So, Im watching this show about airline crashes and apparently, a A380 has gone down because the speed limiter on a spinning engine rotor broke, and the part spun so fast its ultimate yield strength was reached and the material shatterted.(adsbygoogle = window.adsbygoogle || []).push({});

Thats gotta be one really fast spinning rotor! But how fast? It was made of a nickel alloy, but since I dont know exactly what it is lets use steel. Its safe to assume that the part was lighter and stronger than steel, so this will be an underestimate. I also am going to simplify the shape, assume It is rigid (undergoes no elastic or plastic deformation) untile its ultimate strength is reached.

5500MPa and a material density of 7.8g/cm^3. Lets say for simplicity it is a perfect disk of outer radius 1.5m, inner radius 5cm, thickness 5cm . How would you go about calculating the speed at which it hss to spin to break?

Here's what I did, but I get an answer that makes no sense in the end. Can you see where I am going wrong, or is my entire plan of attack wrong?

t = .05 % thickness

r1 = .05 % inner radius

r2= 1.5 % outer radius

rho = 7800 % density

u = 5500000000% N/m^2

The mass of the disk:

m = rho * (r2^2 - r1^2) * t * 2*pi

I assume initial fracture would be at the inner radius, so the effective area:

area = 2 * pi * r1 * t;

force to keep the mass at bay:

F = .5 * (wr)^2 * dm

= .5 * (wr)^2 * rho * t * 2 * pi * dr

Integrating over r on the range r1 to r2:

F = (pi/3) * w^2 * (r2-r1)^3 * rho * t

So the pressure at the inner surface:

P = F/Area

P = 79264.25 w^2

Set that equal to ultimate stresss, solve for speed:

5500000000 = 79264.25 w^2

And I get 263 rad/sec, which I am assuming is wrong, since thats a very reasonable RPM.

Thanks.

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# Disc reach ultimate material strength by spinning too fast

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