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# Roll center and effect on roll stiffness3

## Roll center and effect on roll stiffness

(OP)
As we all know, the roll stiffness ratio effects the load transfers during steady state cornering (Why changing anti roll bars effect handling)

If we have a roll center on the ground, then the full lateral forces from corning acting through the CoG is 100% taken by the spring/dampers and the roll stiffness is calculated from the springs and anti roll bars.
Now if the roll center is at the same height as the CoG then all the cornering forces go through the suspension arms and the spring/dampers take nothing (Hence no roll)
Doesn't this mean the roll stiffness is now infinity? (taking the stiffness of the metal to be infinite?)

So doesn't this mean that a changing roll center height will change roll stiffness and hence change the handling?

I've always been taught that you take the stiffness ratio eg if the total stiffness at the front is 60kn/nm and the rear is the same then roll stiffness is 50/50.

But then this would only be true if the roll center is on the ground?

### RE: Roll center and effect on roll stiffness

While it's true that you would have to use an antiroll bar of infinite stiffness to achieve zero body roll with low roll centers, the effects on the vehicle are nowhere near the same. Consider what happens when the vehicle goes over a one-wheel bump, for example. In both cases, the effects are bad. With a low roll center but infinite antiroll bar, there is no jacking or side-stepping but the wheel that didn't hit the bump is forced off the ground (and, that side of the vehicle now falls down by gravity while the vehicle as a whole gets driven upward by the compressed springs, leading to some nasty ride motions). With an excessively high roll center but weak springing, there is considerable side scrub on the tires and the vehicle body is kicked sideways.

The rule of thumb that you are using falls apart if you are examining the case of a roll center which is excessively high, as you have noted.

Real vehicles aren't designed with suspension having infinite roll stiffness and, for the most part, they aren't designed with excessively high roll centers.

### RE: Roll center and effect on roll stiffness

OP You are confusing roll gain and roll stiffness. If you hold the body still, and move one wheel up and on  wheel down, you are measuring that axles roll stiffness, which is obviously not infinite, whereever the RCH is.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies  http://eng-tips.com/market.cfm?

### RE: Roll center and effect on roll stiffness

(OP)
I understand the difference in a straight line will obviously be different but I am not talking about that. Ill try to rephrase my question better as I've seem to missed the mark.

If we take a steady state corner condition. So corner of x radius with y constant speed (Not accelerating) and we have a vehicle that is completely symmetric, same track width front and rear and CG in the very middle of the wheelbase and the roll stiffness is 0.5.

Then the lateral load transfer for the front wheels will be the same for the rear wheels.

If we have the same tyres then the slip angles of the tyres will be the same and the car will be said to have neutral steering.

But now if we increase the roll stiffness at the front by increasing the stiffness of the anti roll bar or by increasing the stiffness of the springs at the front, then we will have more load transfer at the front, and less load transfer at the rear.

This will cause the front slip angle to be greater and rear slip angle to be less and will cause the car to understeer.

Now... My question is, if we raised the front roll center to the CG height then in this steady state corning condition the rear springs wont get to compress at all because the front suspension setup wont let the car roll at all.
This would cause a massive load transfer at the front and relatively little load transfer at the rear correct?

### RE: Roll center and effect on roll stiffness

Absence of roll due to making the roll moment arm equal to zero is not the same thing as making the roll zero via infinite roll stiffness.  The first item addresses whether a roll moment is even going to exist, the second defines how much roll will be caused if the roll moment is nonzero.

If you only move the front RC up to CG height, while leaving the rear RC at whatever presumably lower height it's starting out at, you will still have some roll, which will divide its lateral load transfer effect according to the relative roll stiffnesses.

Your LLTD would still be heavily front-biased.

Norm

### RE: Roll center and effect on roll stiffness

(OP)
(assuming the tyres and chassis are rigid) and you set the roll axis coincident with the CG to get no roll.
Does the roll stiffness ratio still come into play when working out the lateral load transfer?
If it does how? as this I can't understand yet and if it doesn't then will the load transfer for front and rear be the same regardless of springs/ARBs used for a symmetric car?

### RE: Roll center and effect on roll stiffness

#### Quote:

I've always been taught that you take the stiffness ratio eg if the total stiffness at the front is 60kn/nm and the rear is the same then roll stiffness is 50/50.

