Expansion chambers (Fig. 1) are designed to restrict pressure increase in closed volumes. From basic physics, we, of course, know that the pressure in a closed volume increases as temperature goes up. In case a shaft seal is so tight that it will no longer allow air confined in bearing housings or gearboxes to flow in and out, the trapped air would be pressurized as temperature rises. Creating a larger volume for the trapped air would keep the pressure down. We find expansion chambers advertised for use on process pumps and gearboxes. They can replace breather vents that are commonly found on pump-bearing housings or gear casings.
 |
Fig. 1. A threaded-type
expansion chamber is
sometimes used at the location
where the bearing housing vent
had been installed originally. |
Most expansion chambers incorporate a rolling diaphragm (usually Viton and, occasionally, Teflon). The diaphragm divides the interior volume of the chamber so that ambient air can be aspirated into, or expelled from, the (up-facing) space above the diaphragm. The down-facing surface of the diaphragm is contacted by air (or an air-oil mixture) that exists in, say, a pump-bearing housing or gearbox interior.
Examining the premise is always a good first step.
About two years ago, a shaft-seal supplier started discussions with a wind turbine gearbox manufacturer. The seal supplier wanted advice on calculating the size of expansion chambers for gearboxes with dimensions in the vicinity of 3 m x 2 m x 2 m. A worst-case oil-to-ambient temperature difference of 100°C was anticipated by the two parties. Realistically speaking, temperature differences of 100°C (180°F) are rather unusual in a gearbox. We should always look at the bigger picture and perhaps even challenge the basic premise.
That said, let’s be certain to select the right lubricant and to accommodate thermal expansion which, on a 3-m-long steel gearbox, might be somewhere around 0.14 in. We obtained this number by multiplying the coefficient of expansion for steel, times the length, L (in.), times the anticipated temperature, ∆T, change:
∆L = 0.0000065 3 L 3 ∆T
Anyway, here’s the academic exercise. We might elect to work with a base temperature of, say, 100°F, which would be (100 + 460) = 560 Rankine. Continuing in US units, an increase of 100°C (180°F) is (180 + 560) = 740 Rankine.
Charles’ Law states that the volume of an ideal gas at constant pressure varies directly as the absolute temperature; thus, V2=V1 (T2/T1) = Constant. For equal pressure, the new volume, V2, would have to be V1 (740/560), or 1.32 times that of the original air space (or volume) of 1. Thus, 0.32 volume units would have to be added to the original air space or volume unit of 1.
Also, the volume of an expansion chamber would have to be larger if we had assumed a lower base temperature, say, 0°F. In that case, the needed volume addition would be based on—V1 (640/460)–1—and 0.39 volume units would have to be added to an original air space or volume of 1.
Much of the 3 m-by-2-m-by-2 m overall gearbox volume will be taken up by the gears and oil. So, if the remaining air volume had been 30% of the gearbox total, i.e., 0.3 3 12 = 3.6 m3, one would have to add an expansion chamber with a useable volume of—0.32 3 3.6 = 1.15 m3—in the first instance. In the second instance, the needed addition would be—0.39 3 3.6 = 1.4 m3.
While this might have answered the original question, I now imagined all kinds of different scenarios, including seeing a 1.15 m3 or 1.4 m3 hump on the gearboxes of future wind turbines. Or perhaps none, because someone explained intelligent-sealing options to the gearbox manufacturer. An intelligent-sealing option would be a balanced seal, or a seal that can take the pressure increase that comes with a constant volume. Let me explain.
Pressure increase with constant volume.
Suppose we didn’t add an expanding volume to the wind turbine gearbox and the temperature rose from 0°F (–18°C) to 180°F (83°C). What would be the pressure increase? Well, we might just google “gas law” and observe the before vs. after conditions indicated by the sub-1 and sub-2 characters:
P1V1 / n1T1 = P2V2 / n2T2
The molecular masses, n, probably will not change, and neither will the volume. We assume that our installation is at sea level and atmospheric pressure is 14.7 psia. Therefore, the absolute pressure will change in direct proportion to the absolute temperature:
P2 = P1T2 / T1 = 14.7 psia 3 740R / 560R = 19.4 psia
The ∆P across the seal would be 19.4 –14.7 = 4.7 psi. Now, we could design a seal for that, even if we needed to divert a slip stream of bearing lubricant to provide a bit of cooling for the seal. So, we might not need the expansion chamber, after all? HP
| The author |
Heinz P. Bloch is Hydrocarbon Processing’s Reliability/Equipment Editor. A practicing consulting engineer with close to 50 years of applicable experience, he advises process plants worldwide on failure analysis, reliability improvement and maintenance cost. He has authored or co-authored 18 textbooks on machinery reliability improvement and close to 500 papers or articles. For more, read his book, PUMP WISDOM, Problem Solving for Operators and Specialists, John Wiley & Sons, 2011. |