Fundamentals of Vacuum Technology (1248463), страница 11
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In these cases a higher amount of water vapor partial pressure pwcan be pumped as shown in the diagram. The figures for pW,0 given in thecatalogue therefore refer to the lower limit and are on the safe side.pW [mbar]pL [mbar]2.1.3 Dry compressing rotarydisplacement pumps2.1.3.1Roots pumpsThe design principle of the Roots pumps was already invented in 1848 byIsaiah Davies, but it was 20 years later before it was implemented inpractice by the Americans Francis and Philander Roots. Initially suchpumps were used as blowers for combustion motors. Later, by inverting thedrive arrangement, the principle was employed in gas meters. Only since1954 has this principle been employed in vacuum engineering.
Rootspumps are used in pump combinations together with backing pumps (rotaryvane- and rotary plunger pumps) and extend their operating range well intothe medium vacuum range. With two stage Roots pumps this extends intothe high vacuum range.
The operating principle of Roots pumps permits theassembly of units having very high pumping speeds (over 100,000 m3/h)which often are more economical to operate than steam ejector pumpsrunning in the same operating range.A Roots vacuum pump (see Fig. 2.17) is a rotary positive-displacement typeof pump where two symmetrically-shaped impellers rotate inside the pumpcasing past each other in close proximity.
The two rotors have a cross1Temperature of the pump22Fig. 2.16 Partial pressure pW of water vapor that can be pumped with the gas ballast valveopen without condensation in the pump, as a function of the pump temperature forvarious partial pressures pL of air. The lowest curve corresponds to the water vaporAccording to equation 2.4 an increase in the gas ballast B would result inan increased water vapor tolerance pW,0.
In practice, an increase in B,especially in the case of single-stage gas ballast pumps is restricted by thefact that the attainable ultimate vacuum for a gas ballast pump operatedwith the gas ballast valve open becomes worse as the gas ballast Bincreases. Similar considerations also apply to the general equation 2.3 forthe vapor tolerance pvapor.At the beginning of a pump down process, the gas ballast pump shouldalways be operated with the gas ballast valve open.
In almost all cases athin layer of water will be present on the wall of a vessel, which onlyevaporates gradually. In order to attain low ultimate pressures the gasballast valve should only be closed after the vapor has been pumped out.LEYBOLD pumps generally offer a water vapor tolerance of between 33and 66 mbar. Two-stage pumps may offer other levels of water vaportolerance corresponding to the compression ratio between their stages Ðprovided they have pumping chamber of different sizes.Other gases as ballastGenerally atmospheric air is used as the gas ballast medium. In specialcases, when pumping explosive or toxic gases, for example, otherpermanent gases like noble gases or nitrogen, may be used(see Section 8.3.1.3).3541 Intake flange2 Rotors3 Chamber4 Exhaust flange5 CasingFig.
2.17 Schematic cross section of a Roots pumpsection resembling approximately the shape of a figure 8 and aresynchronized by a toothed gear. The clearance between the rotors and thecasing wall as well as between the rotors themselves amounts only to a fewtenths of a millimeter. For this reason Roots pumps may be operated athigh speeds without mechanical wear. In contrast to rotary vane and rotaryplunger pumps, Roots pumps are not oil sealed, so that the internal leakageof dry compressing pumps by design results in the fact that compressionratios only in the range 10 Ð 100 can be attained. The internal leakage ofRoots pumps, and also other dry compressing pumps for that matter, ismainly based on the fact that owing to the operating principle certainsurface areas of the pump chamber are assigned to the intake side and thecompression side of the pump in alternating fashion.
During thecompression phase these surface areas (rotors and casing) are loaded withgas (boundary layer); during the suction phase this gas is released. Thethickness of the traveling gas layer depends on the clearance between thetwo rotors and between the rotors and the casing wall. Due to the relativelycomplex thermal conditions within the Roots pump it is not possible to base27HomeVacuum generationoneÕs consideration on the cold state. The smallest clearances and thus thelowest back flows are attained at operating pressures in the region of1 mbar.
Subsequently it is possible to attain in this region the highestcompression ratios, but this pressure range is also most critical in view ofcontacts between the rotors and the casing.Characteristic quantities of roots pumpsThe quantity of gas Qeff effectively pumped by a Roots pump is calculatedfrom the theoretically pumped quantity of gas Qth and the internal leakageQiR (as the quantity of gas which is lost) as:Qeff = Qth Ð QiR(2.5)The following applies to the theoretically pumped quantity of gas:Qth = pa · Sth(2.6)where pa is the intake pressure and Sth is the theoretical pumping speed.This in turn is the product of the pumping volume VS and the speed n:Sth = n · VS(2.7)Similarly the internal leakage QiR is calculated as:QiR = n · ViR(2.8)where pV is the forevacuum pressure (pressure on the forevacuum side)and SiR is a (notional) ÒreflowÓ pumping speed withSiR = n · ViR(2.10)By using equations 2.5, 2.6, 2.7 and 2.8 one obtainsη = 1−pV SiR·pa Sth(2.11)SiRSth(2.11a)Maximum compression is attained at zero throughput (see PNEUROP andDIN 28 426, Part 2).
