how to design a bell crank for push rod suspension

[nikhil0078]

hi sir i am nikhil mehrotra age 20 . i am currently working with my team to design an electric car for formula14.
As i am new to the project, i am currently facing problems in designing my bell crank.
Both the front and the rear geometries are completed and now we are working on designing our bell crank.
we are using pushrod suspension for both front and rear.
plzz help me so that i get some idea on how to design my bellcrank.

[acedeuce802]

What problems are you facing? What design work have you done so far?

[MCoach]

First you must connect your shock to the bellcrank.
Then you must connect your pullrod to the bellcrank.

If your geometry is already complete then these points are already defined in space.
Match your motion ratio in your geometry, that's the point it must rotate around attached to the chassis.

Connect the dots and make it a solid part. Done!
Bellcrank is designed. Great victory today!

[nikhil0078]

sir i have no idea on how to calculate the motion ratio. i have completed my 2-D design for front and rear geometries . How should i mount my bell crank and what should be the first criteria in designing bell crank for my car. (only the 16 points of a-arms have been decided so far , next step is to desig a suitable bell crank , how shoul i do it in solid works??)

[nikhil0078]

Hi sir i have completed my 16 points for the mounting of the A-ARMS . now what should be my next step. how should i design my bell crank... what steps should i follow to make it.
I have no idea on how to calculate the motion ratio??? how should i begin??

[Claude Rouelle]

Have you ever followed a course or read a book or watch a video on critical thinking? That is what you need the most I can tell you.

[Claude Rouelle]

Two quick tips and questions

One

- Your lower wishbone outside rod end / spherical joint center (or top wishbone if you have a pullrod)
- The lower pushrod rod end center
- The upper pushrod rod end center (which is also one of the rocker point) (rocker = bellcrank)
- The center of the axis of your rocker
- The damper pick up point on the rocker
- The damper pickup point on the chassis
- The damper axis
- Your antiroll bar droop link

Should all be in the same plane. DO YOU KNOW WHY?

Two

Your front 2 pullrods or 2 pushrods should in a vertical plane (or close to a vertical plane) to the ground. Same on the rear DO YOU KNOW WHY?

Questions:
- How do you come with 16 points? I think you know but I would like to read it from you.
- What Ackermann and what bumpsteer (if any) do you have?
- Why 2D and not 3D?

[nikhil0078]

hi sir, sorry for replying late!!


The answer to your first question should be that all these things need to be in the same plane because the force transfer from the wheel to the bell crank can easily be resolved in a single plane. The force from the pushrod will try to break the bellcrank, the force from bell crank is transferred to the dampers. The advantage of having everything in one plane is that all the forces can easily be resolved.The force transfer is uniformally distributed if it is in a single plane.

got the
Sir my 16 points were decided on a specified geometry which was 3D only( sorry for mentioning 2D in the previous posts). After doing the solid works , we got the main A arm points, those points were then put up to optimum k. Our geometry was stable in optimum k.


We are using 50 percent Ackermann and have a bumpsteer of .05 degrees at 1.5 inches of heave.

[Claude Rouelle]

Nikhil,

OK so in that case, unless huge other compliance, you probably won't have any REIB (Rod End In Bending), good!

So lets's go for the next steps

What are your criteria to chose (assuming you create a double wishbone suspension, not necessarily THE option but let's say)
- your wheelbase
- your front and rear tracks
- your front and rear caster trail and your scrub radius
- your front and rear caster angle and your kpi angle
- your front and rear, top and bottom wishbone upright pick up points on the king pin axis
- your lateral VSAL and therefore you camber variation in roll and heave
- your front and rear roll centers height-
- your ratio between top and bottom wishbone length
- your longitudinal VSAL and your X and Z position of your left and right pitch centers
- your front and rear springs position (that means withinin other things pullrods or pushrods choice) and front and rear ARBs position on the chassis
- your steering rack position
- your steering wheel and steering column (or steering column parts) angle and position
- your front and rear toe link position on the upright
- your ackermann percentage
- your bumpsteer
- your front and rear spring motion ratio
- your front and rear ARB motion ratio


The design of the rocker (= bellcrank) is one part of the puzzle and the answer to the questions above need to be part of thst design. There are no perfect answers but I think the list of criteria question is presented in a logical order.

What do you call a "stable" geometry in OptimumKinematics? Do you have a legal license for this software?

[M. Nader]

Two quick tips and questions

One

- Your lower wishbone outside rod end / spherical joint center (or top wishbone if you have a pullrod)
- The lower pushrod rod end center
- The upper pushrod rod end center (which is also one of the rocker point) (rocker = bellcrank)
- The center of the axis of your rocker
- The damper pick up point on the rocker
- The damper pickup point on the chassis
- The damper axis
- Your antiroll bar droop link

Should all be in the same plane. DO YOU KNOW WHY?



Not all of the mentioned above need to be on the same plane, easier in terms of force calculation yes but geometry can easily change the locations of the following without creating RIEB:

- The center of the axis of your rocker
- The damper pick up point on the rocker
- The damper pickup point on the chassis

Just do realize that most of these are two force members and and not to put bending loads on them and then organize your geometry. a better description would be that any consecutive two points (in reality not the list) mentioned will need to be on the same plane to avoid unwanted/needed loads and have a decent load path.

[Z]

Nikhil,

Why do you want bellcranks?

What is the point?

More specifically, how many more competition points do you think you will get with bellcranks, compared with not having them? Keep in mind that bellcranks cost you more time, money, resources, etc., than not having them.

Please provide at least one good reason for how/why bellcranks will make your car "better".

You might ask Claude why he always wants to complicate things first, without ever making them simple, but I doubt he will "defend his decisions" (DJ privilege, I guess?).

Z

[dynatune]

In principle it is very simple to design a rocker. Start simple and work your way through.

a) make sure that the rotational axis of the rocker is perpendicular to the push-rod angle in the front/rear view and is aligned to the sideview angle of the push-rod
b) on the rocker make sure that the line from push-rod attachment point to rocker axis to spring/damper attachment point is rectangular (90°) and is all in one plane This will give you a linear ratio. By making the angle less than 90° one can create a rising rate motion ratio.
c) the base ratio of the rocker can be calculated by dividing the length of attachment point spring/damper to rocker axis by the length of push-rod attachment to rocker axis. This value is usually greater than 1 and needs to be multiplied with the ratio of the push-rod to wheel. This ratio can be calculated with all kinds of kinematic programs.

happy racings !

dynatune, www.dynatune-xl.com

[Ashir]

I guess on being asked about the genuinity of Software, Nikhil has left.
I want to be sure of my answer to the need of bell crank question. -

*The bell crank multiply the motion of wheel before transmitting the motion to dampers. (this is motion ratio I guess)
*This means the dampers compression/tension is more than the displacement of wheels. This makes the suspension "Stiffer" as compared to the situation when pushrod/pullrod is directly attached to damper.

So we use Bellcrank so that we can make suspension more stiff ?

Just an on spot question which came to my mind while writing this post, if we use pushrod/pull rod directly attached to damper, how Anti Roll Bar is attached in the suspension ?

[JT A.]

I guess on being asked about the genuinity of Software, Nikhil has left.
So we use Bellcrank so that we can make suspension more stiff ?


If that is the only purpose of a bellcrank, why not simply use a stiffer spring to make the suspension more stiff?



Just an on spot question which came to my mind while writing this post, if we use pushrod/pull rod directly attached to damper, how Anti Roll Bar is attached in the suspension ?


The antiroll bar can be attached to any part of the unsprung mass, it's up to you to decide which solution is best. I'd recommend not attaching it to any of the spinning parts for starters. Of course, this also brings up another question- why do you need an antiroll bar?

[Jay Lawrence]

Ashir,

To add to what JT A. said, you may be a bit confused about what a push/pull rod is. If you are not running a rocker or bellcrank then typically you don't have a push/pull rod, because you are attaching the damper directly to the unsprung mass at one end and the chassis at the other. There are many road going cars that have direct actuation (generally the term to describe a suspension without push/pull rods + rockers) combined with anti-roll bars (which are typically connected to the A-arms), but as alluded to above, I think you might need to have a think about what your suspension is required to do. There are a great many posts, particularly by Z, regarding this.

[Ashir]

OK,I went in more depth of search results and visited this topic
http://www.fsae.com/forums/archive/index.php/t-408.html?

Same discussion is already carried out and the conclusion seems good for me.

I myself had thought that by mounting damper directly, we would increase the force acting on it. But then I thought, the force is absorbed by spring not damper.
Then I looked for more information. And turned up with the effect of motion ratio on "effective damper travel" which I interpreted as being stiffer. But again spring's stiffness can be increased in direct mounting of damper as told above.
After this I started thinking about "effective" damper travel. Now I am interpreting it as for the same wheel travel, the damper will push more fluid thus making more effective damping.
Still not completely satisfied, I went for in depth search and visited above mentioned topic. And yes now I would say, my objective is to design the suspension based on the damper we already have. This will save us lot of money (more than what it will be saved on using direct damper mounting by removing bell crank and pushrod costs).
So now I have to make my suspension stiff without changing damper, I will use bell crank to chance motion ratio.
I hope I am on right track. Please correct me if I am wrong or incomplete anywhere!

Edit: I missed out arb question.

ARB: Anti Roll Bar, is used to "fine tune" the suspension. When the chassis roll, the arb blade twists the spring steel rod. The resistance to twist in this rod, creates resistance to roll in chassis. But this resistance is small and thus if required, it can be ommited. When fine tuning is required accounting to track conditions, ARB can play good role.

