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2 hollow cylinders w/ interference fit û decr in ID of inner cyl?

2 hollow cylinders w/ interference fit û decr in ID of inner cyl?

2 hollow cylinders w/ interference fit û decr in ID of inner cyl?

(OP)
Let's say I have an inner hollow cylinder (1) which is interference fit within an outer hollow cylinder (2) as follows:
Hollow Cylinder 1 un-assembled dimensions:  ID = D1, OD = D2
Hollow Cylinder 2 un-assembled dimensions:  ID = D2 – d, OD = D3
where d/2 is the amount of interference per side.

Assume both cylinders have the same Young's Modulus E.
After assembly, what is the expected inner diameter of cylinder 1? (should be slightly less than D1).
Or can you steer me toward a reference that gives this solution?

(I am trying to get rough estimate reduction in shaft-to-bearing clearance for journal bearing which is fit within housing using interference fit).
 

=====================================
(2B)+(2B)'  ?

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