Interference calculation 1

[Mal7]

If I press a hollow cylinder into the bore of another cylinder with a known amount of interference between the two, how can I calculate the force being exerted on the inner cylinder by the outer?

 

[desertfox]

Hi Mal7

Have a look at this thread all the formula you need are there:-

thread404-86905

regards desertfox

 

[Cockroach]

You apply pressure vessel theory noting that force fit means the clearance between shaft and hub. This clearance is treated as an interference.

Lame's Equation for Thick Walled Cylinders therefore reduces to the following quantities:

SHAFT DISPLACEMENT AND STRESSES

Radial: Sr = -P
Tangential: So = -P
Radial Interference: Us = [(1-vs)/Es] P (d/2)

for P=pressure, vs=Poisson's Ratio (shaft), Es=Young's Modulus (shaft) and d=shaft diameter.

HUB DISPLACEMENT AND STRESSES

Radial: Sr = P[(d^2-D^2)/(D^2-d^2)]
Tangential: So = P[(d^2+D^2)/(D^2-d^2)]
Radial Interference: Uh = [P d/2Eh][So + vh]

for P=pressure, vh=Poisson's Ratio (hub), Eh=Young's Modulus (hub) and D=hub diameter.

Obviously at the shaft/hub interface, pressure due to interference is equal, thus equating relating terms and noting C=interference:

P = 2C / d[(So+vh)/Eh + (1-vs)/Es]

This is known in the literature as the interference pressure equation. Just for giggles, the maximum torque that can be transmitted WITHOUT slippage is:

Normal Force: Fn = P {pi d L}
Frictional Force: Ff = U Fn
Torque: T = (d/2)Ff

for U=coefficient of friction, L=hub thickness which defines the length of engagement between hub and shaft.

Hope this helps you out. I'm not sure what the deal is with the thread posted by DesertFox, it never opened for me on this end, maybe a glitch or two.





Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[israelkk]

Any machine design book cover this issue.

 

[desertfox]

Hi Mal7

Sorry the link should have been :-

thread404-86805

regards desertfox

 

[Mal7]

Thanks everyone!