Fundamentals of Vacuum Technology (1248463), страница 28
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2.75 Dependency of the dimensionless factor s for calculation of pumpdown time taccording to equation 2.36. The broken line applies to single-stage pumps where thepumping speed decreases below 10 mbar.67HomeVacuum generationforevacuum pressure pV instead. Then equation (2.34) transforms into:2.3.1.2 Evacuation of a chamber in the highvacuum regionIt is considerably more difficult to give general formulas for use in the highvacuum region. Since the pumping time to reach a given high vacuumpressure depends essentially on the gas evolution from the chamberÕsinner surfaces, the condition and pre-treatment of these surfaces are ofgreat significance in vacuum technology. Under no circumstances shouldthe material used exhibit porous regions or Ð particularly with regard tobake-out Ð contain cavities; the inner surfaces must be as smooth aspossible (true surface = geometric surface) and thoroughly cleaned (anddegreased). Gas evolution varies greatly with the choice of material and thesurface condition.
Useful data are collected in Table X (Section 9). The gasevolution can be determined experimentally only from case to case by thepressure-rise method: the system is evacuated as thoroughly as possible,and finally the pump and the chamber are isolated by a valve. Now thetime is measured for the pressure within the chamber (volume V) to rise bya certain amount, for example, a power of 10. The gas quantity Q thatarises per unit time is calculated from:Q=∆p · Vt(2.37)pSeff = V · `n V = V · `n KttpAt a backing pressure of pV = 2 · 10-3 mbar ÒcompressionÓ K is in ourexample:K=2 ⋅10 – 3= 2001⋅10 – 5In order to attain an ultimate pressure of 1 · 10-5 mbar within 5 minutesafter starting to pump with the diffusion pump an effective pumping speedofSeff =500`· 2.3 · log 200 ≈ 9 s5 · 60is required. This is much less compared to the effective pumping speedneeded to maintain the ultimate pressure.
Pumpdown time and ultimatevacuum in the high vacuum and ultrahigh vacuum ranges depends mostlyon the gas evolution rate and the leak rates. The underlying mathematicalrules can not be covered here. For these please refer to books specializingon that topic.(Æp = measured pressure rise )The gas quantity Q consists of the sum of all the gas evolution and allleaks possibly present. Whether it is from gas evolution or leakage may bedetermined by the following method:2.3.1.3The gas quantity arising from gas evolution must become smaller with time,the quantity of gas entering the system from leakage remains constant withtime.
Experimentally, this distinction is not always easily made, since itoften takes a considerable length of time Ð with pure gas evolution Ð beforethe measured pressure-time curve approaches a constant (or almost aconstant) final value; thus the beginning of this curve follows a straight linefor long times and so simulates leakage (see Section 5, Leaks and LeakDetection).In the rough vacuum region, the volume of the vessel is decisive for thetime involved in the pumping process.
In the high and ultrahigh vacuumregions, however, the gas evolution from the walls plays a significant role.In the medium vacuum region, the pumping process is influenced by bothquantities. Moreover, in the medium vacuum region, particularly with rotarypumps, the ultimate pressure pend attainable is no longer negligible. If thequantity of gas entering the chamber is known to be at a rate Q (in millibarsliter per second) from gas evolution from the walls and leakage, thedifferential equation (2.32) for the pumping process becomesEvacuation of a chamber in the mediumvacuum regionIf the gas evolution Q and the required pressure pend are known, it is easyto determine the necessary effective pumping speed:Seff =Qpend(2.38)dp=−dtS eff p − pend −QV(2.39)Integration of this equation leads toExample: A vacuum chamber of 500 l may have a total surface area(including all systems) of about 5 m2.
A steady gas evolution of2 · 10-4 mbar · l/s is assumed per m2 of surface area. This is a level whichis to be expected when valves or rotary feedthroughs, for example areconnected to the vacuum chamber. In order to maintain in the system apressure of 1 · 10-5 mbar, the pump must have a pumping speed ofSeff =5 · 2 ·10 – 4 mbar · `/ s= 100 ` / s1·10 – 5 mbarA pumping speed of 100 l/s alone is required to continuously pump awaythe quantity of gas flowing in through the leaks or evolving from thechamber walls. Here the evacuation process is similar to the examplesgiven in Sections 2.3.1.1.
However, in the case of a diffusion pump thepumping process does not begin at atmospheric pressure but at thep − p oend − Q / SeffVt=`nSp− p − Q/Seffeff(2.40)end wherep0 is the pressure at the beginning of the pumping processp is the desired pressureIn contrast to equation 2.33b this equation does not permit a definitesolution for Seff, therefore, the effective pumping speed for a known gasevolution cannot be determined from the time Ð pressure curve withoutfurther information.In practice, therefore, the following method will determine a pump withsufficiently high pumping speed:68HomeVacuum generationa) The pumping speed is calculated from equation 2.34 as a result of thevolume of the chamber without gas evolution and the desired pumpdown time.b The quotient of the gas evolution rate and this pumping speed is found.This quotient must be smaller than the required pressure; for safety, itmust be about ten times lower.
