enginners help, comparing strengths of hollow vs solid bars

[Sam_Q]

I figured there would be a few people with engineering backgrounds on here to help me with my lack of it. I would like a rough guide on how to compare the stiffness/strength of solid axles to hollow axles in regard to bikes, with stub and twin supported in mind.

First example that comes to mind is a rear bike axle, ignoring the whole threaded thing it's a 3/8" diameter so 9.7mm. Now if I was to go to a 17mm hollow axle how thick would I have to make the wall to have the same overall strength. The material in question is 4130 steel with no welds or heat treatment. I will have some thin wall sealed bearings which will roll directly on the axle after I grind the outside to the right O.D

With my lack of education all I had to go off was the cross sectional area, with a 1.4mm wall I will have a cross sectional area of a 9.4mm solid axle, however I would of thought that being a larger diameter it would be stronger and more rigid so I could go thinner again. I know if it's too thin the "coke can effect" happens but yeah I don't know much.

I was hoping to gain rigidity and hence loose weight by going for a larger diameter, am I wrong in my approach?

For anyone who answers this thread please be patient and descriptive as I don't know the proper engineering use for many terms like probably even strength, I do however understand elestic limits.

[roadsailing]

I wouldn't bother with hollow axles, as bearing contact complicates things, you may reduce weight a tiny bit but any effect on rotational inertia will be minimal.

For normal applications, like simple beams in bending, there are pretty straight forward formulae to use, likewise for torsion and tension (which is just cross sectional area), compression is a bit more involved due to buckling.

[brett_celicacoupe]

pretty much 3 causes of stresses in your case

1. bending (http://en.wikipedia.org/wiki/Bending)
2. torsion (http://en.wikipedia.org/wiki/Torsion_%28mechanics%29)
3. shear (http://en.wikipedia.org/wiki/Shear_stress) <- id expect negligible


maximum bending stresses occur at top and bottom assuming loaded vertically <- examine side in tension, this is the critical one.

maximum torsion stresses occur furthest from centre

maximum shear stresses occur level with neutral axis. id have to check a textbook but i seem to remember maxstress for a round member is 4/3 * F/A

torsion and bending are a function of moment of inertia and second moment of area about the neutral axis x respectively.

for bending the second moment of area is a 4th order function of radius so large gains in strength can be seen with small increase in R (http://en.wikipedia.org/wiki/Second_..._Cross_Section)

there is the theory, do the math

[Sam_Q]

I wouldn't bother with hollow axles, as bearing contact complicates things, you may reduce weight a tiny bit but any effect on rotational inertia will be minimal.

For normal applications, like simple beams in bending, there are pretty straight forward formulae to use, likewise for torsion and tension (which is just cross sectional area), compression is a bit more involved due to buckling.

yeah I have to disagree with you there, any time I have seen when engineers want to make something stronger and have had the option they have gone for a larger diameter that's hollow over a solid bit of round. Just imagine how easy it is to flex a piece of 10mm rod compared to a 20 x 1.2mm which has less metal in it.

brett_celicacoupe: thats some really full on information. But it feels like I am jumping in the middle and not having much of an idea, do you perhaps suggest maybe a book on the subject or something like that?

[ed]

what exctly do you want to do? remake a rear axle off a pushbike? usually youre stuck with whatever hubs are available. several of which (last i was involved with them) had several big dia, hollw axles. like the big ass fronts on USD forks etc. ive got a set of hugi hubs just like that.

as for the math... bending and shear are the ones youll need. no torsion as the axle is fixed to the frame

[Sam_Q]

I am into bike building, as in the whole thing, this is my current bike that is quite old:



I have for the last year been working away at designing a new model that is three wheel drive, has uni joints and freewheeling axles for the front end. If you don't get why then you would have to ride one of these off-road to know. I wanted a larger diameter axle so I can tottaly get rid of the drop outs. The whole drop out design irritates me and I want to have my two pipes off the frame go to something akin to the way a brake level clamps to a handle-bar, but instead the hollow axle. For the front it's a necessity to allow for the axle to be larger than the uni-joints to let them slide on and off through the bearing.


Now with the calculation of bending force I have this equation for solid:




and this for a pipe:



now plugging my numbers into either one and I am getting some confusing figures. But I will have to explain when I get back from work.

[brett_celicacoupe]

equate the stresses for both beams

bending: M.y/I = M.y/I => y/I = y/I (assume M is same for both cases)

shear 4V/3A = 4V/3A => A = A (assume V same for both cases)

you can see bending stresses dominate so use that inner diameter minimum size for your design

[AdrianS]

If tou have a formula for solid bar, you can derive hollow, as seen by your formula above.
Strength of hollow bar is strength of solid bar with same OD, less strength of solid bar with same ID. This is seen with he 2 formulae you posted above.

As I read it, you are only interested in banding/shear, right? The axle transmits no torque ?

I'll take a look at the numbers tonight.

[Supra967]

Sam, when comparing strenght only for a given load, you can neglect force and go straight to section properties, as the force component in the stress is constant.

As posted by Brett - y/I for bending is what you want, or to simplify even further you want 'Z', or just area for shear, but shear is usually stronger.

Z for solid (pi*D^3)/32 which is approx d^3/10

Z for hollow is (pi/32)*[(D^4-d^4)/D] which is approx (D^4-d^4)/10D

Higher Z means stronger in bending. Higher area is stronger in shear.

The new bike you're making sounds pretty cool.

[Sam_Q]

oh thats just what I need, I can now plug that into my spreadsheet and start playing. Brett thanks for going to the time of showing me that info, it's a bit much for me and I was going to print it off and take it to an engineer friend I see on the rare occasion.

Now Adrian and Supraman this makes sense to me and I will try it out, yes what I had in mind; my rear axle is sheer force only, my front spindles have sheer force but it's pretty understressed. Now is it hard to work out sheer force, do they work with newtons? I have previously had someone work out that I am going to be pushing a max of about 90Nm through each of the front driveshafts and I was thinking of using some 22.22 x 0.9 (4130) pipe, I was going to do a bench experiment to determine if it was acceptable.

Supraman, thanks if your interested I have a little on in here:

http://s-86.com/projects.html

also I have a worklog that's updated whenever I on the very rare occasion make something:

http://www.bentrideronline.com/messa...d=1#post564296

it will happen slowly but I am a very patient man.

[Sam_Q]

oh just to clarify D is outside diameter and d is inside right? I am plugging it into my spreadsheet now

I seem to be getting crazy results, I worked out for a solid 10mm axle: 98.16

then for 17 x 0.5mm wall = 103.84?

I know this is an oversimplification but to what point can I use this as a guide? I am guessing a 0.5mm wall would just crush right?

[Supra967]

yeah, that's right. D outside, d inside

Torsion needs some other properties, and because you're axels will be supporting weight as well you'll have a combined bending and torsion load. 0.9 is pretty thin, bench test might be a good idea.

[Sam_Q]

I understand that it's a combined load however because the spindles are short, a large diameter and relatively thick I am sure it would have little effect. Also the it't more like one side is under torsion and the other is under bending load. Here is a diagram anyway



Spindle axle through the middle, spoke flanges welded to it in the center-left and far left, uni joint on the far right and not drawn in but low profile bearings between the axle and spindle tube, they are low profile (25-37-7)

[Sam_Q]

oh also what do you make of the odd results in post #11?

[Supra967]

results in #11 are right, good question about crushing. If you were to have a pin point load on the outside of the tube it would probably crush. However you have bearing contact which should spread the load pretty well.

Bending may be an issue there with the stub type axle. Just playing around with some numbers now.