Moments about IC's and effects on Roll Center

[Pennyman]

I’m going to shake things up a bit.

I’ve been looking extensively into the importance of roll centers, both kinematic and force-based, and come to some interesting realizations.

All the kinematic RC does is tell us how the instant centers are moving, but not very accurately.

The kinematic RC can fool us into thinking the instant centers are not going crazy, when they are. For example, the kinematic roll center could stay put while the IC’s shoot off towards infinity and climb in altitude by 2 feet or so, but because the lateral IC motion is so much bigger, the roll center stays put.

This leads me to my next point. Vertical and lateral tire forces have since been used to find the force based roll center, but they are usually used independently of the locations of the instant centers. But why leave IC position out?

Let me explain. Tire force creates a resultant vector that we can translate to a point along that resultant line. The magnitude/direction of this vector interacts with the height and distance of its individual instant center, creating a moment, wanting to cause suspension movement and thus chassis roll. I have never seen a definition of the force-based roll center take the position of the IC into account. You can see from the picture below that the height and the distance of the instant center contribute to the moment.

http://img38.imageshack.us/img38/7798/forcevector.png

It makes total sense that the height and distance of the IC’s contribute to a moment about the IC itself, and that the magnitude of that moment determines the ratio of elastic to geometric weight transfer.

http://img525.imageshack.us/img525/6091/asdfjadgfa.png

For example, in a case with a below ground kinematic roll center, the altitudes of the IC’s are also underground. The resulting moment about the IC will be much greater due to the increased vertical distance (larger D), hence more elastic weight transfer.

So the question is where is the roll center? I think a better question to ask is, how linear is the increase in the difference between the two moments? I think the point the chassis rolls about is pretty dependant on how linear the roll stiffness of the suspension is through its travel, then comparing that to the difference in the moments around the instant centers.

[jrickert]

This message board seems to be slowly converging on the solution. Suspensions are made out of forces and moments not woobly points that migrate.

[Jersey Tom]

http://fsae1000.blogspot.com/2...-geometric-load.html (http://fsae1000.blogspot.com/2009/06/thoughts-on-roll-centers-geometric-load.html)

Shameless plug...

[Drew Price]

Dood, Pennyman, you're going to confuse sooooo many people in the next day or so, I love it.



Originally posted by jrickert:
.... Suspensions are made out of forces and moments not woobly points that migrate.

^^ I love this. ^^ Woobly. *haha*



Best,
Drew

[Raechel]

Have you read Bill Mitchell's SAE paper on force-based roll centers? I think it may answer your question... He doesn't explicitly mention the importance of the IC position, but it's kind of implicit in his analysis because he talks about resultant forces in the directions of the A-arm linkages.

[John Block]

Somewhere an old dynamics professor rolled over in his grave. I’m going to coin a new phrase here and let it be known ever after that I said “Roll Centers fact or fiction subtitled, The greatest lie ever told in racing!”

Has everybody forgotten Dynamics class? Poor old ICs should not be so misused by folks who should know better. Why doesn’t somebody show me a free body diagram. Then maybe the light bulb will come on and you will remember the IC was a nice trick we used with velocity vectors when working with an object on rotational translation, but you missed a bunch of forces on the system. Some how the concept has been pushed to the idea of a fixed connection that the chassis roll on. If this were English rather than Engineering, you would be rightful charged with mixing your metaphors.

Now, think about the big picture! Are you missing forces? A good engineer will say “Sure, how about aero?” However, a really good Engineer will think about frequency inputs and say “Oh my gosh, why were we so locked on that silly roll center idea?” Think about system input and response.

Don’t jump on Google and expect to find the answer. That is just like looking in the back of the book for the answer, which is a common complaint I hear from Engineering Professors. When you get a job where are you going to look?

So, where does all this ranting and raving lead? Are you looking for a quick answer here on the forum or are you scientifically curious and willing to develop the answer?

Remember, summer is not vacation time, you must never stop thinking like an engineer.

[Pennyman]

John, I'll take that as a compliment...

[Adambomb]

Yes, John, what is that rant about? I saw no ignorant question posted here, this appeared to be the development of some interesting discussion.

In fact, I'm not sure what your rant was about. For example, what IS the effect of aero on IC migration? And frequency response??? I suppose you could delve into frequency response of IC migration, but I'm having a hard time believing that would yield anything useful. That's like saying, "oh yeah, what about shock hysterisis?" A worthy topic on its own, but not really useful to the subject at hand IMO.

