Mbaron

<ul><li><a href="http://store.summitracing.com/partdetail.asp?autofilter=1&amp;part=INT-15-7-061&amp;N=700+4294924653+4294907586+4294903976+429 4923769+115&amp;autoview=sku">Summit</a></li></ul>

J. Patterson

One of my favorite mods. If you do them pregrease the poly bushings real well.<ul><li><a href="http://www.purems.com/products/product.php/II=2119">http://www.purems.com/products/product.php/II=2119</a</li></ul>

InTTruder

Tubular is alos stiffer for the same diameter.

joe@vwvortex

and will depend on the inner diameter as well. A good example is Neuspeeds 25mm hollow rear bar vs their 22mm solid bar. The 25mm hollow bar is lighter and stiffer.<ul><li><a href="http://www.whiteline.com.au/docs/bulletins/Hollow%20vs%20Solid%20Swaybar.pdf">Solid vs Hollow</a></li></ul>

InTTruder

I'll go check my math.

J. Patterson

I'm not an engineer but my instincts tell me that a tube is stiffer by weight than a rod, but in equal outside diameters the rod would be slightly stiffer. The material at the outer edge of the cross section does most of the work due to the greater shear, but not all.
example: If one takes a 1" rod and axially bores it with a long 3/4 inch bit leaving a 1/8 " wall thickness, does it get stiffer torsionally? I would think not. Lighter yes. Stiffer no. Does it lose any torsional stiffness? I would think very little. Does it become more fragile, apt to fail? Yes I would think so. I have no data to support this . Only my instincts which have been known to be wrong. (Ask my former HPDE driving instructors:-) )

InTTruder

There is a point of diminishing returns (light versus stiff): I'll go see if I can did it up.

joe@vwvortex

from Bimmerforums.........

Let me start by saying that I think the original poster's question is a little ambiguous, and that may be why this discussion took the course it did...

Stronger?

For a given diameter, a solid bar is stronger in torsion than a hollow bar. A greater diameter hollow bar can equal or exceed the torsional strength of a solid bar. It just depends on the wall thickness (i.e. how much material is missing out of the middle).


Maximum shear stress (tm)=(Torque [T])/Polar moment of inertia (Ip)
tm=T/Ip
.
.
.

therefor the ratio of tm is .5/.4352 = 1.15 or, more plainly, the tube is 1.15 times stronger than a solid shaft, given the same outer diameter, and material.


Tau Max isn't the bar's ability to resist torsion, it is the max shear stress that will result from an applied Torque. If you apply 5Nm of torque to a plastic straw and to a .25" diameter steel bolt, the straw will see a higher Tau Max. Doesn't mean it is better able to resist torsion.

Before you say it, I know.... 2 different materials. But that's my point; Tau Max is just a measurement of stress, not an indicator of the ability to resist stress. It doesn't take into account things like materials.

With constant OD, a tubular cross section has a lower polar moment of inertia than a solid one. We agree on that part. Keeping the applied torque a constant, dividing by the lower polar moment is how you end up with the higher Tau Max. Do it the other way; assume Tau Max is a constant related to the material's plastic deformation or ultimate strength point. Now the higher polar moment multiplied by the constant Tau Max gives a higher Max Torque before failure.

To actually see how the solid bar handles that stress compared to the tube, you need to picture the cross section. At the center point in the diameter of the bar, Tau=0. At the outer radius, Tau is at its Max. Tau increases linearly from 0 to max. Since the tubular cross section is missing a large amount of material that would otherwise do the job of resisting the stress near the neutral axis, the smaller annular area of the tubular cross section has to carry the same total load as the circular area of the solid cross section.

http://www.tripledistilled.com/swaybars.jpg

Image found via Google image search! Awesome!

Admittedly, the part of the solid bar that is missing with a hollow cross section is the part that resists a Tau closer to zero, so it does not have an overwhelming effect on the bar's ability to resist applied torque.

So....

...they are lighter too.

Even though the tubular bar isn't actually stronger, the advantage of the hollow cross section is a significant weight reduction without significant loss of resistance to torsion. In some (most) cases, this trade-off is worthwhile.

When comparing a solid sway bar with a tubular bar of identical material and arm geometry, you need to subtract the inside diameter (i.e. wall thickness times 2) to the fourth power from the outside diameter to the 4th power, and then take the fourth root of the whole thing.

In "Excel-speak", think (SQRT(SQRT((OD^4)-(ID^4))).

In practical-speak, I haven't seen a sway bar on a BMW break in years. If the original question about "strength" was due to a concern about breakage, don't worry. If you want to compare a tubular bar to a solid bar, then you just need to keep in mind what I said at the beginning: For a given diameter, a solid bar is stronger in torsion than a hollow bar. A greater diameter hollow bar can equal or exceed the torsional strength of a solid bar. It just depends on the wall thickness (i.e. how much material is missing out of the middle).

For a look at how a tubular bar's measurements will compare to a smaller-but-heavier solid bar, check out the page on UUC's E46 M3 sway bars: http://www.uucmotorwerks.com/html_product/sway_barbarian/html_sway_bar/description2.htm

If the manufacturer's whose tubular bars you are looking at doesn't have this kind of comparison page, email me and I will help you write an Excel spreadsheet to calculate it for yourself (TK Solver and Mathcad requests also OK).

BTW, while the bar geometry (width of straight portion, length of arms, position of adjustment holes/blade length, angle of arm to straight portion) has a huge effect on overall stiffness (i.e. effective spring rate), the material does not. The modulus of elasticity of different steels doesn't vary significantly.

--Matt
Jean-Claude


I don't care about weight - the damn car weighs over 3200lbs - I care about stiffness. I run my 21mm bar on full stiff on track days. That's with my V3's on 55% of full stiff on the back in rebound and 50% on compression.

InTTruder

Looks good. I'll do some tinnin'!