water-film bearing with "precompressed" water ? 3

[cbrn]

Hi,
I've got a runner-in-housing assembly which behaves kind like a bearing, whose fluid medium is water.
The fact is that this water is pressurized, i.e. the average pressure inside the "bearing" at rest is not zero.
Does this pressure have an influence on the static behavior of the bearing under load, or will the bearing behave just like if the fluid medium was not pressurized?
I believe it doesn't make any difference, but my application is somewhat critical and I'd prefer to be really sure about this point...
I don't know if I have been clear... Don't hesitate to ask me for other clarifications...

Thanks in advance !

Regards

 

[cbrn]

... I forgot to mention: it's a radial hydrodynamic bearing, not a thrust bearing. Its geometry is like a "plain shell" cylindrical bearing.
Hope this makes things a bit clearer...

Regards!

 

[electricpete]

I agree with you. Static pressure will likely not have a big effect

Below is classic discussion of Reynold’s model which I think is widely accepted and has proven fairly accurate:

http://nptel.iitm.ac.in/courses/IIT-MADRAS/Machine_Design_II/pdf/5_2.pdf

Section 2.3 gives the assumptions of the model.

These assumptions lead to simple relations like 2.6:
dp/dx = d Tau / dy

and complicated equations like the Reynold’s equation for 2-dimensional flow Equation 2.20.

In both cases, you’ll note that p doesn’t show up, only it’s spatial derivatives shows up.

From 2.20 we can develop detailed charts like those of Raimondi and Boyd which tells us the behavior of the bearing (based on a model which does not depend on static pressure).

This shows that within the assumptions of Reynold’s model, the static pressure will not make any difference. There are of course real world effects which I believe will be minor importance such as change in viscosity with pressure. Change in density with pressure could be important in real world, but not in this model because inertial effects were neglected by assumption.

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[electricpete]

Does this pressure have an influence on the static behavior of the bearing under load

As a clarificaiton, when you say "static", I assume you mean that the shaft is rotating but you are interested in the steady state average position and associated film thickness etc.

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[WCFoiles]

Pressure can make a difference. Look for hydrostatic radial bearings. Does this 'bearing' have a high axial flow component?

Regards,

Bill

 

[electricpete]

Hey Bill
I agree axial flow is a different phenomenon as mentioned in a parallel thread here: thread404-300794

I’m not sure why you’re bringing up hydrostatic bearing... a hydrostatic bearing (with oil injected under pressure at one specific point in the bearing) doesn’t seem to have much in common with a bearing immersed in a pressurized fluid system. Maybe you can explain further.

Do you agree Reynold’s model is completely indifferent to the presence of any static/uniform pressure shift P0 applied to the entire spatial domain of the bearing annulus?



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[cbrn]

Hi,
thank you very much Electricpete and WCFoiles!
I'll try to give some more clarifications after your remarks:
- the "bearing" I'm talking about is, in fact, a sealing labyrinth. So it's a "cylinder-inside-cylinder" whose external one is the machine stator and the internal one is the runner.
- there is, in fact, axial flow while the pressure is dropping from about 56 [bar] "upstream" and -0.2 [bar] "downstream" this "labyrinth with bearing effect". The flow is not really big but I'm talking however of orders of magnitude of 0.1 [m^3/s]
- the axial flow and the axial pressure drop are thus orthogonal to the plane in which the eccentricity of the runner takes place, i.e. they are coaxial with the machine-axis
- when I'm saying "static behaviour" I'm referring exactly to what Electricpete said: the factors which govern the equilibrium position of the runner labyrinth inside the statoric one while it is turning around the machine-axis, regardless of the "instantaneous stiffnesses" which could be calculated with the method of the "small perturbations" and which have an importance for instance for vibrations and so on. In my problem, only the static matter has an importance
- currently I am solving the Reynolds equation under the "short bearing" hypothesis as a simplification of the Merker's method. This is a standard for the Group I work for. I'll have a look to the resource pointed out by Electricpete, possibly there is some different hypothesis or some different methodology.
- I had a look to "Externally-Pressurized Bearings", they're beginning to become common in our industry not only for axial (thrust-) bearings but also for radial bearings. However, what strongly differentiates a EPB from my "application" is the equilibrium "flow-path". I have no injection point in radial direction, as it is obvious because otherwise the labyrinth would not seal anything anymore !

I'm looking forward to hearing your comments,
thank you very much in advance,
best regards

 

[electricpete]

I’ll stick with my answer. If all you’re doing is adding some pressure P0 on both sides of the seal (same pressure drop accross the seal axially), there is no reason to suspect it will affect the seal operation.

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[cbrn]

Hi,
I agree. I checked your resource and recognized I already saw it in another form. Everything seems to confirm what I originally thought and that you also point on.
Thanks!

Best regards

 

[JJPellin]

I am reading this to indicate that there is an axial pressure drop from end to end of this "bearing" and thus there is axial flow. Please correct me if I have misread this. But, if there is axial flow then the Lomakin effect will influence the forces within the bearing. Refer to the attached thread.

Johnny Pellin

 

[electricpete]

I have ASSUMED that the comparison of interest involves no change in dp and hence no change in flow ("same pressure drop accross the seal axially" stated assumption in my post). Gotta love those assumptions.

op is welcome to clarify.

