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How to choose a backing pump based on the pumping speed

The gas or vapor quantity transported through a high vacuum pump must also be handled by the backing pump. Moreover, in the operation of the high vacuum pump (diffusion pumpturbomolecular pump), the maximum permissible backing pressure must never, even for a short time, be exceeded. If Q is the effective quantity of gas or vapor, which is pumped by the high vacuum pump with an effective pumping speed Seff at an inlet pressure pA, this gas quantity must certainly be transported by the backing pump at a pumping speed of SV at the backing pressure pV. For the effective throughput Q, the continuity equation applies: 

Leybold - Vacuum Fundamentals graphics


The required pumping speed of the backing pump is calculated from: 

Leybold - Vacuum Fundamentals graphics


Example how to calculate the pumping speed

In the case of a diffusion pump having a pumping speed of 400 l/s the effective pumping speed is 50% of the value stated in the catalog when using a shell baffle. The max. permissible backing pressure is 2 · 10-1 mbar. The pumping speed required as a minimum for the backing pump depends on the intake pressure pA according to equation 2.41a. 

At an intake pressure of pA = 1 · 10-2 mbar the pumping speed for the high vacuum pump as stated in the catalog is about 100 l/s, subsequently 50 % of this is 50 l/s. Therefore, the pumping speed of the backing pump must amount to at least 

Leybold - Vacuum Fundamentals graphics

At an intake pressure of pA = 1 · 10-3 mbar the pump has already reached its nominal pumping speed of 400 l/s; the effective pumping speed is now Seff = 200 l/s; thus the required pumping speed for the backing pump amounts to 

Leybold - Vacuum Fundamentals graphics

How to choose a backing vacuum pump based on pressure ranges

If the high vacuum pump is to be used for pumping of vapors between 10-3 and 10-2 mbar, then a backing pump offering a nominal pumping speed of 12 m3/h must be used, which in any case must have a pumping speed of 9 m3/h at a pressure of 2 · 10-1 mbar. If no vapors are to be pumped, a single-stage rotary vane pump operated without gas ballast will do in most cases. If (even slight) components of vapor are also to be pumped, one should in any case use a two-stage gas ballast pump as the backing pump which offers – also with gas ballast – the required pumping speed at 2 · 10-1 mbar.

If the high vacuum pump is only to be used at intake pressures below 10-3 mbar, a smaller backing pump will do; in the case of the example given this will be a pump offering a pumping speed of 6 m3/h. If the continuous intake pressures are even lower, below 10-4 mbar, for example, the required pumping speed for the backing pump can be calculated from equation 2.41a as: 

Leybold - Vacuum Fundamentals graphics

Theoretically, in this case a smaller backing pump having a pumping speed of about 1 m3/h could be used. But in practice a larger backing pump should be installed because, especially when starting up a vacuum system, large amounts of gas may occur for brief periods. Operation of the high vacuum pump is endangered if the quantities of gas can not be pumped away immediately by the backing pump. If one works permanently at very low inlet pressures, the installation of a ballast volume (backing-line vessel or surge vessel) between the high vacuum pump and the backing pump is recommended. The backing pump then should be operated for short times only. The maximum admissible backing pressure, however, must never be exceeded. 

The size of the ballast volume depends on the total quantity of gas to be pumped per unit of time. If this rate is very low, the rule of thumb indicates that 0.5 l of ballast volume allows 1 min of pumping time with the backing pump isolated. 

For finding the most adequate size of backing pump, a graphical method may be used in many cases. In this case the starting point is the pumping speed characteristic of the pumps according to equation 2.41. 

The pumping speed characteristic of a pump is easily derived from the measured pumping speed (volume flow rate) characteristic of the pump as shown for a 6000 l/s diffusion pump (see curve S in Fig. 2.76). To arrive at the throughput characteristic (curve Q in Fig. 2.76), one must multiply each ordinate value of S by its corresponding pA value and plotted against this value. If it is assumed that the inlet pressure of the diffusion pump does not exceed 10-2 mbar, the maximum throughput is 9.5 mbar · l/s 

Fig 2.76 Diagram for graphically determining a suitable backing pump.

a) Pumping speed characteristic of a 6000 l/s diffusion pump
b) Series of throughput curves for two-stage rotary plunger pumps (V.B. = Critical forevacuum pressure)

Hence, the size of the backing pump must be such that this throughput can be handled by the pump at an intake pressure (of the backing pump) that is equal to or preferably lower than the maximum permissible backing pressure of the diffusion pump; that is, 4 · 10-1 mbar for the 6000 l/s diffusion pump. 

After accounting for the pumping speed characteristics of commercially available two-stage rotary plunger pumps, the throughput characteristic for each pump is calculated in a manner similar to that used to find the Q curve for the diffusion pump in Fig. 2.76 a. The result is the group of Q curves numbered 1 – 4 in Fig. 2.76 b, whereby 4 two-stage rotary-plunger pumps were considered, whose nominal speeds were 200, 100, 50, and 25 m3/h, respectively. The critical backing pressure of the 6000 l/s diffusion pump is marked as V.B. (p = 4 · 10-1 mbar). Now the maximum throughput Q = 9.5 mbar · l/s is shown as horizontal line a. This line intersects the four throughput curves. Counting from right to left, the first point of intersection that corresponds to an intake pressure below the critical backing pressure of 4  · 10-1 mbar is made with throughput characteristic 2. This corresponds to the two-stage rotary plunger pump with a nominal pumping speed of 100 m3/h. Therefore, this pump is the correct backing pump for the 6000 l/s diffusion pump under the preceding assumption.

However, if the pumping process is such that the maximum throughput of 9.5 mbar · l/ s is unlikely, a smaller backing pump can, of course, be used. This is self-explanatory, for example, from line b in Fig. 2.76 b, which corresponds to a maximum throughput of only 2 mbar l/ s. In this case a 25 m3/h two-stage rotary-plunger pump would be sufficient. 

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