But then this would only be true if the roll center is on the ground

Assuming the vehicle to be a reasonable approximation of a rigid body, LLTD is the sum of at least three significant effects, two of which are purely static force resolutions not involving any sort of stiffness (i.e. fully statically determinate).  Work out the load transfers from each of the three effects individually first before attempting to arrive at the total.

Norm

### RE: Roll center and effect on roll stiffness

In the original hypothetical, there is no roll and the weight transfer is based on front and rear CG's and their distance from the ground. The wheel rates, and the roll stiffnesses, can be anything. Consider a cube with a shaft through the center ... subject it to lateral acceleration and there is no tendency for it to want to roll (ignore aero effects).

Yes, if front roll stiffness is 50% of total, Then it's a 50/50 distribution, front vs rear.

This is my way of answering the OP, sorry if repetitive.

Kevin

### RE: Roll center and effect on roll stiffness

" You need to set the roll 'axis' coincident with the cg to get no roll of the sprung body."

Greg, this was always a bit unclear to me... I've seen Carroll Smith's explanation how to obtain inclination of the roll axis in side view, and it didn't 'feel right'; and I've seen explanations with different CoG heights for 'front' and 'rear' sprung mass and that RCs should be at equal distance from their respective CoG (I presumed something like the car was sliced at CoG and then CoG for front and rear part being calculated), but wasn't sure about it.

I've always wondered if this would mean that roll axis should be (in side view) parallel to the car's primary axis of inertia (or that of sprung mass)?

### RE: Roll center and effect on roll stiffness

From my post:

"In the original hypothetical, there is no roll and the weight transfer is based on front and rear CG's and their distance from the ground."

Should be .."front and rear roll centers", not CG's

Wolf: The roll and CG axes do not need to be parallel to ecah other, or to the ground, for sideview. They typically never are. You need the front CG and rear CG, to establish the CG axis and the CG location on that axis. The other axis is based on F&R roll centers. The roll couple is based on the unsprung mass times the vertical distance from the CG to the roll axis. The roll couple will then be reacted at the front and rear, based on relative roll stiffnesses.

The chassis is assumed to be at least 10X any local rate.

Puhn fan, Kevin

### RE: Roll center and effect on roll stiffness

The roll axis IS usually set parallel to the car's primary sprung mass inertial axis.  And, ITS inclined because the masses and inertias of the dominant pieces that make up the vehicle's inertial axis tensor give it such a characteristic. That would be the motor and transmission to name 2.  Forget about the windshield wipers...

### RE: Roll center and effect on roll stiffness

Cibachrome, what is wrong with my descrption of how to set up these two independent axies, per the Fred Puhn method. I'm an engineer and car builder/racer, and saw no flaw in this approach to determining these axies.

### RE: Roll center and effect on roll stiffness

Your statment about roll stiffness when the roll axis at the cg (actually the sprung mass cg) is incorrect. It just means that the moment arm is zero so that any or NO roll constraint is necessary to keep the sprung mass upright.

My bass boat anti-rolls during high speed cornering.  Does that mean that the water provides negative roll stiffness?

The sprung mass is an inverted pendulum.  It would fall over if there was no restraint.  So why don't cars have very high roll centers?  Because the structural reaction loads can be huge, the sensation of confidence is overwhelming, and the likelyhood of exceeding the friction capability of the surface is very likely.  Plus roll kinematics are a great way to tweak insufficiencies in tire or suspension compliances and oror delta payload demands on handling.  Even your race car has a full and empty gas tank load condition.  Did you mount the tank at the roll axis centerline, I hope?

Keeping the roll axis aligned with the inertia ellipsoid (and near it) cuts down the mr^2 component of roll ineria.  So the dynamic roll reaction dances better.

### RE: Roll center and effect on roll stiffness

Plus the jacking effect, I would think (about high roll centers)... Throwing away lateral force to jack up the suspension rather than to generate centripetal force.

As for roll axis, I would think guys at Caterham know a bit or two about the cars, and their car with deDion and IRS have quite a bit different inclination (ISTR that IRS model has 30mm higher rear roll center, while deDion twice as much). Not that I'm making a point here- just a food for thought...

### RE: Roll center and effect on roll stiffness

It is very misleading to compare roll centre heights for an IRS and a live axle.

