ARB Sizing Calcs

[salad]

Hi guys, I'm currently doing the calcs for the ARB sizing on our car and it's giving me a bit of grief.

The biggest problem so far is that my calculations are saying I need a pretty small motion ratio (<0.4) for a solid bar not to exceed yield shear stress (240MPa). For a hollow bar I need less than around 0.3. I don't think the dimensions are too extreme, I'm getting around 2.8deg twist over a 120mm bar. The bars contribute to about 30% of the roll rate, so I wouldn't say that they're hugely stiff either (others may disagree).

I didn't have much of a problem accepting these calcs, but then some other team members pointed out other teams that are running tiny active bar lengths, really short lever arms and what appears to be pretty high motion ratios.

Just wondering if anyone would be kind enough to give me ballpark figures of what motion ratios they run on their ARBs?
Or are people using different materials with higher yield stresses?

Also, after a little bit of pondering, I got the idea in my head that a U-bar will twist twice as much as a T-bar, so therefore the T-bar will need to be twice as stiff to achieve the same roll rate. Makes sense in my head, but then Milliken makes no mention of different stiffnesses required for different bars.

Any help would be greatly appreciated.

Cheers
Showza

[salad]

Hi guys, I'm currently doing the calcs for the ARB sizing on our car and it's giving me a bit of grief.

The biggest problem so far is that my calculations are saying I need a pretty small motion ratio (&lt;0.4) for a solid bar not to exceed yield shear stress (240MPa). For a hollow bar I need less than around 0.3. I don't think the dimensions are too extreme, I'm getting around 2.8deg twist over a 120mm bar. The bars contribute to about 30% of the roll rate, so I wouldn't say that they're hugely stiff either (others may disagree).

I didn't have much of a problem accepting these calcs, but then some other team members pointed out other teams that are running tiny active bar lengths, really short lever arms and what appears to be pretty high motion ratios.

Just wondering if anyone would be kind enough to give me ballpark figures of what motion ratios they run on their ARBs?
Or are people using different materials with higher yield stresses?

Also, after a little bit of pondering, I got the idea in my head that a U-bar will twist twice as much as a T-bar, so therefore the T-bar will need to be twice as stiff to achieve the same roll rate. Makes sense in my head, but then Milliken makes no mention of different stiffnesses required for different bars.

Any help would be greatly appreciated.

Cheers
Showza

[exFSAE]

Depends how you define motion ratio.. but for what its worth I've seen and used MR's up to 4:1 or 5:1 on ARBs.

That's degrees of ARB twist per degree or chassis roll.

[salad]

Sorry, my motion ratio for this is lever arm:wheel, so the lever arm moves less than the wheel (I think I've got that the right way around). Either way, at the moment, the rear ARB has just under 1 deg of twist per degree of roll, and it seems it has to be close to this to keep the stresses down...

[Mike Sadie]

Are you using a T-bar or U-bar? In either case, how long are your lever arms? If U, which part(s) are you considering flexible, the arms or the connecting tube?

[exFSAE]

I would say some of our older ARB's twisted 10+ degrees.

Edit - Wait a minute.. you're using SOLID bars? Try tube...

Edit 2 - Didn't catch this as you are using silly metric units instead of proper Imperial. 240MPa seems really low for a yield stress. Thats what 35ksi-ish? What is that, mild steel?? Even Cond N 4130 should be in the 60ksi / 400+ MPa range. Q&T much higher...

[The AFX Master]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"> Edit 2 - Didn't catch this as you are using silly metric units instead of proper Imperial. </div></BLOCKQUOTE>
This may help a bit..
http://www.digitaldutch.com/unitconverter/
you can try to catch it, silly that i don´t have tutorials for google usage http://fsae.com/groupee_common/emoticons/icon_frown.gif

back in topic, 120 mm for a torsion bar (at least for an u bar) seems pretty short, and if you have short lever arms the problem gets worse, using 4130 tube and widening your bar will solve your problem..as far as you don´t have packaging issues. You can include blades instead of stiff lever arms to reduce the angular displacement of the torsion bar but that seems to be unpractical if you have short levers.

[Lundahl]

look at different spring steels and you could achive yield stresses at 1000-2000 MPa. we'll be using Orvar Supreme from Uddeholm, which after heat treatment can reach 1520 MPa in yield stress.

about the motion ratio. in the front we'll be lying about MR=.07 (~14 deg arb-twist per deg body roll), and i'm not worried about the arbs gonna break... yet =)

[murpia]

A conservative (safe) ARB will result if you design for a peak stress of 500MPa (heat treated steel) at full torsion (one wheel full bump, the other full droop).

If you want to save weight or go for packaging, you can push your material harder and use real data to determine what the maximum difference in wheel displacements will be...

