was like this:
http://i27.tinypic.com/2ewiqzd.jpg

This in fact shows that we have 50:50 front to rear weight distribution and 50:50 left to right. But the way they were distributed in between them wasn't quite ideal.

The unequal length of the srpings meant that they had different spring rates(and we did test this!). I assumed what happend was that:

--The front rolled away from the longer front suspension srping but still had that longer srping compressed(This is very important! thinking of the front end as it started in an inclined angle since one of the srping is longer. The front end then rolls back towards the horizontal position but still hasn't reached it. In this way, the front end will experience a moment from the suspension srpings in an opposite direction to what normal cars will exeprience in the same roll direction.

--The rear rolled in the same direction and behaved like normal cars in roll.

The result of this was that although the front and rear rolled in the same direction, the moment exerted on them from the srpings were in opposite directions! and hence caused opposite weight distribution of the front and rear axles!

Any opinions on that?

[GSpeedR]

Your static wheel loads are indeterminate until you define a crossweight (many FSAE teams desire 50% for symmetry). Yes, the steady-state wheel loading is dependent on the distribution of wheel rates about the vehicle.

"Roll stiffness" is technically defined as the roll torque per degree of roll between the sprung mass and the axle/unsprung masses by SAE, I believe. However, your static and dynamic wheel loads are dependent on the rates to the ground so you will want to calculate your stiffnesees with respect to the ground.

[Bazanaius]

A bit more clarification from one of the guys on the team...

it turns out that the two springs on the front were entirely different. I probably don't need to refer you to the Risse Racing thread to explain this... :-P

having discovered this, we replaced the springs in time for the next event and managed to get things much closer in terms of cross weight. total L:R distro was nearer 50% (realistically our back of the envelope packaging probably accounts for any discrepancies) and F:R was pretty close to design of 48:52. Cross weights were still off by an amount that was perhaps a little more than I'd be willing to attribute to our <STRIKE>bathroom</STRIKE> scales..

we never really got down to exactly what was causing this, but I'd certainly have liked to do some installation stiffness tests to see just how much of an effect this was having on our wheel rates.

nb we certainly designed for symmetry in the cross weights, so I'd imagine Dave's idea of wheel rates being the cause is sensible?

[Yunlong Xu]

Thanks Barney for clarifying that!

This in fact shows that we have about 50:50 front to rear weight distribution and 50:50 left to right. But the way they were distributed in between them wasn't quite ideal.

The unequal length of the srpings meant that they had different spring rates(and we did test this!). I assumed what happend was that:

--The front rolled away from the longer front suspension srping but still had that longer srping compressed(This is very important! thinking of the front end as it started in an inclined angle since one of the srping is longer. The front end then rolls back towards the horizontal position but still hasn't reached it. In this way, the front end will experience a moment from the suspension srpings in an opposite direction to what normal cars will exeprience in the same roll direction.

--The rear rolled in the same direction and behaved like normal cars in roll.

The result of this was that although the front and rear rolled in the same direction, the moment exerted on them from the srpings were in opposite directions! and hence caused opposite weight distribution of the front and rear axles!

Any opinions on that?

[Jersey Tom]

Originally posted by Yunlong Xu:
Thanks for the reply guys, but I don't think our car has got a cross weight problem. Maybe I didn't express it clearly, but the static weight distribution of our car was like this:
http://i27.tinypic.com/2ewiqzd.jpg

I'd call that an enormous cross weight problem.

[GSpeedR]

Originally posted by Yunlong Xu:
Thanks for the reply guys, but I don't think our car has got a cross weight problem. Maybe I didn't express it clearly, but the static weight distribution of our car was like this:
http://i27.tinypic.com/2ewiqzd.jpg

This in fact shows that we have 50:50 front to rear weight distribution and 50:50 left to right. But the way they were distributed in between them wasn't quite ideal.

The unequal length of the srpings meant that they had different spring rates(and we did test this!). I assumed what happend was that:

--The front rolled away from the longer front suspension srping but still had that longer srping compressed(This is very important! thinking of the front end as it started in an inclined angle since one of the srping is longer. The front end then rolls back towards the horizontal position but still hasn't reached it. In this way, the front end will experience a moment from the suspension srpings in an opposite direction to what normal cars will exeprience in the same roll direction.

--The rear rolled in the same direction and behaved like normal cars in roll.

The result of this was that although the front and rear rolled in the same direction, the moment exerted on them from the srpings were in opposite directions! and hence caused opposite weight distribution of the front and rear axles!