Which rather reinforces my general opinion that RCH is damn close to being a busted concept.

Variations in GRC on a particular suspension seem to correlate to useful changes in measured parameters, but if you were to set an IRS up to a RCH = to the SLR of the tire, you would be an unhappy camper, yet it works perfectly well on a beam axle.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies  http://eng-tips.com/market.cfm?

### RE: Roll center and effect on roll stiffness

"Your statment about roll stiffness when the roll axis at the cg (actually the sprung mass cg) is incorrect. It just means that the moment arm is zero so that any or NO roll constraint is necessary to keep the sprung mass upright."

I said: "The wheel rates, and the roll stiffnesses, can be anything."

What's wrong there?

"The sprung mass is an inverted pendulum.  It would fall over if there was no restraint."

A rock supported by a needle would be unstable. If a typical car was stripped of all unsprung elements, and just supported by pins at the upper coil spring perches, it would be stable. It would be unstable if you tried to support it on a long, longitudinal 2x2 below it, if that's what you are implying.

"The roll axis IS usually set parallel to the car's primary sprung mass inertial axis"

Does not sound right. I think that at turn in, the mass polar momment of inertia of the sprung weight, relative to the roll axis set by roll centers, will initially resist body rotation. But for steady state cornering, that polar moment has no effect, and the roll couple will be based on the distance from the sprung weight to the roll axis based on roll centers.

.

### RE: Roll center and effect on roll stiffness

#### Quote:

It would be unstable if you tried to support it on a long, longitudinal 2x2 below it . . .

Isn't that precisely what you are assuming with a LLTD model that sums the load transfers through the geo roll centers with the load transfers through the elastic elements and whatever contribution comes from the unsprung masses?

#### Quote:

If a typical car was stripped of all unsprung elements, and just supported by pins at the upper coil spring perches, it would be stable.

Try to avoid confusing mathematical modeling or structural stability definitions with the absence of roll.

Commonly, a pin support is assumed to have high stiffness in its direction of constraint.  But if you're trying to prove that roll stability exists in the absence of roll stiffness you have to construct your model such that in total it actually has zero (or at most, negligible) roll stiffness.

What do you suppose would happen to the sprung mass orientation in 3D space if you were to release those four pin stiffnesses to very low values but somewhat higher on one side than on the other?  Mathematically, it would still meet the definition of being a stable structure (wouldn't rotate indefinitely about some axis), but you would see more than just heave motion.

Norm

### RE: Roll center and effect on roll stiffness

Edit last sentence to rear

It would still meet the definition of being a stable structure mathematically (you wouldn't be trying to divide by zero, and a computer solution shouldn't show it rotating indefinitely about some axis), but you would see more than just heave motion.

### RE: Roll center and effect on roll stiffness

Thanks for the response Norrm.

First a correction on my last post, last sentence:

"distance from the sprung weight" should be:
"distance from the sprung weight CG"

Norm, the stability issue was a tangent to the main subject of the post, but I see your points.

The softened Y DOF spring supported 3d model is a good thought analysis. first, you would need to minimally constrain other dof's with extremely soft springs. With other convergence tools to be able to run, I would guess the body would wind up hanging off the stiffer springs, with the softer spring pair at lowest points of support. I agree that infinite rotation does not come to mind, but it really is not important, as you said:

" Try to avoid confusing mathematical modeling or structural stability definitions with the absence of roll."

Norm, I'm more interested in comments about my other points in that post, or is there a forum rule about that type of threesome?

### RE: Roll center and effect on roll stiffness

#### Quote:

I think that at turn in, the mass polar momment of inertia of the sprung weight, relative to the roll axis set by roll centers, will initially resist body rotation. But for steady state cornering, that polar moment has no effect, and the roll couple will be based on the distance from the sprung weight to the roll axis based on roll centers.

The sprung mass's mass moment of inertia about its longitudinal-ish axis (that, I agree, would tend to resist acceleration in roll - as well as tending to cause overshoot in roll beyond the steady state attitude) isn't the same thing as the distribution of roll moment along some notional roll axis from some notional mass centroid axis.

The mass MOI effects are transient, but to the extent that the general and local chassis torsional flexibilities affect the final distribution of lateral load transfer, the centroid axis matter also affects steady state.  Loads divide according to the stiffnesses of the load paths (which go all the way down to the contact patches), and it's probably better if you don't have to crutch a less than stiff chassis with a needlessly stiff suspension at one end.

