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# Gearbox casing heat rejection2

## Gearbox casing heat rejection

(OP)
Hi,

I'm looking for an approximate value for the heat rejection to ambient air of a typical transmission casing.

Watts/surface-area for an aluminium casting in free air would be a good starting point.

I need to calculate the size of the oil cooler, but want to subtract the heat rejection of the casing first.

Many thanks, Ian

### RE: Gearbox casing heat rejection

2
Ian,

The heat in a gearbox is generated thru several mechanisms.  If your gears have high pitch line velocities, then oil windage losses can predominate.  Oil churning losses in bearings can also be significant if scavenging and drainage flows are not paid attention to.  And if your gear meshes have lots of sliding, they will require high flows.

If your gears are supported in rolling element bearings, then they are fairly well thermally isolated from the housing structure, and most of the heat transfer out of the gear teeth/rims must be accomplished thru oil jetting.  The difficulty with doing this is that the oil spends very little time actually in contact with the gear teeth, so it experiences only a modest temperature rise before it is flung off.  With a small temperature rise, you must naturally increase mass flow rates to effect your desired heat transfer rate.

My experience is mostly designing aircraft transmissions with aluminum cases.  The total mechanical (gears, bearings, splines, seals, etc.) and windage losses of these systems is usually about 4%.  As a rule of thumb, I would recommend starting with a bulk oil flow temperature rise of about 40degF, from jet to sump, to be conservative.  We typically design for oil inlet temps of 230degF max under normal conditions with mil-spec gear oil, so bulk oil out would be 270degF max.  The oil system volume is also normally kept very small to minimize weight, so the oil turnover rate thru the system is naturally very high.  Usually around 4X per minute.

Having said all that, the heat transfer variables across the wall of an aluminum casing is something you'll have to make some assumptions about until you get your hands on some test data.  You can easily determine the thermal conductivity of the aluminum, you can analyse for the total exterior surface area, you can safely assume that the inner surface of the casing is at (or near) bulk oil temp, but you'll likely have to guess at the local ambient air mass flows and temperature.  Once again, as a conservative rule of thumb to start with, I would recommend assuming about 10% of the heat load being rejected thru the case wall structure with an aluminum housing in static air.

The other 90% of the heat load must be rejected thru your cooler.  Unfortunately, the cooler core always ends up being a lot larger than you would expect, since you must size it for conditions of max power, on a hot day, at high altitude.

Good luck,
Terry

### RE: Gearbox casing heat rejection

Hmm, informative post but orthogonal to the thread I think.

According to my thermo book the heat transfer coefficient in air is

.0005 to 1 kW m-2 K-1

That's right the estimate varies by a factor of 2000!

My Heat transfer book is even less helpful.

Here's what Ye Olde gearbox booke (practically a scroll) says

H=C*A*dT

H in ft lb/min (that'd be hp/33000)
dT in fahrenheit
A in sq in

C is 0.45 for A=0, .33 for A=10000 and .27 for A=20000

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

### RE: Gearbox casing heat rejection

I think the wide variance in transfer coefficient is probalby due to clean vs. oxidized surface. My data for room temperature is 840-1540 BTU/hr./sq.ft./°F.

ISZ

### RE: Gearbox casing heat rejection

FWIW - My old "Machine Design" by Deutschman, Michels, and Wilson says a widely used heat transfer coefficient (C) for bearing heat balance calcs is approximated as 2 BTU/(hr)(ft2)( degree F) for still air. If air velocity is 500 ft/min, then 5.9 BTU.......  is suggested.

### RE: Gearbox casing heat rejection

Sorry if you thought my post was a bit long winded, but the original question posed was more than simply asking for a heat transfer coefficient for aluminum in still air.  Any decent text will give you that.

I just spent a very long time doing exactly this analysis for a large aircraft transmission.  Sizing the oil heat exchanger core was no straightforward task.  It ultimately involves lots of educated assumptions.  And I'm sure the heat exchanger core size will change after both bench testing and flight testing.

What Ian stated is that his real task is to size an oil cooler for his transmission.  And he wished to start by subtracting the heat rejected thru the aluminum case from the total heat load that must be rejected thru the cooler core.  All other things being equal, heat transfer thru the case wall is most affected by the deltaT.  To accurately establish the deltaT across the case wall, you must firstly understand how the oil-to-inner-case-wall heat transfer mechanism works, and what factors drive it.

Some of the oil, like that used to cool bearings, will not have much temperature rise and will likely drain directly into the sump without contacting the case wall.  Other oil flows, like those used to cool gear meshes, will experience much greater temperature rise, and will be flung and wetted-out against almost all inner surfaces of the case.  Thus the oil flow heating the case will be at a higher local temperature than the bulk oil flow temps measured in the sump.

To make a long story short, accurately sizing a transmission heat exchanger (by analysis) is no simple matter.  And that was the real point I feebly attempted to make with my long-winded post.

Best regards,
Terry

### RE: Gearbox casing heat rejection

Yes, and it was a very useful post. In fact have a star. That and 3 dollars will get you a cup of coffee.

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

### RE: Gearbox casing heat rejection

Three bucks for a cup of coffee?  That works out to over $30/gal. And to think people complain about paying$3/gal for gasoline!

In case you're interested regarding the topic of how complicated some gearbox lube system analyses can get, the one I'm currently working on has over 160 separate oil jet orifices in the system.  Thank God for Excel!

Best regards,
Terry

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