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Shaft critical speed calculation

Shaft critical speed calculation

Shaft critical speed calculation

(OP)
Hi All,
I have a shaft supported by 3 bearings (we'll consider them simple supports) on the ends and one in the middle. The shaft has 2 masses, one on each side of the middle bearing. The shaft is indeterminate so I replace the middle bearing with a force and set the displacement to 0.

Now, when I use Rayleigh's method for lumped masses, do I consider the masses to produce a force in the same direction (Static beam), or do I consider them acting in opposite directions (as would happen in dynamic deflection, likely mode 1).

When I sum w*y^2, I get a negative sign which of course cannot be used in Rayleighs equation.  Any help is greatly appreciated.

Thanks,

Tyler

RE: Shaft critical speed calculation

Assuming you are modeling as two lumped masses (one lumped mass between each pair of adjacent bearings), then the lowest-frequency mode will be masses moving in opposite directions.   As I recall, Raleigh requires you to estimate mode shape (or in lumped case, the relative magnitude of deflection of lumped masses), which will be a challenge for you unless you approach it as an eigenvalue problem or have some other way to determine the modeshape.  

I think  Dunkerley is one way to attack this: Choose one of the masses, displace it by a certain amount, , determine associated shaft deflection (which will be opposite on the two sides of center bearing),  compute resonant frequency using Raleigh for that one-mass configuration... repeat for the other mass... combine resonant frequency estiamtes using 1/w^2 = 1/w1^2 + 1/s2^2
 

=====================================
(2B)+(2B)'  ?

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