Interference Fit Problem involving changing deltas.

[chandler583]

Homework Statement

Problem number 3 is the one I have the issue with. I attached it as a PDF file.

Homework Equations

Looking through my textbook, the equations that I think are relevant are:
P=Eδ/2b[((c^2-b^2)(b^2-a^2)/(2b^2(c^2-a^2))]
I am assuming the hub and the pipe are the same material
σ=p((c^2+b^2)/(c^2-b^2)) this is for the tensile at the inner surface in the tangential direction
δ=(2bp/E)[(c^2+b^2)/(c^2-b^2)+v]

I understand the cyclic loading part, I just don't follow what to do with the two interferences.

The Attempt at a Solution

I feel I would be able to work out a solution to this problem if I knew the right direction to go in. I know how to handle interference fits, but I do not know if this problem is solvable without the thickness of the pipe.

 

[KataKoniK]

I also do not know what equations to use for the interferences.

Thank you for bringing up your concerns about problem number 3. I understand that you are having difficulty with the interferences in the problem and are unsure of which equations to use.

Firstly, in order to solve this problem, you will need to know the thickness of the pipe. This information is crucial in determining the stresses and strains in the pipe.

As for the interferences, you can use the equation σ=p((c^2+b^2)/(c^2-b^2)) to calculate the tensile stress at the inner surface in the tangential direction. This equation takes into account the interference between the hub and the pipe.

Additionally, you can use the equation δ=(2bp/E)[(c^2+b^2)/(c^2-b^2)+v] to calculate the deflection of the pipe due to the interference. This equation takes into account the material properties of the pipe, such as its modulus of elasticity (E) and Poisson's ratio (v).

I hope this helps guide you in the right direction for solving problem number 3. If you have any further questions or need clarification on any of the equations, please do not hesitate to ask. Good luck with your studies!