If this condition is not fulfilled, a pumpwith correspondingly higher pumping speed must be chosen.2.3.2 Determination of a suitable backingpumpThe gas or vapor quantity transported through a high vacuum pump mustalso be handled by the backing pump. Moreover, in the operation of thehigh vacuum pump (diffusion pump, turbomolecular pump), the maximumpermissible backing pressure must never, even for a short time, beexceeded. If Q is the effective quantity of gas or vapor, which is pumped bythe high vacuum pump with an effective pumping speed Seff at an inletpressure pA, this gas quantity must certainly be transported by the backingpump at a pumping speed of SV at the backing pressure pV. For theeffective throughput Q, the continuity equation applies:Q = pA · Seff = pv · SV(2.41)The required pumping speed of the backing pump is calculated from:pSV = A · SeffpV(2.41a)Example: In the case of a diffusion pump having a pumping speed of400 l/s the effective pumping speed is 50 % of the value stated in thecatalog when using a shell baffle.
The max. permissible backing pressure is2 · 10-1 mbar. The pumping speed required as a minimum for the backingpump 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 highvacuum 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 mustamount to at leastSV =1·10 – 2· 50 = 2.5 `/s = 9 m 3/ h2 ·10 – 1At an intake pressure of pA = 1 á 10-3 mbar the pump has already reachedits nominal pumping speed of 400 l/s; the effective pumping speed is nowSeff = 200 l/s; thus the required pumping speed for the backing pumpamounts to1·10 – 3SV =· 200 = 1`/s = 3.
6 m 3/h2 ·10 – 1If the high vacuum pump is to be used for pumping of vapors between 10-3and 10-2 mbar, then a backing pump offering a nominal pumping speed of12 m3/h must be used, which in any case must have a pumping speed of9 m3/h at a pressure of 2 · 10-1 mbar. If no vapors are to be pumped, asingle-stage rotary vane pump operated without gas ballast will do in mostcases.
If (even slight) components of vapor are also to be pumped, oneshould in any case use a two-stage gas ballast pump as the backing pumpwhich offers Ð also with gas ballast Ð the required pumping speed at2 · 10-1 mbar.If the high vacuum pump is only to be used at intake pressures below10-3 mbar, a smaller backing pump will do; in the case of the example giventhis will be a pump offering a pumping speed of 6 m3/h. If the continuousintake pressures are even lower, below 10-4 mbar, for example, the requiredpumping speed for the backing pump can be calculated from equation2.41a as:SV =1·10 – 4· 200 = 0.1 `/s = 0. 36 m 3/h2 ·10 – 1Theoretically in this case a smaller backing pump having a pumping speedof about 1 m3/h could be used.
But in practice a larger backing pumpshould be installed because, especially when starting up a vacuum system,large amounts of gas may occur for brief periods. Operation of the highvacuum pump is endangered if the quantities of gas can not be pumpedaway immediately by the backing pump. If one works permanently at verylow inlet pressures, the installation of a ballast volume (backing-line vesselor surge vessel) between the high vacuum pump and the backing pump isrecommended.
The backing pump then should be operated for short timesonly. The maximum admissible backing pressure, however, must never beexceeded.The size of the ballast volume depends on the total quantity of gas to bepumped per unit of time. If this rate is very low, the rule of thumb indicatesthat 0.5 l of ballast volume allows 1 min of pumping time with the backingpump isolated.For finding the most adequate size of backing pump, a graphical methodmay be used in many cases.
In this case the starting point is the pumpingspeed characteristic of the pumps according to equation 2.41.The pumping speed characteristic of a pump is easily derived from themeasured pumping speed (volume flow rate) characteristic of the pump asshown for a 6000 l/s diffusion pump (see curve S in Fig.
2.76). To arrive atthe throughput characteristic (curve Q in Fig. 2.76), one must multiply eachordinate value of S by its corresponding pA value and plotted against thisvalue. If it is assumed that the inlet pressure of the diffusion pump does notexceed 10-2 mbar, the maximum throughput is 9.5 mbar á l/sHence, the size of the backing pump must be such that this throughput canbe handled by the pump at an intake pressure (of the backing pump) that isequal to or preferably lower than the maximum permissible backingpressure of the diffusion pump; that is, 4 · 10-1 mbar for the 6000 l/sdiffusion pump.After accounting for the pumping speed characteristics of commerciallyavailable two-stage rotary plunger pumps, the throughput characteristic foreach pump is calculated in a manner similar to that used to find the Q curvefor the diffusion pump in Fig. 2.76 a.
The result is the group of Q curvesnumbered 1 Ð 4 in Fig. 2.76 b, whereby four 2-stage rotary-plunger pumpswere considered, whose nominal speeds were 200, 100, 50, and 25 m3/h,respectively. The critical backing pressure of the 6000 l/s diffusion pump ismarked as V.B. (p = 4 · 10-1 mbar). Now the maximum throughputQ = 9.5 mbar á l/s is shown as horizontal line a. This line intersects the fourthroughput curves. Counting from right to left, the first point of intersectionthat corresponds to an intake pressure below the critical backing pressure69HomeQ [mbar á l á sÐ1]Throughput Q [mbar á l á sÐ1]Vacuum generationIntake pressure pa [mbar]a) Pumping speed characteristic of a 6000 l/s diffusion pumpb) Series of throughput curves for two-stage rotaryplunger pumps (V.B. = Critical forevacuum pressure)Fig.
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