Roll center and effect on roll stiffness 3

[PAG24]

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?

 

[KevinK2]

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?

 

[NormPeterson]

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

 

[KevinK2]

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?

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.

.

 

[NormPeterson]

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

 

[KevinK2]

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.

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?

.

 

[KevinK2]

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

.

 

[WolfHR]

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.

 

[NormPeterson]

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

 

[cibachrome]

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.

 

[KevinK2]

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

 

[KevinK2]

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!