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
pumpbearing housings or gear casings.

Fig.
1. A threadedtype
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
(upfacing) space above the diaphragm. The downfacing surface
of the diaphragm is contacted by air (or an airoil mixture)
that exists in, say, a pumpbearing housing or gearbox
interior.
Examining the premise is always a good first step.
About two years ago, a shaftseal 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 worstcase
oiltoambient 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
3mlong 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, V_{2}=V_{1}
(T_{2}/T_{1}) = Constant. For equal
pressure, the new volume, V_{2}, would have to
be V_{1} (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—V_{1} (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 mby2mby2 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
m^{3}, one would have to add an expansion chamber with
a useable volume of—0.32 3 3.6 = 1.15
m^{3}—in the first instance. In the second
instance, the needed addition would be—0.39 3 3.6 = 1.4
m^{3}.
While this might have answered the original question, I now
imagined all kinds of different scenarios, including seeing a
1.15 m^{3} or 1.4 m^{3} hump on the gearboxes
of future wind turbines. Or perhaps none, because someone
explained intelligentsealing options to the gearbox
manufacturer. An intelligentsealing 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 sub1 and sub2 characters:
P_{1}V_{1} / n_{1}T_{1}
= P_{2}V_{2} /
n_{2}T_{2}
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:
P_{2} =
P_{1}T_{2} / T_{1} = 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 coauthored 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.
