How To Calculate Vacuum Pump Speed
Pumping Speed
Of the numbers used to characterize a vacuum system, pumping
speed is the most fundamental. Unfortunately, it is a common
mistake to accept the pump manufacturer's quoted pumping speed as
if it were the effective pumping speed from the chamber.
This error is easily exposed. Think of two identical pumps and
chambers: one set is connected via a short, wide-diameter tube; the
other is connected by a long, narrow tube. Which arrangement pumps
the chamber faster and why?
From the first great principle, 'vacuum doesn't suck', we know
that gas molecules enter the pumping mechanism via a series of
random collisions with each other and with chamber walls. The
narrower the tube, the lower the probability that a molecule will
enter it. The longer the tube, the greater the chance of the
molecule hitting a wall while passing through. But molecules,
unlike light, do not bounce off walls at the same angle as they
arrive. They are just as likely to bounce backward as forward.
That is, the shorter, wider connection gives the faster
pump-down, since its higher conductance leads to a higher effective
pumping speed from the chamber.
Effective Pumping Speed
If we attach a 500 L/s pump to a chamber with a 500 L/s
conductance port, what is the effective pumping speed (EPS) from
the chamber. Before calculating, let us set some limits
intuitively:
- A 500L/s pump is connected to the chamber by some magical
'infinite' conductance port, would the pump's pumping speed be
affected?
Answer - No. EPS is 500 L/s
- Two 500L/s pumps are connected to the same chamber by separate,
'infinite' conductance ports, what is the EPS?
Answer - EPS is 1000 L/sec.
- A 500L/s pump is connected to the chamber by a 500L/sec port,
would the EPS be higher or lower than 500L/sec?
Answer - Lower.
This indicates that adding pumping speed and conductance in
series lowers the overall pumping speed, while adding them in
parallel increases the pumping speed. This sounds identical to the
series/parallel connections of electrical capacitances. Indeed,
pumping speeds (PS) and conductances (C) are added to give
effective pumping speed (EPS) using exactly the same mathematic
form as capacitances. To calculate series connection of chamber and
pump noted above:
1/EPS = 1/PS + 1/C
Substituting the numbers from our initial example, we find 1/EPS
= 1/500 + 1/5001/EPS = 2/5001/EPS = 1/250
EPS = 250 liter per sec That is, when the pumping speed and
conductance are of equal value, the effective pumping speed is half
the quoted pumping speed. Newcomers to vacuum technology, and even
some old-timers, are surprised by this number.
Adding other components only worsens the problem. For example,
what if we put an LN2 trap with 500L/sec conductance between the
port and pump?
1/EPS = 1/500 + 1/500 + 1/5001/EPS = 3/5001/EPS = 1/167
EPS = 167 liter per sec
Clearly, using the quoted PS as the effective PS will cause
serious errors in estimating base pressure and pump down
time.
Now, we will take the ridiculous situation and connect a 2000L/sec
pump to a chamber by a tube with 10L/sec conductance and calculate
the EPS. 1/EPS = 1/2000 + 1/101/EPS = 201/20001/EPS = 1/9.95
EPS = <10 liter per sec
Conclusions
One critical fact should be extracted from this segment. The
effective pumping speed never exceeds the value of the minimum
conductance (or pumping speed) of the individual parts that are
stacked together. Expressed differently, if one component in the
stack has a 10L/sec conductance, the effective pumping speed cannot
exceed 10L/sec even if a 2,000,000L/sec pump is attached to it!
Remember - vacuum doesn't suck!
