Lateral Kinematic RC Migration

[R. Alexander]

Hi Guys,

I know I'm going to get someone saying that this has been asked a million times, but it's a pretty specific question.

I've been trying to figure out practically what happens with kinematic roll centre lateral migration and haven't come up with much at all.

I've seen it written many times that the following equations are valid:

Geometric weight transfer = Latg* SM*(RC_Z) /(Contactpatch_Y)
Elastic weight transfer = Latg* SM*(CG-RC_Z) /(Contactpatch_Y)

However, I've stumbled upon some WT equations in a thesis paper written by someone implementing force based roll centres into OptimumK (I'd love to link it, but it appears to be broken. The title is: Implementation of the Force Roll Center into OptimumK by Sébastien Allibert):

Geometric weight transfer = Latg* SM*(RC_Z) /(Contactpatch_Y-RC_Y)
Elastic weight transfer = Latg* SM*(CG-RC_Z) /(Contactpatch_Y-RC_Y)

The effect of the vertical location of the RC seems clear to me because it creates 'the' moment arm which creates your chassis roll, however I'm troubled with throwing the lateral position of the roll centre into the mix.

Here's the golden question:

Doesn't this mean that if I have RC migration to infinity (is this possible?) that there will be 0 WT? I haven't got an RC to migrate to infinity, but maybe it's possible. Maybe those equations are just wrong, and he really means to use the real roll centre location, not just the kinematic location.

Hopefully I'm not being too confusing.

Please give me some input as I'm about to decide that lateral kinematic RC migration doesn't really do anything and I should therefore neglect it in my design and instead focus on getting the points done quickly.

Sincerely,
Ryan Alexander

[R. Alexander]

Even weirder, doesn't that mean that as you approach putting the RC under the contact patch that your WT approaches infinity.

That cant be right, granted that its possible!

[R. Alexander]

Heres the linkhttp://dspace.lib.cranfield.ac.../1/Allibert-2007.pdf (http://dspace.lib.cranfield.ac.uk:8080/bitstream/1826/2097/1/Allibert-2007.pdf)

[Bobby Doyle]

While I can't comment directly on the validity of your equations, I can tell you with a fair degree of certainty that no matter how magical your kinematics are, you unfortunately cannot defeat the laws of physics. If your CG is above the ground, you will have weight transfer.

[Pennyman]

Ok, I'll bite...

There's been a lot of this covered in the past on this site, but every once and a while it's good to dig it back up..i guess...

I've read the paper you've referenced, and there some interesting topics covered, but let's not forget some very important things here.

First, the "roll center" is an effect of many different things including spring stiffness and motion ratio linearity in bump and droop, kinematics, compliance (yuck) and probably some other stuff. It's not a cause, it's an effect.

The paper you reference mentions that the height and lateral migration of the roll center affects the ratio of elastic to geometric weight transfer. If the RC is at the CG, there's only geometric weight transfer. The lower the RC is, larger the net moment reacted to the sprung mass and thus more elastic weight transfer. If the RC migrates to the inside wheel, that spring will act more "stiff" meaning the weight transfer off the inside tire takes place more geometrically than on the outside. Really the instant centers are a better way to analyze this phenomenon anyway IMO.

In a situation where the roll center migrates past the half track or even farther, I think roll center analysis is only the beginning of your problems, and you should probably begin by looking at what your individual instant centers are doing relative to each other to create such unstable RC movement. You probably don't have the best camber compensation at this point either.

Again, I've heard people mention that a RC past the half track will cause both springs to extend or compress, causing the car to theoretically "heave" instead of roll through a turn. But other things like motion ratio and spring stiffness also affect this as well! Everything is interconnected with this stuff.

In my opinion, don't over-think it, keep it simple stupid, and keep those tires upright! http://fsae.com/groupee_common/emoticons/icon_smile.gif

[rjwoods77]

Kinda off topic but there is another article about FBR centers in the new RaceCar Engineering,

[R. Alexander]

Yeah, I know this subject has been exhausted too many times. Appreciate the input regardless.

I just haven't seen the lateral WT formula include lateral RC location before. Even odder is that they specify using the geometric RC, not the 'real' force based RC.

Do parallel arms make kinematic RCs that migrate to infinity? Does that bring it to 0 WT again?

I guess I'm just trying to disprove that formula.

I've been going through tons of iterations in optimumk and have noticed a couple scenarios in which I can get a lot of RC migration while maintaining practically the same camber curves (however, my optimumk rolls about the kinematic roll axis so that is maybe playing a role that might not happen in real life).

Penny mentions that if the roll centre is actually outside of the track that the car will either compress or extend all springs in roll. While it might be possible to get the kinematic roll centre out there, I don't know if it would be possible to actually get a symmetric car to roll about that point. Has anyone seen that?

Probably rambling. What do you all think?

Cheers

[Pennyman]

R. Alexander, listen to me VERY carefully.

The total amount of steady state weight transfer is only caused by 4 things:

Distance between wheel centers (track width)
CG height
Mass of the vehicle
Amount of lateral acceleration experienced

Do not forget it.

