To debunk that all you need to know about your sway bar is

[Pissoff]

I have read many many posts about sway bars. Everyone seems to think that diameter is the only thing you need to know about a sway bar. I have even read posts saying that a hollow bar and a solid bar gives the same resistance as long as they are the same diameter. Here are some solid facts about m3 front sway bars.
http://www.turnermotorsport.com/t-te...sway-bars.aspx

This shows that one needs to know what the true resistance of a bar is not just how big or small it is.

[dojk]

Just think of a sway bar (anti-roll bar) as a straight spring.

Essentially that is what it is, that ties the suspension to each side.

The torsional stiffness is based on the material, thickness of the of the spring.

[_Ryan_]

Do a search, there is far more detailed data available on this forum than on that single link.

[Suhb]

Do not forget that a hollow sway bar = less unsprung weight

[MightyMouseTech]

A bar being hollow makes almost zero difference in torsional stiffness.

[ShocknAwe]

only way is to measure spring rate. being hollow or solid is contributing an unknown quantity, especially considering differences in materials, dimensions, wall thickness, pinch, etc.

[MightyMouseTech]

Originally Posted by ShocknAwe

only way is to measure spring rate. being hollow or solid is contributing an unknown quantity, especially considering differences in materials, dimensions, wall thickness, pinch, etc.

Any mechanical engineer would beg to differ. There are very simple calculations to figure out torsional stiffness of a tube. The most important factor is the outside diameter of the tube. .

The torsional stiffness is related to the diameter to the forth power. For a hollow bar you substract the inner diameter cubed.

So, a 28mm solid bar is proportional to 28x28x28x28 or 614656, if you make the bar hollow, say an inner diameter of 15mm, it would be proportional to 28x28x28x28 - 15x15x15x15 or 564031, which is an 8% difference.

Going up 1mm would be a much bigger difference.

[ShocknAwe]

Originally Posted by MightyMouseTech

There are very simple calculations to figure out torsional stiffness of a tube. The most important factor is the outside diameter of the tube. The difference between hollow and solid is less than 1%.

No arguments there.

[tracer bullet]

Originally Posted by dojk

Just think of a sway bar (anti-roll bar) as a straight spring.

LOL I always think of a spring as a coiled bar. I guess it's whichever makes the most intuitive sense can be translated to the other.

[amsnow440]

Originally Posted by MightyMouseTech

Any mechanical engineer would beg to differ. There are very simple calculations to figure out torsional stiffness of a tube. The most important factor is the outside diameter of the tube. .

The torsional stiffness is related to the diameter to the forth power. For a hollow bar you substract the inner diameter cubed.

So, a 28mm solid bar is proportional to 28x28x28x28 or 614656, if you make the bar hollow, say an inner diameter of 15mm, it would be proportional to 28x28x28x28 - 15x15x15x15 or 564031, which is an 8% difference.

Going up 1mm would be a much bigger difference.

Not trying to nit pick here but this is incorrect. You subtract the fourth of the inner diameter.

Here is some raw data that will hopefully clear things up for some people.

The equation for torsional deflection is:

Θ = (L * T)/(G * J)

Where Θ is the angle of deflection of the bar in radians, L is the length of the tube, T is the applied torque, G is the modulus of rigidity of the material, and J is the Area moment of inertia.

For a solid tube J = (pi/2)*r^4.

And for a hollow tube: J = (pi/2) *(R^4 - r^4).

We will assume that everything else constant the only factor that differs is the Area Moment of Inertia for a given load scenario.

I've created a chart of the area MOIs for the varying wall thicknesses of a 28mm bar in a hollow configuration and compared it to a solid 28mm bar. You can see how quickly a hollow bar approaches the stiffness of a solid bar, with a 28mm(1.1") bar that has a 4mm(.150") thick wall (ID of 20mm) being 75% as stiff. But a 1mm wall thickness only yields a relative stiffness of 28%. And to make things simple, if you think about J in terms of the above equation it follows that by doubling J you will cut the deflection in half. So the stiffness is HEAVILY dependent on the wall thickness because it directly effects the area MOI.



We can take this further and use a common steel tube size of 1.125" (about 28mm) with a .1875" (4.75mm) wall thickness (ID of .75"). According to the chart, this is about 83% as stiff as the solid 1.125" bar. Quickly running the numbers it came out that the hollow bar is 55% the weight of the solid bar with 83% of its stiffness.

NOTE: For all you imperial people (like me haha) 28mm ~ 1.1" and 1mm ~ .040".

Here's a list of Area MOIs

[MightyMouseTech]

The "cubed" was a typo. All my calcs were to the forth power. My bad.

[amsnow440]

No worries. I see that I misread your calcs now and I agree with you.

