Quote:
Originally Posted by humfrz
WOW! ....... what a dissertation ......impressive ...... 
A couple of comments.
You mentioned "It's not speed that does it, it's load". Well, I know this is an apple and orange thing but, I have sat on the top of transmissions (literally) for hours on end, with a big diesel tractor engine putting tons of torque through the transmission to pull heavy ground working equipment. The transmission just felt warm to the touch after pulling hard till I needed to re-fuel (or stop under an oak tree to take a nap).
You mentioned " So, in 15 minutes, we have put enough energy into the oil to heat it from room temperature (15C) to 1348.8 Degrees C." YIKES, I suspect your math/physics calculator overheated on that one ....... how could the transmission oil reach a temperature of 1348.8 degrees C ....... when that same oil would boil at roughly 300 degrees C ..... ?? Hell, at that temperature the oil would be lucky to be called tar and the transmission case would glow like an overheated pot belly stove ...... 
humfrz
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Correct. To settle your comparison, it's load measured in power, not torque. Torque is just force, and doesn't make any heat at all. Power is a rate measurement. Force x distance / time.
A crude example: if you hold the brakes and mat the gas pedal in an A/T car, the brakes make enough torque to hold it still (assuming they're big enough) but do no work. That's a lot of torque, but they build no heat, because they make no power.. Stop that same car from 60, the discs will burn your hand, even though they made less torque.
The heat over time example... I'm sure an hour of highway traffic makes enough heat to make similarly absurd numbers in the brakes, yet they don't glow red. The heat does dissipate. I also didn't account for the rate of heat
transfer to the aluminum case, the capacity of the case to act as a heatsink, the capacity of the case to dissipate heat, etc.
You put enough energy through a header in track session at WOT to melt it to liquid hundreds of times over, yet it doesn't even reach sufficient temperature to glow... Because that heat is rapidly dissipated, and the absorption is limited.
Yes, the oil doesn't get anywhere near that hot. I refined the example to the potential increase in temperature per minute to illustrate the point.
Here's the relevant point from all the math, boiled down. The rate at which heat is added, through purely mechanical work, is very high.
Much higher than people think. The rate of subtraction has to keep up, otherwise it will heat to failure very quickly. Other than that, it's not unreasonable to have very short oil change intervals in the transmission if you're applying a lot of sustained power to it. The more power you make, and the longer you do it, the more true that statement is.
Mainly, however, it explains that a street driver can get away with rarely or never changing the transmission oil, while a track driver can break down that same oil in a matter of hours, which answers the original question.