[Ashir]

Ashir,

To add to what JT A. said, you may be a bit confused about what a push/pull rod is. If you are not running a rocker or bellcrank then typically you don't have a push/pull rod, because you are attaching the damper directly to the unsprung mass at one end and the chassis at the other. There are many road going cars that have direct actuation (generally the term to describe a suspension without push/pull rods + rockers) combined with anti-roll bars (which are typically connected to the A-arms), but as alluded to above, I think you might need to have a think about what your suspension is required to do. There are a great many posts, particularly by Z, regarding this.
Sorry I didn't include your reply in above post as I went for a bath while writing above and didn't see your post.
The link joining bell crank to lower wishbone can be push rod if it is in compression, and pull rod if it is in tension. To add to the benefit of using bellcrank, they allows to adjust ride height without changing spring stiffness.

I am sorry I am not a suspension guy but I have read basics. So please excuse me for my lack of research. I will do some more research and come up with better answers ;)

Till then any help and/or comment is apritiated.

[Jay Lawrence]

Where did you get "effective" damper travel from? There is wheel motion, and this is translated to the damper. There isn't really anything "effective" here. Don't confuse yourself with motion ratio. It doesn't necessarily make whatever suspension mode stiffer; it can make it stiffer or softer or leave it the same, or it can be rising/failing rate.

[mdavis]

Ashir,

Just because you have an existing damper does not mean you cannot mount it in a direct acting fashion. We (University of Cincinnati) and Monash both ran TTX25's (I believe Monash ran TTX25s, if not, someone please correct me) in a direct acting manner in the past year, and those are about as small of a damper as you're going to find. There is no reason you cannot use your current damper in a direct acting installation, you may just have to be a bit more creative in your packaging/frame design.

-Matt

[jpusb]

LOL about the software license haha

Ashir,

I recommend you take a look at a Honda Civic (just the first that came to my mind) front suspension arrangement (any Civic from 88 to 2001, at least). Many dirtbikes (and bicycles) do not present rockers and they still get the desired motion ratio (and motion ratio curve, which in long travel applications may be way more important than in our toy FSAE cars). Other dirtbikes (and bicycles) present rockers with their designers claiming that this way they could control better motion ratios curves. In many cases, packaging drives a lot of this, in other cases, even marketing can drive design tendencies (bicycles, many times). Note that in any of these applications (with or without rockers) you can adjust ride height without changing spring stiffness.

In FSAE (as in dirtbikes, and bicycles), there are fast cars with all kinds of configurations. So, you don't need to know anything from vehicle dynamics and chassis tuning to understand that there isn't a holy winning formula.
The answer to "why am I using rockers" and conceptual questions like that (these type of question I find EXTREMELY important) may well be particular for your team's needs, realities, targets, etc.

JP

[Ashir]

Where did you get "effective" damper travel from? There is wheel motion, and this is translated to the damper. There isn't really anything "effective" here. Don't confuse yourself with motion ratio. It doesn't necessarily make whatever suspension mode stiffer; it can make it stiffer or softer or leave it the same, or it can be rising/failing rate.

Searched for details of damper to get more in depth. Came across this article by "Kaz Technology".
http://www.kaztechnologies.com/fileadmin/user_upload/Kaz_Tech_Tips/FSAE_Damper_Guide-_Jim_Kasprzak_Kaz_Tech_Tip.pdf
(http://www.kaztechnologies.com/fileadmin/user_upload/Kaz_Tech_Tips/FSAE_Damper_Guide-_Jim_Kasprzak_Kaz_Tech_Tip.pdf)
While reading I was finding what effect damper travel will have on its characteristics. When damper travels more, the fluid is pushed more and since the cross section area of valve is same, better damping is achieved. (This was taught to us in no further detail). But after going through the article, first of all its not just travel but its travel per sec which affects damping. In it they have explained how fast, medium and slow speed dampers differentiate in rebound and compression. Then I came across this:

There are several reasons for using high motion ratios. The first is higher motion ratios require lower spring rates for the same wheel rates. Lower spring rates are also lighter, and result in less spring and shock friction as well as lower component loads. The other reason is greater damper travel and higher shock velocities. Since dampers perform better at higher velocities, and the wheel displacements are quite small on a FSAE car, higher motion ratios produce better shock performance.

By higher motion ratio they meant as close to 1.0 i.e the spring displacement or damper displacement is same as wheel displacement.

So I concluded, if we can bring motion ratio very close to 1 by direct mounting the damper, the benefits of easy frame design, load paths etc can be achieved without losing on shock performance.

[Z]

Ashir,

You have enlightened me to the sheer "genius" of modern engineering.

I used to think that the modern approach to engineering, as seen in a lot of FSAE, simply involves COPYING whatever the current fashion happens to be, and then justifying your "engineering decisions" by offering up some lame, half-baked, CALCULATIONS as support.

But, no, I was completely wrong. Absolutely NO calculations are required! Not even any sort of rational, or well-reasoned, qualitative analysis. Instead, you only have to regurgitate a few HALF-TRUTHS, and then back them up with a mountain of IRRELEVANCIES, and BLATANT BULLDUST. Sheer genius!!!
~o0o~

For example...


I went in more depth of search results and visited this topic
http://www.fsae.com/forums/archive/index.php/t-408.html?

... conclusion seems good for me.

... my objective is to design the suspension based on the damper we already have. This will save us lot of money (more than what it will be saved on using direct damper mounting by removing bell crank and pushrod costs).
So now I have to make my suspension stiff without changing damper, I will use bell crank to chance motion ratio.

It seems that your decision (in that post) is to use "bell cranks" (= pushrod-and-rockers) because your previous car already has them, so it is easier for you to keep doing the same. Is this your thinking?

(Edit: I just read your above post more closely, and it now seems that you may move to direct-acting SDs, but only if they have MR close to 1?)

So far, in your decision making, you seem to be happy with the following arguments. (These are taken from the above-linked thread, and are my main reason for ranting here... :)).
~o0o~


For the shock to work well, and also to allow lighter springs (both in rate as well as in mass), the MR needs to be somewhere near 1:1. Modern formula cars strive for 1:1 for the front (if not higher), and even higher for the rear. This allows the springs to be of lighter rate and mass, ...

Pure BULLDUST!!! (And, frankly, pure STUPIDITY!) For a given wheel-rate and travel, more spring travel (ie. higher MR = damper/wheel motion) requires a lower spring-rate, but also a proportionally LONGER SPRING!

Thinking about it "big-picture-wise", the integral of wheel-force x wheel-travel = strain-energy to be stored in the spring. So, for springs of equal strain-energy/mass capability (ie. for the same quality of spring steel), a given wheel-force x wheel-travel requires the same mass of steel, regardless of MR!

(Of course, fibreglass, or rubber-band, or gas, (or other...), springs ARE lighter for the same total strain energy storage, again regardless of MR...)
~o0o~


[the magical MR=1] ... also pumps more fluid for every increment of wheel movement.

The more fluid that the shock can pump - especially with the high wheel rates we have on modern cars - the easier it is for the shock to be fine tuned for good spring and tire contact patch control.

The "high wheel rates" come when incompetent suspension engineers eventually discover that "any suspension will work, if you don't let it...". However, these incompetents believe that they got the suspension working by "fine tuning" it.

As for "pumping more fluid", just how much fluid needs to be pumped (ie. how much energy needs to be dissipated) to control these teeny-weeny racecars, as they race around their billiard-table smooth tracks? (Please do the calculations, and see that it = SFA.)

Also, if you double the MR, then you double the "static friction" forces felt at the wheelprint due to stiction in the damper seals, etc. Generally, this is a bad thing.
~o0o~


... the higher the MR the less force that is put into the frame where the Coil-over dampener attaches.

This is one of those half-truths that obscures several more important facts. Namely, for given Fz wheel forces the stresses felt by the main portion of the chassis are, quite obviously, the same regardless of suspension details (as explained by The-Man). A pushrod at the same angle as a DASD, has, quite obviously, the same forces acting on it. The addition of a rocker with high MR simply transfers this same force to two, hopefully smaller, forces at two separate chassis nodes (ie. the rocker node, and the SD node).

"So, hey, why not 10 x pushrods, rockers, and dampers per corner!? Yeah, then the force into each of the, err... 10, no that's 20 chassis nodes, is only, err... 1/20 of what it was before... Genius!!!" :)
~o0o~


If you practice with 39 C ambient temperature, and 53 C track temperature (like we do here at our country), radiator flow is really critical, and a shock in the way is a big problem.

Groooaaannnn... See below...
~o0o~

The above-linked thread had some discussion (by Big Bird ++) along the lines of,
"If you are in close competition with Stuttgart at the front of the field, then tiny details such as the exact MR of your rockers might make the difference between 1st and 2nd place.".

Sounds plausible... Except that Monash won the most recent FSAE event, Oz-2013, with direct-acting SDs. And they won by the proverbial country mile! And they have an aero car, so it seems that DASDs don't mess up aero flows too much. And Monash have a side-mounted radiator, and they test and race in Oz, "the sunburnt country", with the FSAE comp held in summer. So DASDs don't seem to kill radiator flows too much either...

But Monash are not a Northern Hemisphere team like Stuttgart. Does that make a difference? Should it? They were briefly at the top of the FSAE ladder (IIRC, sometime last year?). And they have been hovering around there for quite some time...