Anyway, I'm amused with where the original topic is going. I've never really thought about it too much in depth, I just imagine the added effects of tire and suspension compliance, which sort of effs the rest of it up, at which point my head hurts. http://fsae.com/groupee_common/emoticons/icon_biggrin.gif Could very well be onto something here though, at least for the hard-core vehicle dynamicist.

[John Block]

No time right now, but tomorrow we can continue.

The rant is roll center, roll center, roll center. When is somebody going to talk about static margin or something fun like elastic conjugate points or any thing but the roll center?

Remember the roll center is the result of the motion and not the cause.

[exFSAE]

Originally posted by John Block:
When is somebody going to talk about static margin or something fun like elastic conjugate points or any thing but the roll center?

When? When this isn't FSAE and people aren't struggling to retain the understanding of the basics from year to year. Until then...

[Chris Allbee]

I'd say I agree with John on this one. I think that with the number of tools and amount of information now available, new people shouldn't have to learn incorrect knowledge just to have to re-learn the truth later on.

My advice, go ahead and calculate that roll center. Convince yourself that constraining its movement is the holy grail to a good suspension. Then spend some time scratching your head wondering why you still see your tires develop loads of positive camber in every corner.

[flavorPacket]

Too true, Chris! I think you just described 95% of all FSAE suspension designers right there...

IMO Ch. 17 in Milliken does more harm than good these days.

[John Block]

Sorry, for not getting back sooner, between teaching a class, a Board meeting and a separate Presentation the yesterday just evaporated. Pennyman, actually I admire you curiosity and willingness to think outside the box. However, I’m not sure I understand your fascination with the IC.

Remember from Dynamics Class that the IC is a point where a perpendicular line to any velocity vector on a slab in rotational translation will intersect a perpendicular line from any other velocity vector on the slab. Bottom line was we ended up with a point and angular velocity about the point for the slab. All we had was velocity and not acceleration, so no acceleration then no force(s) can be backed out even if we know the mass. As such, we really cannot use a single IC to back out the forces on the object.

Granted we can pick a point and take forces and moment arm and start summing up moments (but it might be better to use a moment arm perpendicular to the resultant’s line of action and not orthogonal to the picture’s orientation). Anyway, in taking your approach you may have inadvertently missed some simplifying assumptions never stated, such as uniform spring rate left & right and a linear wheel rate (compression/rebound), ditto on damping (shocks), etc. which seldom happens in the field.

There was also an assumption with the resultant force at the tire. The lateral component can be assumed or derived from vehicle speed and turn radius, etc, but magically a vertical component was introduced to create a resultant vector. I take the vertical components to be the result of the load transfer due to the overturning moment of the half model (front or back of the car). The line of action for your resultant is a product of the vertical component. So in essence your moment arm at the IC back to the resultant force’s line of action is a function of the vertical component. At this point it is getting pretty cloudy with assumption and number of unknowns in the problem.

Not to totally rain on your parade, but the statement that “the smaller moment around the IC the less suspension motion” goes back to the simplifying assumptions. This neglects spring constants and ARB constants. Plus think about this: no racing surface is a true plane. We don’t have to get into spectral density or anything, but the wheels always have some sort of input signal due to the undulations in the surface. That frequency input is my secret weapon used with the dampers. Heck, before they milled Lowes Speedway the corners were rougher than the straights. I actually got the car to roll backwards (to the inside) in the turns and proved it on the data acq. Anyway, my point is there are many factors you have not accounted for in your approach such as wings (in the last two years I’ve used aero to do some pretty trick things with platform orientation on Indy Lights cars).

At this point let’s shift gears. Please do not try to use the roll center for anything but a convenient point to sum moments and calculate load transfer. Truly, the roll center is the result of the motion and not the cause. In one of my online classes I show how some publications make what I call the compass mistake. This is where the person placed the compass in the paper at the roll center and makes an arc at each pickup point to find a new body position, WRONG! DO NOT PROPAGATE THIS MISTAKE. At that point the roll center is the cause and not the result. What if I have different springs left & right, what if there is there is superelevation, or, or…?

As best I can tell Olley is the one to popularize the kinematic roll center way back (like 80 years ago). It was clever for the time but still not a very good solution and even then field observations were a bit different than the model.

I like the force-based model much better, not just due to the frame of reference problems with kinematic model, but we are starting to account for restoring moments (springs etc) so this model has fewer simplifying assumptions.

