Hertzian Pressure in a Bearing

[VibFrank]

Hy,
I try to calculate the stress inside a journal bearing, if the shaft gets into contact with the bearing housing during shocks. I calculated with the formulas of Hertz (cylinder inside cylinder) and I found very low values for the pressure. This results from 1/r1+1/r2 (r1=radius of the shaft=100, r2=radius of journal housing=-100.3) in the numerator of the formula, which becomes very low due to the different signs in the radius. Some questions..

Is the calculation correct because the values are so low ?
Are there other formulas for this problem ?
Is the use of Hertzian pressure allowed for this problem ?
What other calculation/check would you make for this shock-contact-situation ?

I'm concerned, because the values for the pressure are so low for typical journal bearing geometries (radius nearly identical but different sign), that theoretically there would nearly never be problem..

Thanks for your comments
Frank

 

[btrueblood]

???

No such thing as a negative radius, unless you have bearings with imaginary cross sectional area. A radius is the (always positive) distance from the center of a circle to its circumference. Change the sign back to a positive value and re-compute.

 

[GregLocock]

Oh, that's just the way that Hertzian contacts are worked out. You can have a ball resting on a ball, in which case both radii are positive, or a ball in a cup in which case one of the radii is negative.

The reason I guess is that we are really talking about curvature.



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[btrueblood]

Oops, sorry, Greg is right -- though I hadn't seen the equations written out that way before (glanced at an online reference last night that showed that convention).

 

[VibFrank]

I also did not realize the "sign-convention" at the beginning. Or perhaps from another point of view: are the formulas valid for r1 nearly equal r2 but with different sign ?
frank

 

[GregLocock]

So far as I know they are valid. The first example in roark C14 is for a 1.5 ball in a 1.6 groove, so he obviously thinks it is OK!

EXAMPLE
A ball 1.50 in in diameter, in a race which has a diameter of 10 in and a groove
radius of 0.80 in, is subjected to a load of 2000 lb. It is required to find the
dimensions of the contact area, the combined deformation of ball and race at
the contact, and the maximum compressive stress.
Solution. The formulas and table of case 4 (Table 14.1) are used. The race is
taken as body 1 and the ball as body 2; hence R1 = -0.80 in, R01 = -5 in, and
R2 = R02 = 0.75 in. Taking E1 = E2 = 30,000,000 lb=in2 and n1 = n2 = 0:3, we get sigmac-252,000 lb=in2



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[GregLocock]

Here's Roarke's formula for your exact case if nu=0.3 and both parts are the same E and nu

kd=D1*D2/(D1-D2)

sigmamax=0.591*sqrt(p*E/kd)

p is the load per unit length

so as D1 approaches D2 the stress approaches zero.



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[btrueblood]

Roark also mentions that some of the references note deviations from the simple equations as the cylinders approach the same diameters. The whole mix of contact stress, stiction/adhesion (galling), fluid-dynamic shear, and (in some cases) cavitation come into play in a well-made journal bearing...to the extent that the whole black art science of tribology was created to study the phenomena.

 

[zekeman]

Moreover, how do you account for shock loads that the OP refers to using the Hertz formula, which is linear in the load P?

What do you use for P?

You really have to model the impact using momentrum and energy equations, make some assumptions on elssticity before you can apply that formula.

I haven't done this for some time but I know that any valid result will depend on these factors, and not simply writing an equation and making up some amplification of the load. I suppose the current literature has something on this.

 

[VibFrank]

P is the load from earthquake: P=mass*acceleration