Bearing Contact 1

[prost]

This month's Machine Design had an article about modeling bearing contact in a crankshaft. The author first made the point that a "...widely used technique to simulate crankshaft bearing load is with a simple linear arc of loads, say 60 degrees around a reaction-force vector." This seems like a terrible idea, by the way, especially if you care at all about the stresses near this hole where you applying the load. Nevertheless, here's the rest of the article.

http://machinedesign.com/ContentItem/71865/FEUpdateUsesurfacecontactformoreaccuratesimulations.aspx

He further makes the point that actually modeling the connection directly with a pin and contact surfaces produces more realistic results. Unfortunately, he added some twist to the model, so I couldn't make a direct comparison to the results using our standard technique for modeling bearing of pins against holes.

My question to this forum is: is this '60 degree constant arc of loads' (which I take to mean constant pressure, distributed 60 degrees around the hole) widely used by FEA forum participants? It would seem very easy to apply a distributed normal traction (AKA 'pressure' since it's in compression) of some form, A*cosine(theta), or B*cos(theta)*cos(theta). Of course maybe that 60 degree constant pressure is used because it's the easiest to implement, and users do not have capability to apply a pressure with a functional distribution like A*cosine(theta).

For comparison, our standard practice is to use one of 3 methods: 1) bearing traction, cosine distributed, 180 degrees on the hole surface or 2) normal springs, 180 degrees around the hole--allow the springs to react out an applied load or 3) modeling the pin-hole contact directly with contact surfaces between pin and hole.

The preferred method is 1) above, mainly because a) seems to work very well, and b) is really fast computationally! 2) above is pretty good too.

 

[corus]

I'd agree with the use of 1) making the bearing pressure as a cosine function so that the sum of forces is equivalemnt to the total bearing load. As the article suggests though, it all depends on clearance, and if there is sufficient clearance then the bearing load will act as more of a point load on the surface. In most cases, however, the bearing load will not be uniform along the bearing axis, say due to bending of the shaft, and in that case I'd use contact between the two surfaces. You could of course not use contact and just assume a cosine function of load around 180 degrees of the shaft circumferentially, and a triangular load distribution axially, depending on your assumption of the load distribution which would err on the conservative side for your final results.

corus

 

[GregLocock]

Well, for plain bearings in engines there is a fair amount of data around. Heywood has a conrod bearinsg distribution, for example.

Cheers

Greg Locock

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

 

[johnhors]

Back in July 1980 Ozzy Gencoz of the Boeing company published an article in the International Journal of Fatigue entitled "Application of Finite Element Analysis Techniques for Predicting Crack Growth in Lugs". In it he proposed an empirical formula to describe the distribution of bearing pressure for pin and lug contact. This formula produces peak pressures roughly 40 degrees either side of the load direction. The pressure is spread over 180 degrees.

 

[corus]

I'd think that the real pressure distribution depends to a certain extent on the relative stiffness of the lug to the pin and I'd treat Gencoz's results with caution for every application you might have. I've also seen measurements before that showed that the cosine distribution gave a good comparison with measured results for applying the pressure distribution around the circumference. The axial distribution is probably mroe significant to the stresses than the circumferential distribution. In a simple pin and lug case, as shown in the paper, would the centre of the stiffer region at the centre of the lug/pin take more of the load, and the less stiff free edges of the lug take less?

corus

 

[prost]

What is 'conrod bearinsg distribution'? I take it "conrod" is short for connecting rod. This is some particular functional form, like cosine() or cosine*cosine? Or something else?

Regardless of which method you use, however, which one is better than the others? corus seems to think that 'it depends' is the most reasonable answer; I tend to agree. We do a lot of lap joints, which generally have a few small holes in large plates, located a couple of diameters away from edges, so that cosine() seems to work pretty well. But if you have a rod end with a pin, cosine() might be a terrible distribution to use.

Better question yet--how do you know which method is better? I have tried to locate some experimental measurements of stress fields around loaded holes; I managed to find a limited set of photoelasticity results by Hyer, and got mixed results. I've uploaded the two comparison figures to Engineering.com

 

[prost]

Durn; only one of the files uploaded. Here's the other one.

 

[prost]

The reference for the photoelasticity data is
Hyer, M.W. and Liu, D. "Stresses in a Quasi-isotropic
Pin-loaded Connector Using Photoelasticity"
Experimental Mechanics, Vol. 24, pp. 48-53, March 1984

 

[prost]

As far as interference of the pin relative to the hole is concerned, I believe this is an entirely different discussion. I'd be happy to start with getting the hole pressure distribution for 'neat fit' or 0.0 interference holes right. Or should I say "most correct", since there will always be a difference between the reality of the connection and our model?

 

[GregLocock]

A con rod is the connecting rod in an engine.