Anyway, on that linked thread from 2010 there was a post from Fil (who seems to have been on the Monash team?) who said that he did a study of DASDs and concluded that they "actually made sense". I recall Monash at Oz-2013 pointing to a bucket full of pushrods and rockers (= dead weight and $$$s) as justification for their move to direct-acting SDs.

So, does anyone know how long Monash have been running DASDs, and what their competition record with them is?

(Important point: Your decisions should NOT be swayed by what some other team does, except, perhaps, as confirmation of your calculations!)
~o0o~

Bottom line;
Know thyself!

Are you doing what you are doing because it really makes sense, or simply because it is easier to follow the flock?

Z

[Z]

For those interested in Motion Ratios, I should add some more comments here, because the situation is even worse than suggested above.

(Note that in the following,
MR = spring-damper-change-of-length/wheelprint-vertical-displacement.
So, for given size bump, larger MR means more spring-damper movement. (Sometimes MR is defined as the inverse of this.))

"Expert" opinion nowadays has it that, in general, a higher MR is better (see all the lame reasons in above post). In fact, one expert FSAE Design Judge has advised students several times that by increasing MR the "unsprung mass may be DECREASED...". This advice applies when using the same damper. And as noted in above post, for given wheel-rate and wheel-travel, the spring's mass also stays the same, regardless of MR.

So, regardless of MR, the same mass of spring and damper must be accelerated whenever the wheel hits a bump and is itself accelerated. But, with an increased MR, the acceleration of the SD must also increase. Doesn't this effectively INCREASE the "unsprung mass", by adding to the wheel's mass, the SD's mass, err.... multiplied by the MR?

Well, dear students, it is actually even worse than that! Let's do the calcs.
~o0o~

Consider a Wheel-Assembly of mass Mwa (= tyre/wheel/upright/hub/axle/moving-bits-of-suspension...), which is the nominal "unsprung mass".

At the end of some push/pullrod&rocker linkage (which we consider massless, or roll into Mwa) is a Spring-Damper that has a part with mass Msd (= perhaps the piston/piston-rod/spring-seat/first-few-coils-of-spring...) that must move at a velocity relative to the wheelprint that is determined by the above definition of Motion Ratio.

Now, let's assume the Wheel-Assembly of mass Mwa hits a bump, and after a short time dt, it is moving upward with extra velocity dVwa.

By Newton II, the WAs "rate of change of quantity of motion", namely,
dP/dt = Mwa*dVwa/dt,
is proportional to, and caused by, an upward acting force Fwp (force from-ground-to-wheelprint).

So, in appropriate units,
Fwp = Mwa*dVwa/dt.

(Note: Newton's "quantity of motion" is nowadays called "momentum" (ie. P = m*V, or for "rate of change", dP/dt = d(m*V)/dt). And while NII is, strictly speaking, F ~ P-dot = dP/dt, in this case you can use F = m*A if you find it easier...)

In the same small time period dt, the moving part of the SD must also increase in velocity, but now by MR*dVwa (from the definition of MR). The force needed to cause this change of quantity of motion of the SD is,
Fsd = Msd*(MR*dVwa)/dt.
This is the force acting from the rocker, to the moving-part-of-SD, via the ball-joint connecting these two parts.

BUT!!! As the reaction to this force, namely -Fsd, is passed backward from the SD, through the rocker and pushrod linkage, to the WA, it is necessarily multiplied by MR (Law of Levers).

So, whenever the WA is "changing its quantity of motion" (ie. accelerating), it is also feeling the inertial reaction of the SDs "change in motion". The total force at the wheelprint required to cause BOTH these "changes in motion" (ie. accelerations) is thus,
Fwp(total) = (Mwa + MR*MR*Msd)*dVwa/dt.

Bottom line here, the effective "unsprung mass" is INCREASED by the mass of the moving-part-of-Spring-Damper, multiplied by the MOTION RATIO SQUARED!
~o0o~

Are the above theoretical calculations backed up by any empirical examples? I can think of quite a few in the automotive world, but here are two from further afield.

1. To survive, an animal must be able to accelerate its feet very rapidly (and not just when running, but also when kicking out at predators, etc.). The typical Motion Ratio of an animal's muscles to whatever they are driving/controlling is very low. For example, a "gluteus maximus" (= bum muscle) might only move 0.1 metres while it drives the animal's foot 1 metre backwards. So here MR = 0.1 (with the muscle = the SD, and the foot = the wheelprint).

If the moving part of the "glute" has mass of, say, 1 kg, then the above calcs with MR = 0.1 suggest that this only adds 0.01 kg (= 0.1*0.1*1 kg) to the effective "unsprung mass" of the foot. If the Motion Ratio was 10, as suggested by extrapolating some of the lame reasoning in the above post, then the foot would be effectively burdened with an extra 100 kg (= 10*10*1 kg) of "unsprung/glute mass"!

2. A "trebuchet" is a Medieval siege engine that throws stones at castles. It has a large wooden lever-arm pivotted several metres above ground. The short end of the lever-arm attaches to a large basket full of several tons of stones, and the long end of the arm (plus a sling) does the throwing. Gravitational force acting on the heavy basket powers the machine (a bit like a muscle, or SD). But, quite obviously, the basket itself can't accelerate any faster than "G" (~9.8 m/s.s).

Do the calcs and you should see that the only way to throw stones a long way (ie. with high speed) is to have a very low MR (= basket-motion/throwing-end-motion). Incidentally, the same principles apply to the similar, but much older, torsion-spring powered "ballista".

In suspension terms, the above examples suggest that if you want the wheel to rapidly move up and down so that it can follow a bumpy road, and if the stuff controlling this movement (eg. the SD, muscle, etc.) has significant mass, then a LOWER MOTION RATIO IS BETTER.
~o0o~

So, bottom line is that hundreds of millions of years ago Nature used trail-and-error to figure out that low MRs are good. A thousand years ago Medieval turnip farmers had the common sense (ie. inspiration from Nature) to do the same. But today some Engineers in the uppermost echelons of motorsport do not seem to have figured it out yet. Well, not the "experts"...

Maybe some of you students can help them? :)

Z

(PS. Some F1 teams have figured it out, and have their springs and dampers at quite low MRs. (Hint: torsion springs and rotary dampers attached directly to the rockers.)

[Moop]

For teams with direct acting dampers, how do you balance your cross weight? I've found that by adjusting a pushrod about a turn, I can change the cross weight by about 0.5-1%, whereas I've not found much change in the cross weight when adjusting a spring perch. Granted, I've been dead tired every time I've tried it with the perches and never bothered trying afterwards.

We've used pushrods and bellcranks for the longest time and I've never really given direct acting dampers much serious thought. I thought that it would be difficult to get the motion ratio I wanted and difficult to package an ARB other than a passenger car style torsion-and-bending tube. The ideas I came up with mostly involved smaller bellcranks to connect a conventional u-bar, which sort of defeated the purpose of eliminating the bellcranks.

One solution I've seen is what looks like a shuttle bar ARB on the rear of the new Monash car. Our team has had a shuttle bar in the past, but we ditched it because its motion ratio varied quite a bit through bump travel, although maybe they've been able to fix this since theirs is mounted over a much larger width than ours was.

While I'm in favour of simplifying the system by eliminating the pushrods and bellcranks if the same or similar performance can be achieved, I wouldn't want to do so at the cost of losing roll stiffness distribution adjustment with the ARB. Changing springs is quite a PITA compared to adjusting an ARB blade or swapping a torsion bar if you want to reset your cross weight as well. I think the weekend autocrosser would certainly much prefer it, even though that mindset went out the window a long time ago.



Regarding motion ratios: I've honestly never really thought too much about picking a motion ratio. If you have a target wheel travel, a coilover travel fixed from the manufacturer, and want a roughly constant motion ratio, then it's already defined for you. Anything other than that will require you to put a really thick bumpstop on the damper or a hardstop somewhere else in the system, unless you're cool with the possibility of your suspension bottoming out on something other than a bump stop. It sort of makes sense to use all the travel you have in the damper though.

The arguments I've always heard for "high" motion ratios have been the same; lighter springs, lessened effects of friction, hysteresis and play, and better "use" of the shock. I bought the lighter springs argument without actually thinking about it, but it seems that's not actually a valid argument. As Z mentioned, a higher MR amplifies any frictional force felt at the damper, although it does attenuate any play in the damper(not that there should be any).

On the con side, increasing the speed of the damper will increase the mass flow/dynamic pressure though the piston, which will decrease the minimum pressure in the piston for a fixed minimum Cp. This increases the potential for cavitation and requires a higher shock pressure, increasing friction in the damper. Then there's the increased amplification of the damper/bellcrank mass effect that Z mentioned.

A crazy idea I just had is that maybe, the usual recommendation for "high" motion ratios stem from digressive damping knee speeds. I've noticed that the knee speeds for most digressive damping curves I've seen have fallen in the range of 25-50 mm/sec, with higher damper speeds being labelled as controlling road input and lower damper speeds being labelled as controlling chassis motions. For a fixed knee speed, you don't want your motion ratio getting too low, as while you can still increase the damping rate to keep the wheel damping rate the same, the knee speed at the wheel increases. This results in your damping blowing off later under larger bumps, or maybe even not at all, and would probably make tuning the dampers give unexpected results.

This is pure speculation, as I don't exactly have experience with a wide range of damping curves. It may explain why some F1 teams use the low motion ratio rotary dampers, since they probably design their own damper anyways and could change the knee speed to be in line with their lower motion ratio.

[mdavis]

We adjusted corner weight with spring perch position. It did take a lot of adjustment to make a big difference, but that was the price we paid.