[Mikey Antonakakis]

Pennyman, maybe I am missing something, but doesn't roll stiffness at least have a small effect on weight transfer?

EDIT
Or maybe this is better wording:
Could a fifth (but less important factor) be roll stiffness (speaking in terms of roll/lateral acceleration)? Because the mass center of the vehicle would move laterally, slightly. Again, this is a small amount of WT though (Unless you're driving a box truck lol).

[Pennyman]

Mikey, weight transfer is time-based, so the ratio of elastic to geometric weight transfer and the roll stiffness have an affect on HOW FAST the weight transfers, not the total amount, so let me explain a couple of simple scenarios for ya http://fsae.com/groupee_common/emoticons/icon_smile.gif

1: high roll center, low roll stiffness: so there's little elastic weight transfer, weight transfer takes place very quickly through suspension links in the from of geometric weight transfer. (but more jacking forces experienced, but that's a new topic)

2: Low roll center, low roll stiffness: So there's a lot of elastic weight transfer, but because of the low roll stiffness, the weight takes longer to transfer and therefore the car takes longer to settle, rolling much more. The total amount of weight transfer remains the same.

3: low roll center, high roll stiffness: so there's still a lot of elastic weight transfer, but now because of the high roll stiffness, the weight transfers more quickly with less body roll, but the total amount remains the same (if the turn is long enough, so to speak)

[Mikey Antonakakis]

Oh I certainly understand the difference that roll stiffness makes in time response, maybe I still didn't word my question properly.
Let's say there is a car that has achieved a steady-state condition in a constant radius turn. The weight transfer at this point depends on the mass center height, track, mass, and lateral acceleration, as you said. That is a simple mechanics problem. But, let's say the car is undergoing a few degrees of body roll, and as long as the body does not roll around the mass center (I'm trying to avoid the whole RC discussion), I am fairly certain the mass center would migrate laterally (and vertically) slightly, with respect to the tires. I think some books would say the same thing by saying "b1 and b2 change in roll." If we started with a perfectly symmetrical car, i.e. b1=b2, then we would see that there is a slight change in l/r weight distribution due to the fact that the mass center now does not sit directly between the tires, but slightly offset. This is mainly for the sake of argument, as I doubt it has a significant impact (although I can't say for sure until I have some good equations). I'm not saying the total weight transfer would change or not, just that the fact that the vehicle's mass center has shifted left or right with respect to the tires at least contributes a small amount to that total weight transfer.

Also, I'm assuming my whole "mass center migration" talk is the same as you saying elastic weight transfer.

I guess your previous statement is still completely true given l/r symmetry and knowing the CG height in a turn.

Sorry, been doing too much vehicle dynamics HW lately, I'm going a little crazy.

[Mikey Antonakakis]

Oh man I am going to actually have to draw a FBD to put my mind at rest http://fsae.com/groupee_common/emoticons/icon_frown.gif

Okay so I drew one, and here's what I got.
2 equations:
-W*b2+F*y+F2y=0 and W*b1+F*y-F1y=0
where W is weight, F is lateral force, b1 and b2 are the horizontal distances from the mass center to each tire, y is mass center height, and F1y and F2y are the vertical forces on the tires. Those vertical forces change if I change the values of b1 and b2 (isn't that what you mean by elastic weight transfer?), that is pretty obvious. I plugged in some numbers and the total weight transfer does change if I leave the mass center height, mass, and lateral force constant while changing the values of b1 and b2 to reflect this elastic WT. However, I think for most FSAE cars the elastic weight transfer is probably less than a few percent, which only changes the weight transfer a few percent.

[Bobby Doyle]

The distribution and rate of your elastic WT can be controlled by your springs, dampers, ARB's, etc. It is not the term for the WT you are speaking of, the lateral translation of the CG due to body roll, which is usually negated in most equations at least from my experience.

[Yellow Ranger]

Has someone ran the numbers to see how much extra weight would be on the outside for 2 deg vs 1 deg? I imagine your time would be better spent elsewhere. Hell, many of these team's can't even properly set cross weights.

[Zac]

Cross weights are one thing, but I've found many teams struggle with static alignment settings.

[Chris Allbee]

To follow up on something Pennyman said:

The ONLY thing that affects weight transfer are the 4 things he mentioned.

I'm not talking about contact patch reaction forces to road input or frequency responses to transient loading, just pure unadulterated weight transfer. Equal and opposite reactions and everything you learned in middle school.

I think the terms "geometric" and "elastic" can be misleading to most when learning about suspension and weight transfer. Better terms would be "undamped" and "damped".

Undamped would be the instantaneous weight transfer that results from buildup of lateral accelerations on the mass of the vehicle. Indeed this will be a function of the aforementioned 4 items above and the reaction forces (or transferred weight) is what keeps your car from defying the laws of physics and sinking into the pavement.

