Thermal expansion coefficient of gear oil

[blckwtr]

We have an application with an enclosed gearbox, which is to be put down into a reservoir with temperature of up to 200°C, from an initial temperature of -20°C or so... The challenge is that we want to balance the pressure, since the outside pressure is very high, giving far too much friction on the seals which keeps the transmission fluid inside of the gearbox... So we want to make an equalizing chamber, which we now has to make extra room for if ouir calculations are correct...

Initial volume of gear oil; 1,66 litres
Temperature difference; 220°C
Estimated beta factor (thermal expansion coefficient); 700*10^-6 / °C(K)

Volume difference; 255,6 mL (15,4%)(!)

Is this correct, and do we need to make extra room for our chamber, which can take only 10 mL ?

 

[Oldhydroman]

Is your gearbox absolutely full to the brim with gear oil (and gears) or is there an air space?

If you assume the vessel to be completely full, the fluid to be a mineral oil, the vessel to be unchanging in volume (both because of temperature increase and internal pressure increase) then you can estimate a pressure increase of about 11.5 bar per degree Centigrade. A temperature rise of 220 deg C would cause a pressure rise of over 2500 bar. I suspect your gearbox case couldn't take this sort of pressure so you probably do have air in there as well.

If so, try re-calculating separately for the oil volume and then for the air pressure. Work out the expansion of the oil (your figures are good, although personally I would have used 0.00064/K for a mineral oil) and then see what effect this has on your air volume. The air will be compressed in volume because of the expansion of the oil and the air will itself also try to expand because of the increase in temperature. Remember to use Kelvin for the temperatures, and use "absolute" values of pressure.

So if your 1.66 litre gearbox case actually contained 1 litre of oil and 0.66 litres of air at -20 deg C, then at 200 deg C the oil will have grown to 1.154 litres. Your gas calculation would give you an internal pressure of about 1.4 bar above atmospheric. It is possible that by adjusting the amount of air in the gearbox (i.e. the percentage of oil fill) you could get the internal pressure at 200 deg C to rise enough to balance the external pressure.

DOL

 

[blckwtr]

Thank you very much for the good input, Oldhydroman, we would certainly look into this, with having an amount of air inside at atmospheric pressure... If we in addition to this have our balancing piston, which can balance the inside and outside pressure, it would almost not move at all... This is of course dependent on the temperature at a given pressure. We would not want the piston to go into end positions in either direction...

We don't know exactly what kind of oil we would use for the gearbox, but is it fair to estimate an incompressible fluid at these pressure/temperature ranges?

 

[Oldhydroman]

Well you haven't actually said what your external pressure is, but as a rule of thumb you could use a bulk modulus of 14,000 bar (which equates to 1% decrease in oil volume for every 140 bar increase in pressure). If you are using an air space in the gearbox then the compressibility of the gas is so many orders of magnitude above the compressibility of the oil that you would be right to consider the oil to be effectively incompressible.

There are other possibilities which you might like to consider: when working out how much air space to leave so that the pressures will balance at the new temperature you could consider pre-charging the gearbox case (using an inert gas such as Nitrogen) or you could consider evacuating the case (this gives room for the oil to expand without it increasing the internal pressure - although you did say you the high pressure differential caused you a problem).

Would it be possible to fit a pressure relief valve to limit the pressure differential across the seals? If your air gap was on the small side then the rise in temperature would cause the case pressure to rise more than the ambient pressure - then the releif valve could let gear oil out into the reservoir.

DOL

 

[blckwtr]

Sorry about that, we willl work in temperature range and pressure range between 20°C and 200°C / 0 - 10000 psi...

So there is no way to predict which pressure and temperature occurs at the same time...

 

[Oldhydroman]

Oh, that's definately some external pressure!

I suspect you are going to have to try to find room for your pressure equalisation system to be able to cope with the full thermal expansion volume of your oil. Any air gap you started off with at atmospheric pressure will have shrunk to less than 0.2% of its original volume when you pressurise the case to 10,000 psi. You would be better off having no air gap at all but being able to accommodate the 260 mL of oil volume change via your moving piston.

You might be able to reduce the volume change by filling your gearbox with a load of incompressible [metal] spacers so that you have less oil. Then look at using a synthetic lubricant - the stuff that is used to fill the sealed-for life gearboxes. This stuff has more service life in it - which you might need if there's less actual gear 'oil' doing the rounds. You might want to investigate something like Shell Tivella.

DOL