We didn't run an ARB last year, but we had one designed. It used some aluminum elements in bending, and I wasn't all that fond of it. It wasn't completely manufactured when we did our first test, and the results were good enough without it that we simply developed the package that was done, rather than trying to change things up. To run the front ARB would have meant so much dive under brakes that it would not have been funny.

As for quick adjustments to roll stiffness distribution, we used spring rubbers (similar to NASCAR) that we cut and modified to fit our spring diameters/wire diameters. They were for much larger springs, but some time on a bandsaw took care of that. We had 3 different durometer spring rubbers, and could interchange them as we pleased. Some people had a lot of doubts about them staying in place, but we ran 2 competitions with the same rubbers in place and had no troubles.

-Matt

[Adi_97]

Dear Z,

I know it has been over 3 years since you put up this post. But, I really seem to find something fundamentally wrong with what you said. I am new to the world of FSAE and please do pardon me if I sound stupid.

Let me first state the things I agree upon.
dP/dt = Mwa*dVwa/dt
Fsd = Msd*(MR*dVwa)/dt.
BUT!!! As the reaction to this force, namely -Fsd, is passed backward from the SD, through the rocker and pushrod linkage, to the WA, it is necessarily multiplied by MR (Law of Levers).

Now, this is where I do not agree upon.
Bottom line here, the effective "unsprung mass" is INCREASED by the mass of the moving-part-of-Spring-Damper, multiplied by the MOTION RATIO SQUARED!

From what I understand, you are basically increasing the effective spring rate of the car as a whole ( i.e. ride rate, by changing your wheel rate) when you increase your MR.
This does not is any way increase the 'unsprung' mass of the car. Your argument about how the force needed to produce the same wheel centre deflection along the Z axis of the car increases with increasing MR cannot
be attributed to the 'effective' increase in mass . The equation to be considered here is not F=mx(double dot) but F= mx(double dot) + kx + bx(single dot), where b is the damping coefficient. So, increasing your k increases the F you have to apply for the same wheel displacement.

Moreover, I do understand how your suspension's response time would increase if you were to increase your unsprung mass ( f = squareroot(k/m), where f= undamped natural frequency of the suspension )
But, what is happening here is that you are effectively increasing your 'k' and thus your suspension's response time should decrease, and not increase.

Also a progressively increasing MR in my opinion would help as you would be able to take care of your pitch and dive issues without having to increase your spring stiffness considerably which would in turn enable you to get
your desired ARB Roll contribution.( As in the percent by which your ARB contributes to the roll rate).

The only fault that I can see with higher motion ratios is that they considerably increase xSD(single dot, velocity of SD)= xW(single dot, velocity of W)*MR and this causes heating up of the damper. This heating up of the damper fluid causes it to change
it's viscosity and other properties which leads to undesired hysteresis.

I know that I am no expert. So, please feel free to point out mistakes.

Adi

[Z]

...please feel free to point out mistakes.

Adi,

You have made several mistakes. Don't worry, the experts also make those same mistakes, over and over again.
~~~o0o~~~

MAIN MISTAKE.
=============

Now, this is where I do not agree upon.
[Z quote->]"Bottom line here, the effective "unsprung mass" is INCREASED by the mass of the moving-part-of-Spring-Damper, multiplied by the MOTION RATIO SQUARED!"
From what I understand, you are basically increasing the effective spring rate of the car ... when you increase your MR.
This does not in any way increase the 'unsprung' mass of the car.

Effectively, it does.

If you keep exactly the same spring (ie. with the same spring-stiffness K), and you then increase that spring's MR (wrt the wheel), then, yes, you do increase the "effective spring rate of the car" (= "ride-rate", or "wheel-rate"). In fact, and as I am sure you know by now, the "effective wheel-rate" goes up by ... MOTION RATIO SQUARED!

And if you keep exactly the same damper (ie. with exactly the same settings), then the damper forces also go up, but by an amount that depends on the shape of the damper curves, multiplied by ... MOTION RATIO SQUARED.

And similarly, the inertial resistance of the Wheel-Assembly+Spring-Damper to acceleration goes up by ... MOTION RATIO SQUARED (multiplied by mass of moving-parts-of-SD, as explained in my previous post).

It is true that the "net unsprung mass" of the car remains the same, being simply the sum of the masses of Wheel-Assemblies and Spring-Dampers. But by fitting the SDs at the end of a linkage with increased MR, you do, MOST CERTAINLY, increase the force required to accelerate the WA+SD.
~o0o~

In the previous post I explained this behaviour in terms of classical Newtonian "changes of momentum". I guess many students struggle to understand this approach these days (because failed eduation system), so below is another way to look at it.

This time consider two simple examples, with some simple numbers thrown in, and forget all about "Newton's Laws".

Instead of tricky "changes in momentum", think about the WORK and KINETIC ENERGIES involved. (Note, of course, that these two concepts are derived from N's Laws.)
Define:
Work = Force * Distance (with * being the Scalar-Dot-Product of the F and D vectors),
Kinetic-Energy = 1/2 x Mass x Velocity-SQUARED,
with both having units of Joules.
~o0o~

EXAMPLE 1 - Consider a "one-piece" WA+SD, with combined mass M = 10 kg. That is, consider a Motion Ratio = 1.

This one-piece mass M is forced to move upwards at constant acceleration A = 1 m/s/s, perhaps because the wheel hits a bump with parabolic profile. (<- Think about why "parabolic" implies "constant acceleration".)

After 1 second of this constant upward acceleration A, the mass M has an upward velocity V = 1 m/s/s x 1 s = 1 m/s, and has travelled an upward distance D = 0.5 metres. (<- These V and D being calculated with the very simple 1-D Kinematics that used to be taught in high-schools.)

So the Kinetic-Energy of the mass M is now,
KE = 1/2 x 10 kg x 1 m/s x 1 m/s = 5 Joules.

If (to keep this example simple) we assume no dissipative forces such as friction, and if we believe in olden-day concepts such as "CONSERVATION OF ENERGY", then we must conclude that this newly acquired KE of mass M must be the consequence of some Work done on the mass. That is, an upward force F must have acted on the mass M over an upward distance D.

So, for the books to balance, Work-done-on-mass must equal the mass's final Kinetic-Energy.

So, Work-done-on-mass = F * D = 5 Joules (= KE).

We conclude that the upward force F that acted on the mass M over the whole of the distance D = 0.5 m, is given by,
F = W/D = 5/0.5 = 10 Newtons.

(Note that this force is in addition to any "static wheel-load", say that due to gravity.)
~o0o~

EXAMPLE 2 - Now let's split the one-piece WA+SD mass into two separate masses.

The Wheel-Assembly part has mass Mwa = 9 kg, and is forced to move upwards exactly as before, namely with upwards acceleration of Awa = 1 m/s/s.

The moving-part-of-Spring-Damper has mass Msd = 1 kg, and is at the end of a pushrod & rocker linkage that causes it to move (in any direction!) 10 times as far as the WA. That is, the SD has Motion Ratio = 10.

So the SD's acceleration is necessarily Asd = MR x Awa = 10 m/s/s. (<-Think about it.)

After 1 second of the WA's constant upward acceleration of Awa = 1 m/s/s, it has upward velocity Vwa = 1 m/s, has travelled distance Dwa = 0.5 m, and has acquired Kinetic-Energy,
KEwa = 1/2 x 9 x 1 x 1 = 4.5 Joules.
This is almost the same as the first example, just slightly less because slightly less mass.

After the same 1 second the SD has a velocity of Vsd = 10 m/s (BECAUSE ITS MR = 10), so it has acquired Kinetic-Energy,
KEsd = 1/2 x 1 x 10 x 10 = 50 Joules!

So the TOTAL Kinetic-Energy of WA+SD is now KEwd+sd = 54.5 Joules!

Note that although the SD has the much smaller mass of only 1 kg against the WA's mass of 9 kg, the SD nevertheless carries by far the majority of the total Kinetic-Energy, because it has the greater VELOCITY SQUARED (<- Edit - added emphasis, because important!).

Again from Conservation of Energy, we conclude that the Work done, by an upward force Fwa+sd, acting on the Wheel-Assembly+SpringDamper, over the distance Dwa = 0.5 m, must be,
Fwa+sd = Work/Dwa = 54.5 J / 0.5 m = 109 N.

So the inertial resistance to acceleration of the COMBINED WA+SD has increased by more than ten times over Example 1, even though the total masses of both systems are identical.

By similar reasoning, we find the force Fwa to accelerate ONLY the WA is,
Fwa = 4.5 J / 0.5 m = 9 N.
Similar to Example 1, just a bit less because bit less mass (9 kg vs 10 kg).

And the force Fsd@wp, ACTING AT THE WHEELPRINT (and thus only moving distance D = 0.5 m) required to accelerate ONLY the moving-parts-of-SD, is,
Fsd@wp = 50 J / 0.5 m = 100 N!

Yikes!!! That is a lot of force to accelerate a small mass. And it will certainly increase wheel loads on the uphill side of bumps, and keep the wheel hanging in the air over the downhill sides!

(Note that the force Fsd, acting DIRECTLY on the moving-parts-of-SD, and thus moving the much greater distance of MR x D = 5 m, is given by,
Fsd = 50 J / 5 m = 10 N, as expected.
The MR, or "leverage", of the pushrod & rocker linkage multiplies this force to give the much higher force at the wheelprint.)
~~~o0o~~~

OTHER MISTAKES.
================

...progressively increasing MR in my opinion would help as you would be able to take care of your pitch and dive issues without having to increase your spring stiffness considerably which would in turn enable you to get your desired ARB Roll contribution.

