Hertz Contact pressure when R1=-R2
Hertz Contact pressure when R1=-R2
(OP)
Pals
I have a cylinder to stay fit in a groove. According to text books the effective radius is
1/R=1/R1+1/R2
and the effective bearing width b happens to depend on that value
now when R2=-R1 this one becomes 0. I expect cylinders in groove to reduce contact stress but I can not find the number.
I can not find a way around that
respects
IJR
I have a cylinder to stay fit in a groove. According to text books the effective radius is
1/R=1/R1+1/R2
and the effective bearing width b happens to depend on that value
now when R2=-R1 this one becomes 0. I expect cylinders in groove to reduce contact stress but I can not find the number.
I can not find a way around that
respects
IJR





RE: Hertz Contact pressure when R1=-R2
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes for fun rides
http://www.levitans.com : Air bearing pads
RE: Hertz Contact pressure when R1=-R2
what would be the practical value to be considered or at least assumed?
respects
ijr
RE: Hertz Contact pressure when R1=-R2
In structural calculations that situation, that is typical for bolts and other fasteners in shear, is handled with a nominal contact pressure, equal to the shear force divided by the diameter and the thickness of the plate with the hole; this stress is compared to an allowable stress that may be typically two times the normal allowable (that depends on the applicable code).
prex
http://www.xcalcs.com : Online engineering calculations
http://www.megamag.it : Magnetic brakes for fun rides
http://www.levitans.com : Air bearing pads
RE: Hertz Contact pressure when R1=-R2
a value for R2 equal to (R1 - x) and input
x=.001, x=.0001, x=.00001, etc to approximate
some value?
RE: Hertz Contact pressure when R1=-R2
prex's comment that as R1 approaches -R2 contact stresses gets down to zero is a very good comment. Dinjin, that limit approximation wont be helpful and it will simply bring zero contact stress and some very large contact width.
I found out that when R1 approaches -R2 then we stop talking of contact stresses and start talking of bearing stresses using area of projection of contact surfaces.
And so it becomes a simple bearing problem
Here is a good and simple book(though it discusses elastomeric bearings more than it does mechanical bearings):
Bearings in Structural Engineering by J.E.Long, John Wiley and Sons ISBN 0-470-54456-2
respects
IJR
RE: Hertz Contact pressure when R1=-R2
BW www.akeng.com
RE: Hertz Contact pressure when R1=-R2
As far as the suggestion of using load over a simplified bearing area--that will work if you don't care what the stresses around the hole are; you are merely transferring load through the hole or groove. But that won't work if you need to know the stresses around the groove, or you are analyzing the case of say a roller bearing in its groove.
RE: Hertz Contact pressure when R1=-R2
For the OP, if you are concerned with failure of the joint remeber that for "pin in plate" there are a half dozen different failure modes that can be checked by hand (or all at once with FEA).
Brad Woodward
www.akeng.com
www.appliedkinetics.ca
RE: Hertz Contact pressure when R1=-R2
what you are describing and at one time used fat
to lubricate the journal bearings. They finally went
to tapered roller bearings in these applications.
Interesting problem!!!