What I learned from reading
 

ok I know Im gonna get alot of heat from this post but here it goes. On my free time when Im feeling lazy, I like to read Car Mags like Sport Compact Car, and Car and Drive, and Grossmans Motorsports, and every now and then maybe a Honda Mag just to see whats new in the world of cars.

Anyway I was reading about suspension upgrades and and I thought you guys might like to know this if you didnt already.

The topic at hand is SWAYBARS and The technical stuff on them.

First off I leanerd Tublar sway bars are better then solid sway bars, They are much lighter.

Here is the Technical stuff

"The concept of hollow Bars is simple. The stiffness of an anti-roll bar goes up with the FOURTH power of the the DIAMETER. In other words, if you double the diameter of the bar its stiffness will go up by 16 times or 2 to the 4th power. This means the metal on the outside of the bar's cross section is far more important than the metal core. SO WHY NOT JUST TAKE THE CORE OUT?
If a 1-inch bar is 16 times stiffer then a 1/2 inch bar, then a 1 inch bar with a 1/2 inch hole in the middle is still 15 times stiffer than the original, but FAR LIGHTER." THIS IS WHY HOLLOW SWAY BARS ARE BETTER .

Just thought you guys might find that intresting.


:D

Very interesting. I wondered why a small amount of increase in diameter seemed to be much more expensive. Pelican just started selling hollow sway bars...

you can read?


j/k :D

From an engineering standpoint, "stiffness" is a property of the material, not a function of the radius or diameter. I think a better explaination would be that the torsional force exerted on the outside of the bar is the same regardless of whether the bar is hollow or not, so removing the core will just save weight. I'm not sure how the "stiffness" (modulus of elasticity) can change with the radius, unless the bar is made of two different materials.

As the diameter is doubled, the radius is quadrupled, and the yield stress (the point at which the bar fails) at the outer radius of the bar will increase by a factor of 16 , regardless of the diameter of the bar. It can't go up by a power of 4 in relation to the diameter.

Clear as mud? Good. Test tomorrow.

so what is that, about half a pound total saved weight?
instead ill just drive with out shoelaces tomorrow and call it even.

and i dont think the modulus of elasticity varies with diameter, but the change in length will

Then I guess the ultimate would be a hollow titanium alloy (6% aluminum, 4% Vanadium) sway bar about 2 inches in diameter, with Ti mounting bolts...strong, stiff light. Shouldn't cost much more than my car. :D

Nawww...just take a dump before you drive and save a pound!

The age old question! "Does size matter"??:D :D

Huh?

Yup. One time I was getting my exhaust welded and some weird guy went up to my gf and said "Big guys like small cars huhhh" and she got scared but she told me the guy was right ;).

I think he was refering to the torsional stiffness of the swaybar which is torque (T)/(angle of twist (d). Torsional stiffness is a function of the polor moment of inertia (J), the modulus of rigidity (G), and the length of the bar (L). T/d=G*J/L. Since J = (Phi/2)*(radius (r) to the 4th), doubling the radius does yield a 16 fold increase in torsional stiffness. Hollow bars are a little different since J=(Phi/2)*(r-outer^4 - r-inner^4). For an example, I took 2 951 sway bars (25.5mm solid and 27MM hollow) and compared them. Again assuming same material, length and torsional stiffness, the 27mm bar will have an inside diameter of 18.15mm.

And...doubling the diameter does NOT quadruple the radius, it only doubles it. :D

Rob

You're right, sorry about the radius thing. However, where tmin/max = shear stress, tmax will be the same at max rho, regardless of whether the shaft is solid or hollow. tmin will be greater than zero because of C(1), and tmin will be zero at the center of a solid shaft. So, tmax=(c2/c1)tmin in the case of a hollow shaft. The stress is still distributed linearly across the radius.

I do agree that as the shaft lengthens, phi will increase with gamma, but tmax should remain the same at max rho.

Rob,

I see what you're saying now: to get the same torsional stiffness (GJ/phi*L), C2 has to increase to account for c1>0.

So, it seems to me that hollow bars still aren't any "better" than solid bars, they just do the same thing with less weight but a larger diameter.

-Tom

That's correct Tom. The benefit is really the weight reduction. Because as you can see with my previous example, increasing the r-outer by .75mm allows you to have an r-inner of ~9.1mm.

In essence, your removing material that doesn't resist much of the applied torque and instead put it were it will.

If you look at the same 27mm bar but instead as a solid bar, it would result in a sway bar that was 25% torsionally stiffer than it's hollow counterpart.

Rob

Rob, did you weigh the two bars? What weight savings do we get? Can you cut one open to see how large the hollow center is so we can caculate its effective stiffness in a solid bar?

The calculations for rigidity (not stiffness) is pretty interesting in that you subtract the stiffness of an equivalent bar as the hollow center, from the overall stiffness of a solid bar of that size. But this is for thickwall tubing only, once the wall-thickness gets below 10% of the diameter, there are more complicated factors that come into play.

Hey Danno,

I haven't weighed or cut apart anything. I just used these 2 bars as examples and as stated earlier, used the assumption that the 2 bars have the same torsional stiffness, material properties, and length.

And as always, you bring up some good points that it does vary for each instance and not really applicaple to thin walled tubes because of the torsional buckling.

Rob

Rob,

I finally noticed your location....do you know a guy named Derek Redding? He worked at Los Alamos last summer, I think

No, I sure don't. He might have worked for the national laboratory here as a summer student, but the labs spread out all across Los Alamos.

Rob

sorry, ill try to complete my thoughts more often.
i think i was saying that modulus of elasticiy only depends on the material but the stiffness or rigidity or resistance to compression (im not sure of the correct term here) is dependant on the area.