What Is the Maximum Speed of a Hollow Shaft Given Specific Shear Stress Limits?

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SUMMARY

The maximum speed of a hollow shaft with an internal diameter of 72 mm and a wall thickness of 24 mm, designed to transmit 90 kW of power without exceeding a shear stress of 150 MPa, is calculated to be 22.66 rad/s. To determine the external diameter, the formula for the outer diameter (OD) must be applied, which is essential for accurate stress calculations. The discussion highlights the importance of understanding the relationship between internal diameter, wall thickness, and external diameter in torsional stress problems.

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Homework Statement



A hollow shaft has an internal diameter of 72 mm and wall thickness of 24mm is to be used to transmit a power of 90 kW.

what would be the maximum speed of shaft rotation if the shear stress must not exceed 150 MPa ??

Homework Equations



http://www.amesweb.info/Torsion/CalculationStepsForTorsionalStress.aspx

The Attempt at a Solution



I got 22.66 rad/s. I am getting stuck at finding the external diameter
 
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The OP states the ID of the shaft is 72 mm and the wall thickness is 24 mm. It's not clear why you are stuck calculating the OD of the shaft.
 
is there an equation to find the OD
 
Yes there is. Do you know what the terms 'internal diameter' and 'wall thickness' mean? How did you work the problem in the OP without doing this calculation first?
 

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