ARB contribution to wheel rate?

[highboost]

Hi guys,

Long time reader, first time poster.

I understand you need the spring rate and motion ratio of the roll bar, but mathematically, how do you include this value into your overall wheel rate?

This has been bugging me for a while now.

Thanks

 

[hemipanter]

Swaybars are often made of a bent steel bar where the "arms" that goes out to the A-arm's has an angle, in the vicinity of 45 dgr or so. This will affect the rate of the torsion section, which is the straight portion of the bar in between the chassis attachment clamps of the bar (by partially serve as a transverse leaf spring). The torsion section should be activated throught the use of stable 90 dgr levers out to the A-arms.
That said, we can now calculate torsion spring force on ordinary way, and then wheel-rate through Mr ^ 2.
When the car roll, thus we can say that swaybar remains stationary in its absolute center because the inner wheel springs out as much as the outer wheel springs in. We should therefore use half the spring force per suspension side.

There are a lot ideas around concerning swaybar function, like "lifting the inner wheel" and the like. It can create false ideas about what is happening, but it requires as much strength to lift up one side of the car as it takes to pressing it down on the other side.

I've heard ideas that the car's ordinary springs helps to lift the car on the inside wheels, but it is so that the lifting force of these springs decreases by as much per mm as the car is lifted. So it is all about that the swaybar is getting twisted in proportion to the roll of the car.
Goran

 

[WolfHR]

I think the problem is that it's no longer independent suspension, so wheel rate will depend on position of the other wheel. In pure bounce ARB will not affect wheel rate, but any roll angle will change that.

 

[hemipanter]

Wherever the possition of the wheel travel are, the spring wheel constant will remain the same, the only thing changing is the spring pressure at the wheel in Kg. Well, provided there are no progressive springs or lever arms included.

The swaybar will only add to wheelrate in ROLL, with as much as the bar is twisted. (Times the Mr).
Goran

 

[GregLocock]

Couple of things

The single wheel bump rate is roughly half way between the roll rate and the bounce rate.

If you have grippy D blocks then they affect the bounce rate

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[TrackRat]

From the little that I've researched ARBs they can change a lot more things than I'd like when they have a high spring rate. If I had a choice I'd prefer stiffer primary springs and a lower rate ARB, but that tends to be more of a track oriented approach than for street. It can reduce traction on bumpy surfaces and make for a harsher ride so it's all a compromise.

The link below is a ARB spring rate calculator. I have not confirmed the accuracy but offer it as a visual aid for those interested.

http://buildafastercar.com/tech/Sway-Bar-Rate-Calculator

 

[NormPeterson]

TR - for a simplified derivation from basic structural beam formulas, it's not too bad. A more rigorous effort including a few more flexibility terms (but stil not considering the ffect of bend lengths) typically gives stiffness values a few percent lower (5% or so in most cases that I've checked). "Exact" material Youngs modulus vs the assumed value (I forget what it worked out to have been) could perhaps be a few percent more. A finite element analysis will give answers that don't agree with either of those.


Norm

 

[NormPeterson]

Greg - use of the qualifier "roughly" has me wondering if the geometric changes due to roll are sufficient to affect what the sta-bar sees as displacement inputs on one side vs the other. It would seem that the geometrically carried LLTs would become unsymmetrical, forcing the elastic roll resistances to either do likewise or add some coupled 'heave'.

I recall that adding a moderately stiff sta-bar to the front of a car that was not originally fitted with any bars at all gave the distinct impression of holding the front end up in a turn, relative to its earlier behavior (this being in addition to keeping it more level). Some of that may have been due to parallax or other illusion, but I don't think it all was.


Norm

 

[TrackRat]

I'm no expert but it appears to me an ARB is a reasonable compromise for street use but far from the ideal when you are approaching the limit of traction or for optimum handling. It's a useful tool to reduce roll while allowing softer springs for improved ride, but it has it's negatives also including lifting the inside wheel, rate change with large angle changes, etc.

 

[hemipanter]

I did a "thinking problem" to a Swedish forum for the discussion swaybars.
It consists of two parts ...

A, a number of different swaybars that have different angled arms. The first is at 90 degrees and it gets a deflection of 120 mm at the load 185kg. The figures come from practical full-scale experiments I have made. Problem solution is to resolve how much the deflection will become with the other described angles of arms.

http://www.hemipanter.se/Kr%E4ngningsfj%E4der.jpg

B, the second problem is to solve the spring constant of two springs working against each other, which is linked to swaybars against the usual feathers.

http://www.hemipanter.se/Springs.jpg

Perhaps no direct marvels but about what we are discussing here. I will show the answer within a coupple days if anyone like to try to come up with some figures.
Goran

 

[NormPeterson]

In thinking problem "A", may we assume that there are chassis side pivots at the intersections of the center section and the arm(s)? Or are they offset along the torsional section by some distance?