Regards, Ian

[salad]

Thanks for the replies guys, I will be using tube, but just did the calcs for a solid bar anyway. The 120mm active bar length is for packaging mainly, the lever arms are long though, 200mm at it's softest, mainly to keep the stresses down and 200mm makes it almost inline with the bellcranks.

The 240MPa that I used was from the calcs done by one of last year's guys and is for 4130 tube. I will contact our supplier and find some finer details soon.

Thanks again for everyone's help.

Cheers
Showza

[billywight]

240MPa is wrong as others have said, that's less than the yield strength of 6061-T6. Perhaps that number has an included factor of safety? 4130 in an annealed or normalized state is about 460MPa YTS and when heat-treated can be in excess of 1100MPa. Essentially the more agressive the heat-treat, the higher the hardness; yield strength increases and elongation at break decreases (more brittle). See:

http://www.matweb.com/search/QuickText.aspx?SearchText=4130

for material properties. Also, I believe someone (Jersey Tom?) posted some good material spec sheets on alloy steels a while back. Try the search function to find them.

[salad]

Correct me if I'm wrong as I'm not that strong with materials (I'm a mechatronics engineer), but in an ARB, wouldn't we want the Shear strength? Not the Tensile strength?

I have been using Matweb a bit but will do more now as I just found out the relationship between shear and tensile strengths... (pretty damn crap at materials really...)

Cheers
Showza

[murpia]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by salad:
Correct me if I'm wrong as I'm not that strong with materials (I'm a mechatronics engineer), but in an ARB, wouldn't we want the Shear strength? Not the Tensile strength? </div></BLOCKQUOTE>
There are 'rules of thumb' for shear stress vs. UTS:

http://www.roymech.co.uk/Useful_Tables/Springs/Springs_helical.html
http://www.roymech.co.uk/Useful_Tables/Springs/Springs_Materials.html
http://www.tech.plym.ac.uk/sme/desnotes/Springs1.pdf

I would advise you check other references though, I've discovered errors on that first site.

Regards, Ian

[billywight]

for most steels, shear strength is generally 58% of the tensile strength.

[murpia]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by billywight:
for most steels, shear strength is generally 58% of the tensile strength. </div></BLOCKQUOTE>
Yield or ultimate? Do you have a reference you can post?

Thanks, Ian

[salad]

Sorry, I meant shear yield stress in my original post.

[flavorPacket]

that's the standard von Mises yield criterion (it's actually .577)

[Christopher Catto]

shear stress and tensile stress are governed by:

G = E/[2*(1+PoissonRatio)]

So for a steel of Young's modulus E=210GPa, the shear modulus is 80.7GPa. Assuming a poisson ratio of 0.3 to 0.33

If this is then the same for the yield and UTS stresses, then it should not be a problem to check the ARB is not going to fail

[exFSAE]

It's been a while but I'm not sure that the relationship between shear and tensile modulii holds up for shear and tensile strength...

[murpia]

Not the moduli, but the stresses.

For a bar in torsion, shear stress in torsion is dictated the relationship between twist angle, cross section, torque etc. given here (http://en.wikipedia.org/wiki/Torsion_%28mechanics%29). G appears here because a 'stiffer' material generates more torque per twist radian.

The relationship between tensile yield stress and shear yield stress is therefore the key to determine if your bar will yield given a certain twist and / or torque.

If you're making a bar, why not twist a material sample to yield in a rig? That way you don't need to rely on an internet forum for results...

Regards, Ian

[salad]

Yeah, I'm not taking everything that has been said as gospel, there will be testing first to make sure the thing doesn't yield.

I seem to be struggling to find a supplier for 4130 with suitably high yield stress at the moment though.
Just throwing this out there, has anyone used 4140 for an ARB? Matweb says the shear modulus is the same, it's just got much higher yield strength.

[billywight]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"> I seem to be struggling to find a supplier for 4130 with suitably high yield stress at the moment though </div></BLOCKQUOTE>

I assume you're going to weld this? You will need to heat treat it afterwards anyways. Just get whatever they have in stock (probably normalized condition) weld it up, and heat-treat it. Make sure you use the proper wleding rod; you should probably be looking for about 37-38 HRc for the heat treat.

[flavorPacket]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by salad:
Just throwing this out there, has anyone used 4140 for an ARB? Matweb says the shear modulus is the same, it's just got much higher yield strength. </div></BLOCKQUOTE>

Watch out for notch sensitivity with 4140. the fracture toughness will limit you more than you think.

[salad]

No worries, thanks for all your help guys.

[BilletB]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">I seem to be struggling to find a supplier for 4130 with suitably high yield stress at the moment though.
Just throwing this out there, has anyone used 4140 for an ARB? Matweb says the shear modulus is the same, it's just got much higher yield strength. </div></BLOCKQUOTE>

Many, many arb's are made from 4140, 4340, etc. and it will be used in some hardened condition. Fundamentals show that quality, hardened steel makes the best springs whether coil, torsion, or something else.