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Figures I found on the web indicates 3% is a fairly
standard figure used for a planetary gearbox efficiency.
So if that figure is close and you are producing in cruise
- say 160 HP- then the gear box will produce heat with about 3% of the
input power. So 3% of 160 HP = 4.8 HP which is
mostly converted to heat.
I assume the oil is already cooled by the oil
cooler before it is fed to the PSRU. So the temp of the oil going
into the gear box might be around 180F. I am not certain how many GPM of
oil Tracy's PSRU flows but the old Ross flowed around 1 to 1 1/2
pint/minute, but that was apparently rather marginal. So assume
Tracy's flows 8 times that or 8 pints/minute = 1 gal a
min. Probably not that high but lower flow just means the temperature
calculation will be higher than in this example.
The Cp of oil is around 0.4 and its mass is approx 7.3
lbs/gallon.
4.8Hp converts to 203 BTU/Min, so we need to find out what
temperature rise that might cause in the oil.
Delta T = Heat/(Mass flow *Cp) or if we start out
with 180F oil (Ti) then we need to find the final temperature (Tf) .
So Tf = Ti + (Heat/(mass flow *cp)
Tf = 180F + (203/((7.3 *.5) *0.4) = 180F
+ 69F = 249F
So using this example and assuming I haven't screwed up,
I would expect the oil temps coming out of the gear box to be around
249F.
Less efficiency would mean higher temps. More oil
flow would lower the temp and less would increase it. Less power being
produced would also decrease the temperatures. There may be some heat lost
through air flow around the gearbox, but probably offset by heat from the engine
through the spacers and plate.
In my case, I would likely producing around 80 HP
at cruise based on fuel burn numbers (8 gph). My oil temp at that power is
around 170F.
So Tf = 170F + (102/(7.3*0.4) = 170F + 35F = 205 F.
So don't know if that tracks or not with what you guys are
seeing, but that's my 0.02 on it.
Ed
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