Thermal resistance of ball bearings (rotating)

[dirkschiller]

Hello all,

Im am looking for some information about the heat transfer through rotating ball bearings. This is probably a function of the bearing dimensions, the lubricant and the rotational speed.
Does anyone have an idea where to find such information?

Thanks,

Dirk

 

[Skogsgurra]

I have got very useful information from "the horse's mouth" at SKF in Gothenburg. Try phoning an SKF office near you. Or have a look at

http://www.skf.com.

 

[electricpete]

FAG Publication WL 81 115/4 EA - Rolling Bearing Lubrication page 18 addresses heat generated within the bearing and how to quantify dissipation of this heat through the housing.

Is this what you are interested in? If so you should be able to find the file somewhere on

http://www.fag.com

I think. I tried to cut/paste from the pdf file but it may not work perfectly. I didn't spend too much time because I'm not sure this is what you're looking for. Let me know if you wnat more clarification of what is in the document. (I may be able to put it in a better format)


The heat flow QR generated by the
bearing is calculated from the frictional
moment M [N mm] (section 1.2) and the
speed n [min –1 ].
QR = 1.047 · 10 –4 · n · M [W]
The heat flow QL dissipated to the en-vironment
is calculated from the differ-ence
[K] between bearing temperature t
and ambient temperature tu , the size of
the heat transfer surfaces (2 dm · ??· B)
and the heat flow density qLB customarily
assumed for normal operating conditions
(fig. 19) as well as the cooling factor Kt .
For heat dissipation conditions found in
the usual plummer block housings,
Kt = 1, for cases where the heat dissipa-tion
is better or worse, see below.
QL = qLB · [(t–tu )/50] · Kt · 2 · 10 –3 · dm · ??· B [W]
qLB [kW/m 2 ] rated heat flow density,
see diagram, fig. 19
dm [mm] (D + d)/2
B [mm] bearing width
Kt cooling factor
= 0.5 for poor heat dissipation
(warm environment,
external heating)
= 1 for normal heat dissipation
(self-contained bearing
housing)
= 2.5 for very good heat dissipa-tion
(relative wind)
With oil circulation lubrication, the
oil dissipates an additional share of the
heat. The dissipated heat flow Qöl is the
result of the inlet temperature tE and the
outlet temperature tA , the density r and
the specific heat capacity c of the oil as
well as the amount of oil m [cm 3 /min].
The density usually amounts to 0.86 to
0.93 kg/dm 3 , whereas the specific entro-py
c – depending on the oil type – is
between 1.7 and 2.4 kJ/(kg . K).,
QÖl = m · r · c · (tA – tE )/60 [W]
For a standard mineral oil with
r = 0.89 kg/dm3 and
c = 2 kJ/(kg . K) the following simplified
equation is used:
QÖl = 30 · VÖl · (tA – tE ) [W]
where
Völ amount of oil flowing through the
bearing [l/min]
The bearing temperature t can be
calculated as follows
QR = QL + QÖl [W]




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[dirkschiller]

Thanks a lot guys for your suggestions. I have contacted the supplier regarding this issue. The question is really how much heat is transported from the inner bearing ring to the outer one. It seems to be not a well explored field.

Greetings,

dirkschiller

 

[EnglishMuffin]

When I saw this thread it piqued my interest because I once investigated this subject a little, but I thought I would just sit back and see what everyone else had to say first. There was a paper that I used to have in which the author derived a quasi steady-state equation for the contact resistance of rolling bearings, which in reality is a transient thermal problem. I believe that it was only valid for the case where the heat source is at the contacts - but I could be wrong. The equation he produced seemed vaguely reminiscent of Block's flash temperature equation. There were also some aspects of it that seemed questionable to me. Unfortunately, I can't locate it at the moment. However, the fact is that if you consider (for example) the total thermal resistance of a bearing between the inner and outer races, even in the non-rotating case, it's much more complicated than just a conduction problem. There is an old rule of thumb that says that if you place a hot cup of coffee on a table, the heat loss is initially about one third due to conduction, one third free convection, and one third radiation. So considering conduction alone probably won't give you very meaningful numbers in this case, since in the case of bearings we are usually talking about temperatures of a very similar order of magnitude to the coffee example. I once carried out an experiment with a large non-rotating taper roller bearing (about 6" ID), in which the heat source was simulated by electrical heating tape placed on the inner race. From memory, it's effective conduction was roughly equivalent to what you would have got through a steel torus of about half the bearing width.

 

[dirkschiller]

Hello EnglishMuffin,

thanks for sharing your experience. I agree the problem with a rotating bearing is somewhat complicated. It must be some kind of transport effect either via the ball material close to the surface of the ball or via the oil film on the ball. The reason I have to know this in detail is that the bearing is running under vacuum, which means no air conduction or convection. Radiation I can calculate, so the only remaining unknown factor is the friction and thermal conductivity of the bearing.

Regards,

dirkschiller

 

[EnglishMuffin]

Oh! Well, without too much convection, which is always the toughie, your problem might be somewhat more amenable to theoretical analysis, assuming you don't have large amounts of oil present. It's not entirely clear to me whether your problem involves a bearing which is itself the sole heat source, or whether there is an additional heat source somewhere else and the bearing is part of a conduction path for that also. The heat generated at the contacts (usually greatest on the inner) may or may not be significant, depending on how fast the bearing is rotating. If it is significant, it is still hard to calculate theoretically, since it depends strongly on the amount of excess lubricant present. Only a tiny amount at the contact is actually needed for the elastohydrodynamic lubrication regime which applies to bearings, and if there is any excess then it is this, rather than the phenomena taking place in the contact zone, that is usually responsible for most of the heat generation. If you had marginal lubrication, as would be the case with grease for example, it would considerably simplify the analysis on all counts. I will again try to locate that paper on rolling contact resistance, but as I say, I had problems with it since I seem to recall that it predicted infinite resistance at zero speed. The gist of the approach was that, in the case of a ball passing over a fresh portion of race, the thermal gradient in the race close to the moving contact will be greater the faster the ball is traveling, consequently leading to a lower contact resistance with increasing rolling speed. The theoretical predictions were backed up with experimental results. But I think the guy's analysis only made sense if the sole heat sources were the contacts themselves, which may not be the case here.

 

[EnglishMuffin]

One other thought occurs to me. A few years ago, Joe Poplawski of Poplawski Associates was developing a computer program (with government assistance) which was supposed to generate all the data one would need to interface with a thermal finite element model of whatever the bearing is connected to. I think he initially decided to make it compatible with ANSYS. Heat generation and contact resistance were certainly going to be among the generated data, although I do not know what his method of calculating them was going to be .

http://www.bearingspecialists.com/software.asp

I don't know how far he has progressed with the program - maybe not as far as his web site suggests, but you might want to talk to him, since bearing heat generation and its effects on surrounding structures is one of his consulting specialties. There is an old finite difference mainframe program called SHABERTH, which may actually now be in the public domain, and his intent was to supplant that with his more up to date approach. Of course, bearing manufacturers have their own proprietary software for this sort of thing.