Stress due to rotation in a ring mounted on a shaft

[ladil123]

Hello!



I would like to know how to calculate the stress in a ring that is mounted on a solid steel shaft. The shaft and ring is rotating at a couple of 100 rounds per minute up to a 1000 rounds per minute.

The density for both materials are know, the geometry is know and material properties as well such as the E-modulus.

The ring is assumed not to rotate faster or slower than the shaft, as they are connected well enough...



Any tips or equations on how to solve this one?



Thanks

Daniel

 

[skeleton]

If the angular speed is constant, then the stress develops from centrifugal force.

If the angular speed is changing, then the stress has an additional component - torsional stress from the angular acceleration.

If E.ring < E.shaft Then
The ring and shaft will expand from centrifugal forces, but the ring is inclined to expand more than the stiffer shaft. I would assume that the shaft is "driving" with an applied torque and the ring is "driven". Essentially, the ring might swell to become larger than the shaft, but then it would loose its grip and want to not increase its speed any further. I would presume that kinematic friction would develop at the interface as the ring would rotate slightly slower than the driving ring.

If E.ring > E.shaft Then
The ring will expand from centrifugal forces, but there is more ...
The shaft will expand at a rate more than that of the ring, thus applying a pressure against the inside face of the ring. This needs to be included with the centrifugal force.

Interesting problem.

 

[ladil123]

Thank you.

For my problem E.ring will always be larger that the shaft. And the angular speed is constant as well. The ring is assumed to never loose grip.
Is there anyway to put up equlibrium for this and solve?

 

[skeleton]

For first order approximation (good enough for most applications), I would ignore the compression force that the inner shaft imparts on the outer ring. So, the stress on the ring is predominately:

1) If the angular speed is constant, then the stress develops from centrifugal force. This usually is primary.

2) If the angular speed is changing, then the stress has an additional component - torsional stress from the angular acceleration. This usually is secondary.

 

[ladil123]

Yes, how do I use the centrifugal force to calculate the stress?
What would the equlibrium be?
I got the density and all geomtrical data.