Cheers

Greg Locock

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

 

[prost]

OK, think I guessed that correctly. When you say 'conrod bearing distribution,' what is the functional form of the distribution? cosine? cosine*cosine? something else?

 

[prost]

Looking at that Gencoz distribution more closely, I am not sure what advantage it has over say a contact model, other than computation speed. The resulting FEA computed stress distribution with the Gencoz distribution seems to be farther away from the Hyer photoelasticity measurements compared to the FEA computed results with the contact model.

 

[GregLocock]

Heywood's diagram is taken from sae paper 821576, I don't have it.

Having studied it more closely it is very complex shape since they've plotted the polar plot of the force vector during one cycle of operation - so it isn't what you wanted. Sorry.

Having said that,

http://www.pump-zone.com/articleimages/283_6.jpg

is in line with my memory - a sine wave is a reasonable approximation.

However

http://www.me.berkeley.edu/PREM/hydrodyn.htm

would make me cautious about such a simplistic assumption.

Cheers

Greg Locock

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

 

[cbrn]

Hi,
1) Prost, it's no surprise that a full contact schema reproduces experimental data in a much more consistent manner than any equation-based schema. The important thing with Gencoz form is that it reproduces experimental data much better (in this case) than the cosinusoidal form. At this point, I have two questions:
- how must the Gencoz series be read? I mean, which is the meaning of the "comma-separated double value" for the index "n" in the summations? Never seen anything like that in my math volumes...
- when is the Gencoz schema more appropriated, and when instead the cosinusoidal? Because, in the basic engineering books, what "thet" give you for a direct bearing-like contact is the cosinusoidal form...

2) GregLocock, the first reference you give relates to a deviated, eccentric bearing-like contact and is effectively a cosinusoidal schema, corrected in order to take into account eccentricity.
The second reference, instead, has in my opinion nothing to do with the original question, because it's a Reynolds-based pressure distribution which is valid for fluid-film hydro-dynamic bearings only.

Regards

 

[johnhors]

cbrn,

Here is a fortran function to evaluate gencoz:-


FUNCTION GENCOZ(A)

IMPLICIT DOUBLE PRECISION (A-H,O-Z)

GENCOZ=COS(A)

IF (GENCOZ.LT.0D0.0D0) THEN
GENCOZ=0.0D0
RETURN
END IF

OLD=-1.0D0
J=1
K=-1
10 J=J+4
K=K+4
RJ=FLOAT(J)
RK=FLOAT(K)
GENCOZ=GENCOZ-COS(A*RJ)*5.0D0/((RJ-8.0D0)*(RJ-1.0D0)*14.0D0)
* -COS(A*RK)*2.0D0/((RK-4.0D0)*(RK-4.0D0)*5.0D0)
IF (GENCOZ.LT.1.0D-8) RETURN
DIFF=ABS((GENCOZ-OLD)/OLD)
IF (DIFF.LT.1.0D-6) RETURN
OLD=GENCOZ
GO TO 10

END

 

[johnhors]

that should be :-

IF (GENCOZ.LT.0.0D0) THEN

in the fourth line of code !

 

[cbrn]

Hi,
ah, OK, the meaning should be, if I understand well, "for n=5 to infinity step (9-5)" and "for n=3 to infinity step (7-3)"; i.e. the index "n" grows "step 4" in both summations, starting from 5 in the first one and from 3 in the second one... Not really a standard mathematical notation, I guess...

Thank you, regards !

 

[gurmeet2003]

One of the factors that has not been considered so far is the presence of the oil film between the crankshaft pin and the connecting rod bearing. The actual pressure is obtained by mobility study of the lub oil. So to consider the real load, contact alone is not sufficient.

This creates a difficulty. Because if one applies the oil pressure obtained from the study to the bearing without the pin, then the conrod bore is too flexible. On the other hand
if pin contact is included then there is no way of applying
the actual oil pressure. The best study would be what is called the elasto-hydro dynamic study. But that is computationally very expensive.

Gurmeet

 

[prost]

Oops! My bad! I misread the Gencoz formula; the last picture I posted isn't representative, since it didn't take enough terms. I wondered why my FE solution had more 'bumps' than the figure in the Gencoz.pdf posted here.

 

[cbrn]

Hi,
Gurmeet,
yes, this is a very special case and I have no knowledge on how to consider it.
In general, however, if you want to simplify, it's either one of these two situations:
- fluid-film hydrodynamic bearing: Reynolds equation applies, at least until the pressure of the fluid-film is not high enough to "strip" the film itself (overload), until the relative speed is not so low as to make the film creation impossible (lack of lift), or until the relative speed and load are not such as to create whirls in the film (instability) - this is however out of the original question
- dry contact between bodies: you can choose from cosinusoidal, Gencoz, or whatever pressure distribution is best appliable to your problem. The question is still: which distribution goes better for which situation?

Regards