Damped weight transfer isn't weight transfer in the same sense as above, it is the reaction forces generated from the relative movement of objects within the system. In this case, the chassis movement relative to the suspension and tires. It is the result of built up momentum and inertia WITHIN the system, and this can modify the distribution left-to-right with respect to time.

No matter where you roll center happens to end up, because it IS a result of the input forces and not the cause of them, it will not change the amount of weight transferred when your vehicle is subjected to an acceleration. Nor does its position dictate the fluctuations due to the damped inertial forces in the system. Its location is a result of those movements and it has been said before that it will be a function of input load, input velocity, spring rates, damping rates, and motion ratios. And thats without going into mass ratios.

The fastest and easiest way to get a good suspension, one that all but the most advanced team would certainly be happy to have, is to design a geometry that maintains the desired camber position (focus on roll) and get an adjustable high quality damper. Spend your time dialing in the damping rates to get the car to settle and not "rock-n-roll" through the corners.

If you have a data aq with strain gaged push/pull rods and damper displacement sensors, then you can even extract a frequency spectrum for your car and develop your own damper curves if you so desire.

Remember that just because everyone has used a certain method for however many years doesn't mean it's right or that you should accept it at face value.

Good luck with your designs.

[ed_pratt]

Good job and thanks Chris,

That was probably the clearest and most succinct explanation of this topic that I've read.
I agree, it can be confusing talking in terms of geometric and elastic transfer, and your analogy to undamped and damped systems seems to be a pretty close fit.

Ed

[R. Alexander]

Hey Guys,

Thanks for all the input.

I agree that TOTAL weight transfer depends on the for above mentioned things (CG height, accel, vehicle mass, track or wheelbase).

However it makes sense to me that the weight transfer distribution between front and rear depends on the relative anti roll stiffness of the front and rear.

For example, if you put lots of front anti roll, you'll have more weight transfer in the front than the rear, although the total weight transfer will be the same.

The front or rear RC position affects your elastic vs static weight transfer, which affects the roll stiffness at that end, and therefore changes the weight transfer distribution between front and back.

Does that make sense so far?

What I'm thinking is that the equations in my first post may be attempting to explain how anti-roll stiffness changes with lateral roll centre position in addition to vertical position. Could this be so?

Please keep the input flowing.

[Pennyman]

Originally posted by R. Alexander:
What I'm thinking is that the equations in my first post may be attempting to explain how anti-roll stiffness changes with lateral roll centre position in addition to vertical position. Could this be so?

Please keep the input flowing.

Lateral kinematic RC migration is solely dependent on instant center position and migration on either side of the car. I think analyzing RC migration begs the question of what your IC's are doing, whether it be changes in IC length or height. Looking at the component forces (generated from the contact patch) through the IC for geometric WT or calculating a moment about the IC for elastic WT for each side of the car is probably a better place to spend your time in my opinion.

[R. Alexander]

Originally posted by Pennyman:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by R. Alexander:
What I'm thinking is that the equations in my first post may be attempting to explain how anti-roll stiffness changes with lateral roll centre position in addition to vertical position. Could this be so?

Please keep the input flowing.

Lateral kinematic RC migration is solely dependent on instant center position and migration on either side of the car. I think analyzing RC migration begs the question of what your IC's are doing, whether it be changes in IC length or height. Looking at the component forces (generated from the contact patch) through the IC for geometric WT or calculating a moment about the IC for elastic WT for each side of the car is probably a better place to spend your time in my opinion. </div></BLOCKQUOTE>

Would you say that the equations are incorrect?

[Pennyman]

I wouldn't say they are incorrect, just that they do not take into account additional variables for more complex situations. In other words, its probably a good place to start. If there's one thing I've learned in all this vehicle dynamics stuff it's that there's always more to learn.

Listen, I'm not here to prove or disprove anyone, just trying to lend some insight. However I don't know whether or not Claude would appreciate your use of one of his student's papers when he judges your suspension though. http://fsae.com/groupee_common/emoticons/icon_wink.gif

EDIT: knowing him, he probably wants you to derive the equations on your own haha!!

[R. Alexander]

I don't see why Claude would have an issue with me looking into the formulas of a public thesis paper that he's probably approved. He said to me himself that he's not the bible...

I've derived that equation numerous times, it's just a moment balance to see what additional wheel normal load counters the force acting at the CG height.

The denominator is the moment arm that the wheel normal load acts about.

When you look at the derivation, it makes sense to use the distance from the contact patch to the point of rotation wherever it may be since that's the moment arm.

I guess it comes down to where is the body actually rolling about and how do you find that point. I think the point to use would be the force based roll centre, not the kinematic roll centre since the car doesn't actually roll about the kinematic RC.

Assuming that the force-based roll centre migrates towards the unloaded wheel, I'm not sure how much of the lateral force gets resisted by the inside vs outside wheel, nor am I sure how much of the added normal force gets resisted by the inside vs outside wheel.

I'll think about it and hopefully post with some more insight. It's probably going to be complicated and use the actual wheel ICs as Penny suggested...