Shaft critical speed calculation

[TyVan07]

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

 

[electricpete]

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


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(2B)+(2B)' ?

 

[desertfox]

Hi TyVan07

Have a look at this site:-

http://www.roymech.co.uk/Useful_Tables/Drive/Shaft_Critical_Speed.html

Go down till you see Dunkerley's method as E.Pete suggested.
Can you post a sketch or pic of your situation?

desertfox