How to calculate an interference fit over a large temperature range 1

[Andy001]

Hey gents,

I have a problem. I am currently trying to calculate the required interference fit of a bush inside a thick walled cylinder, whilst taking into account the effects of a large temperature range (-40 to +150 degrees).
I have the dimensions for both bush and bore but that is it….
I have looked at some of the calculators and they are great, but what I need is to see the equations as well and not just the resultant figures. Can you HELP???
Thanks

 

[israelkk]

Graduate school books for mechanical design

 

[rb1957]

well i don't think it's just a matter of seeing the equations (they're easy enough ... metal expands when it gets hot). the trick is how does your structure respond ? ... is it unconstrained so that the plate can expand in size as it gets hot (so the hole gets bigger, and maybe the bushing too), or is the expansion constrained by "the rest of the world" ... but it'd take a lot of constraint to prevent the hole from opening up as it wants to. then the bush wants to do it's thing (probably it's alpha is different to the surrounding material's).

 

[desertfox]

Hi Andy001

The formula for force fit I have here:-

Here are the formula you need:-



Pa= f*3.142*d*L*Pc

where f=friction coefficient
Pc=contact pressure between the two members
d= nominal shaft dia
L=length of external member.
Pa= axial force required to interference fit
to calculate Pc for a given interference use the formula:-

Pc=x/[Dc*[((Dc^2+Di^2)/(Ei(Dc^2-Di^2))+....................
((Do^2+Dc^2)/(Eo*(Do^2-Dc^2))-((Ui/Ei)+
Ui/Eo))]



where x = total interference
Dc=dia of shaft
Di = dia of inner member(this is zero for solid shaft)
Do= outside dia of collar
Uo=poissons ratio for outer member
Ui=poissons ratio for inner member
Eo=modulus of elasticity for outer member
Ei=modulus of elasticity for inner member

This formula for Pc will simplify if the materials are the same.
what you need to do is calculate your stresses for each interference and then recalculate your stresses based on the extreme temperature ranges and see if your fit comes loose.
Hope this helps.


regards desertfox

 

[eromlignod]

A hole thermally expands by the same amount that the removed cylinder of metal would have under the same temperature conditions. So if the bushing is made out of the same material as the housing, they should expand or contract the same amount and retain the same interference. If the materials are different, then their coefficients of thermal expansion need to be taken into account accordingly.

Don
Kansas City

 

[Clyde38]

If you are an EXCEL user, try this link....

http://www.excelcalcs.com/repository/Machines/Miscellaneous/Simple-Press-Fit-Calculator/

While your there look around. There are a lot of helpful calculaitons and ExcelCalcs is very helpful.

 

[Andy001]

Thanks guys,

thats a great help. I should also mention as well that the bush is cold drawn steel and the bore is cast aluminium.
The bush is free to expand longitudinally.

 

[rb1957]

as cast Al i imagine that the body is pretty rigid, would that make it less likely for the hole to expand with heat ? i think the bush would expand or shrink, but maybe in your case the hole is stable ?? it would be conservative (if you're trying to estimate the forces involved) to assume the hole is stable, but it would be unconservative if you're trying to ensure a level of interference.

 

[eromlignod]

"as cast Al i imagine that the body is pretty rigid, would that make it less likely for the hole to expand with heat ?"

Are you talking about localized heating? The structure doesn't matter much when you're talking about thermal expansion as a whole. A solid object expands and contracts thermally like one giant crystal. That's why the hole gets larger and not smaller when the item is heated.

Think of the object as being made up of tiny elements connected into one big truss structure (like FEA). Then imagine that each of the little members grows by 1%.

Aluminum thermally expands/contracts more than steel, so hotter temperatures would make the bushing looser and colder temperatures would make the bushing tighter. You need to calculate how much.

