Calculating a push up load

[Oldandconfused]

Hi Guys...I just registered on here after someone recommended the site to me. I need help with a calculation and as my name suggests, the ol' grey matter just aint doing it for me right now!
Okay, I got a taper shaft which is 2.88" dia at the large end and 2.715" at the other. I've also got a bush with an internal taper. The outside of the bush is 3.25". I need to force the shaft through the bush. The bush is a thin wall cylinder so will expand in diameter. I know how much I need to expand the bush (4 thou on dia) but don't know how to calculate the force required to achieve that expansion.
Can anyone point me in the right direction?
Thanks.
....maybe I shoulda posted something less difficult but it's important for work that I come up with a solution.

 

[MikeHalloran]

Isn't that a textbook problem?



Mike Halloran
Pembroke Pines, FL, USA

 

[GregLocock]

Lame's equation probably applies as the bush is fairly thick walled. So you also need to work out the taper angle and the friction coefficient.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Oldandconfused]

Hi Mike,

Yeah, most definitely a textbook problem. Without the textbooks and seemingly no answers to be found anywhere on google, I thought I may benefit from the experience of the guys on here.

Hi Greg,

Thanks, I have worked out the taper angle to be 1:40 on diameter. I'll have a look under Lames equation. Thanks again.

 

[GregLocock]

Well, before you do that just see if a thin wall tube answer looks in the ball-park.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[zekeman]

You need to give us the length of the bush ---- and 1/4" wall is not exactly thin walled.

 

[GregLocock]

Why do you think we were talking about Lame's equation?

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Oldandconfused]

Guys... apologies for the delay in adding to this thread...I kind of put the file to one side and hoped the problem would go away!!...it hasn't. I looked up Lame's equation which seems applicable for thick walled cylinders. I'd kind of concluded that I was dealing with a thin walled cylinder here?
In any case, to add more meat on the bones:-
The bush has an od of 3.25". Its internal diameter at the large end is 2.88" (i.e.its flush with the shaft) so t (being the thickness) is 0.185" radially. The bush inside diameter of the taper at the small end is 2.717" so sits slightly inside the shaft.

 

[vpl]

I don't know if you noticed Zekeman's post of 11 Feb:

You need to give us the length of the bush ---- and 1/4" wall is not exactly thin walled.

Patricia Lougheed

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[Oldandconfused]

Apologies for not spotting the question further up..the bush is 6.63" in length...

This is where I got to so far..
I calculated a circumferential stress in the bush based on the required expansion of 4 thou over the mean bush diameter

From that I looked at calculating an interface pressure based on the above stress, modulus of elasticity, poissons ratio, thicknes of the bush etc etc...this threw up a figure of 7832 psi (interface pressure)

So now i need to calculat the force required to achieve the required expansion...assomebody said way up there..its prob a textbook question but I'm certainly struggling to find it!!

 

[chicopee]

Since it appears that you have a fit-on- fit situation why don't you do a shrink fit of the shaft by using dry ice. It will be better than forcing the shaft in the bush.

 

[desertfox]

Hi Oldandconfused

If you have the interface pressure then this formula may help but it is for mating cylinders:-

Force = 2*pi*mu*Rb*L*p

where mu= coeff of friction
Rb = radius of outer diameter of inner cylinder
L = length of interference (engagement length)
p = interface pressure
Force= axial force req to assemble cylinders

not perfect by any means but might get you in the ballpark

regards

desertfox

 

[Oldandconfused]

I'm sure the regulars on here get loads of paople coming on and asking for help. As soon as they get what they want, they disappear without saying thanks.

I used the calc offered by desertfox....we applied the load using hydraulics and achieved the interference fit we were aiming for. As you say desertfox, it may not be perfect but ballpark it certainly appears to be. A note to chicopee...appreciate exactly where yr coming from but our H&S dept are crazy about dry ice (don't ask...much source of bemusement here too!)

So thanks to Greg and the above mentioned contributors...marvellous.

 

[desertfox]

Hi Oldandconfused

Your welome.

desertfox