Any opinions on that?

Nope. Load is transferring in the same direction for both axles unless you are striking a curb or are experiencing additional external forces (aero/banking). The fact that you have different spring rates across an axle does not change the resistive moment applied to the chassis...both the inboard and outboard spring resist roll so long as there is positive load on their respective tire.

Edit: I misunderstoodyour post and thought you meant during cornering...not static.

[Yunlong Xu]

To Jersey Tom,

Sorry, maybe I didn't quite understand what a cross weight is... I thought it was the weight bias towards on side of the car.

To DohertyWins!,

I still think it is possible for the resistive moment to be in the opposite direction.

Imagine, now all the four srpings are in their original length so no moment is applied to the chassis.

The front: Since the front springs are different in length, so it rolls an angle (say 10 degrees clockwise) even under no load at all

The rear: Stays horizontal as it should do.

When the loads are applied, the front rolls 5 degrees anti-clockwise and the rear rolls 5 degrees clockwise so the whole chassis stays 5 degrees clockwise. In this scenario, the front and the rear will experience opposite resisitve moment since they've rolled in opposite directions from the original position.

Of course this is just a made-up scenario, but I'm just trying to say that opposite static lateral load distribution on axles can happen in circumstances like ours

[Zac]

Imagine, now all the four srpings are in their original length so no moment is applied to the chassis.

The front: Since the front springs are different in length, so it rolls an angle (say 10 degrees clockwise) even under no load at all

The rear: Stays horizontal as it should do.

When the loads are applied, the front rolls 5 degrees anti-clockwise and the rear rolls 5 degrees clockwise so the whole chassis stays 5 degrees clockwise. In this scenario, the front and the rear will experience opposite resisitve moment since they've rolled in opposite directions from the original position.

How is the front suspension going to roll more than the rear?

[Jersey Tom]

Originally posted by Yunlong Xu:
To Jersey Tom,

Sorry, maybe I didn't quite understand what a cross weight is... I thought it was the weight bias towards on side of the car.

Cross percentage is how much load is taken up by one diagonal. I use RF + LR. In your case, 60.6%. That's huge.

It's generally used on oval racing. High cross percentage through a left corner means excellent power-down at the expense of mid-corner understeer. It does have some application on road courses, depending on the the track layout and critical corners. Lime Rock Park might as well be NASCAR in reverse.

In your case if you take the car on a skidpad I bet it understeers left and oversteers right, all other things being equal.

[Philipp Bachmann]

Hello Yunlong Xu,
you should do exactly, what i described in my first post. This should solve your Problem, and your crossweights should be the same.

[ben]

Originally posted by Jersey Tom:
Lime Rock Park might as well be NASCAR in reverse.


Road America too, although less obviously from a quick look at the track map.

Ben

[Bazanaius]

Just to butt in again, Philipp this is exactly what we did :-) Replacing the front springs with two that were the same stiffness and length helped enormously in getting the pretensions the same!

I don't think Yunlong was there when we did that, so he might not have been aware.

Back to leaving alone...

[Jersey Tom]

Thought about this... this shouldn't be statically indeterminate should it? If you set the wheel rates (which are in effect the "compliances") you can solve for the corner loads at any heave, roll, and pitch displacement (or applied Mx, My, Fz).

[Zac]

You're only half right. You need to use the wheel rates to figure out your deflections (ie. using compatibility equations), but the problem is statically indeterminate since you don't have enough equations to solve for the loads just by summing forces and moments.

You could also use Castigliano's theorem.

[Jersey Tom]

Funny that I have this handy Matlab code that solves this indeterminate problem in the manner I outlined above...

[Zac]

I'm not saying your method isn't capable of solving a statically indeterminate problem (the contrary actually!), just that this is a statically indeterminate problem.

[Jersey Tom]

True fact. So yea. Compatibility is key, but you don't necessary need to get to the level of upright and bearing compliances.

http://img.photobucket.com/albums/v163/Gamer674G/nbc_the_more_you_know.jpg

[Yunlong Xu]

Hi guys, thanks for the tips.
I agree with what Zac is saying. I believe this is a statically indeterminent problem.

"Statically indeterminent" refers to problems that can't be solved by equilibrium only(equilibrium of forces and moments). And statically indeterminent problems are normally solved by combined equations of equilibrium and compatibility (deflections, extensions,etc and as in your method, the body roll angle)