1. "Progressive MR" (aka "rising-rates") on corner/wheel-springs is, in general, VERY BAD for circuit racing cars.

2. I see nothing "desirable" in ARBs.

Z

[Scott Rinde]

2. I see nothing "desirable" in ARBs.

Z

Hi Z,

Loooooooong time lurker, first time interlocutor, to protect myself from Claude's etiquette wrath I'll tell you that I'm an old guy, not a current student, forgotten most of the higher math I learned in getting a degree in it, club racer, kart racer, life long student and power user of suspensions.

How undesirable do you find ARB's? Are they a packaging complication? Are they practically unnecessary and an abomination unto The Lord? Or something in between to the extent that they're not the same thing (been there, thought that).

I thought it had been proven that for a given roll stiffness, achieving it with Spring And ARB gives a lower single wheel rate than achieving it with Spring only. Correspondingly then the warp stiffness too is lower with the spring/ARB combination.

Here's an entertaining thread in which the subject of ARB's is taken up: https://honda-tech.com/forums/road-racing-autocross-time-attack-19/did-you-see-nicholas-cage-movie-national-treasure-2761537/ A consolidated treatment appears in this thread: https://honda-tech.com/forums/road-racing-autocross-time-attack-19/scientific-truth-about-sway-bars-there-one-you-know-2903722/

Can you expand on your position on the subject?

Thanks,

Scott

[Claude Rouelle]

Z, Yes you Z i am speaking to you! :)

1. IMO the main reason why variable motion ratio are used is getting the most of aeromaps. You need a "soft" car at low speed and a "stiff" car at high speed to make a compromise between mechanical grip and exploitation of the aeromaps which often are very front ride ride height sensitive.
Other solutions such as bump rubber or variable spring rate can be used. Test made on 7 post rigs in wind tunnel and on track has shown (at least to me and many of our customers) that sometimes yes you lose a bit in mechanical grip but you gain much more in aerodynamic downforce and aerobalance consistency.
Do you have any experience with such car.

2. Simplified problem: you driver complains about oversteer. 2 solutions: soften the rear or stiffen the front. To decide which way to go one more question to the driver: is the car too lazy or too nervous? If the car is too lazy you will stiffen the front. if the car is too nervous you will soften the rear.
Lets' say your diver says he as oversteer and he finds the car too nervous. So yo decide to soften the rear but oh surprise there isn't any rear ARB. OK so you will do it with the soften rear springs but if you do so you change the car pitch and heave frequencies (which affect both mechanical grip and aerodynamic platform)
For me front and rear ARB gives you the possibility to modify the TLTTD without affecting ride and aero ride height control Your comments?

3 Unless I miss something.... in your last post Example 2 you give a Mass wheel assembly of 9 Kg and a Spring damper assembly of 1 Kg. These are good generic realistic number.... but a motion ratio of 10?

Claude

[JT A.]

Claude,

I think just about anyone with experience in professional motorsports would agree with you that you can possibly exploit an advantage from properly designed rising rate motion ratios, front and rear antiroll bars, etc if you have you have a good understanding of your vehicle. The important things you mentioned like having a good aeromap, ability to quantify mechanical grip changes, access to a 7 post or virtual 7 post software, and you can definitely improve performance of the car.

However consider the context of a hypothetical FSAE team, one that-

-Has no idea where their wings are dynamically (no simulation tools or post-processing methods to calculate wing positions from sensors)
-Has no idea where their wings should be (no aeromap)
-They are vaguely aware that a concept called "mechanical grip" exists, but they don't know how to define it or calculate any metric associated with it.
-They have no access to a 7 post rig or virtual 7 post rig software, and wouldn't have the first clue what to do with it even if they did.
-They know that generally "softer ARB in rear = better rear grip, stiffer ARB in rear = worse rear grip" but can't explain why.

I'm curious to know your opinion on this-
Do you believe such a team gains any advantage from having pushrod/pullrod actuated bellcranks, front and rear ARBs, etc? Are those parts worth their weight to a team like that?

Do you think it is more productive for a team like that to dedicate 2-3 members spending the whole design stage debating pushrod vs pullrod vs monoshock vs 3rd heave spring style suspensions (with none of the tools or knowledge required to make the best choice and fully exploit it's advantages), repackaging the ARB, and "optimizing" the bellcranks. Or would they be better off leaving all that crap alone and work on filling in the gaps in their knowledge so they can actually make better choices in the future?

And lastly -
How would you score a team in design judging with the lack of understanding that I listed above, if they had non adjustable dampers, direct mounted from A-arm to chassis, and no ARB's?
How would you score a team with the same lack of understanding, but they have the most expensive 4 way adjustable dampers money can buy, front and rear titanium blade electronically adjustable ARBs, pushrod or pullrod bellcrank actuation, and their design report says that their ride and roll frequencies are somehow "optimized"?

[Z]

Scott,


How undesirable do you find ARB's?
...Can you expand on your position on the subject?

If less than one-tenth of my posts here are on this general subject (in truth, probably many more), then I still have well into triple figures of posts ranting about it! :)

So, very briefly, of the many ways to interconnect wheels with springs, the "ARB" (or "lateral-U-bar", which interconnects "end-pairs" of wheels) is one of the worst. Yes, it does stiffen the Roll-mode, which can be beneficial for some types of car (sometimes, but not always), but it also EQUALLY stiffens the Twist-(aka-Warp)-mode, which is generally VERY BAD for all cars.

A much bettter choice of wheel-pair interconnection is the "longitudinal-Z-bar", which interconnects "side-pairs" of wheels. (Note: "Z" is the shape of the bar in plan-view, and not any relation to me. :) "U-bars" resist opposite movements at their ends (eg. up+down), and "Z-bars" resist same movements (eg. up+up, or down+down).)

"Side-pair-Z-bars" are good because they stiffen Heave and Roll, while NOT affecting Pitch and Twist. They also make it easy to adjust Elastic-Roll-Moment-Distribution (~ LLTD) to allow easy adjustment of US/OS. And packaging complexity is similar to ARBs. In principle, a complete (and very good!) suspension for a car can be made from two side-pair-Z-bars, and a third end-pair(=lateral)-Z-bar, typically at the heavier end of the car. No more is needed!

The only real downside of side-pair-Z-bars is that almost no one in the entire auto-world knows about them! Oh, ... and if, say, someone in F1 stumbles onto them, and they start winning races because of them, then the organisers start jumping up and down, shouting "It's FRIC-ing cheating!!!", and they immediately ban them as being against the spirit of motorsport. ("FRIC" was a hydraulic Front-Rear-Inter-Connect ... Z-bar.)

Aaaarghhhh, ... progress!!!
~o0o~

Getting back to FSAE, it is desirable for the car to have the lowest possible CG-Height, to allow the narrowest possible Track-Width for better slalom speed. Bumps are almost non-existent on the tracks, but some damped suspension movement is beneficial to suppress "bouncing on the tyres', which can start by "stick-slip" of the tyres during hard cornering.

So, what sort of "springing" to use?

Since the major masses are distributed mainly along the centreline of the car (eg. IA and pedals at front-centre, driver's bum in middle-centre, engine at rear-centre), it follows that to have a low CG, this car-centreline should run at a minimum ride-height, and it should NOT be allowed to move up-down much. So it should be STIFFLY SPRUNG.

So end-pair(=lateral)-Z-bars are well suited. These, of course, are also known as "third-springs" (actually seventh and eighth), and work well at controlling changing aero loads. More below in reply to Claude, but rising-rate is GOOD here!

That only leaves the Roll-mode to control, since Twist-mode can be left soft. So side-pair-Z-bars can be added. Or, for easier packaging, simple, softish, corner-springs can be used (ie. they only connect to one wheel, so simplest type of spring).

Note that with appropriate suspension kinematics there is NO disadvantage (on the smooth FSAE tracks) of having a soft Roll-mode. Here "good kinematics" are those that give ~100% "camber recovery". So, beam-axles, or independent suspensions with Front-View-Virtual-Swing-Arm = ~half-Track-Width. With these the car can have low CG and also considerable Roll-Angles, but nothing touches the ground (since main masses along car-centreline and any undertray can be "unsprung"), and tyres maintain high grip because always close to zero camber.

Note that for very bumpy roads the preferred kinematic behaviour is ZERO camber recovery, mainly because of the gyroscopic forces involved. But that ain't FSAE!
~o0o~

More coming next post.

I haven't had time to read your links, but may add more later after checking them.

BTW, you can "Search" this Forum for my ranting on "Z-bars", starting back in 2005 (there was a sketch in one of the posts back then).

Z

[Z]

Claude,

Posts are arriving like buses. Nothing for ages, then all at once! :)
~o0o~


1. ... main reason why variable motion ratio are used is getting the most of aeromaps.

As I touched on in above post, I see rising-rates as being GOOD for the so-called "third-springs". These, in effect, control the ride-height of the centreline of the car at its front and rear. They can thus be used beneficially to change the "attitude" of the car (ie. rake, or F&R heights) at different speeds. For example, large rake at low speed for better downforce, but less rake at high speed for less drag and less axle-busting DF, and so on. Similary, such rising-rates are good on motorbikes, where these "centreline" springs have no influence on cornering.