Very bottom line, there is no proof that a non-migrating roll center is the holy grail to suspension design. Here is where I get on my soap box, what is the top priority in suspension design? In my online class I stress camber as the top priority of geometric parameters. I back this up with logic and examples from data acquisition. Granted there are writers all over the place that will argue the point, but I don’t see them in the pits putting me to shame. In fact, I don’t even see them at the track. To close let me say that if automotive engineering was easy then there would be no need for proving grounds. We use our education as best we can to calculate, model and design only to find in the field that we totally forgot something, or got tripped up on a known-unknown or my favorite on the unknown-unknown. But, by no means stop thinking outside the box, you just never know what you will find. Imagine poor old Copernicus saying the earth was not the center of rotation, but rather the sun (he surely would have poopooed the whole roll center dealhttp://fsae.com/groupee_common/emoticons/icon_wink.gif.

[exFSAE]

Originally posted by John Block:
Very bottom line, there is no proof that a non-migrating roll center is the holy grail to suspension design.

Who said it was?

The only thing I give a shit about is as follows:

With the chassis constrained, if you apply a lateral force at the tire's ground contact point, there is a resultant vertical force change. Can see it plain as day on the SPMM.

I can use the rate at the left and right tire at an axle to define a "roll center" or "force center" or whatever you'd like to call it. I want to know how far off that is from the kinematic RC.

That's all I'm interested in, but in all the handwaving RC explanations (which everything in this thread so far counts as) I've never seen data to that point.

[Pennyman]

John, thank you for the lengthy response. I like hearing from people with more experience than I.

You are correct in that I made a lot of assumptions.

The lateral force is calculated from a theoretical lateral g load and the mass on that end of the car.

The vertical force is calculated based on a steady state assumption using CG height, track width, axle weight and lateral g.

The moment about the IC is very similar to Bill Mitchell's broomstick analogy from Wingeo3.

However, I never stated that a larger moment about the IC means more suspension motion. It only means there is a larger percentage of elastic weight transfer. I am well aware that stiffer ARB's will reduce suspension motion, which in turn will affect your roll gradient, and thusly the amount the IC's migrate.

It was never my intention to incorporate aero into my analysis, or road irregularities. All I wanted to do was cross reference different suspension designs based on a net moment applied to the sprung mass. It was only a side affect that I realized in the process that the roll center is an effect, and is influenced by things like motion ratio linearity.

It's like FEA, sometimes it's better as a comparison tool rather than an end-all-be-all decision maker. Better to make a few assumptions to get a few miles closer to the ballpark than use a RC method which is basically a rule of thumb based on (what I believe to be) motion of the IC's in the first place!

At this point ALL I'm using the kinematic RC for is, like you said, a point to sum moments around. It doesn't seem to be good for much else.

[Chris Allbee]

exFSAE, why do you really care what an imaginary point is doing and where it is in relation to another imaginary point? What are wanting to get from the exercise?

The tires are what is important. The whole point of the suspension in a racing vehicle is to provide the tire with optimum operating conditions. Geometrical constraints (suspension linkages) need to be arranged to provide the appropriate amount of camber to the tire (check the tire data, or survey other suspensions). Springs and dampers are there to provide a consistent contact patch force and keep the chassis from touching the ground.

If you really must know the point the chassis is going to roll around kinematically, then plot the transformations in Excel. Bump one wheel by a unit, drop the other the same amount. Reposition the points representing the vehicle so that the dropped contact patch point is at your ground plane, then rotate the points representing the vehicle about the dropped contact patch point until the bumped contact patch point intersects the ground plane. Measure the roll angle and roll center location from that. You can now use different amounts of suspension bump and droop to get different roll angles.

Determining a force based roll center seems a bit strange as well. I understand determining the force vectors from the contact patches, this is all well and good information to have. But again, what is the point of determining the contact patch force vectors? What do forces act on? Mass. So one calculates the force vectors and uses them to apply moments and forces to masses to determine accelerations. WHY do you care where they intersect? Does that change the effect on the mass (provided you keep the system instantaneously rigid)? It all just seems to be an unnecessary intermediate step.

You know, its not all that difficult to whip up a very simple dynamic model in excel or matlab that will provide much more usable information than drawing lines and random points in space will.

Just a thought *WAVES HANDS AROUND* http://fsae.com/groupee_common/emoticons/icon_wink.gif