Press Fit Stresses - Three Ring?

[Airfix]

I'm working a problem with a three ring press fit situation and I'm trying to find the stresses in the middle ring. Can anybody point me to a method for calculating this by hand/excel?

Analysis of the stresses as a reult of the press fit between two cylinders is fairly well established in general engineering texts such as in Shigley's Mechanical Engineering Design section 2-18 Press and Shrink Fits. However when you have a press fit assembly, pressed onto another thick cylinder it becomes a much harder problem.

Any tips or links are welcome.

Thanks,

Airfix

 

[JStephen]

It seems to me, that if you take two cylinders and press-fit or heat-fit one inside the other, you wind up with a composite cylinder that you can treat as a single element in the analysis and then combine with the third. You'd be adding all the stresses in each of the first two cylinders to that obtained from the second combination. This assumes that you stay in the elastic range and all.

 

[Airfix]

JStephen,

I thought about that but when you press the first assembly onto the third cylinder it will cause a change in the pressure between the first two cylinders. Depending on the stiffness of each of those cylinders will change the stress within the middle cylinder.

The inner two cylinders are of the same material and same coefficient of thermal expansion the outer cylinder has a much bigger CTE than the inner two. I need to look at the stresses on the middle cylinder at room temp and at cold conditions.

Airfix

 

[EdStainless]

Years ago I looked at some of these with 3 different materials.
I did the calcs iteratively by hand.
In every case I found that one of the members ended up with so little stress that I could ignore it.
The problem was I never figured out a quick way to tell which one it would be.
I wouldn't approach this as fit 2 and then add a third.
Wright out all of the equations and solve them at once.
Should be straight forward matrix algebra.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

 

[DAVIDSTECKER]

Here is an article from Machine Design that might be what you are looking for.

 

[sreid]

At some point it's time for FEA.

 

[Airfix]

EdStainless that's a good article. Thank you but only looks at a 2 ring system which I've analyzed many times in the past. I've manage to work up a solution using iteration to get close to what I need for a 3 ring system.

sreid,

While FEA is great in lots of scenarios it is not the case here. I'm analyzing a gearbox with 20 bearings and I have to carefully set up the press fits in each shaft to prevent unwanted thermal effects on the fit and to ensure the bearing IRC remains positive. Excel is the engineers choice for such a situation as it gives instant results that I can see across the whole system. Using FEA to analyze 20 bearings would be overly time consuming.

The difficulty in my analysis from typical is that this time I have an aluminium housing lined with a steel tight fit liner that then houses the bearing outer race at a small clearance. At cold conditions the clearance between the liner and bearing OD closes up creating a 3 ring press fit.

Airfix

 

[kawamatt2]

Link

Good luck with the translation (unless you are Russian). Figure 7.16 on actual page 603 has what you need. We have used these concepts in my department to calculate contact stresses and dimension changes for a sleeve frozen into a larger sleeve, then a pin frozen into the smaller sleeve (basically a 3 ring system).

 

[Airfix]

Ha ha kawamatt2,

That's probably exactly what I'm looking for and by chance my brother is dating a Russian girl. I wonder if she'll translate it for me! How the hell did you find that?

Airfix

 

[kawamatt2]

Google translate is not bad, but could still be difficult with a very technical topic like this. In our case we were trying to figure out how long to freeze a pin to fit into a sleeve, which itself had been frozen into a larger sleeve. We weren't controlling the middle sleeve ID dimension after it was frozen in, so these calculations helped us understand how much its ID permanently changed, which helped us determine how much the pin OD would need to change (shrink) and the resulting stresses and final theoretical interface dimensions when its all together.

One of the guys in the department (Russian lineage) found it through google somehow, since he speaks and writes the language.

 

[sreid]

If the third outer "Ring" is the transmission Aluminum case the problem might be looked at differently.

1) Interference between a beqring race and the steel ring it's mounted in is well established.

2) When hot the steel ring must not get loose in the Aluminum.

3) When cold the aluminum must not crack. The strain between the Al Fe where they touch is identical.