But the problem with rising-rates, especially the agressively rising-rates found on motorbikes, is when they are used on the corner-springs. Here, whenever the car is cornering, there is a "Lateral Load Transfer" OFF the inside-wheels, and ONTO the outside wheels. The changing spring-rates then make the inside of the car-body necessarily LIFT MUCH MORE than the outside falls. So the CG necessarily LIFTS, and it lifts quite a lot if the rising-rates are similar to those on motorbikes.

Note that a high CG is NO problem when travelling in a straight line. Even during longitudinal accel/braking it is not too bad, because wheelbases are typically much longer than track-widths. Really, the only important time to have a low CG is when cornering. So rising-rate corner-springs = BAD.

Note also that a common solution to the problem of the inside of the car lifting too much during cornering is to "droop limit" the corner-springs. Look at the force-deflection curve of such springing, and see that it gives an agressively FALLING-RATE! The springs are very stiff in extension, but softer in compression. So the car "jacks down" in corners, which is good because it lowers CG height.
~o0o~


2. Simplified problem:
... driver complains about oversteer.
... is the car too lazy or too nervous?

Well, several problems there, so many possible solutions.

For the "too lazy or too nervous" problem, I would start (and possibly end) with toe-adjustments. Especially at the rear. Toe-in for stability, toe-out for agility. This is something that can, and should, be done on any and all cars. Even cars with NO suspension can have their toe-angles adjusted. For high-speed racing the next step is to look at aero-stability, mainly by having aero-DF behind CG. This is not so important in FSAE, because it is very low-speed racing!

For the "oversteer" problem, there are a whole host of solutions, starting with changes to tyre-sizes, pressures, +++. The very last thing that might need adjusting is LLTD. As noted by Matt earlier (U of Cincinnati), this can be done very easily with some coil-spacers stuffed into the corner-springs. And as noted by JT A. directly above, in FSAE conditions ... who cares about "optimum" pitch and heave frequencies!?

FSAE teams should focus on building a car that:
1. Can RELIABLY drive 30 kms, at an average speed of ~50 kph.
2. Then, chase less mass, and more aero-downforce.
3. Then, chase less cost (roughly equal to quicker build), and less fuel-consumption.

Fine details such as optimum spring-rates for optimum handling/aero-platform-control are a long way down the list.
~o0o~


3 ... a motion ratio of 10?

Just using round numbers. (I also had D = 0.5 m of upward wheel travel, which was only half-way up the parabolic bump!)

Also, MR = 10 follows the line of thinking that if a bit more is a bit better, than much more must be much better! :)
~o0o~

Final BTW for now.

Students wanting to learn more about "energetic" approaches to solving Mechanics problems can google "Lagrangian" (1700s), "Hamiltonian" (1800s), and Principles of "Virtual Work", or "Least Action".

However, IMO these are NOT very useful for solving FSAE type problems because they do not like friction, which dissipates energy, nor the irregular input of energy, such as a driver getting on and off the throttle. Better is to use Newton's Laws directly. Very easy these days, because computers do all the boring work for you.

(Hint: Simply time-step NII, "F causes P-dot". Or, spelling it out in detail,
DO
dP = F * dT
LOOP.)

Z

[Scott Rinde]

Scott,

If less than one-tenth of my posts here are on this general subject (in truth, probably many more), then I still have well into triple figures of posts ranting about it! :)

BTW, you can "Search" this Forum for my ranting on "Z-bars", starting back in 2005 (there was a sketch in one of the posts back then).

Z

Hi Z,

Well aware, versed, and very appreciative, of your writings on the board as well as RCE. But if in all of that you ever restricted yourself to just the spring/bar tradeoff ala conventional production cars, I must have missed it because I'd surely have remembered.

Please do, if you have the time, read thru those two threads I linked - there is mathematical treatment of the subject as well as my comic book antics.

Thanks,

Scott

[Z]

Scott,

Thanks for the entertaining posts on ARB-rates. Also good to see a forum intended, I guess, for amateur rev-heads, that has more in-depth calculations than most of this forum intended for (wannabe?) engineering students.

I agree there is not much good advice out there on how to calculate such spring-rates. This boils down to modern society's almost total abandonment of DEFINITIONS. Poor Euclid tried so hard to show how it should be done, but now he is totally ignored. Anyway, once you give a clear definition of what you want to know, say, an ARB's contribution to Roll-rate, then the right "equation" is there in front of you.

Also amusing are those units. Ahh..., I keep thinking of the Mars Climate Orbiter. A billion dollar rocketship that was going quite well, made it all the way to Mars, and then ... came in a little low and got burned to a crisp! The main contractor, Lockheed Martin, used your good-ol'-fashioned imperial units, while NASA did its figuring in those new-fangled metric thingies. Poor confused little rocketship never had a chance. :)

Getting back to things like Roll/Pitch/Twist-modes, even with metric units there is the problem of angles. Degrees? Radians? Other? The French did manage to squeeze 100 "gradians" into a right-angle. My solution is to abandon angles, and measure the suspension modes with LINEAR dimensions only.

As briefly as I can:

Single-Wheel-Mode - Defined as displacement, Dn, vertically in Car-coordinates, with +ve = "up", of the given wheelprint "n", in units such as metres, cms, mms, or inches/feet/fathoms/cubits...

Two-Wheel Axle-Bounce-Mode - Defined as HALF THE SUM of vertical displacements, Dl and Dr, of the two wheelprints "l" and "r", again in linear units. So "Axle-Bounce = 1/2 x (Dl + Dr)". This is the displacement that a "third-spring" would feel, and would have to react against. This gives the AVERAGE vertical displacement of the two wheels.

Two-Wheel Axle-Roll-Mode - Defined as HALF THE DIFFERENCE of vertical displacements, Dl and Dr, of the two wheelprints "l" and "r", AGAIN IN LINEAR UNITS. So "Axle-Roll = 1/2 x (Dl - Dr)". Easy! This is the distance each wheel moves AWAY from the average given above, with one wheel moving up, the other down. Only tricky bit here is deciding which wheel gets the negative sign. But same problem in Single-Wheel-Mode, in deciding whether up or down is positive. You can bet that if half the world chooses one way, then the other half will go the other way!

So "Roll" is conveniently defined as a distance, just like a single-wheel displacement. In fact, it is quite straightforward to convert back and forth between Axle-Bounce&Roll displacements, and Single-Wheel-Left&Right displacements, using simple arithmetic. To convert to "roll-angle", simply throw in the half-track dimension, with Roll-Angle = ~Axle-Roll/(T/2), in radians (using "small angle approximation").

Continuing in a similar manner:
Four-Wheel Twist-Mode - Defined as "Twist = 1/4 x (+Dfl - Dfr - Drl + Drr)". In words, it is the "averaged amount" by which the FL&RR diagonal-pair go up (+ signs), and the FR&RL diagonal-pair go down (- signs). (IIRC, this gives twice as big a value as you put in one of your posts, where you only had one diagonal-pair moving.) Again, this approach gives a simple LINEAR measure of Twist (aka Warp) motion. This is convenient, because it is not obvious how such a Twist motion can be described with an angular measure. For example, would it be the difference of the angles of the two axles in end-view, or difference in angles of the two side-pairs in side-view?

Similarly, the Heave, Pitch, and Roll displacements have essentially the same equations as above, just with different + and - signs. Heave has all pluses, thus giving the "average" vertical displacement of all four wheels. Pitch and Roll have two pluses and two minuses, in the obvious way.

Not so obvious is that each Dn can have a weighting coefficient in front of it. My preference is to have all four coefficients summing to 1, with these replacing the 1/4 in front of the brackets. So the Heave-Mode for a 60%R-weight car might have coefficients of 0.3 for the rear-wheels, 0.2 for the front-wheels, thus always making Heave a direct measure of CG vertical movement wrt ground (err, to first order approximation).

The next step is to find the "spring-stiffnesses" of each of these modes (2 or 4 wheel). This really depends on what you want from such numbers, but the bottom line is that if you clearly define the quantity, then the appropriate equation should fall straight out of the definition.
~o0o~


...the spring/bar tradeoff ala conventional production cars...

Well, I cannot be totally opposed to ARBs, because one of my favourite cars of all time has them. But it is hardly a "conventional" car!

The front-drive Citroen DS (launched ~1955) has front and rear ARBs, of conventional U-bar shape. After that things get a little UNconventional. The DS has NO CORNER SPRINGS. It does have an "oleo-pneumatic" unit at each corner, with these being best described as very rugged, gas-pressurized dampers. The (nitrogen) gas is typically at around 50 bar (~750 psi) when the unit is at full "extension", but rises towards 200 bar (~3,000 psi) under full load (= heavily loaded car hitting big bump).

But, importantly, the L and R units at each end of the car are hydraulically connected such that each "end-pair" of these dampers acts as a lateral-Z-bar. That is, each end-pair only resists "Axle-Bounce" at their end of the car. They provide no "spring" resistance to Axle-Roll (or 4-wheel Twist) motions, although they do provide damping resistance. Taken together, the two end-pairs only control Heave and Pitch of the car. Furthermore, each end-pair senses the centreline height of the car at their end, via a mechanical link connected to the centre of their end's ARB, and a simple hydraulic valve then maintains a set ride height (...with a ~3 second delay) regardless of changing loads.

So, taken in terms of earlier discussions, the car has only four "springs". Each end of the car (F & R) has a reasonably conventional lateral-U-bar (= ARB), together with an oleo-pneumatic lateral-Z-bar, which has a smoothly rising-rate (via the increasing gas pressure).