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[cbrn]

Hi,
I should have read better the assumptions of Electricpete...
I hope I will be able to clarify a little bit:
- the labyrinth seal is supposed to behave like a radial bearing (hydrodynamic, no stiffness at zero eccentricity)
- there is indeed a strong pressure difference axially between the "upstream" side of the labyrinth and its "downstream" side. The pressure difference is more or less 5 [bar] and the flow (leakage flow) is of the order of magnitude of 0.1 [m^3/s].
- however, in a section immediately upstream the labyrinth (section plane orthogonal to the machine-axis) the pressure is completely uniform, there is no unbalance in the circumferential path around the runner. The same can be said downstream.

Now I recognize that my own calculation hypotheses may be a little contradictory: if I consider that, at each section (plane orthogonal to the machine-axis), it's "like if" I add a uniform P all around the fluid film and superimpose to this the equilibrium solution in the radial direction, then is this idea compatible with the "short bearing" formulation, or should I find a more adequate and complete formulation which takes into account the pressure gradient in the axial direction?

Thanks again, regards

 

[cbrn]

... oops, sorry, please don't consider my last question, let's reformulate like that:
it seems it is not really a matter of pressure (intended as "total pressure") because the total pressure is uniform circumferentially, rather a matter of velocities (and hence static pressures). Axial flow (which in my case is not high in absolute but relevant for the single labyrinth stage) seems to play a role, then, via the Lomakin effect which I will study in the shortest delays !
PLease correct me if I am wrong.
Regards!

 

[cbrn]

Hello all,

I've been searching through the net for analytical solutions of the "short bearing with axial flow", thus combining hydrodynamical effect due to rotation and Lomakin effect due to axial flow, for a shaft having an eccentricity "epsilon", but...
- sources as D.W. Childs give solutions in closed form for the short seal with Lomakin effect but without hydrodynamic effect (i.e. they allow to determine a direct stiffness "at rest" with zero eccentricity)
- sources as Merker and others give solution for the "classic bearing theory" of hydrodynamic fluid-film forces, but without Lomakin effect...

I'm a bit lost: does someone know a good resource giving indications in order to combine both effects?

Thank you in advance,

Regards

 

[electricpete]

I don’t get how Lomakin effect applies with zero eccentricity.

I’m no expert in this stuff. My general impression is that the more recent publications concerning seals will be more relevant to analysing seals than the older publications concerning hydrodynamic bearings. Seals have more complicated dynamics than bearings whose implications for rotordynamics have not been understood for as long. The newer formulations for seals tend to supersede the older simpler Reynold’s hydrodynamic bearing model applied to a seal for a number of reasons (assumptions are not met). Things like preswirl become important. Building rotordynamic models for seals remains an area of active recent research.

Some textbook references:
Vance – Machinery Vibration and Rotor Dynamics, Chapter 6.
Rao – History of Rotating Machinery Dynamics section 14.12
Adams – Rotating Machinery Vibration, Chapter 5


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[electricpete]

According to Adams, Child’s is the man for seals:

However, the most complete
treatment and information resource for seal dynamics is contained in
the book by Childs (1993). Childs’ book covers a wide spectrum of rotor
dynamics topics well, but its coverage of seal dynamics is comparable to the
combined coverage for journal bearings provided by Lund et al. (1965) and
Someya et al. (1988). It is the single most complete source of computational
and experimental data, information and references for seal rotor dynamic
characteristics, reflecting the many years that Professor Childs has devoted
to this important topic.

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[cbrn]

> I don't get how Lomakin effect applies with zero eccentricity.

Sorry, I called it like that a bit improperly. I wanted to say that Childs derive a solution for anular fluid film with turbulent (high axial Reynolds) flow: anular implies inner and outer borders of the fluid field are coaxial. There is indeed a direct stiffness K which is far from being zero with the geometry I have. Childs' solution takes into account two self-centering stiffness terms, one of which is directly derived from the Lomakin effect and the second, antagonist one, is the Bernoulli effect.
Calculation of the pressure drop through the labyrinth stage, made following Childs' theory, matches very well what our fluid-dynamists calculate usually with other theories. This seems an index of the fact that Childs' theory is appropriate for our case, of which it represents the "limit condition" without eccentricity.

By working on the origin of the Lomakin effect, however, I was able to build a mathematical model which is able to "simulate" the Lomakin effect with eccentricity (but no contribution of the rotation speed) and whose extrapolation to null-excentricity approaches Childs' solution with an error of less than 10%, which is acceptable for me at the time present.

In my application, the direct stiffness due to Lomakin-type effect at near-to-zero eccentricity is of the same order of magnitude (1E+07 [N/m]) as the direct stiffness produced by the bearing effect at relative eccentricities approaching 0.94 !!!

To cut the long story short, simulating the two contributions altogether allowed to demonstrate that there was no risk of interference between rotating and stationary faces of the labyrinths, while with the "short bearing" theory alone there seemed to be a somewhat important one.

As regards the resources you have indicated, thank you very much ! I already knew some of them, you confirm my impression that they are "must-have" texts !

Thanks again, regards !
... and a star from me !