Contact stress for pin in hole.

[garycvv]

Hello,
I'm looking at a problem on an assembly in tension. This could be assumed to be a clevis pin arrangement where several plates are joined together using a pin. The holes in the plates are clearance holes and are a slightly larger diameter hole. I'd like to calculate the contact stress around the hole cirumference assuming that the plate is made of an elastic isotropic material and the pin is rigid. Can someone point me in the right direction?
Thanks

 

[drawoh]

garycvv,

Look in your machine design text under ball bearings. There should be literature on how curved surfaces interact with each other.

--
JHG

 

[Tmoose]

"the pin is rigid"

That may overstate the stress around the hole the first time max force is applied, but then again assumptions about fits, surface finish and edge loading may be pretty optimistic.

 

[boo1]

Cylinders Contact Stress should be used not spheres (ball bearing)
Cylinder in a cylindrical groove (a cylindrical groove is a cylinder with a negative radius)
The maximum contact pressure between two curved surfaces depends on:
– Type of curvature (sphere vs. cylinder)
– Radius of curvature
– Magnitude of contact force
– Elastic modulus and Poisson’s ratio of contact surfaces

Design of Machine Elements, Spotts, 6th ed PP443
Po = Maximum compressive stress
P1 = Force

Po=0.591*((P1*E1*E2)(1/R1-1/R2)/(E1+E2))**.5

 

[dhengr]

Garycvv:
Look in most good Strength of Materials, Theory of Elasticity, or Machine Design text books, and look for Hertz bearing stresses. The tighter the fit btwn. the pin and the hole the lower the peak bearing stress. Some yielding in bearing is almost unavoidable to cause a satisfactory bearing condition, and this is usually o.k. Also, look at the design of structural eye bars, as in bridges and the like; and lifting lug plates and clevis pin holes, as in ASTM BTH-1. There is more to the problem than just the bearing stress btwn. the pin and the hole in the plate. The pin does bend a little even if you protest to the contrary, and the clear space btwn. the plates and/or clevis (the faying surface clear space) causes some of this. If the plates are not wide enough and thick enough you can get substantial tension and bending stresses at about 3 & 9 o’clock on the pin hole, at the I.D. of the hole, a combined stress condition.

 

[BUGGAR]

When you do a FEA on a pin connection you invariably get high "theoretical" forces at the pin that you learn to accept since in reality there is some yield that allows it to work. Every time an analysis is presented, that's the first thing everyone notices, those bright red overstress contours at the pins.

 

[drawoh]

BUGGAR,

You get that message because the FEA is seeing a contact area of zero, resulting in a divide by zero error. I don't know enough about any FEA software to have any confidence in results showing computing errors.

Roark's Equations for Stress and Strain has a section on Bodies in Contact Undergoing Direct Bearing and Shear Stress. This might help.

--
JHG

 

[JStephen]

Note that in many real-life situations, the gross average stress is allowed to be approximately the yield stress of the material, without consideration of the theoretical contact stresses. See the approach used ASME BTH, for example. This is typical where the pin is used for hoisting and the like (ie, clevis pins through plates or lifting lugs), not where it is a rotating machine part. This assumes that some minor yielding may occur around the hole without loss of utility.

 

[garycvv]

Thanks for the help, I had checked Roark but had missed the section on contact. I'll check Roark as that's the book I've got to hand.

 

[chicopee]

I agree with Boo1. Keeping your elastic deformation small, then you have two different radii for contact stress between two different cylinders. Having large elastic deformation, then you have two cylinders of the same radius.

 

[boo1]

here is a presentation showing graphically what happens with additional info