elastic and plastic deformation - pin in hole interference

[dasgne]

I need to know how to calculate the amount of interference allowed for a pin (metal-1-hard) in hole (metal-2-soft) to remain in the elastic deformation area and not get plastic deformation after freezing to a certain temperature.
Appreciate any help?

 

[unclesyd]

P=E[Δ](b²-a²)(c²-b²)/2b³(c²-a²)

P=radial pressure (PSI)
[Δ]= Interference (in) = OD of die-ID of retainer/2
a = inside radius of die
b = nominal outside radius of die
c = outside radius of retainer

S_tMax = P(c² + b²)/(c²-b²)

S_cMax = 2Pb²/(b²-a²)

If you keep your interference between .003"/.004" you should be OK.
You want the retainer to be around 350 HB
You want your pin and hole to finished to .0005" with straight sides.

 

[dasgne]

Thank you unclesyd.
I am surprised that Young modulus is not part of the decision. from your formula's it seems purely dimensional.
I am in acoustics and not familiar with some of the terms you use. Could you please explain: S(t), S(c) and HB.
Thanks again.

 

[unclesyd]

The E is the Modulus of Elasticity (Young's).

S_t is the tensile stress in the retainer

S_c is the compressive stress in the die or pin

HB is the Brinell hardness number.
300 HB is about 38 Rockwell C

 

[rb1957]

Unclesyd,

how about the thermal effects ?

btw, E would be for the plate material
looking at your equation, E is for the material that you're calculating P for (be it plate or pin

 

[dasgne]

Ok, so you don't need the E of the pin.
Thermal effects, I can calculate the dimensional changes based on the CTE.
Is it possible to determine the excact amount of interference which makes the shift from elastic to plastic deformation?

 

[rb1957]

unclesyd's equation is for radial pressure (i think).

there is also a circumferential pressure.

with these you have bi-axial stress, so use von mises stress criteria (or octahedral stress).

then it's just trial and error (should be less than 1/2 hr) to fine tune the interference so that the bi-axial yield criteria you choose is met at either room temperature or at the cold temperature.

 

[unclesyd]

This is just a formula for a simple shrink fit converting radial pressure to tensile and compressive stresses in each component.

It doesn't take into account temperature, pressure, or spin as you would see in something like a sleeve or liner.

 

[rb1957]

oops, i didn't notice you'd included stresses ...

so you'd recommend a uniaxial yield stress criteria ?

 

[unclesyd]

rb1957,
Yes I would for a simple pin in a hole. Normally I would just use this approach on this problem and not consider the axial stress and thermal stress or even the combined stresses. To do much more you have to look a the stress in form of a combined plot vs radial distance.

dasgne,

Yes that is the way to go approch the heating/cooling problem. I have several graphical representations of TE plotted with RT and 0 expansion as the center lines. I limit the high temperature to a temperature below the tempering temperature of the metal and carry the low down LN₂. The expansion scale is 0 to .004" on both sides. Assume all are linear, makes it simple.

I need my grandson’s math book for graph nomenclature.