Polar moment of inertia for a shaft with slot

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Homework Help Overview

The original poster seeks assistance in calculating the polar moment of inertia for a hollow shaft that includes three circular slots, specifically in the context of its application in diverters used in oil and gas. The problem involves understanding the geometry and dimensions of the shaft and slots.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need for a diagram and specific dimensions of the slots to facilitate the calculation. There are suggestions to subtract the inertia of the slots from that of the hollow shaft. Some participants express uncertainty about the appearance of the slots and how they might affect the moment of inertia.

Discussion Status

Participants are exploring various interpretations of the problem, including the geometry of the slots and their impact on the overall moment of inertia. Some guidance has been offered regarding the use of the parallel axis theorem and approximating shapes, but no consensus has been reached on a definitive approach.

Contextual Notes

There are constraints related to the dimensions of the slots and their placement within the shaft, which are still being clarified. The original poster has provided some measurements, but further details may be necessary for a complete analysis.

chaitac
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Homework Statement


HI
Can anyone help me in finding out the polar moment of inertia of a hollow shaft with 3 circular slots . Its used in design of DIVERTERS in oil and gas application.


Homework Equations





The Attempt at a Solution

 
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Do you have a diagram?

Do you know the dimensions of the slots? If you do, then you can just subtract the inertia of the slots from the inertia of the hollow shaft.

J= πd4/32
 
The slots are 1.031 long and 0.688 wide Like a Mill Slot . they are rounded at the end(Radius of the rounded ends 0.344). they are 3 slots at 120 degree apart place radially.

Thanks
 
I think the polar moment of inertia for a hollow shaft is J = π(D4-d4)/32 when derived from its center. I have the slots 0.250 distant from the end of the shaft. How does it change the MOI?
 
chaitac said:
The slots are 1.031 long and 0.688 wide Like a Mill Slot . they are rounded at the end(Radius of the rounded ends 0.344). they are 3 slots at 120 degree apart place radially.

Thanks

I think then, you can assume that they are like cylinders then, and just subtract them from the inertia of the entire thing. But I'm not too sure what a Mill Slot looks like so it is possible that I may suggesting the wrong thing.
 
_____
(_____)

I hope you got how the slot is looking .
 
Last edited:
chaitac said:
http://www.lukescustoms.com/Page11_Rail_Milling/Foregrip_Slot.JPG

my part is similar to the pic in the link (its a section view) its a hollow shaft with slot in it. how can we calculate the moi for the part.

Well in that case, I'd just approximate that shape to a cuboid.

Just find the inertia about its own center and then use the parallel axis theorem to find the inertia about the axis of the shaft.
 

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