Don
Kansas City

 

[desertfox]

Hi Andy001

What thickness is the aluminium and diameter of steel shaft?
The interference fit should be based on the service loads the joint will see and then we can look at the temperature
ranges.

desertfox

 

[rb1957]

sorry, don't see how you can separate one from the other (ie the interference required and the temperature the part is operating at)

 

[davidh729]

Unless you have a situation where coefficient of friction depends on temperature the interference vs. load capacity of the press will not depend on temperature. So the interference required doesn't change. What does change is the actual interference. If we assume the original poster's design point is a minimum interference to react some load, the other boundary will be the material strengths. It is important to remember that the design documentation must reflect the interference at manufacture and the calculations should include the tolerances of the hole and bush.

Dave Hyman
Mechanical Engineer

 

[eromlignod]

"sorry, don't see how you can separate one from the other (ie the interference required and the temperature the part is operating at)"


A bushing and a hole in a block made out of the same material expand by the same amount (diameter) if the parts are heated uniformly (not localized). So a .001" interference fit remains a .001" interference fit regardless of temperature or diameter of hole & plug.

Think of a solid block of annealed steel with a circle drawn on it. If the block is heated, it expands, and the circle grows. The material inside the circle is just like the bushing; the material outside the circle is like a housing with a hole where the circle is. No metal crosses the boundary. The bushing (inner material) gets bigger by the same amount as the imaginary hole.

If it didn't, there would be internal stresses in our solid block located near the imaginary cylinder bounded by the drawn circle...and there aren't. If there were, how would the stresses know to form about an arbitrary cylindrical boundary?

Don
Kansas City

 

[desertfox]

Hi rb1957,davidh729

The joint might have to transmit a torque and therefore
will require a particular interference to enable it to do this, then we need to see what interference is left at each extreme temperature and adjust that interference to enable the joint to function correctly if possible at the temperature extremes.

desertfox

 

[rb1957]

all well and good if the bushing and the body were the same material ...

but they aren't ...

the interference at elevated temperature will be higher than at room temperature, 'cause of the dissimilar metals; unless the body is rigid (so that it reacts to the temperature by developing internal stresses, similar to plane stress).

 

[desertfox]

Hi rb1957

Yes I can see the materials are different which is why I said we need to workout the interference at both temperature extremes so that we can ensure that the stresses
at the higher temp don't cause the joint to loosen and at the other end the stress in the aluminium doesn't get to high.
However in order to do that we need a starting point ie:-
what function does the joint serve, does it transmit torque
etc.
Once we know whether the joint carries load and assuming it does, we can calculate a starting point for the intereference, which then needs to be adjusted for the temperature extremes if possible.

 

[rb1957]

desertfox, the dangers of simultaneous posting ! ... that's what i'm saying too (calculate the interference at temperature extremes); my post was directed towards don in KC.

i guess you could push some torque across an interference joint, in my business they're used to create beneficial compressive stresses around the hole (but to do this you need to ensure a level of interference).

 

[desertfox]

Hi rb1957

Yes I see that now and agree that Don is correct with reference to same material.

desertfox

 

[Andy001]

Hey guys,

first of all, thanks for your help, i really appreciate it.
Ok, i agree that the most logical step is to calculate the interference at the worst cse scenario (low temperatre to prevent loose fit).

With regards to your questions on transmition of torque, no the joint does not transmit torque.

With regards to your question about temperature variation. The temperature change is not due to localised heating. The temperature change is transmitted through the entire mechanical system and the max and min temperature values are the boundaries of the lubricant oil.
Thanks

 

[desertfox]

Hi Andy001

Firstly if the joint isn't heated uniformly then that makes the calculation a lot more complicated and not one we can solve with the formula I posted above unless you know the temperature of the steel and aluminium at any given time.
You would need to do a heat transfer analysis with respect to time to see how both parts rise in temperature.
The worst case for your joint would be the upper temperature
limit because the aluminium expands more than steel for a given temp rise and therefore there is a greater chance of the joint loosening.
I suppose the most conservative method would be to assume that the aluminium rises to maximum temperature and the steel doesn't see any temperature rise at all, then choose
an interference fit that ensure's no joint loosening.
The downside might be that at the lower temp the stress in the aluminium might be to great.
What are the sizes of the aluminium and steel parts?

desertfox