There isn't any forum rule about having to reply to a post in its entirety all in one shot either.

Norm

### RE: Roll center and effect on roll stiffness

#### Quote:

The sprung mass's mass moment of inertia about its longitudinal-ish axis (that, I agree, would tend to resist acceleration in roll - as well as tending to cause overshoot in roll beyond the steady state attitude) isn't the same thing as the distribution of roll moment along some notional roll axis from some notional mass centroid axis.

By distribution, do you imply front and rear roll moments?

By notional, do you imply they don't exist, theoretical or actual?

#### Quote:

The mass MOI effects are transient, but to the extent that the general and local chassis torsional flexibilities affect the final distribution of lateral load transfer, the centroid axis matter also affects steady state.  Loads divide according to the stiffnesses of the load paths (which go all the way down to the contact patches),

Which "centroid axis" ?

I thought with a "torsionally stiff" chassis, where the F to R torsional rate is 10X+ any equivenant front or rear local wheel rate, it was sufficent to just use the distance between the roll axis and the sprung WT CG (on a normal vector) to develop the total roll couple. This would not apply to typical convertables.

For a flexible chassis, I can see adding a torsioal spring rate between F and R wheel rates, for a simplifed closed form solution, with no need to consider any axis related to the MOI, if that's what you meant. A simple FEA beam approach would consider incremental loads and stiffnesses, from front to rear wheels.

.

### RE: Roll center and effect on roll stiffness

#### Quote:

By distribution, do you imply front and rear roll moments?
No.  I'm referring to what you'd draw up with the roll axis modeled as a torsionally loaded beam, with the effects of all of the infinitesimal longitudinal length masses and their eccentricities plotted as a non-uniformly distributed torsion.

Notional, because they aren't "real" axes about which anything actually rolls.  Because a mass centroid "axis" is likely to be anything but straight, and because its distance from the roll axis tells only part of the story.  The value of considering them at all lies in distinguishing mass moment of inertia in roll effects from a very detailed picture of chassis torsion caused by steady state lateral inertial loading.

By "centroid axis" I was referring to that mass centroid axis, as that is where the chassis torsion in steady state cornering is coming from.

10x may or may not be appropriate, never mind that a car that meets a 10x criteria in stock form may not when its suspension tuning is substantially modified for competition.  At which time you might prefer a greater than 10:1 ratio for "efficiency of chassis tuning" reasons if the rules permit you to do what it might take.

Norm

### RE: Roll center and effect on roll stiffness

#### Quote:

I'm referring to what you'd draw up with the roll axis modeled as a torsionally loaded beam, with the effects of all of the infinitesimal longitudinal length masses and their eccentricities plotted as a non-uniformly distributed torsion.

#### Quote:

Because a mass centroid "axis" is likely to be anything but straight, and because its distance from the roll axis tells only part of the story

I think I see your points ... mabe

For a 2d straight beam approximation of the sprung weight, including front and rear roll stiffnesses as end constraints, say 100+ beam elements were used to model the sprung chassis. Each element would have a torsional stiffness, and an offset mass center.

Can I then assume the roll axis, for determining all the torsional loads/couples on each unsprung chassis beam element representation, has ends at the front and rear instant roll centers, assuming small rotation and constant roll centers?

.

### RE: Roll center and effect on roll stiffness

#### Quote:

From Norm: -> Absence of roll due to making the roll moment arm equal to zero is not the same thing as making the roll zero via infinite roll stiffness.  The first item addresses whether a roll moment is even going to exist, the second defines how much roll will be caused if the roll moment is nonzero.

If you only move the front RC up to CG height, while leaving the rear RC at whatever presumably lower height it's starting out at, you will still have some roll, which will divide its lateral load transfer effect according to the relative roll stiffnesses.

Your LLTD would still be heavily front-biased.

This would be my exact response too. Why do you think this Fred Puhn (how to make your car handle) approach, which I have been describing and I used for years, is wrong? I used this method to designed and build a small rear sway bar (9/16") that made a big improvement on my tracked D-Production GT-6 with a transverse leaf spring with all but one leaf allowed to pivot at the connection to the top of the diff'l.

Also, what does GRC and SLR stand for?

Thanks

.

