Roll Center Migration

[^_^]

For those of you who consider it, how do you minimize your roll center migration (kinematic RC)? Anybody have a good closed-form solution that they use? Iteration? Trial and error? Just trying to get a feel for how everybody goes about it.

[kwancho]

Lots of trial and error.

[CMURacing - Prometheus]

there are some basic correlations you can find through trial and error, and quite a few of them i've found to hold true.

[Patrick W. Crane]

trial and error.

is discussing what final numbers people are getting too secrative? i'm just stuck between 1 and .5 inches... i dunno how much more it's worth chasing it at this point.

[Andrew Nabb]

I think most people have examined these through trial and error. One of the big trade offs you will probally have to make is camber gain vs roll center migration. I have not fully examined the situation, but what i have seen from my own work is that as the IC's (instant centers) get longer (ie further from the car) the migrations will go down. This also generally leads to less camber gain. (think horizontal control arms in the front view)

Of course realize with the limited travel we have, migrations are probally not as big of an issue as some other factors will be (like RC center heights front to rear, camber change, ect). It is not a street car with 7 or 8 inches of travel.

[F1engineer]

I set up an numerical optimizer and at let it do the trial and error. I define parameters to allow the analysis to move the suspension points within specifed limits in specified directions as appropriate to the packaging constrains. The constain limits are for example max and min camber, mean anti dive, mean roll centre hieght etc. The optimization typically does about 60 iterations in 30 mins of running and finds a solution for all the limits. Having set up the basic 5 bar linkage. I then add the pushrods rocker , springs and arbs and optimize the linkages for sping and arb velocity ratios and rising rate. Can't see the point in doing days of trial and error!

[Marshall Grice]

you're right, months of writing code is much better.

[F1engineer]

You must be an Adams user!

[Marshall Grice]

ADAMS? that is definitely the long way to a design. I am a 2d sketch guy. I don't claim that my way is superior to yours. However for a couple days work i end up with a fairly solid design. If i were doing this for a living i would certainly invest the time to write some code but the reality is most suspension designers in FSAE only do one maybe two cars during their time.

[Buckingham]

There are ways to define 3d sketches in programs such as solidworks that eliminate the need for iteration. Through careful definitions, you can work backwards by defining the output and solidworks will give you the unique input solution. I've always used ADAMS because it only takes a day of trial and error once you get good at it (and once you decide what you want), and it allows you to visualize your linearity very easily.

quote: "as the IC's (instant centers) get longer (ie further from the car) the migrations will go down"

If you think outside of the box, there are other ways of getting the migration down. In fact, there is a way to get them to zero "in theory". There is also a feasible way to get them down to the .050" and under range (save for manufacturing tolerances)

[Kevin Hayward]

I took an approach similar to F1Engineer. It took time to program our own 3d kinematics package and optimization routine. I was involved in suspension design for 4 years. The first year it was 2-d and solid edge. By the second year (2002) we had the optimization routines and our own 3d kinematics package.

The time invested was well worth it as the tool is still in use today ... with quite a few enhancements. What took time in 2001 and 2002 saved a huge amount of time in 2003 and 2004. The program was hooked up to the Solid Edge model so all suspension changes were made in one place and all the files associated to it were changed instantly. The moment you had the suspension curves you also had the Solid Edge model. This made it really easy to assess the effects of changes to the suspension due to packaging constraints, and more importantly how to get it back to a good design when changes were necessary.

What came from the optimization was a bunch of simple rules that have not failed yet for our FSAE cars. Trial and error should show these rules. My main suggesttion would be not to think of the suspension as xyz points. Think of it in terms of SAL, upright height, upright angle, ratio of arm lengths etc. When you look at it this way and change those variables you will see relationships quite quickly.

Kevin Hayward
ex- UWA Motorsport

[Kevin Hayward]

By the way I have used ADAMS a few times for suspension design. It was one of the programs we used for correlation in the first year. I think it is unsuitable for FSAE cas it takes too long to setup and then once it is setup changes to the suspension systems are not very quick.

It is an incredibly powerful package. Most of the power a FSAE suspension designer does not need. I would always recommend investing time into your own packages rather than the training and time required to use ADAMS.

Kev

[Andrew Nabb]

I have used both Adams, Altair's Suspension Gen and also the Wingeo released by bill mitchell. The mitchell software has been the easiest for me, allthough it is fairly basic in its appearance and utility. Is it as powerful as Adams...of course not. With a retail price of around 700 bucks (usually free for FSAE teams) you get what you pay for. However it does everything most teams would need and is fairly straight foward.

It is geared towards nascar teams down here in NC....so it can't be too complicated.

[Marc Jaxa-Rozen]

I think it is unsuitable for FSAE cas it takes too long to setup and then once it is setup changes to the suspension systems are not very quick.


That was pretty much why I made ours as well, ADAMS is needlessly complex when you're just looking for RC positions and camber curves. I think the learning process involved in making your own software also ends up paying dividends for the actual design as well as its justification to the judges.

Marc Jaxa-Rozen
École Polytechnique de Montréal

[F1engineer]

It is worth looking at Matlab which is available cheaply in a student version. The Optimization Toolbox includes all the optimization software you will need. If you have a dos type suspension analysis software which uses a text files for input and results, you can write matlab code to call edit the input file run the dos program and read the results files quite easily.
Alternatively you can write you own suspension software in matlab or use the SimMechanics kinematics package in matlab.
I know of several people who use matlab optimizations routines calling Adams models in batch mode.

[CMURacing - Prometheus]

Originally posted by F1engineer:
It is worth looking at Matlab which is available cheaply in a student version. The Optimization Toolbox includes all the optimization software you will need. If you have a dos type suspension analysis software which uses a text files for input and results, you can write matlab code to call edit the input file run the dos program and read the results files quite easily.
Alternatively you can write you own suspension software in matlab or use the SimMechanics kinematics package in matlab.
I know of several people who use matlab optimizations routines calling Adams models in batch mode.

unlike the fsae.com forums, if you ask matlab nicely, it will give you the answer to any problem you may have. however, asking nicely usually involves a good deal of programming.

[swong46]

I want to bring this thread back because I am using a 2D Solidworks model along with Lotus and am having a hard time finding a correlation with geometry changes and roll center lateral migration.