But it is perhaps even simpler than that. The rear ARB is really quite thin and offers little Roll resistance (so 4-wheel Twist is also very soft). It seems to be there mostly to provide the height-sensing function. And with the front Track being considerably wider than rear (1.5 m vs 1.3 m), and the front ARB being a lot thicker than the rear, its seems that the front ARB provides almost all the anti-Roll for the car. (One day I should measure these numbers.) So the DS is not far from a 2F-1R three-wheeler, with only 3 springs!

But wait, there's more! In terms of conventionally accepted VD-wisdom, it gets even weirder. The front suspension is equal-length, parallel wishbones. So the nominal "RC" starts at ground level, then goes below ground during cornering (whilst shooting off to infinity!). More accurately, the outer-wheel's lateral-n-line slopes down-to-centre during cornering, and it slopes down quite a lot because of the highish roll-angles. So the front kinematics are "pro-roll" (in Mark Ortiz's terminology), and they jack the front of the car down.

Conversely, the rear suspension is pure trailing-arm, so its outer-wheel lateral-n-line slopes up-to-centre during cornering, giving progressively more "anti-roll", which also jacks the car up. Since the suspension is so soft, this gives a noticeable change in pitch-angle during hard cornering (nose down, so lowering the CG). It also moves the Total-LLTD rearwards as cornering G's increase, so presumably moving the car's handling more towards oversteer at the limit. But, in practice, the DS "corners on rails". The long wheelbase (3.125 m) and very soft suspension, especially at the rear (both in Bounce and Roll), means it is almost impossible to unstick the rear.

Waaaaay too complicated to work? Well, as noted, it only has two springs (the ARBs), plus the four, extra-heavy-duty, gas-pressurized, dampers. The suspension control-arms are also simple and strong. As for its dynamic capabilities, the early cars did win the 1959 Monte Carlo Rally, and countless other rallies like it. In later years Citroen focussed more on proving the car in the harsher, long-distance, off-road rallies. To quote the head of the competitions department at that time, Marlene Cotton,"Whenever the roads were really bad, that was when the DS was happiest...".

So, yes, I can accept ARBs, when they are done right. :)

Z

[Scott Rinde]

Thank You Z.

I was looking for a different heuristic, but I appreciate your response.

About our old gang on that board - Very Serious "rev-heads" laboring to understand how to get the most out of our stupid front wheel drive cars. When I first started there was a setup orthodoxy, not uncontested, but no why beyond this is what works. A group of us worked out the why very publicly and had great fun doing it. Like every community, it has run thru a life cycle and currently exhibits the barest signs of life. Kind of like this board. Students graduate and move on with life, Honda track rats move up in the world of hardware, expend the sum of their motivation, succumb to the normal mandates of life, etc. We're lucky if we get to ride the peak of a wave, but we feel it's absence after keenly.

Maybe thinking and working really are in the main driven by necessity, and relatively few of us carry a necessity within us. A love of learning joined to the opportunity to apply that learning in pursuit of pleasure and fulfillment is a magic combination. My most basic motivation is not sucking with respect to the competition and the bliss of being in the zone behind the wheel of a sorted car.

I can understand how one day it all seems trivial. Wrestle a big vehicle dynamics problem to the ground and after the satisfaction fades the next one isn't as all consuming. Win, and forget, enough races and one day you find yourself asking what it means to you now and maybe even what it ever meant. When you look around and most or even all of your old friends are gone it gets lonely and eery. And you feel your accumulated philosophy as a barrier between yourself and the new people.

Beyond numbers this is all really about souls.

:)

Scott

[Claude Rouelle]

JTA,

I judge much more what the students have between their ears that what the car has between its tires.

A team with the lack of understanding with a car with nonadjustable dampers, direct mounted from A-arm to chassis, and no ARB's will do poorly with me.

A team with the same lack of understanding, and a car with expensive 4 way adjustable dampers money can buy, front and rear titanium blade electronically adjustable ARBs, pushrod or pullrod bellcrank actuation, and their design report says that their ride and roll frequencies are somehow "optimized" will do miserably because the ratio exploitation of resources divided by resources will be even worse.

If you come to Formula Student and you put wings you are expected to understand aerodynamics. Putting wings because it is faster (and because it is cool- yes, I heard that) won’t do the team any good.

Coming to FS without an aeromap is ridiculous. If you do aero, do aero. I expect the team to show me a 5 D aeromap of downforce, drag, aerobalance, yaw moment, pitch moment and roll moment Vs front and rear ride height, yaw angle, roll angle and steering angle and, yes, speed.
I expect that CFD simulations are made with rolling floor and rotating wheels.
I expect the team to exlain why and by how much the CFD is too optimistic compared to reality.
I expect the team to show me how they use their aeromaps to simulate and develop the car on track.
Last year at FSG a team show me their 3rd front and rear springs. I ask them why they had such device. They told me “because it helps to maintain the downforce distribution aerodynamic platform (a concept they could not define). I asked them if they had a aeromap at least downforce and downforce distribution (aerobalance) Vs front and rear ride height. They didn’t. How do you think they did with me in design?

I agree that like tires and aerodynamic, dampers are complex models that are difficult to understand, measure model, exploit. That said, there are basic simulations that can be run in the time and frequency domain to see the transmissibility and the phase shift between road input, suspended and non-suspended mass accelerations. There are basic “mechanical grip” 101 simulations that should be run before you decide your suspension stiffness and damping. They won’t be perfect but they will be useful. I expect teams to do such simulations before they even think about going on a 4 or 7 post rigs if they have that luck (more and more teams do)

If the only think a team know is: "softer ARB in rear = better rear grip, stiffer ARB in rear = worse rear grip" but can't explain why” they should stay home.

As far as the debate between the direct actuation and pull push rod it is more about the criteria that was used to make that choice than the choice itself. The existing resources are part of this criteria.

If you team is only 2 or 3 members forget it: it is not reasonable. Not at the competitive level that Formula Student is today. If you want to go in the playground with the big kids you need to stop wearing shorts.

Some whiners will tell me they do not know how to acquire such knowledge. Quick story to illustrate my reply. A few years ago during a meeting I ask my team “How do you define a good programmer?” One of them (A guy who has been at OptimumG for now 10 years) answered “How good are you with Google? Because most of the answers are there". This forum, the many, many books available on the market (books list in the sticky section of this forum), the OptimumG seminars are some of the many ways to acquire such knowledge. It is there.

Again, this is not racing; this is an engineering and project management competition. If there was a design event in Formula One it is not sure that the winner would be Mercedes or Ferrari.

[Adi_97]

Dear Z,
Thanks for the reply.
Just for clarification purposes. I did understand the Newtons Second Law approach you adopted earlier. In fact I feel your Newtons approach is definitely more explanatory and
correct in comparison to the KE method you adopted. ( We conclude that the upward force F that acted on the mass M over the whole of the distance D = 0.5 m, is given by,
F = W/D = 5/0.5 = 10 Newtons. This does not have to be true. Just the integral of Force times displacement in the interval b/w 0 and 0.5 should be 5. Telling you nothing about
the instantaneous force. Although I do realise you have done it to make life easier.)

(<- Think about why "parabolic" implies "constant acceleration".) I guess this is because y = kx^2( where y is along the bump height and x along the car's forward velocity)is the eqn of a parabola and upon differentiating it twice w.r.t time we
would end up with y(double dot) = 2k*( x*x(double dot) + x(single dot )^2). Assuming you don't accelerate or decelerate while on the bump, i.e maintain the same 'x' component of velocity, you are left with
y(double dot) = 2k*(x(single dot)^2) , where x(single dot) is a constant.

Yikes!!! That is a lot of force to accelerate a small mass. And it will certainly increase wheel loads on the uphill side of bumps, and keep the wheel hanging in the air over the downhill sides!
This I do agree. But if you were to consider two cars with different springs but same damping ratio ( i.e b1/sqrt(k1*m1) = b2/sqrt(k2*m2) , where b is the damping coefficient) won't the car with the stiffer spring come back to it's steady state load distribution
quicker than the on with softer springs. Isn't that desirable? How do you come to a reasoning on where you should draw that line b/w better response and road holding ?

Always welcome to criticisms.
Adi

[DougMilliken]

But if you were to consider two cars with different springs but same damping ratio

Must be time for my annual(?) plug for our Olley book, "Chassis Design" SAE R-206, (C) 2002. As well as this thread, an email just came in from a retired Swiss engineer interested in some Olley history, and friend wants a copy of the book for his new hire to read...

For a simple linear damper, Olley presents an analysis that ends up with a plot of ratios and a line for equal damping of sprung and unsprung. Figure 6.25 page 353. Perhaps someone here can reproduce the plot, with their FSAE car spotted in.

[Claude Rouelle]

Z,

".....Here, whenever the car is cornering, there is a "Lateral Load Transfer" OFF the inside-wheels, and ONTO the outside wheels. The changing spring-rates then make the inside of the car-body necessarily LIFT MUCH MORE than the outside falls. So the CG necessarily LIFTS, and it lifts quite a lot if the rising-rates are similar to those on motorbikes."

Did you calculate how much the CG would raise with rising rates?

Claude

[DougMilliken]

Did you calculate how much the CG would raise with rising rates?

Not the answer to your question, but a related story:

I measured CG rise on a C3 Corvette cornering on a circle. This version (1968 - 1982) had high roll centers F and R (rear fixed-length half-shafts were also the "upper control arms" for the independent rear suspension). Roll was around an axis that connected (approximately) the tire contact patches on the outside pair of wheels. There was droop on the inside wheels, but negligible bump travel on the outside. CG height increase was approx 1/2 the amount of droop (rebound) on the inside suspensions.