### RE: Roll center and effect on roll stiffness

KevinK2- I'd say GRC would be geometric roll center (as opposed to force roll center), and I understood SLR to be static loaded radius.

### RE: Roll center and effect on roll stiffness

#### Quote (KevinK2):

Why do you think this Fred Puhn (how to make your car handle) approach, which I have been describing and I used for years, is wrong?
I don't recall suggesting that his method is way off the mark, although since it is a model set up at 0° roll there will of necessity be some error introduced by however much roll is developed and how much the geo roll centers migrate as a result.

It is also simplified in that the entire sprung mass is lumped at one point.  The stiffer that your suspension becomes, relative to the chassis, the greater the error introduced becomes.  Like you said, convertibles (but they might not be the only cases).

What I was getting at was closer to replacing that single mass "lollipop" with perhaps a hundred of them (might as well use your number) taken at stations along the chassis, all with different mass values and eccentricities.  Now visualize a 3-D curve drawn through them all.  The rotational inertia effect of the lollipop balls about themselves as far as steady state is concerned is, of course, zero.

Another way of looking at the condition where roll is nonzero is that the geometries of the left and right sides of an independently sprung pair of wheels are no longer symmetrical.  This implies that the relationship between load transfer carried geometrically and load transfer carried elastically is not fixed like the Puhn model assumes.  Further, I'm pretty sure that this effect can be noticed from the driver's seat if you make a big enough roll stiffness change.

Norm

### RE: Roll center and effect on roll stiffness

Actually, you don't need a hundred elements you only need about 4.  I started out with 16,000 and eventually whittled it down to the basics. (see http://papers.sae.org/790376/)

The front suspension section, passenger compartment section, rear kick up and rear suspension areas are the low hanging fruit in studying this issue.  The rear kick up is often the major player in many architectures because of the need to package the rear wheelhouse.

In studies (like that shown in the SAE example), the geometric roll center concerns become apparent as the g levels get near the maximum sideforce.  To do the studies properly, you also need to run K&C type tests iteratively with corresponding handling model forces and moments applied for the next iteration and on and on.  This is referred to as 'bootstrapping': You get some initial compliances, put them into a handling model, recover all tire forces and moments, apply these to the next compliance test, recover the next set of compliances, rerun the handling model and carry on thru for a few more iterations, advancing the g-level as you go along.

In the NASTRAN example case, I also used Solution2 (inertia relief).  This applies lateral forces and aligning moments to the element assembly as if it were in a force field.  The net result is a 2D plot of the distorted body/frame model showing where and how much bending is occurring. Then you can condense out the modes doing the most movement and build up your 4 or 5 element equivalent package and make up some braces to fix the real vehicle. Your other choice would be to somehow accurately estimate the sectional properties of each portion of the vehicle. The matchboxing view of the body/frame is usually the most eye-opening. It often makes people run out and want to start stringing cross cables under the car to keep it square. And, it works!

All this boils down to a recommendation to use a lateral load transfer based roll center approximation instead of a geometric one.  If you have an asymmetric suspension at either end (like a Panhard bar for example), you have no other choice if you want accurate answers. The proof is in the comparison of model results versus road test results. When they agree, the methodology gets hardened up and confidence in the approach will be high.

Obviously the use of solid body mounts, tube frames, solid engine mounts and spherical chassis ball joints lessens the need for any of this. But, you'd be surprised at all the flexing that can occur at a steering gear mount, front upper control arm mounts, or strut rods, etc, which if not addressed, can really screw up your day at a race track.

### RE: Roll center and effect on roll stiffness

Thanks for the detailed responses Norm and Ciba*.

Ciba, I did use Nastran for my design of Lance's 3-spoke wheel(attached), and gave a paper at an MSC conference in LA about the inconsistencies in buckling prediction using 3 different Nastran methods. Also used it in one of the 1st efforts to model thread stresses in a breech loacked high pressure vessel, and co-authored an ASME paper under "Ed Perez, et al".

I need to take a bit of time to carefully study your latest, generous contributions to my understanding of suspenson analysis.

Thanks again, Kevin

### RE: Roll center and effect on roll stiffness

Note that the wheel project managers, Mark and Frank, tried to take credit for the wheel design using a Cray, for the Bicycling Magazine article. I suspected this would happend, so I put my name in very large font on the screen shot!

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