I read in Competition Car Suspension that the FSAL has a lot to do with the migration, but I have exaggerated the SAL to be VERY large and small and the migration changes by 1-2 inches. However during normal trial and error, I have seen migration to be upwards of 16-30 inches.

Right now, I have settled on 7 inches. What is the ball park I want to be in?
And what should I modify to better limit the migration?

[OspreysGoSWOOP]

No OptimumK love in this thread?

OptimumK is a $400 software available to FSAE teams from OptimumG.

http://www.optimumg.com/

It does exactly what you're asking about and it does it really really well. Easy to use, great interface.

It's purely geometric so it doesn't account for tire spring rates or spring/damper constants. But it's great for analyzing camber gain vs body roll, bump steer, RC migration etc etc.

Plus you can import DAQ from your ECU to run your simulations. Cheers

[Adambomb]

I'd say there's on OptimumK love yet because it came out in 2007 or 2008 if I remember right, and all but the previous two posts are from 2006...

I'll vouch for it though, we used Solidworks 2D sketches in the past, and even continued to use them until this year, mostly because they cost nothing and we already had them developed. Although working out the constraints was a huge pain, not to mention the circus act involved in switching between "let's change the kinematics" mode and "let's see what the rates are" mode. And then every time someone else touches it you have to wonder to yourself if they did anything bad to it. Then teaching someone else to do it takes another 2 hours or so.

