roll centers

[Schumi_Jr]

I have a few questions about roll centers...
first, why does a lateral migration of the roll center cause the spring rate of that side to effectively increase? Second, why does a roll center below ground cause a weight transfer from the outside to inside tire (obviously to a lesser extent from that of the weight transfer from the inside to outside tire due to the centrifugal force on the chassis )?

I must have a flawed perception of what a roll center is, can someone answer these questions or refer me to a book (besides Milliken, Dixon and Smith) thanks!

[danW]

Here is my simplified explanation.

The major contributor to weight transfer is the sprung weight.

The roll center is the point that the sprung mass (at that end of the car) is rolling or pivoting about at that instant. The roll center is idealized as a pin joint (ie reacts forces but not moments).

In a cornering situation, the side force on the sprung mass is reacted by the suspension at the roll center. The weight transfer due to sprung weight(at that end of the car) is the moment due to the side forces and the distance between the cg of the sprung mass and the roll center.

Drawing freebody diagrams of the sprung mass and the suspension will show you how the roll center affects weight transfer.

Remember, you shouldn't just focus on the front and rear suspensions independently. Roll center movement not only affects traction at one end but also affects the front to rear traction balance of the car.

I hope that helps!

[Jeff Curtis]

The lateral-anti method is currently the preferred method of calculating non-rolling weight transfer. In this method the NRWT is calculated individually for each wheel.

In a LF hand turn

NRWTLF=-(lat-LF)*(LF IC Height)/(LF IC Length)
NRWTRF=(lat-RF)*(RF IC Height)/(RF IC Length)

then same is done with the rear.

Then the chassis roll is iterated into the roll stiffness distribution until the overall weight transfer=Ay*CG-height/TW=(Rolling WT+Non Rolling WT)

Remember that jacking force=NRWTLF+NRWTRF

So as RC moves up and the the right there will be less chassis roll but more jacking. Effectively more of the weight transfer is occuring throgh the RF linkage rather than through the RF spring.

Unfortunately these calculations need an estimate of lateral force on both the tires to work. It is also interesting to note that NRWT occurs(or changes) instantaniously with a change in lateral accelertation. So whether or not two different roll center height, spring-bar combinations you choose might have the same steady state balance the transient feel of a car with lower F-RC vs. higher R-RC, will feel more "oversteery" in a transient menuver.

Jeff

[ben]

Could I just get some clarification - Is rolling weight transfer, weight transferred by the springs and bars, and non-rolling weight transfer, weight transferred through the suspension links?

Also, I assume Lat-LF and Lat-RF are the left front and right front cornering forces?

Ben

[This message was edited by ben on October 03, 2002 at 09:28 AM.]

[Jeff Curtis]

Yes, you are correct on all points. The same priciples apply for anti-pitch and anti-dive. Your discription is probally the most clear(non-rolling transfer is through the linkage, rolling weight transfer goes through the springs and bars). In the real world everything is a spring, but hopefully your suspension linkage and frame are stiff enough not to behave as one.

Jeff

[Mark Ortiz]

I have for some time been telling people to pay attention to force line slopes rather than force line intersections. (By force line I mean the front view or side view line from contact patch to instant center, whose slope together with lateral or longitudinal tire force determines jacking force at an individual wheel.)

I have thought I was a lone voice in the wilderness on this, but it appears there is a body of opinion out there that substantially agrees with me. My question to Jeff: where did you learn this method? Is there any book or paper out that advocates it?

I'm not sure you've got it 100% right calculating a load change at each wheel as being equal to the jacking force at that wheel. Seems to me it's necessary to calculate the total anti-roll moment for the wheel pair due to jacking forces, and then divide that again by the track to get a load transfer on the wheel pair that is equal in absolute value for each of the two wheels - in other words average the right and left lateral anti forces. Otherwise, we end up predicting a change in the total wheel pair loading when the jacking forces are anything but equal and opposite.

Or do you handle the apparent wheel pair load change as a total spring load change (unloading for net upward jacking), to keep the total wheel pair load unchanged?

Also, how does this method deal with the unsprung masses?

[Jeff Curtis]

I just wanted to say that I read you column in Race Car Engineering magazine each month, and I learn something each time. It is refreshing to read stuff that is actually correct:) Or shall I say stays true to "real" vehicle dynamics principles. (Something that is a rarity in the Charlotte region, if you know what I mean.)

Originally, I was looking at some K & C compliance rig data for one of our Cup cars. One of the many graphs included was for for normal force change vs. lateral force (also normal force change vs. long. force).

At first I didn't know what this meant. At the time, I was trying to understand what it meant for a roll center to be off the centerline of the car.

About a month later I got the new Milliken book and in a footnote on page 470 mentions the lateral-anti method of calculating non-rolling weight transfer.

I talked to Doug Milliken at last year's FSAE event and he suggested that I invest some time in figuring out how it works. From there I looked at the K & C data again and it all made sense.

In the data, it gave a R.C. value for each the LF and the RF. The value for the RF was higher than the LF. I thought, how could there be two different RC values? These values were actually where the "IC to center of tire" lines crossed the centerline of the car.

In other words the R.C. was actually to the right of centerline for this car (common as you know for a Winston Cup car). From there I more or less figured out the lateral-anti method.

Mark: "Or do you handle the apparent wheel pair load change as a total spring load change (unloading for net upward jacking), to keep the total wheel pair load unchanged? "

YES.

Unfortunately, I am not a skilled enough writer to explain my method without confusion. I am better at showing it though my model and explaining it in words.