Those calculations weren't directed at you specifically. I wanted the community to understand how the math works and to show with data how you can achieve almost the same stiffness with a hollow bar.

[DieGrüneHölle]

Whiteline discussion paper on hollow vs solid sway bars.

http://www.whiteline.com.au/docs/bul...%20Swaybar.pdf

[BrokenVert]

Originally Posted by amsnow440

Not trying to nit pick here but this is incorrect. You subtract the fourth of the inner diameter.

Here is some raw data that will hopefully clear things up for some people.

The equation for torsional deflection is:

Θ = (L * T)/(G * J)

Where Θ is the angle of deflection of the bar in radians, L is the length of the tube, T is the applied torque, G is the modulus of rigidity of the material, and J is the Area moment of inertia.

For a solid tube J = (pi/2)*r^4.

And for a hollow tube: J = (pi/2) *(R^4 - r^4).

We will assume that everything else constant the only factor that differs is the Area Moment of Inertia for a given load scenario.

I've created a chart of the area MOIs for the varying wall thicknesses of a 28mm bar in a hollow configuration and compared it to a solid 28mm bar. You can see how quickly a hollow bar approaches the stiffness of a solid bar, with a 28mm(1.1") bar that has a 4mm(.150") thick wall (ID of 20mm) being 75% as stiff. But a 1mm wall thickness only yields a relative stiffness of 28%. And to make things simple, if you think about J in terms of the above equation it follows that by doubling J you will cut the deflection in half. So the stiffness is HEAVILY dependent on the wall thickness because it directly effects the area MOI.



We can take this further and use a common steel tube size of 1.125" (about 28mm) with a .1875" (4.75mm) wall thickness (ID of .75"). According to the chart, this is about 83% as stiff as the solid 1.125" bar. Quickly running the numbers it came out that the hollow bar is 55% the weight of the solid bar with 83% of its stiffness.

NOTE: For all you imperial people (like me haha) 28mm ~ 1.1" and 1mm ~ .040".

Here's a list of Area MOIs

Its like I'm taking senior structures again! Gotta love MOIs - so useful.


And to those wondering, MOIs are used all the time in design to make structures lighter and, sometimes, stiffer than using a solid, dimensionally equivalent, piece. An I-Beam would be the most common example of this idea.


But great chart Mike! Very informative.

[tjswarbrick]

Great. Brought me right back to Structures, too.
So, are all OE and aftermarket BMW sway bars mild steel with a modulus close enough to be nominally equivalent?
I see from the Turner link that the e92 (26.5mm) and e93 (28mm) M3 bars are hollow - as are the E81 M-Sport bars.
Fascinating.

[amsnow440]

Originally Posted by tjswarbrick

Great. Brought me right back to Structures, too.
So, are all OE and aftermarket BMW sway bars mild steel with a modulus close enough to be nominally equivalent?
I see from the Turner link that the e92 (26.5mm) and e93 (28mm) M3 bars are hollow - as are the E81 M-Sport bars.
Fascinating.

My gut says yes, but until someone cuts a bar in half it's pure speculation. Has anyone done this or found a source that has this information? I'm considering the e93 M3 bar myself.

[BrokenVert]

Originally Posted by amsnow440

My gut says yes, but until someone cuts a bar in half it's pure speculation. Has anyone done this or found a source that has this information? I'm considering the e93 M3 bar myself.

I couldn't bend my e93 bar by hand when I got it. But I'm not that strong, so take it with a grain of salt!

[ShocknAwe]

I'd love to know where the numbers from the TMS page came from.

[John_01]

I think the difference between stock and M3 bars seems larger than what Turner motorsport claim. On the other hand, maybe the measured the stiffness of the bars, but didn't account for the stiffness of the firmer sway bar bushings on the M3 items.

[aloksatoor]

I have the e93 bar. The bushings for sure seem way stiffer than the stock ones. Maybe that contributes to better stiffness overall. Since the actual roll resistance will be a combo of bar and bushing.

[chris82]

Originally Posted by MightyMouseTech

Any mechanical engineer would beg to differ. There are very simple calculations to figure out torsional stiffness of a tube. The most important factor is the outside diameter of the tube. .

The torsional stiffness is related to the diameter to the forth power. For a hollow bar you substract the inner diameter cubed.

So, a 28mm solid bar is proportional to 28x28x28x28 or 614656, if you make the bar hollow, say an inner diameter of 15mm, it would be proportional to 28x28x28x28 - 15x15x15x15 or 564031, which is an 8% difference.

Going up 1mm would be a much bigger difference.

Thanks for this

[dtla1]

What do you guys think adding a few layers of wet lay carbon fiber to our from anti-roll bar? I thought about doing this to the end-links also.