We switched to OptimumK this year, not sure how long it took but I remember that into the semester (ie competing in time with classwork) our suspension team leader went from "hey let's use OptimumK" to showing me plots in like less than 2 days.

~~~~~~~~~~~~~~~~~~~~~~
I'd say 7 inches of RC migration is pretty huge for an FSAE car. As for what you want, that's for you to decide! As the previous posts have suggested, see what happens when you move your ICs around.

[PaulKennedy]

The same for me. I love this since when it is launched. What I feel when I read the comments of others is there is no as such discussion on Optimum desktop. Optimum Desktop is a program which gives you the opportunity to increase the abilities of standard desktop, and if required to change its appearance completely. With the help of animation your desktop will refresh for day. I was also using the 2D till last year. Now, the new Optimum has a lot of changes and it developments so I feel it has to use once.

[Shebert]

There is a formula in Milliken's Chassis design book, wich is a function of upright points height and a-arm lenght. Try it in bump and roll... in OptimumK for sure http://fsae.com/groupee_common/emoticons/icon_wink.gif

[Z]

Fasten your seatbelts boys and girls, this pot needs a good stir...
-----------------------------------------------------

The original question asked by ^_^, and again by swong46, is;

"How do you minimise lateral roll centre migration?"

I ask "Why bother?"

I guess the answer is to impress the Design judges. I'm guessing that you get extra points by saying "We managed to keep it down to about N millimetres. Here, look at our pretty pictures...".

If so, then there is something seriously wrong with both the students and judges understanding of this subject. From my brief reading of the many threads about roll centres on this site, I counted about seven people who seemed to "get it". (I blame the education system for this, and might rant about it later).

My point is, (IMHO) there is absolutely nothing wrong with lateral RC movement, per se. Many a good suspension has its RC zoom off to infinity with the slightest chassis movement. And then, with a bit more movement, it comes back from the opposite infinity. Wow! But nothing bad happens!

This behaviour is covered at the end of a 2005 thread "Roll Center vs. Jacking". Also in a Racecar Engineering article August 2010 p77. (Note that the boneheaded sub-editor at RE decided to sex-up the article by chopping the text to bits and scattering the pieces hither and thither. The remnants of the relevant words are at the beginning of the main text and under Figure 13.)

But it seems that the message is not getting through...

So, as students, what do you do?

1. Show the Design judges your pretty pictures of a "well constrained RC" and get good marks.

2. Study the subject from first principles, then tell the judges that if they think RC migration is a bad thing they are imbeciles and should get another job. And, err..., maybe lose marks?

3. Study the subject, but explain it more diplomatically. (I'm not sure how to do that...)

----------------------------------------------------------

Soooo....., to get the ball rolling...

Would someone like to explain why RC migration is such a bad thing?

(Please don't use religious arguments, such as "because it is written in <racing-guru's> bible".)


Z

------------------------------------------------------

PS. Mini-rant: I reckon someone should do a thesis on this. Not in Engineering, but in one of the Social Sciences. That is, how is it possible that so many supposedly highly technically educated people could believe such nonsense? It is not a difficult problem! Is it head-in-sand mentality? Herd mentality?? What??? End mini-rant.

[Big Bird]

Z!!!!!!!!!!!!
Welcome back!!!!!!!!!!!!!

My god we have missed you around here!

[Big Bird]

I've often wondered the same thing. I would suggest you don't need to worry about your rotational centres as much as the movement of the car itself.

Consider your vehicle's yaw centre. You are driving along a straight road, and you "swerve" 0.0001 degree to the left to avoid running over a microbe. You realize that if you continue on this trajectory, some time in the next 1500km your car will leave the road - so you swerve back 0.0001 degree to the right.

Now it would take some sort of super-accelerometer to notice that anything had happened at all, and I'd challenge anyone to convince me that was a particularly severe operating condition. Yet this worrisome instantaneous centre has travelled from near infinity to the left, to near infinity to the right.

So the question becomes - who cares??

[Dash]

I have to admit, whenever I joined my team I was taught that it was a sin to have the roll center move all over the place. I believed it for a little while even though I thought it was a pain in the ass to try and minimize movement. And then I had Mechanisms class and realized that the kinematic roll center doesn't really matter much at all. I'll just drop this link for anyone to read a little further on: http://www.neohio-scca.org/com...e%20Dynamics2007.pdf (http://www.neohio-scca.org/comp_clinic/hand_out_reprints/Vehicle%20Dynamics2007.pdf)

Now all I REALLY look at are camber curves in roll/bump.

[Mike Cook]

I would argue that the car is much more sensitive to vertical roll center movement. Because the lateral force is acting at the RC, any vertical movement will change the lateral load transfer distribution. If the roll center moves a lot during the roll of the car, the LLTD will change through the entry and exit of the corner. I suppose this could be bad or good, depending on what you want, but I think an easier way to tune this behavior is with the dampers.

Now, on to lateral motion. Any jacking forces will act at the RC and if the roll center moves enough, this could really cause a lot of vertical travel of the chassis. In an aero car, this could upset the handling. Also, the jacking force times the offset of the roll center will cause an extra roll moment that will change the LLTD too.

Jacking forces aren't that significant until you start to pick up inside tires, which is fairly common in fsae.

For reference, changing our roll center height by 1/16 to 1/8" was very significant in the tuning of our car.

Mike

[PatClarke]

Hello Erik, Long time no see! http://fsae.com/groupee_common/emoticons/icon_smile.gif Your re-emergence certainly beats the 'How do I Dsin a car?' posts of late!

Mike, where is the roll centre on that axle when you do pick a wheel up?

And Geoff, this thread is now starting to remind me of a conversation you and I had at the Melbourne Motor show a few years ago!

Cheers

Pat

[Big Bird]

It certainly is, Pat. But on these boards I get to choose my words a little more carefully - so I don't sound anywhere near as scattered as I do in person http://fsae.com/groupee_common/emoticons/icon_smile.gif

Cheers!

[Mike Cook]

If you pick up a wheel then that axles roll center migrated to the outside tire contact patch or even further outboard of that. Which is a pretty bad thing if you run an aero car.

Mike

[PatClarke]

And I wonder, Mike, where the kinematics say the R/C is under these circumstances?? Different for differing designs, but probably nowhere the contact patch.

Remember the immortal words of Colin Chapman, "Any suspension will work if you don't let it". Then Z would probably want you to paint it brown http://fsae.com/groupee_common/emoticons/icon_wink.gif

Pat

[Kevin Hayward]

Z,

I don't think the judges are particularly concerned with RC migration nor should they. I remember talking to Carroll Smith about it in 2002 and he certainly wasn't fussed. I think most students worry more about what the judges are worried about than what they should be worrying about.

I have often wondered where the idea of RC migration minimisation actually started, and it appears most likely to orginiate from "paddock talk" rather than any basis in thorough engineering testing. In most of the more engineering based texts on it is barely mentioned. Most likely it would have been a case of:

Car is fast so the supsnsion was analysed and kinematic roll centre didn't move about. Therefore low kinematic RC movement causes fast cars.