Norm

 

[hemipanter]

Torsion springs are solidly fixed to the right side, so we have a torsional spring length of 700mm. The difference lies in arm length and angle. We do not anticipate any friction in the bracket where the lever goes out. The entire spring is of the same material. We do not need to care about the figure at the bottom with two arms.

Goran

 

[evelrod]

I've used several of the "plug and play" sites lately. I'm not near the engineer that most of y'all are and I'm fairly inept with the PC. However, I've a good deal of experience in the field as it pertains to race cars. What works for production cars usually does not translate well to the track. It is often better to change spring rates than worry with all the eccentricities of ARB's. Still it is also most difficult to do in an expeditious manner at the track so, enter the ARB. It makes for an easily adjustable and tunable setup, even from the cockpit in some cars. Certainly not the end all for chassis setup, just another factor.

"Grippy D blocks"---Well, you try to not do that.
Wheel rate, I just factor in the max of the bar rate per wheel and let it go at that. No matter what the paperwork says, it never works out perfectly at the track.
Much like setting up the dampers, ARB's, Panhard bars, require a LOT of track testing and adjustment to achieve a proper setup. I suspect that this is also done on the production side as well...It's just not publicized since, how would that look to John Q. if he knew that "science" was not all it takes to make his Toyahonda?

Rod

 

[hemipanter]

Rod, I agree with you, you have to test the car on the track.

If I may allow myself to be a bit philosophical.

I think the great value of engineering knowledge is to acquire the right understanding of the events so that you can work more rationally on the track. This swaybar problem is actually also an experiment I did in real life to get just a practical evidence to show why different types of swaybars produce different effects on the cars. I have seen several formulas for swaybars not taking everything into account, which easily creates distrust of computations. It is therefore important to understand "both sides of the coin".
In many discussions with amateur racing team, I come across another kind of problem, you have a knowledge of the nature of a design but wrong idea of how important it is. It makes you prioritize errors both in the building of a car and pit stop.
Goran

 

[highboost]

Thank you for all the very insightful posts everybody, here's a little background so you can understand why I asked this question.

I have a B8 A4, and B8 S4. These cars have the same motion ratio front and rear. I have a susp. setup on the A4, and am trying to achieve the same chassis frequency F/R on the S4 I have on the A4.

I have a roll bar of known stiffness and motion ratio. I have a spring of known stiffness and motion ratio of rear suspension.

I know how to find the wheel rate JUST using the spring, how do I mathematically include the ARB?

 

[hemipanter]

Here is the answer for the swaybar deflection (D).
In the first 90dgr example we had D of 120mm.
If we had another arm,like the last figure,
there will be D of 60 mm each arm,
Number two 67,5 dgr have a D of 140mm.
Number tree 45 dgr have a D of 160mm.
Number four 22 dgr have a D of 430mm.

Here is the answer for the other problem (hope I can explain it properly).

In example A1-A2 the spring rate will include one single spring when moving the plate C for a rate of 1kg/mm.

In example B1-B2 there are two springs involved since the springs are preloaded against each other. The result is that in now takes 2kg/mm to move plate C to the left. In other word the same rate per mm as if the springs where standing in parallel under the plate C.

The explanation is that in the starting position the left spring is preloaded to 10 kg. By pressing it further together by 10mm we must add another 10 kg of force for a total of 20kg for this spring. Since the right side spring now is loose it will provide no “help” any longer.
In stead of giving us assistance moving the plate C to the left it is actually LOOSING 1 kg mm of assistance for every mm the plate C is moving to the left. This might be worth thinking of in the case of the sway bar loading up against the ride spring during cornering. A situation looking a bit of the reverse since the bar starts out unloaded against the ride spring that is preloaded by the weight of the car.

Goran Malmberg

 

[TrackRat]

Strange world...

I contacted an aftermarket mfg. who's company name would resemble the initials in a High Rate ARB, regarding the swaybar that I purchased from them, to see if they would provide either the ARB rates for the replacement ARB at the different link positions or the wheel rates for the different link positions. They refused to provide any info. which makes me wonder if they actually know the rates?

You've got to love good customer support - if you can find it any place. <LOL>

 

[hemipanter]

Is not this a reminder of our experience with shock absorbers?
Goran

 

[evelrod]

It's pretty pointless to post a lot of theory in a thread as there are so many different approaches at the problem. Try the "plug and play" sites plus reading a couple books---they don't need to be complicated, e.g., Carrol Smith or Fred Puhn paperbacks. Especially the ARB/wheel rate section in Puhn's book.

For anything more than approximation, I should think a simple scale and test rig should suffice. The actual determination of wheel rate is not rocket science. Still, the final "at track" setup CAN be a bit of the "black art", especially when you factor in all the other variables---.

Rod

 

[TrackRat]

Goran-

Yeah, I forgot this stuff was National Secrets... <LOL> As if the competition can't measure the rates if they wanted to. It's all so silly to me.