[Claude Rouelle]

Z speaks about motion ratio with rising rate and you speak about jacking forces. Not the same thing.

[Z]

Adi,


But if you were to consider two cars with different springs but same damping ratio (ie. b1/sqrt(k1*m1) = b2/sqrt(k2*m2), where b is the damping coefficient) won't the car with the stiffer spring come back to it's steady state load distribution quicker than the one with softer springs? Isn't that desirable? How do you come to a reasoning on where you should draw that line [between] better response and road holding ?

I assume you are asking about a quarter-car model driving over a single bump, where the wheel is forced up by the bump, then the suspension-spring pushes the wheel back down, and then after some damped oscillation of the wheel-mass between the suspension-spring above it and the tyre-spring below it, the wheel eventually "comes back to its steady state load distribution". Furthermore, you say that a wheel-oscillation that dies down quickly is better, because "better response" time is "desirable".

Ahh, if only it were so simple!

If it was so simple, then inspection of the relevant (and overly simplistic) equations, such as Oscillation-Frequency = sqrt(K/M), suggests that all you have to do for "optimum suspension" is to keep increasing the spring-rates! Higher K => faster response time => better. Too easy!

But ... you also have to increase damping-rate, in order to keep the same damping-ratio. Err, ... so now the stiffer dampers will increase wheelprint loads on the uphill side of bumps, over and above the increased loads already coming from the stiffer springs. So this doubly increased vertical force, between wheel and car-body, launches the car-body upwards whenever it goes over a bump. And the stiffer dampers also reduce the wheelprint loads on the downhill sides of bumps, which, coupled with the car-body now shooting upwards, can leave the wheelprints hanging in the air. Hmmm, .. so NOT good for tyre-grip. And then there is also the greatly increased drag (= rearward wheelprint-force component) coming from those damper induced wheelprint load changes on the bumps. Aaarrghh, ... not so simple!

Fact is, good suspension on very bumpy roads has long-travel springs with very LOW rate, and VERY LOW values of damping force. Minimum values of wheel-mass also help, but this is limited by stuctural considerations, as well as the fact that larger diameter (= heavier) wheels roll more smoothly over rough roads than smaller diameter (= lighter) wheels. Note also that "wheel-mass" is usually called "UN-SPRUNG" mass, even though it sits between, and oscillates between, the suspension-spring and tyre-spring. It is exceedingly well "sprung" mass!

But, most importantly here, FS/FSAE TRACKS HAVE NO BUMPS!!!

Well, none worth fussing over. :)
~~~o0o~~~

Claude,


Did you calculate how much the CG would raise with rising rates?

It is a trivially simple calculation.

The more important point is that students say they want rising wheel-rates, usually via rising-MRs, because such rising-rates are supposed to be great at absorbing bumps. The students say this because they see it on motorbikes, and the motorbike PR people are always pushing it. So what the students want is ... to BLINDLY FOLLOW FASHION!

I have yet to hear students ask "What is the best way to get falling-rates? And what shape of a falling-rate curve should we aim for?"

This is despite the fact that a large number of circuit racing cars (perhaps most?) end up with aggressively falling-rates, because these give the fastest lap-times. These falling-rates are arrived at by pure trial and error, and most of the race-teams/engineers who use them do not even realise that their corner-springs have "falling-rates".

Yes, I am talking about "droop limiting" here, which, despite the fancy name, is nothing more than aggressively falling wheel-rate.

Two more points:
1. Some years ago I had quite a few PMs from a student working on rocker geometry with the aim of getting "rising-rates". He eventually managed to get a nice "J"-shaped MR curve, with lowish MR at lower-left of the curve (= full droop), and progressively higher MR towards the top-right (= full bump). But, on closer inspection the curve had its vertical axis (= MR) extending from something like 0.98 to ... 0.99. The MR was all but CONSTANT!

In practical terms, the whole exercise was an utter waste of time. Or "intellectual mastur...", as you might call it :). A DASD would give exactly the same performance, but be much quicker to design and build, and have less mass, friction, slop, cost+++.

2. Rocker-geometry is limited in how much "shape" it can put into the MR-curve, and hence also the wheel-rate-curve. Essentially, there are only two sinusoids to work with. At best you get a "U"-ish shaped curve, or part of an "S" on its side. However, a combination of different springs and/or bump rubbers, connected in series and/or parallel, and with optional mechanical-stops to control the ranges of the various elements, allows almost any shape of curve to be produced.

In fact, "droop limiting" is just such a system, in that it uses a "droop stop" (usually the damper-rod) to increase the wheel-rate below static ride-height. This is an exceedingly simple mechanical linkage (so simple that few people recognise it as such) that produces a car performance enhancing wheel-rate curve that cannot be achieved with rocker-geometry alone.

Z

[Claude Rouelle]

Z,

We ran a few simulation in OptimumDynamics, but the differences between the results are very small.

I used linear suspensions with all other parameters (roll center height, camber/toe gain, aerodynamics, etc.) as constants to make sure the differences in the results were only due to the MR variation. I also ran the simulation with a rigid tire stiffness model, to eliminate the effects of tire deflection.

The main conclusion is that you are correct when you say that rising-rate corner-springs pushes the CG upwards. This effect, however, is very small.

You are not correct when you say that, when you have falling-rate corner-springs, the car "jacks down". The car always jacks upwards if you have roll centers above the ground. In a cornering situation, the jacking effect of the tire forces has much higher impact on the attitude of the suspended mass than the rising or falling rates of corner-springs.

I ran lateral acceleration sweeps from zero to 20 m/s^2 at 100 km/h. The baseline setup has a constant MR of 1.0. The setup 1 has an increasing MR that goes varies 0.9 to 1.2 (from full droop to full compressed state). The second setup has a MR that varies from 1.1 to 0.8. These variations were implemented both in the front and rear suspensions.
• Baseline: constant MR=1.0
• Increasing MR: MR from 0.9 to 1.2
• Decreasing MR: MR from 1.1 to 0.8

As expected, the inside spring (left) has a larger deflection for an increasing MR and a smaller deflection for a decreasing MR. On the outside spring (right), the deflection is smaller for an increasing MR and larger for a decreasing MR. See z1

The argument that you wrote in the FSAE Forum is indeed true. The variation of the CG position is larger when you have an increasing MR. However, the difference is very small. See z2.
In this plot, you can see that the CG position is always positive, regardless of the variation of the MR. This is due to the fact that the jacking forces have a higher impact on the variation of the CG position, than the MR.

To illustrate this effect, I removed the jacking forces by placing the roll center of both front and rear suspensions at the ground level: see z3
Now you can see the effect of the variation of the MR. The CG position varies by +0.1 mm for an increasing MR and -0.1 mm for a decreasing MR. This is an exaggerated case, where the MR varies by 0.3. Most suspensions have a smaller variation of MR, so the impact on the CG position will be even smaller.

The reason we removed the tire deflection and the kinematics was to isolate the effect of the varying motion ratios, since it was so small.

When I was running the first few simulations, I was using the full kinematics. The roll center position changed as car rolled, so the jacking forces were also changing. Since the chassis movement in the vertical direction is mainly dictated by the jacking forces, it was very difficult to identify what was the change in cg position caused only due to the variation of motion ratios.

Adding the tire stiffness would only make the effect even smaller, since you would have another spring in series with the suspension.

The change in CG movement with varying MR is so small that it would be "diluted" in the other kinematic effects (migration of roll center).

Claude

[Z]

Claude,

I think it is quite obvious that if you make VERY SMALL changes to the MR-curve, then

... the differences between the results are VERY SMALL. (My added emphasis.)

I am sure that if you modelled a rising-rate MR-curve similar to that used on many motorbikes, namely the type of curve most newbie-students seem to think they need, then the resulting CG-height changes will be much more dramatic.

In fact, that was the point of my Point-1 in previous post, in that spending time tailoring a MR-curve that ends up with only a tiny MR change is ... quite pointless!
~o0o~

The second point of my previous post was to point out that there are simpler ways to get much more dramatic changes to the shape of wheel-rate-curves than using rocker-geometry. Specifically, "droop-limiting" puts a sharp bend in the curve at, or just below, ride height. Very stiff wheel-rate below ride-height, and softer wheel-rate above. It follows that the resulting effects of that sudden change in wheel-rates, such as CG-height, are much bigger.

Coincidently, the resulting body-roll behaviour of droop-limiting is similar, but opposite, to the example that Doug gave in his earlier post. That is, the car-body nominally "rolls" about its inside pair of wheelprints, with no suspension movement of the inside-wheels, and only the outside-wheel springs compressing.

Here is a thread from 2005 about "Zero Droop Behaviour".
http://www.fsae.com/forums/showthread.php?4047-zero-droop-behaviour

If you care to model the CG-height change of a Zero-Droop car, then please give it the same roll-stiffness as the baseline car (and with RCH = 0, no ARBs, etc.). That means the ZD corner-spring-rates have to be HALF that of the baseline car's springs.

(Note the interesting discussion regarding ZD roll-stiffness in the 2005 thread. Nothing changes! Well, maybe I was more polite back then. :))
~o0o~

Also, from your previous post.

You are not correct when you say that, when you have falling-rate corner-springs, the car "jacks down". The car always jacks upwards if you have roll centers above the ground...

And from the top of your earlier post.

CG height : Let's not mix causes.

Z

(PS. On the 2005 thread linked above I mention the aero advantage of droop-limiting at the bottom of page 2. I think this can be a big factor. Claude gets a mention on page 5 (last page).)