It is spoken of being very important in Competition Car Suspension by Alan Staniforth. Unfortunately I think too many people take it on board without considering Alan's background. This book should only be treated as an introduction to suspension, although it is an excellent read and well worth your time.

Carroll Smith deals with it more clearly by dismissing it as being at best a second order effect and most likely of no real importance. At the same time he leads readers to consider the camber gains as being much more important.

I also believe there is some discussion of it in Costin and Phipps, but I cannot remember the importance they place on it. This however is a much earlier text and to my great sadness I have misplaced my copy. (Somebody PLEASE run a reprint of this book)

Herb Adams mentions it in Chassis Engineering. However I would warn any serious designer away from this text as being any serious reference.

I think the most appropriate treatment of the roll centre in texts is in Dixon's Tires Suspension and Handling which states that the roll centre is an interesting idea that can be used to summarise the effects of suspension links, but the idea should be approached with caution as it is not very applicable in a dynamic situation.


When the kinematic roll centre moves close to the ground there can be considerable lateral migration. This is inevitable, but not a sign of anything good or bad by itself.

The kinematic RC migration may be able to be used as an indicator, but I doubt it is a very good one. Practically when designing it is a trivial exercise minimising the RC movement when the RC is away from the ground, once the Swing Arm Length is set you can do it by simple variation of the length of either the lower or upper arm. You can decide to do it if you want, but it is more likely that your lateral scrub is the larger concern when altering a-arm lengths. I would keep a note of what the RC is doing in the same way you would track the behaviour of many suspension parameters and try to find correlations.

Practically there area few things that are much more important:

Tyre temperature
Camber angles
Steering Geometry (Caster, KPI, Offsets, Ackermann)
Damper settings
Wheel loads

I pity the student that tries to sell their car in design to someone like Terry Satchell based on a graph showing low lateral RC migration.

Kev

[ben]

Here you go Kev:

http://www.scribd.com/doc/5079...s-Car-Chassis-Design (http://www.scribd.com/doc/50792969/Costin-and-Phipps-Racing-and-Sports-Car-Chassis-Design)

Ben

[ben]

Good post from, I believe, Damian Harty of Prodrive:


blackbirdblue (Automotive) Jun 10, 2002
Roll Centre (excuse my UK spelling) has to be one of the biggest areas of confusion in suspension design that there is.

First, it isn't any sort of centre of motion, it's really a force centre. Second, for an independent suspension you can't arbitrarily combine the characteristics of both sides of the vehicle at the centre line.

The reason it matters is that it determines what proportion of suspension forces are transmitted via a "fast" mechanical route and what proportion are transmitted by a "slow" suspension spring/anti-roll bar/damper route.

The only things that matter in vehicle dynamics are forces on the tyres. A high roll force centre gives more load via the "fast" route and less via the "slow" route. Thus for a typical vehicle with higher rear roll force centre than front, the rear tyres load up faster during turn-in. This helps reduce the phasing between yaw and lateral acceleration and is generally A Good Thing.

If the roll force centre is below ground it means the suspension is "pro-roll" - the roll moment carried by the
sprung elements is greater than the inertial moment one might calculate using CG height and lateral acceleration. Motorcycle front suspension forks are similar in pitch.

In fact, the whole subject is better approached using the "anti-dive" logic applied to pitch motions rather than all this roll centre voodoo. Track down any half decent vehicle dynamics book and look at the anti-dive definitions then imagine them applied to roll.

One thing that isn't so obvious is that limit behaviour is helped by a low roll force centre and so some race cars have a rear roll force centre that plunges from above to below the front one to aid both turn-in and limit behaviour.
So you might find that lifting the rear roll force centre on your friend's car makes it technically faster but much more scary to drive and hence he'll return slower lap times.

As for camber, it has a lot to do with tyre wear but is really quite a small modifier on fundamental vehicle dynamics. There are a lot of people who will dispute that statement but none of them use any coherent maths to do it, only some very flawed reasoning.

In summary, think of roll-centres like anti-dive, reject any attempts to turn it into voodoo and find a good vehicle dynamics book. And set your static camber to maximise tyre life with the camber change characteristics you have, use tyre temperatures to predict tyre life without actually wearing them out.

Ben

[FWBcut]

I'll just drop this link for anyone to read a little further on: http://www.neohio-scca.org/com...e%20Dynamics2007.pdf (http://www.neohio-scca.org/comp_clinic/hand_out_reprints/Vehicle%20Dynamics2007.pdf)


I'm assuming people in this thread saying to not worry about RC migration are refering to kinematic RC. I'm also assuming that the force based roll center SHOULD be looked into.
If a kinematic RC was designed to have no migration in roll, the N lines would have a constanst angle, and the FAP's would remain at constant height. Because of the relation of kinematic RC and N lines, would this be a case were you WOULD want to look at the kinematic RC, just as a tool to determine FAP's?

[Mike Cook]

Pat, It has been awhile, but I think there is an article by Mr. Bill Mitchell that has some modified roll center equations based up the percentage of the weight transferred. Maybe a good article for students to read.

Our team is approaching the brown car more and more every year. The funny thing is, most of those students were in diapers when Z was talking about it.




Originally posted by PatClarke:
And I wonder, Mike, where the kinematics say the R/C is under these circumstances?? Different for differing designs, but probably nowhere the contact patch.

Remember the immortal words of Colin Chapman, "Any suspension will work if you don't let it". Then Z would probably want you to paint it brown http://fsae.com/groupee_common/emoticons/icon_wink.gif

Pat

[PatClarke]

Mike,

Thats the paper Dash linked to earlier
http://www.neohio-scca.org/com...e%20Dynamics2007.pdf

Pat

PS, use some other colour please, brown photographs like sh*t =]

[Z]

The Many Definitions of RCs.
===================

Please make yourselves comfortable. This is a long one...
-----------------------------------------------------------------

I'll address some of the above posts later, but first a rant about our declining education system (it is relevant).

The rot set in about 50-100 years ago when they stopped teaching Euclid. "The Elements" is a book that teaches the student how to THINK. It uses geometry as the example (a quite useful one), but once the student has "got it" they can think reasonably and rationally, completely and concisely, longitudinally and laterally, etc and etc, about ANY subject. (Eg. Google Abe Lincoln, the small town lawyer who, before any important case, would spend the night reading the Elements.)

How does it work? Let's start at the beginning;

"THE ELEMENTS.
=============
Book 1, Pg 1.
=============
DEFINITIONS.
=============
1. A point is that which has no part.
2. A line is breadthless length..."

And so on (it's quite poetic, really...).

These Definitions are followed by the Postulates and Common Notions (nowadays called "Axioms"). These Axioms are a clear statement of what is NOT KNOWN, but assumed so that we can make progress. Then, in the Thirteen Books (nowadays chapters), follow almost 500 Propositions. These are useful factoids that are proved by an irrefutable, step-by-step process from the previous clearly stated Definitions and Axioms. (Eg. The quite useful Theorem of Pythagoras, or "Bride's Chair", is Prop. 47 of Book 1.)

