Bushing ID after Shrink Fit - Interference Fit 1

[NB02]

Hello,

Looking for some help on calculating the ID of a bushing that has been shrink fitted into a larger bushing. I can't seem to find an equation for this. I have calculated the interference pressure, and the hoop stress'. Application is we have two manufactures of the parts that are shrink fitted together. We would like to tolerance the the interference fit and ID of the inner hub to allow for +/- .005" of the inner hub ID after the shrink fit into the outer hub.

Material Assumptions - Modulus of Elasticity = 30,000 ksi - Poisson's Ratio = .3
Outer Hub OD = 32"
Out Hub ID = 22"

Inner Hub OD = 22.050"
Inner Hub ID = 18"

Interference Pressure ~ 8693 psi
Outer Hub Hoop Stress ~ 24,276 psi
Inner Hub Compression Stress ~43,899 psi

So I am trying to calculate what the ID of the inner hub would be after the shrink fit operation assuming the above is true? We would like to get away from having to do a final machining of the bore after assembly if possible. I was able to find a few old threads on this website about calculation of area but they didn't really make any sense to me. Any help in the right direction would be appreciated.

Best Regards,

 

[israelkk]

The inner hub OD and the outer hub ID have tolerances too. Those tolerances affect the result too.

Any mechanical engineering book such Shigley's or Norton has the explanation and formulations.

If the end result is +/- 0.005" then the OD tolerances of the inner hub and the ID tolerances of the outer hub must be much smaller than +/-0.005".

 

[israelkk]

The outer hub is 5" thick, the inner hub is 2" thick. Therefore, the outer hub will expand much less than the shrink of the inner hub. Therefore, we can assume that almost all the 0.05" (without added tolerances) difference between the OD of the inner hub and the ID of the outer hub will go to shrink the inner hub. Therefore, I do not see any option to control the inner hub ID after shrink fit to +/-0.005" without final machining.

 

[gruntguru]

The OP states he will tolerance the shrink fit so tolerance of the outer hub ID and inner hub OD are irrelevant. If the fit is tolerances, that should define the reduction in inner hub ID and the pre-fit dimension can be adjusted accordingly.

Now over to the experts who can calculate that reduction.

je suis charlie

 

[TheTick]

Usually I use conservation of cross-section area. I assume the housing is nigh-undeformed, and the bushing compresses to meet the housing. Calculate cross-section area of uninstalled bushing from ID and OD, then calculate new ID from area and installed OD.

This has worked well enough for my applications in the past. If you need a really tight tolerance, you should be reaming bushings post-install anyhow.

YMMV

 

[Tmoose]

Along with the reduction in the 18" ID, the cylindricity, taper, and etc will likely follow the 22" hub ID condition.

If you require good a precise finished ID then boring the assembled ID may be the only solution.

Co-linearity/concentricity of the finished ID to 32" OD will require careful shepherding of all the ID and ODs as well.

If both materisls' E = 30,000 ksi Sounds like the "bushing" is made of steel as well. Is that OK for wear, or a manufacturig convenience?

 

[tbuelna]

If you want to control the ID of the inner bushing to +/-.005" after installation, then you need to consider a couple things. First, you need to control the tolerance stack-up of the 4 dimensions involved- the outer bushing ID and OD, and the inner bushing ID and OD. Then you will also want to do a sensitivity study of how variations in the tolerance of each dimension affects the inner bushing ID after installation. If you need to control the inner bushing ID to +/-.005", then the tolerance of each bushing's ID/OD before installation will need to be much smaller than that. What you'll likely find is that it is more economical to finish machine the inner bushing ID to +/-.005" after installation than it will be to machine the 4 surfaces of the bushings to a tighter tolerance prior to shrink fitting.

 

[GregLocock]

It's called Lame's formula

http://www.roymech.co.uk/Useful_Tables/Mechanics/Cylinders.html

or

http://www.tribology-abc.com/calculators/e3_8.htm

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[tbuelna]

Thanks professor. But you seemed to have missed the point I was making. If you wish to hold a +/-.005" tolerance on the inner bushing ID after installation, and machining cost is a concern, then wouldn't it be smarter to machine the inner bushing ID to size after installation and use much looser tolerances on the individually machined bushings? If the inner bushing ID tolerance must be held to +/-.005" after installation, then it would need to be machined to a much tighter tolerance prior to installation. So how does that reduce cost?

 

[gruntguru]

I assume there is some difficulty (greatly increased cost) associated with in-situ machining.

je suis charlie