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

[josh16]

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

 

[SteamKing]

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.

 

[josh16]

is there an equation to find the OD

 

[SteamKing]

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?

 

[rezeew]

of shaft.

I would approach this problem by first understanding the physical principles involved in hollow shaft rotation and the factors that affect its maximum speed. I would start by researching the equations and principles of torsion and shear stress, as these are the key factors in determining the maximum speed of rotation for a hollow shaft.

Next, I would use the given information about the internal diameter, wall thickness, and power transmission to calculate the maximum shear stress using the equation for torsional stress. This would give me a value of 150 MPa as the maximum shear stress.

To find the external diameter of the shaft, I would use the equation for torsional stress again, but this time solving for the external diameter. This would involve rearranging the equation and plugging in the known values for the internal diameter, wall thickness, and maximum shear stress. This would give me the required external diameter of the shaft.

Finally, I would use the equation for maximum speed of rotation, which takes into account the maximum shear stress and the external diameter, to calculate the maximum speed of rotation for the given power transmission. This would give me the final answer of 22.66 rad/s.

In conclusion, as a scientist, I would approach this problem by understanding the underlying principles and equations involved, and using them to systematically solve for the required variables. By doing so, I can ensure the accuracy and reliability of my solution.