---------------------------------------------------------

So what's the above ramble got to do with roll centres?

Well, from the many posts on this and other "Roll Centre/er" threads, I see at least SIX different types of RC, most of them discussed WITHOUT ANY DEFINITION AT ALL! No wonder it gets confusing...

So...

The Six Most Common Types of "Roll Centre".
============================================
(These are only the simplified 2-D versions for one axle. Please imagine a 2-D front-view sketch of double-wishbone suspension, as in Mitchell's paper ref'd by Dash/Pat above.)

1. KRC, or Kinematic RC. This is the intersection point of the two wheelprint's n-lines (ie . lines of "no-motion" from WP to IC). This is probably the oldest and most common "RC", and called "kinematic" because it is derived from the kinematics of the four-bar (or whatever) linkage.

2. FBRC, or Force-Based RC. Of variable definition, but often same as 1 above. Called "force based" because the Control-Arm forces are directed along the n-lines and can be combined at the intersection point. (Note that, for obvious reasons (?), the CA forces can ONLY be directed along n-lines, and any otherwise directed forces are carried by the spring-dampers.) On the thread "Force Based Roll Centre VS Kinematic Roll Centre", poor Yunlong Xu set out to prove that KRC=FBRC. Yunlong got it mostly right (a few typos), but was then jumped on by people who were assuming different types of RC without stating clearly which ones they were using.

3. FAP, or Mitchell's Force Application Point(s). I've lots to say about Mitchell's paper, but to keep it brief... http://fsae.com/groupee_common/emoticons/icon_eek.gif Based on algebraic reasoning Mitchell assumes, WITHOUT ANY CLEAR STATEMENT, that vertical components of control-arm (or n-line) forces (ie. jacking forces) MUST PASS THROUGH THE CG. This is arbitrary and misleading. Mitchell does acknowledge his mea culpa ("my bad") in telling students that "RC migration is bad".

4. RLRCH, or Ortiz's Resolution Line RC Height. Again, based on algebraic reasoning Ortiz puts the jacking forces at his (arbitrary) coordinate origin, which this time is at the mid-track position. Again misleading because not clearly stated. Nevertheless, I do like Ortiz's writings because, most of the time, he starts by clearly defining terms he is going to use.

5. SAERC, or the SAE definition of RC. This is called a "point" but is then described in such a way that only its height can be determined. Mitchell quite correctly says this is the work of a "committee".

6. MC, or Motion Centre (my term). This is very commonly used (and abused!) to refer to the 2-D motion of the car body relative to some other, INVARIABLY UNSPECIFIED (!!!), reference frame. This other frame might be the ground, in which case KRC=MC, but only if BOTH WHEELPRINTS ARE PIN-JOINTED TO THE GROUND, which they never are. There is a tenuous connection with beam-axles here, where the two WPs have a fixed distance between them. Much more to be said on this (ie. 3-D Motion Screws...), but maybe later...

-----------------------------------------------------------------

Deep breath, almost there....


Soooo..., you're in the Design tent;

Design Judge,
"So, Suspension Boy, tell me about your roll centre movement during cornering."

Suspension Boy (folding arms, rocking backward on heels and looking down nose),
"And just which of the six most common roll centres are you talking about? Well!?"

(Z thinks - Err... Oops, no, no, no. That won't work. How about...)

Suspension Boy,
"Yes Sir. Well, there at least six different concepts just for 2-D roll centres...
blah, blah, blah...
BUT!
We, Sir, prefer to take a holistic 3-D view of the car, which, in its simplified form, has five bodies, namely the main chassis-body and the four wheel-assemblies, each with their own mass distributions. We then see these bodies interacting via the n-lines and spring-dampers of the respective suspension linkages. The n-lines, determined by the relevant 3-D motion screws, carry the fast acting "geometric" forces, also referred to as "inelastic" forces, but that's a poor term. The spring-dampers carry the remaining forces, usually referred to as the "elastic" and "viscous" forces...
blah, blah, blah..."

And so on...

More later (if anyone can take it???).

Z

[ZAMR]

http://i1230.photobucket.com/albums/ee496/zmoor/RC.png

Alrighty...

If we create a vector from the tire contact patch to the same tire's instant center we can take that vector to describe the direction that any force must take from the sprung mass to that tire's contact patch. Some say a roll center is not important, that it is an imaginary woobly point that does not matter. Sure, but the vector in question and how it changes with time is a very real, and DOES effect the handling of the car, as it determines the geometric weight transfer of the car wrt time.

When designing your suspension, you can choose the characteristics of this vector. If it has a positive z component (out of the ground plane), you will inevitably have some instantaneous weight transfer before the car starts to roll. If your IC's are on the ground plane, you can see how there will be no instantaneous weight transfer, since you cannot react any vertical forces through a vector with no vertical component.

If you want to truly understand the weight transfer characteristics of your car, you would have to create a model that can balance the forces and moments acting on the car's mass and the tire contact patch (TCP), accounts for IC-TCP distance changes, etc. Your roll center is moving all over the place, but your model is solving for forces in real time so who cares.

Or,

Instead say you wanted to create a simpler model. You can constrain your roll center, calculate an equation for jacking forces wrt lateral force, and input all your camber curves. This gives you a very easy way to model the transient and static weight transfers taking place in your suspension, and a pretty good one too. Just make sure you haven't messed up your camber curves in the process.

So where do you want to spend your time? You can spend a lot of time in kinematics trying to lock down that KRC (actually, making sure your IC's move along the original IC-TCP vector) or you can spend a lot of time writing code that accounts for all the changes in your IC-TCP vector wrt tire displacement. Either way you can understand the behavior of your car, but I'd argue that one way is slightly more intuitive.

So is KRC confinement the holy grail of suspension design? No. Either way you can arrive at a good solution, but you have to spend time looking at it. Simply ignoring the IC-TCP vector is not OK. Either constrain it, or write equations that keep up with it. Just my view.

[Z]

ZAMR,

I'm being picky here, but I hope this helps everyone with their understanding.

You say "[a WheelPrint's n-line is] the direction that ANY force MUST take from the sprung mass to that [WP]" (my emphasis).

No! The Spring-Damper exerts a force on the WP that is not in the n-line direction. It is important to understand this distinction. Note that the SD forces are very rarely shown in sketches, etc. So, if we assume for VD analysis that the SD is vertically above the WP, then the n-lines carry no forces in straight running (assuming zero toe angles, etc.) The combination of lateral and longitudinal n-line forces, and a notionally vertical SD force, gives the resultant force between WP and ground.

Furthermore, for this sort of dynamic analysis we don't need to know the IC positions, only the n-line slopes. Camber change is another matter, somewhat second order, say, compared with toe/slip angle combined with Fz, coefficient of friction, etc.

Lastly, not "forces and MOMENTS acting on the car's mass" but "forces and COUPLES acting...". Sorry, I know they teach you to say "moments", but there is a difference.

Z

[ZAMR]

Originally posted by Z:
ZAMR,

I'm being picky here, but I hope this helps everyone with their understanding.

You say "[a WheelPrint's n-line is] the direction that ANY force MUST take from the sprung mass to that [WP]" (my emphasis).

