Polar moment of inertia for a shaft with slot

[chaitac]

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

 

[rock.freak667]

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

 

[chaitac]

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

 

[chaitac]

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?

 

[rock.freak667]

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.

 

[chaitac]

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I hope you got how the slot is looking .

 

[chaitac]

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.

 

[rock.freak667]

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.