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elastic and plastic deformation - pin in hole interference

elastic and plastic deformation - pin in hole interference

elastic and plastic deformation - pin in hole interference

(OP)
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?

RE: elastic and plastic deformation - pin in hole interference

P=EΔ(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

StMax = P(c2 + b2)/(c2-b2)

ScMax = 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.

RE: elastic and plastic deformation - pin in hole interference

(OP)
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.

RE: elastic and plastic deformation - pin in hole interference

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

St is the tensile stress in the retainer

Sc is the compressive stress in the die or pin

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

RE: elastic and plastic deformation - pin in hole interference

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

RE: elastic and plastic deformation - pin in hole interference

(OP)
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?

RE: elastic and plastic deformation - pin in hole interference

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.

RE: elastic and plastic deformation - pin in hole interference

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.

RE: elastic and plastic deformation - pin in hole interference

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

so you'd recommend a uniaxial yield stress criteria ?

RE: elastic and plastic deformation - pin in hole interference

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.   

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