No! The Spring-Damper exerts a force on the WP that is not in the n-line direction. It is important to understand this distinction. Note that the SD forces are very rarely shown in sketches, etc. So, if we assume for VD analysis that the SD is vertically above the WP, then the n-lines carry no forces in straight running (assuming zero toe angles, etc.) The combination of lateral and longitudinal n-line forces, and a notionally vertical SD force, gives the resultant force between WP and ground.

Furthermore, for this sort of dynamic analysis we don't need to know the IC positions, only the n-line slopes. Camber change is another matter, somewhat second order, say, compared with toe/slip angle combined with Fz, coefficient of friction, etc.

Lastly, not "forces and MOMENTS acting on the car's mass" but "forces and COUPLES acting...". Sorry, I know they teach you to say "moments", but there is a difference.

Z

Of course, I mispoke. Any force applied in a stepwise manner, before the car starts to roll, must travel through the "n-lines" to get to the TCP. The model I drew would not be possible if the SD's did not exert a force, the car would simply roll over!. The springs and dampers (and arbs) exert force as the car rolls.

And we're saying the same thing, you say keep n-line slopes the same, I say keep the ICs on the original (by original I mean car at rest, no lateral force) vector as the car moves. Same thing.

If you want to get picky about couple moment stuff ok. If I balance forces and moments, I will have the same result if I balance couples and forces. In the US we balance moments.

[Z]

ZAMR

In the US we balance moments.

I think all of the English speaking world uses "moments". "Couples" are so 19th century... My point is (and I acknowledge that I'm totally outnumbered here), what most people are saying is similar to,

"Black and White? Same thing really. Just call them all Black! You're splitting hairs Z!"

I think both Mitchell and Ortiz got to their unnecessarily complicated versions of RCs by not fully understanding what they were doing. That is, they used the various short-cuts inherent in algebraic "balancing of forces and moments", and overlooked the fact that they were making ARBITRARY AND UNSTATED ASSUMPTIONS. Namely, their choice of an origin of coordinates. Doing it with "old school" geometry doesn't require such arbitrary assumptions, and also gives better understanding (IMO).

As an example of what I'm ranting about. We have a horizontal force at the left wheelprint Fhl. We use the vector cross product to calculate that there is "a moment Mhl, at the CG, due to the force Fhl". Now we draw a second picture with Fhl acting at the CG, and , err..., also Mhl, err..., yes, also at the CG (???). But how can these two very different pictures represent the same situation. In the second picture, how can Fhl exert any moment about the CG, when it is AT the CG???

The answer is that in the second picture we have moved Fhl away from its original line of action, to the CG, and therefore have had to add the couple Thl to compensate for this move. The "new" Fhl, at the CG, is in fact a totally different force to the old Fhl, at the WP, but we just use the same name to save letters. And where do we place the couple Thl?. Well, as all small boys know http://fsae.com/groupee_common/emoticons/icon_biggrin.gif , a couple is a free vector, so we can place it anywhere.

Note that we only need one force to create a moment, but we need at least two forces to form a couple. They are very different things.

Z

[ZAMR]

Not arguing here, I don't see why we have to translate forces and moments and couples and doohickymabobs all over the place. Centrifugal (Oh no! there's no such thing, or whatever) force and weight act at the CG of the sprung mass (and unsprung masses too) and then normal and lateral tire forces exist at the contact patch. Just draw your statics/dynamics diagram and solve it over time.

There seems to be an anti-pay-attention-to-the-roll-center group out there because no one can tell them what a roll center is or what it does, so why should they pay attention to it? Congrats, you are an engineer! However that also means that you have to think critically about these tings, draw some pictures, and figure it out for yourself.

If the only thing you look at is camber change in bump/roll, then you have no real idea how your car transfers forces elastically/inelastically. If you don't want to mess with the KRC, fine, as long as you can look at the "holistic 3-D view of the car" etc. I personally believe constraining "n-line slope" or whatever is beneficial to the engineer because it gives a way to easily define elastic/inelastic weight transfer characteristics of the car (also easy to model), and it shows that the engineer understands what a kinematic roll center is and how it truly works.

[Z]

ZAMR,

I agree 100% that you can use "Centrifugal force at the CG".

The reason Mitchell, Ortiz, and many others, "translate forces and ... doohickymabobs all over the place" is that they have been taught that the forces have to act AT the CG in order to accelerate it. Hence they move the wheelprint forces up to the CG, and lose a lot of the clarity in the original picture.

I also agree that the common view is that "Oh no! there's no such thing" as inertial (eg. centrifugal) force. In some circles, more the physics community than engineering, it is almost a hanging offence to mention "inertial force". Funny thing is, the standard argument that the physicists use to "prove" that inertial force is NOT real, is actually a very good argument in favour of it being just as real as any other "real" force.

Long live d'Alembert!

Z

[exFSAE]

This whole topic may be a bit less confusing or grey if it were just looked at in what I consider the practical and meaningful part - what are your jacking coefficients at each corner of the car. When I started to think of it like that it was much easier to comprehend the significance, rather than dicking around with translating forces into force / moment equivalents here and there.

In my experience all this talk of RC location, force application points, etc etc... all it is, is a way of showing or linking jacking coefficients (which as an aside are only half the story if you're not talking about relative lateral force on each tire).

Ultimately to be a GOOD engineer with this stuff you have to understand the relative significance of things. It's funny, in college doing FSAE I got in this mindset of having to chase down "all the little stuff that adds up" to be competitive. Double edged sword in that you can easily get caught up in the minutiae and waste time that can be more effective elsewhere. For example, if your "RC" is right around ground level and your jacking coefficients are tiny... lateral movement probably doesn't amount to anything. Perhaps more significant if your "RC" is generally higher.

Or as another example, since all of this relates to vehicle balance changes through load transfer effects... plenty of FSAE students like to dick around with roll centers. If you were asked in the design event to give some numbers for how much your tires' overturning moment affected your total and relative load transfer numbers, or even "pneumatic" track width change.. how many would have an answer for it? Is it more or less significant than some arbitrary amount of RC movement?

[PatClarke]

Quote exFSAE "you can easily get caught up in the minutiae and waste time that can be more effective elsewhere"

Very well said!

Pat

[wil oberlies]

The following was sent to me by an engineer working in American motorsport (and seems to be a really bright guy). Again, the following are not my thoughts....I'm not this smart.

'Obtaining your jacking coefficients is actually similar to obtaining a KRC, but it doesn't take those extra (invalid) steps and uses the coefficients in a different way. Things get more muddy when you deal with mechanically coupled suspensions such as live axles. Your Kinematics texts will describe how to calculate an instant center and what can be done with it. For independent suspensions, the equivalent swingarm theory is important, which basically replaces the upper and lower control arms with a single swingarm in the Front-View of the chassis. This is functionally equivalent so long as you remember that the swingarm mount is not locked in space, but free to move as the control arms would require. It is also important to understand that Instant center creation (from a 4-Bar linkage) is a 2-D representation of reality. We attempt to account for this by calculating in both the Front-View and Side-View (and determine independent instant centers for both cases), but there is still error involved compared to a 3-D kinematic analysis.