It is designated as k0:k0 = (Sth) =SiR η 0(2.12)k0 is a characteristic quantity for the Roots pump which usually is stated asa function of the forevacuum pressure pV (see Fig. 2.18). k0 also depends(slightly) on the type of gas.For the efficiency of the Roots pump, the generally valid equation applies:η = 1− kko(2.14)From thisk=SpV= η · thpaSVk = η · kth(2.15)(2.16)Equation (2.16) implies that the compression k attainable with a Rootspump must always be less than the grading kth between Roots pump andbacking pump since volumetric efficiency is always < 1. When combiningequations (2.13) and (2.16) one obtains for the efficiency the well knownexpressionη=When designating the compression pv/pa as k one obtainsη = 1− kSV · pV = Seff · pa = η · Sth · paThe ratio Sth/SV (theoretical pumping speed of the Roots pump / pumpingspeed of the backing pump) is termed the gradation kth.
From (2.15) oneobtainsVolumetric efficiency of a Roots pumps is given byQ effQ thNormally a Roots pump will be operated in connection with a downstreamrough vacuum pump having a nominal pumping speed SV. The continuityequation gives:(2.9)i.e. the product of speed n and internal leakage volume ViR.η=Fig. 2.18 Maximum compression k0 of the Roots pump RUVAC WA 2001 as a function of forevacuum pressure pVk0ko + k th(2.17)The characteristic quantities to be found in equation 2.17 are only for thecombination of the Roots pump and the backing pump, namely maximumcompression k0 of the Roots pump and gradation kth between Roots pumpand backing pump.With the aid of the above equations the pumping speed curve of a givencombination of Roots pump and backing pump may be calculated.
For thisthe following must be known:a) the theoretical pumping speed of the Roots pump: Sthb) the max. compression as a function of the forevacuum pressure: k0 (pV)c) the pumping speed characteristic of the backing pump SV (pV)(2.13)The way in which the calculation is carried out can be seen in Table 2.3giving the data for the combination of a Roots pump RUVAC WA 2001 /E 250 (single-stage rotary plunger pump, operated without gas ballast). In28HomeVacuum generationthis the following is taken for Sth:The power losses summarized in NV are Ð as shown by experience Ðapproximately proportional to Sth, i.e.:Sth = 2050 Ð 2.5 % = 2000 m3/hThe method outlined above may also be applied to arrangements whichconsist of a rotary pump as the backing pump and several Roots pumpsconnected in series, for example.
Initially one determines Ð in line with aniteration method Ð the pumping characteristic of the backing pump plus thefirst Roots pump and then considers this combination as the backing pumpfor the second Roots pump and so on. Of course it is required that thetheoretical pumping speed of all pumps of the arrangement be known andthat the compression at zero throughput k0 as a function of the backingpressure is also known.
As already stated, it depends on the vacuumprocess which grading will be most suitable. It may be an advantage whenbacking pump and Roots pump both have the same pumping speed in therough vacuum range.(2.20)Depending on the type of pump and its design the value of the constantranges between 0.5 and 2 Wh / m3 .The total power is thus:Ntot = Sth (pv Ð pa + const.)The corresponding numerical value equation which is useful for calculationsis:Ntot = Sth (pv Ð pa + const.) · 3 á 10-2 Watt(2.21)with pv, pa in mbar, Sth in m3 / h and the constant Òconst.Ó being between18 and 72 mbar.Power requirement of a roots pumpCompression in a Roots pump is performed by way of externalcompression and is termed as isochoric compression.
Experience showsthat the following equation holds approximately:Ncompression = Sth (pv Ð pa)∑ Nv = const · Sth(2.18)In order to determine the total power (so-called shaft output) of the pump,mechanical power losses NV (for example in the bearing seals) must beconsidered:Ntot = Ncompression + ∑ NV(2.19)ForevacuumpressurePvPumping speedSv of theE 250kth = Sth / Sv= 2001/Svk0 (pv) ofthe RUVACWA 2001η = k0 / k0+kth(Volumetric.efficiency)Seff = η Sth(equation 2.14)1002508.012.50.611.22021402508.0180.691.3807.2102508.0330.81.6001.652508.0420.841.6800.7512508.0410.841.6800.155 á 10Ð12209.1350.791.5807 á 10Ð21 á 10Ð112016.6230.61.2001 á 10Ð24 á 10Ð23067180.214203 á 10Ð3↓↓The values taken from the two right-hand columns give point by point the pumping speed curve for thecombination WA 2001/E250 (see Fig. 2.19, topmost curve)Intake pressurepa = pv á Sv / SeffPumping speed characteristicfor the combinationWA 2001 / E250Table 2.329HomePumping speed SVacuum generationIntake pressure pa →Fig.
2.19 Pumping speed curves for different pump combinations with the corresponding backing pumpsLoad rating of a roots pumpThe amount of power drawn by the pump determines its temperature. If thetemperature increases over a certain level, determined by the maximumpermissible pressure difference pV Ð pa, the danger exists that the rotorsmay seize in the casing due to their thermal expansion.
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