More or less, the usefulness of this knowledge for our Winston Cup cars is to run high IC's on the Left side (RC to the left) as to keep a better aerodynamic attitude under lateral accelerations.

As for unsprung mass, I have yet to refine this portion on my model. I have them calculated in the simplistic sense:

WT=Unsprung_Mass*lat_g*UM-CG-Height/TW

I am sure this is not entirely accurate because a small percentage of the unsprung mass's force is probably being transmitted into the springs.

I am sure a good ADAMS model accounts for all of this mess; I just need to get onto a team that has one or wants to invest the time and money into developing one! For now a good, well developed steady state model is still quite valuable.

Jeff Curtis

[Dick Golembiewski]

Those of us who lived in Charlotte (in my case for a year) understand completely!

[Mark Ortiz]

New Milliken book? I guess I've thrown away too many mailings from SAE Bookstore. Have they come out with a revised version of Race Car Vehicle Dynamics, or is this something else?

[ben]

The book Jeff's referring to is the Milliken's publishing of the Olley papers as "Chassis Design".

One thing they are doing though is republishing the RCVD workbook. Sadly any hope of more detailed exploration of lateral-anti has been dispelled by Edward Kasprzak who said that the EOMs for it are pretty much 'trade secret' for those who've got them.

Ben

[Schumi_Jr]

Now that some good vehicle dynamics discussion has errupted, what is everyones opinion on the height of roll centers? A roll center below ground should see a momentary loading of the inside tire on corner entry resulting in added grip (prior to the load transfer throught the springs and ARB). However, the car will roll more and will have a higher moment of inertia in roll. To compensate for the added roll a stiffer ARB must be used making the suspension "less independant". Suspension jacking forces will lower the chassis (good thing?)

Conversely, a roll center above ground will see a momentary transfer of normal force to the outside tire, reducing grip. It will roll less and have a lower moment of inertia in roll. Suspension jacking forces will raise the chassis.

So which is better? I would think for FSAE a r/c above ground is better because it will be more responsive (low inertia) and you can use a softer ARB. I recall that Pontiac was pretty bumpy so one wheel bump should be a concern. Also, any comments on pitch centers?

[Jeff Curtis]

I would state the claim the roll center stability is the most important goal to shoot for. This of course is a function of IC stability. A-Arm lengths as well as point positioning are both critical variables towards this.

However, In my opinion controling cambers has a more significant effect on vehicle handling than small changes in roll center position. Remember that caster and Kingpin Axis Inclination has it's effect on your cambers while steering.

To sumarize, start by setting a guideline on where the cambers need kept with in your pitch, roll and steering gradient. Then design a stable geometry that most closely fits your camber requirements.

Jeff

[ben]

In the absence of the sort of analysis Jeff and Mark are talking about (and I am perpetually going to do tomorrow :-) ) I would suggest designing the roll centre to maintain a fixed roll moment and not move laterally at all during roll.

Simple is better I would say in this situation.

Ben

[Mark Ortiz]

I have for some time been working on an article for Racecar Engineering on this whole subject. When done it will have to be in at least two installments, due to its length.

A few brief further comments here:

It is definitely an error to think of the roll center as a pin joint. Vertical forces do not act through it, nor does the car pivot about it. Think of it as the height of a level Panhard bar.

It is also an error to use the height of the force line intersection as the roll center height. Here's a better method:

1) Estimate the distribution of lateral forces generated by the tires. In the absence of better information, use a default assumption that the loaded tire generates 75% of the total.

2) Draw a vertical line in your front view, that
percentage of the track away from the loaded wheel. I call this the front view resolution line.

3) Find the two force line intercepts of the resolution line.

4) Average the heights of those two intercepts. Use that average height as your roll center height when estimating wheel loads at a given lateral acceleration.

This method will give a better approximation than using the force line intersection height in most cases, and avoids the large errors that can occur if you use the force line intersection when the force line intersection lies far to one side of center.

You will find that if the force line intersection is above ground and moves toward the loaded wheel in pure roll, the roll center as determined by this method rises.

The distance between the two force line/resolution line intercepts is also a rough predictor of the amount of overall upward jacking: more spread, more jacking. Note how the jacking increases as the resolution line moves toward the unloaded wheel (load distribution departing further from equal). This explains why swing axle suspensions jack so little in gentle driving, yet so much in hard cornering.

If you try to create a geometry where the force line intersection does not move in pure roll, you will find that the force line intersection moves up and down with the sprung mass in ride, by an identical amount. If you create a geometry where the force line intersection does not move up and down in ride, then in pure roll it will move toward the loaded wheel if it is above ground; will move toward the unloaded wheel if it is below ground; will become undefined if it is exactly on the ground (in which case its lateral position will also be undefined at static).

Controlling force line angle is a problem similar to controlling camber. If you achieve zero change in roll, you get big changes in ride, and vice versa. Therefore, as with camber control, a compromise is in order.

Camber patterns are an independent issue from roll center heights, except that keeping camber change rates more constant involves more nearly equal control arm lengths, and this leads to more force line slope change in ride and less in roll, at least for "normal" geometries.

My general-purpose recommendation is to have a static front-view swing arm length between 63 and 95 inches in all suspension positions, a static force line slope of 2 to 4 degrees above ground at static (force line intersections 1 to 2 inches above ground), slightly more force line slope(higher intersection) at the rear than at the front, and a force line slope between 0 and 8 degrees above ground in all combinations of ride and roll. Force line intersection height change in pure ride should be between 0.5" and 1.0" per inch of ride, preferably around 0.8".

Finally, try to keep all these rate-of-change parameters as nearly equal as possible at both ends of the car.