Once you've got an instant center, there is a "force-line" between the instant center and the tire contact patch. This "force line" describes the transfer of the lateral tire load through the suspension to the chassis. The angle of this force line is important, because that designates the Fz/Fy coupling...essentially how much vertical jacking force is present per unit of lateral force.

Now you've got you coefficient, if you have lateral force to apply then you can determine jacking loads at each side of your suspension (Coeff=Fz/Fy)...these jacking loads are in parallel to the spring/shock/bar loads, meaning they can be summed at an instant of time. The jacking loads create anti-roll moments (like springs) or pro-roll depending on the coefficients values. As mentioned by some, you can probably calculate an accurate-enough total axle lateral force from F=ma (m being the front static mass), the assumption required is how to split up that load between inside and outside tires. Depending on what kind of analysis you are doing (Simple Excel spreadsheet, a Dynamic Sim, or something in between) you may not even have to assume the lateral load split.

If you don't want to split lateral force, then you can simply compare your jacking coefficients between setups. For an Excel spreadsheet type analysis, this is fine. If your sim is more complicated then use a calculated lateral force...use a constant load split for every case if necessary. Lots of proponents of RCs wish to "split up" their load transfer through elastic (springs/bars) and geometric (suspension jacking) load paths. What they fail to realize is that the "geometric load transfer" depends on lateral force split, so they are no better off (and have a less valid analysis).'

Thoughts?

[exFSAE]

I'd say that's pretty much on point, Wil.

[Z]

Wil,

Yes, pretty much spot on... Some comments:

It is also important to understand that Instant center creation (from a 4-Bar linkage) is a 2-D representation of reality .... but there is still error involved compared to a 3-D kinematic analysis.
If you do the proper 3-D analysis (it's not hard) you get 5 n-lines for the single degree of freedom motion of the wheel (up-down). This accurately models the kinematics (but not the compliance, which, hopefully, is a second order effect!).


Once you've got an instant center, there is a "force-line" between the instant center and the tire contact patch. This "force line" describes the transfer of the lateral tire load through the suspension to the chassis. The angle of this force line is important, because that designates the Fz/Fy coupling...essentially how much vertical jacking force is present per unit of lateral force.
This "force-line" is one of the "n-lines". Note that IC position is NOT important for this analysis of instantaneous dynamics. 2-D IC position does relate to camber change (in a slightly faulty 2-D way), but toe change (bump steer) is more important, and better worked out in 3-D.


...these jacking loads are in parallel to the spring/shock/bar loads ... the "geometric load transfer" depends on lateral force split.
Firstly, as a first approximation of "lateral force split", try the vertical force split. If left wheel carries twice Fz of right wheel, then left Fy = ~ 2x right Fy. Then add second order corrections for different toe angles, cambers, tyre load sensitivity, etc.

Secondly, this "jacking/geometric load transfer" is also called "inelastic LT" quite often on this site. "Inelastic" is not a good name (IMO) for 2 reasons:
1. It means "not springy" so it includes ALL non-spring types of LT, such as the "viscous/damper" LT, which is not what is meant.
2. Technical communication generally works better when you call a spade a spade. So imagine soldiers in enemy territory, sitting and having a rest. One hears a sniper bullet whistle past his ear and shouts "Don't STAND UP!". You can bet someone will stand up and get their head blown off! Better to shout (in big Arnie S. accent) "GUT DOWWWN!"

---------

So, how about these 3 types of ground-to-wheel forces for 3-D VD analysis (together with gravity and inertial forces at the CG);
1. "Virtual Control Arm" or "geometric/kinematic/n-line" force, which lies in the plane of the n-lines at the WheelPrint. This can be decomposed into horizontal (lateral and longitudinal), and the vertical (jacking) components. (H and V are relative to car floor.)
2. "Virtual Spring" or "elastic" force, acting vertically through the WP.
3. "Virtual Damper" or "viscous", also vertical through the WP.

These "virtuals" simplify the picture for dynamic analysis - all forces are either horizontal or vertical wrt car, and all are at the WPs. Of course, when you do stuctural analysis you have to account for spring-damper angles, etc., which can load up the control arms even when stationary...

Enough rambling for now...

Z

[wil oberlies]

Please accept my apologies, but does anyone know of a visual representation of jacking forces as a result of lateral force; it would be helpful to me to be able to see a drawing of the forces at work. I assume the n-lines could be resolved into equivalent vertical and lateral forces....?
Thanks in advance.
Wil

[Z]

Wil,

Try Racecar Engineering July 2010 (V20N7) page 62, Figure 10. (As noted earlier the text has been scattered around, but it is mostly under the figure.)

One day I'll figure out how to post pics here, but at the moment all this photobucket stuff sounds too hard http://fsae.com/groupee_common/emoticons/icon_frown.gif (Is there an easy way?)

https://lh5.googleusercontent.com/-arTDwLtqt_A/TuasCHP62vI/AAAAAAAAAHk/TMOt63WgDmc/s800/MechAntiFg10.jpg

(Edit) Added the above for anyone trawling the backpages. Shown is a car accelerating longitudinally (eg. forward), but same principles apply for lateral acceleration (ie. cornering). Black arrows are the forces acting on the wheelprint or car. White arrows are some of the possible components of the black arrows. Fca = Control Arm force. Fsd = Spring-Damper force. H = horizontal. V = vertical. G = Gravitational. I = Inertial. Etc...(End Edit)

Z

[wil oberlies]

Thanks Z, much appreciated.

[ben]

The diagram on page 138 of Costin and Phipps makes far more physical sense to me than any of the big discussions on roll centres.

The one that just confuses me massively is the models that consider an asymmetric lateral force distribution and still arbitrarily place the roll centre at mid-track.

Ben

[wil oberlies]

Ben, thank you...helps a great deal. I share your bafflement with the models you refer to, also with concept writ large, given the number of different types of RC and thier alleged significance. Seems some (most?) people agree that jacking forces are worthy of consideration, regardless.

[exFSAE]

Originally posted by ben:
The one that just confuses me massively is the models that consider an asymmetric lateral force distribution and still arbitrarily place the roll centre at mid-track.

RC at mid track just implies that the jacking coefficients (dFz/dFy) are equal left and right due to the geometry at that condition. Can certainly have that with asymmetric lateral force distribution.

[ben]

No problem :-)

In my experience any LMP and GT car I've ever worked with have kinematic RCs close to ground so the jacking forces don't do a whole lot of bad things, with the rear a little higher so that you get faster load transfer at the rear relative to the front. This keeps the yaw and lateral acceleration in phase (as perceived by the driver.) If the car's lazy on turn-in raising the rear RC (not by ride height) can help, conversely lowering the rear RC (not ride height) can help if the car lacks entry stability.

It's important to know the underlying physics, which is what we're discussing, but the rule of thumb is just fine in practice despite the scoffing of certain people.

