What is the Formula for Sizing a Shaft at 150,000rpm?

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max11
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Hiya

I was hoping that somebody would be able to help me.

I need to size a shaft coming from a turbocharger spinning at 150,000rpm the shaft needs to transmit 9Nm and 200mm in length, the shear stress of the material is 457MPa.

I need to size the diameter of the shaft and know that it is going to be very small but can't seem to find a formula that gives me a sensible answer, right now I am using a formula from engineering toolbox (http://www.engineeringtoolbox.com/torsion-shafts-d_947.html)

D = 1.72 (Tmax/σmax)1/3

But this give me a diameter of 0.46mm which seems so small that it would just twist and break.

an y help greatly appreciated.

Cheers
 
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