G-Force calculation
 

I decided I'm going to build a DIY centrifuge, and I was going through the paces figuring out where to source some materials, etc...

So I thought about using a brake drum from a large truck, with a diameter of ~ 15" (380cm)

I used a G-Force calculator because I'm kinda special when it comes to the more advanced maths and just wanted a quick answer... plugging in the numbers I was asked for [radius and RPM] yielded an answer of almost 24,600g.

The numbers I gave are r=190cm, RPM = 3400.

This is basically representative of a 15'' drum spinning at 3400RPM, but it doesn't seem right that the (g) experienced at the outer edges of the drum will be around 24,600g...

I'm not even positive that a cast iron brake drum would hold itself together at that force.

Edit:

Nevermind, I really shouldn't math when it's so late. Stupid decimals.

If you change 190 cm (75") to 19 cm (7.5"), you will get 2460 G. Those decimal points are sneaky little devils, and just waiting for an opportunity to slide around and mess you up.

...gotta love "slide-ruler" accuracy -- always had to keep track of the decimal point(s) in your head...or, better yet, on paper!

Also, 3400 rpm seems rather high for the axle speed of a large truck. Assuming a 30" tall tire (probably too short), I get 300+mph at 3400rpm.

You were probably thinking engine speeds, rather than axle speeds.

I'm thinking industrial motor speed, actually. 3400-5000 RPM that I'll be spinning the drum at. Remember, this is for a centrifuge.

On average, if a large truck engine spun at 3400 RPM, it'd rip itself apart. The only thing that may spin that fast is the output of the transmission.

G = (2.8416*10^(-5))*(radius, inches)*(rpm)^2

...example: 1G = 351.9" rad @ 10 rpm.

Centripetal Acceleration:
α = V^2 / R
(In SI units)
α = (67.65m/s)^2 / .19m
α = (4576.4m^2/s^2) / .19m
α = 24086m/s^2

Convert to g's
1g=9.81m/s^2

α = (24086m/s^2)*(1g)/(9.81m/s^2)
α = 2455g

Anyone have any clue if a brake drum will even hold up to 2500-3000g's?

I know they can handle quite a bit of torsional force and a great amount of torque in shear, but I duno if the thing is just gonna blow apart spinning at 3450 RPM, and I'd rather not be a personal testament via injury to what happens if it does..

Guess the first thing will be to find out what speed they're balanced at.

Apologies for using SI units. That is what I have formulas for and am comfortable using - the result should be easily converted or the formulas work with imperial units:

If the ratio of radius to thickness is greater than 5, a rotating cylinder (= drum) can be treated as thin wall, and the stress as ~uniform through the wall thickness:

r = 0.19m

t = ? but let's call it 20mm = 20x10^-3m

r/t = 0.19/(20x10^-3) = 9.5; which is >5 so treat as thin wall.

Hoop stress:

fh = rho x v^2; Hoop stress (Pa) = material density (kg/m^3) x linear velocity of rim squared (m/s)^2

Need the linear velocity of the rim:

v = (r x pi x N)/30; velocity (m/s) = radius (m) x (pi x rpm)/30 (s^-1)

v = 0.19 x (pi x 3450)/30 (m/s)

v = 68.64 (m/s)

Plug that into the hoop stress formula, using a density for cast iron of 7200 (kg/m^3):

fh = 7200 x (68.64^2) (Pa)

fh = 33.9 (MPa)

I have the Ultimate Tensile Stress of grey cast iron as 170 (MPa) and, being brittle, that's the stress at which it will fail, so it should be OK.

There will be some margin in the design of the drum because the brake shoes will be pushing out against the drum wall, in addition to the stress due to the rotation of it's own mass.

Depending on what it is you will be centrifuging you might want to add that in (simplistically and conservatively, increase the density by assuming the extra mass is acting within the same volume as the cast iron drum wall) because that will add to the force causing the stress but not act to resist it. It's unlikely to be a problem though.

Jargonjargonjargonjargonanswer.

Good answer. LOL

I'm 'fuging used motor oil with random densities, probably a quart or less will actually fit in the area inside the bowl after I attach the cap to it.

Really, short of someone saying 'yeah, that should work', I was just going to build the whole plan inside a cage, turn it on and walk away for about 3 days, checking on it once in awhile and then ultimately checking it for signs of fatigue, cracking, or an out-of-round condition after running full speed for that period of time.

Seemed like a good enough stress test to me.

True, however the rim is moving 225 ft/sec (154 MPH). If it breaks apart, the pieces will make big dents in a concrete block wall. I'd have a scattershield around it, just to be safe.

The two relevant formulas are actually pretty simple, even if that is somewhat hidden by the clumsiness of word processing absent Greek symbols, subscripts and superscripts.

Unfamiliar units might not help either :) . You will be able to get the same result using the appropriate Imperial units.


With the last sentence I was referring to the additional force due to the fluid being centrifuged. If that is just one quart and motor oil it will weigh about 1/75th of the drum rim itself (assuming ~3/4" wall thickness), so not add appreciably to the stress in the drum.

Otherwise, yes, as general advice, it would be wise to be conservative. Perhaps a couple of inches of cloth or wadding backed by 1/4" mild steel plate?

Actually, a bigger risk than the extra mass of the oil is spinning the drum a lot faster than 3450 rpm. The stress is a function of the square of the rim velocity. At 3450 rpm there's a lot of room for error. At 5000 rpm the stress will be (5/3.45)^2 = 2.1 times greater. I consider that's still OK but wouldn't want to go too much higher.

Spinning it twice as fast (as 3450 rpm) will result in a stress 4 times greater and closer to the failure stress: 136 MPa vs 170 MPa. Checking the motor speed is what it is supposed to be might be sensible.

To put it into perspective, a car flywheel will spin at similar speeds, be of similar size and made of the same material, although of different configuration.

Yes, I actually changed the design to something more... proven.

A torque converter. It's already the proper shape, no modification [other than cutting and gutting] needed, I can bolt it directly to the existing flexplate, which bolts directly to the end of a crankshaft, which I can have a machinist center drill, cut a keyway, and re-balance for me, enabling me to sit the whole assembly on the motor head like a hat of sorts, and we all already know that torque converters on average can spin 7k+ RPM FULL of fluid and counter-rotating forces inside them without blowing apart at modest power levels attached to automobiles, so I'm thinking it should be fine [i.e. less potentially catastrophic] spinning at 5k RPM generating ~5,000g with about a quart of oil in it. [probably less in practice]