I think Edward Kasprzak's review of "Think Fast" was excellent because he realised that the lack of equations wasn't a problem because it was clear that the author knew the underlying physics. That for me is the key difference between trackside and a design office - knowing when do a big calculation or (in this case) just dropping the rear KRC.

Ben

[Z]

Some final thoughts regarding Migrating Roll Centres (supporting some previous posts by others above).

Say you're an inexperienced team and you've gone through Geoff Pearson's Level 4 and 3 "Reasoning ..." processes. You've narrowed your front and rear suspension designs down to two options;

Option 1. This has horizontal n-lines that stay horizontal wrt the car floor with wheel bounce. Practically this might be SLA double-wishbones with ground level ICs, or 2cv style leading and trailing-arms, or Morgan style vertical sliding pillars.

Option 2. This has lateral swing-arms pivoting about a low axis along the car centreline.

Option 1 has nominally ground level KRCs, FBRCs, etc. (but NOT MCs, which can be anywhere). However, these Option 1 RCs zoom off to "infinity", or at least the next county, with the slightest roll angle (because "parallel lines meet at infinity").

Conversely, Option 2 has rock solid RCs that are guaranteed never to migrate anywhere. You can actually touch these RCs, as they are the BJs that the arms swing on (assuming all BJs co-linear). However, since these RCs are about 5cm (2") above ground, you can expect some jacking.

So, the big question is, which is the, err..., "OPTIMAL" design?

I would argue that the best design is the one that can be built most QUICKLY, CHEAPLY, and ROBUSTLY, so that you can get on with the far more important (and fun http://fsae.com/groupee_common/emoticons/icon_smile.gif ) matter of wearing out tyre rubber during testing.

Issues such as RC migration or jacking are relatively inconsequential in the big scheme of things. Either effect can be easily swamped by other tuning factors.

Eg1. Too little LLT because of low KRC? Add a stiffer ARB or more low-speed damping.

Eg2. The 0.5cm jacking due to a "high" RC is reducing the aero from your front wing? Add a stiff "third-spring" (aka a "camber compensator" or "lateral Z-bar").

RC migration and jacking can be fun to talk about, but they won't help or hinder you when it comes to finishing Endurance.

Z

[ZAMR]

Originally posted by Z:
Eg1. Too little LLT because of low KRC? Add a stiffer ARB or more low-speed damping.

Eg2. The 0.5cm jacking due to a "high" RC is reducing the aero from your front wing? Add a stiff "third-spring" (aka a "camber compensator" or "lateral Z-bar").

RC migration and jacking can be fun to talk about, but they won't help or hinder you when it comes to finishing Endurance.

Z

Just don't tell Billings you used your dampers to tune LLT on turn entry. He'll ask why you didn't use a high rear KRC (Even though I'm firmly convinced that low speed damping will not effect tire load variation due to road input, so using high rear damping coefficients is fair game if it makes the car turn faster IMO).

Also I think finishing endurance is way in the back of ppl's mind at this point. We're talking about design points right now!

[flavorPacket]

Originally posted by ZAMR:

I'm firmly convinced that low speed damping will not effect tire load variation due to road input, so using high rear damping coefficients is fair game if it makes the car turn faster IMO).

You may be convinced without proof, but this actually isn't that challenging to prove.

[dynatune]

Technically speaking the RCH as is being used in modern suspension design is "only" valid at the very beginning of lateral vehicle movement. As Wolfgang Matschinsky quite extensively demonstrated in his book, the theory of how to calculate the vertical roll center height or lateral roll center migration is only valid if we assume that the vehicle would actually run on rails which would allow a rather precise location of a contact patch point. Since we do however have a tire on a car that is far from consistent as a railway steel wheel the actual position of that contact patch becomes more and more less defined with more and more lateral acceleration. Hence, we do not know where the rollcenter is, neither in height nor in lateral position. We do know however that having a low roll centre is reducing jacking forces so that is a good thing. Also we know that "if the roll center migrates" it should migrate towards the inside wheel, for the very simple reason that - still assuming that the vehicle body is rolling about the roll axis - an increase of roll angle would lead by definition towards more wheeltravel on the outside wheel than on the inside wheel and thus work against jacking. This info should help you avoiding to make the most common mistakes.

Cheers
dynatune

[Z]

Dynatune,


Technically speaking the RCH as is being used in modern suspension design is "only" valid at the very beginning of lateral vehicle movement...
... with more and more lateral acceleration ... we do not know where the rollcenter is, neither in height nor in lateral position.

If so, then "modern suspension design" needs a big kick up the backside!

As long as the "Roll Centre" is adequately DEFINED, and all the ASSUMPTIONS used are also clearly stated, then there should be no problems finding the RC at any time.
~o0o~


Also we know that "if the roll center migrates" it should migrate towards the inside wheel, for the very simple reason that - still assuming that the vehicle body is rolling about the roll axis - an increase of roll angle would lead by definition towards more wheeltravel on the outside wheel than on the inside wheel and thus work against jacking.

Wrong! You are confusing two very different versions, or DEFINITIONS, of "roll centre/axis".

The "roll axis" you use above to describe motion of the car-body with respect to its four wheelprints (which, strictly speaking, is an impossibility!) is in no way related to the KRC, or FBRC, as these more usual definitions of RCs are defined half-way down page 4 of this thread. (That earlier post was written over four years ago, and it seems that the lack of people using clear definitions in these discussions is getting worse! :().

Here is a post from another thread (almost two years ago...) showing the difference between two different types of "Centre". "Where is the Motion Centre?" (http://www.fsae.com/forums/showthread.php?6945-anti-dive-setup&p=118084&viewfull=1#post118084)

Z

(PS. When Matschinsky's book drops below ~$100 I might buy it. But if he believes that the RC "should migrate towards the inside wheel", then maybe I shouldn't bother?)

[dynatune]

Z,

With "modern suspension design" I meant after 1989 when the book that you are still considering to buy came out. Actually the rest of the quote came out of that book (page 141/142, first edition).

And as you said most correctly:

As long as the "Roll Centre" is adequately DEFINED, and all the ASSUMPTIONS used are also clearly stated, then there should be no problems finding the RC at any time.

Independent of what definitions are being used, the point I was trying to make was, that not having a correct contact patch location, any calculation of RCH (for that condition) is equally difficult leading to a correct result (with whatever method), and thus needs to be treated with some care.

With respect to the roll centre migration, I take gladly all the blame for that . Back in 1995/1996 I did participate in quite a long study - most of it in virtual in ADAMS, some of it on a real car - that was focused on finding out more about the vehicle body movement in relation to the suspension roll centres position and find out any possible correlations. We did execute lot's of sensitivity DOE's on a virtual K&C test rig where we did change in an orderly matter various parameters of the suspension and looked at what happened on the virtual vehicle. Besides the fact that a lower roll centre height on the virtual rig reduced jacking of the virtual vehicle, we did also notice that if the RC migrated "in roll" on the virtual rig towards the inside wheel this also reduced jacking on the virtual car, hence the conclusion -at that time-seemed logical that there was a correlation and we explained it to ourselves with the explanation above. That's all.