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How does a Roots pump work?

The design principle of the Roots pumps was already invented in 1848 by Isaiah Davies, but it was 20 years later before it was implemented in practice by the Americans Francis and Philander Roots. Initially such pumps were used as blowers for combustion motors. Later, by inverting the drive arrangement, the principle was employed in gas meters. Only since 1954 has this principle been employed in vacuum engineering. Roots pumps are used in pump combinations together with backing pumps (rotary vane or dry pumps) and extend their operating range well into the medium vacuum range. With two stage Roots pumps this extends into the high vacuum range. The operating principle of Roots pumps permits the assembly of units having very high pumping speeds (over 100,000 m3/h) which often are more economical to operate than steam ejector pumps running in the same operating range.

Operating principle of a Roots pump

A Roots vacuum pump (see Fig. 2.17) is a rotary positive-displacement type of pump where two symmetrically-shaped impellers rotate inside the pump casing past each other in close proximity. The two rotors have a cross section resembling approximately the shape of a figure 8 and are synchronized by a toothed gear. The clearance between the rotors and the casing wall as well as between the rotors themselves amounts only to a few tenths of a millimeter. For this reason, Roots pumps may be operated at high speeds without mechanical wear. In contrast to rotary vane and dry pumps, Roots pumps are not oil sealed, so that the internal leakage of dry compressing pumps by design results in the fact that compression ratios only in the range 10 – 100 can be attained. The internal leakage of Roots pumps, and also other dry compressing pumps for that matter, is mainly based on the fact that owing to the operating principle certain surface areas of the pump chamber are assigned to the intake side and the compression side of the pump in alternating fashion. During the compression phase these surface areas (rotors and casing) are loaded with gas (boundary layer); during the suction phase this gas is released. The thickness of the traveling gas layer depends on the clearance between the two rotors and between the rotors and the casing wall. Due to the relatively complex thermal conditions within the Roots pump it is not possible to base one’s consideration on the cold state. The smallest clearances and thus the lowest back flows are attained at operating pressures in the region of 1 mbar. Subsequently it is possible to attain in this region the highest compression ratios, but this pressure range is also most critical in view of contacts between the rotors and the casing. 

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Fig. 2.17 Schematic cross section of a Roots pump

  1. Intake flange
  2. Rotors
  3. Chamber
  4. Exhaust flange
  5. Casing

Check out the video below to see a pumping animation of a roots pump in action

RUVAC - The dry compressor roots principle

Characteristic quantities of roots pumps

The quantity of gas Qeff effectively pumped by a Roots pump is calculated from the theoretically pumped quantity of gas Qth and the internal leakage QiR (as the quantity of gas which is lost) as:

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The following applies to the theoretically pumped quantity of gas: 

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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: 

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Similarly the internal leakage QiR is calculated as: 

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where pV is the forevacuum pressure (pressure on the forevacuum side) and SiR is a  (notional) “reflow” pumping speed with 

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i.e. the product of speed n and internal leakage volume ViR

Volumetric efficiency of a Roots pumps is given by (2.10) 

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By using equations 2.5, 2.6, 2.7 and 2.8 one obtains (2.11)

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When designating the compression pv/pa as k one obtains 

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Maximum compression is attained at zero throughput (see PNEUROP and DIN 28 426, Part 2). It is designated as k0: (2.12)

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k0 is a characteristic quantity for the Roots pump which usually is stated as a function of the forevacuum pressure pV  (see Fig. 2.18). 
k0 also depends (slightly) on the type of gas. 

2.18 Maximum compression k0 of the Roots pump RUVAC WA 2001 as a function of fore vacuum pressure pv

For the efficiency of the Roots pump, the generally valid equation applies: (2.13) 

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Normally a Roots pump will be operated in connection with a downstream rough vacuum pump having a nominal pumping speed SV. The Continuity equation gives: (2.14) 

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From this (2.15) 

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The ratio Sth/SV (theoretical pumping speed of the Roots pump / pumping speed of the backing pump) is termed the gradation kth. From (2.15) one obtains (2.16) 

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Equation (2.16) implies that the compression k attainable with a Roots pump must always be less than the grading kth between Roots pump and backing pump since volumetric efficiency is always < 1. When combining equations (2.13) and (2.16) one obtains for the efficiency the well known expression (2.17) 

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The characteristic quantities to be found in equation 2.17 are only for the combination of the Roots pump and the backing pump, namely maximum compression k0 of the Roots pump and gradation kth between Roots pump and backing pump. 

With the aid of the above equations the pumping speed curve of a given combination of Roots pump and backing pump may be calculated. For this the following must be known: 

a) the theoretical pumping speed of the Roots pump: Sth 
b) the max. compression as a function of the fore vacuum pressure: k0 (pV
c) the pumping speed characteristic of the backing pump SV (pV

The way in which the calculation is carried out can be seen in Table 2.3 giving the data for the combination of a Roots pump RUVAC WA 2001 / E 250 (single-stage rotary plunger pump, operated without gas ballast). 

Table 2.3 The values taken from the two right-hand columns give point by point the pumping speed curve for the combination WA 2001/E250 (see Fig. 2.19, topmost curve)

In this the following is taken for Sth

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The method outlined above may also be applied to arrangements which consist of a rotary pump as the backing pump and several Roots pumps connected in series, for example. Initially one determines – in line with an iteration method – the pumping characteristic of the backing pump plus the first Roots pump and then considers this combination as the backing pump for the second Roots pump and so on. Of course, it is required that the theoretical pumping speed of all pumps of the arrangement be known and that the compression at zero throughput k0 as a function of the backing pressure is also known. As already stated, it depends on the vacuum process which grading will be most suitable. It may be an advantage when backing pump and Roots pump both have the same pumping speed in the rough vacuum range. 

Power requirement of a roots pump

Compression in a Roots pump is performed by way of external compression and is termed as isochoric compression. Experience shows that the following equation holds approximately: 

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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 be considered: (2.19) 

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The power losses summarized in NV are - as shown by experience - approximately proportional to Sth, i.e.: 

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Depending on the type of pump and its design the value of the constant ranges between 0.5 and 2 Wh / m3
The total power is thus: 

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The corresponding numerical value equation which is useful for calculations is: 

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with pv, pa in mbar, Sth in m3 / h and the constant “const.” being between 18 and 72 mbar.  

Load rating of a roots pump 

The amount of power drawn by the pump determines its temperature. If the temperature increases over a certain level, determined by the maximum permissible pressure difference pV – pa, the danger exists that the rotors may seize in the casing due to their thermal expansion. The maximum permissible pressure difference Δpmax is influenced by the following factors: forevacuum or compression pressure pV, pumping speed of the backing pump SV, speed of the Roots pump n, gradation kth and the adiabatic exponent κ of the pumped gas. Δpmax increases when pV and SV increase and decreases when n and kth increase. Thus the maximum difference between forevacuum pressure and intake pressure, pV-pa must - during continuous operation - not exceed a certain value depending on the type of pump. Such values are in the range between 130 and 50 mbar. However, the maximum permissible pressure difference for continuous operation may be exceed for brief periods. In the case of special designs, which use gas cooling, for example, high pressure differences are also permissible during continuous operation.

Types of motors used with roots pumps

Standard flange-mounted motors are used as the drive. The shaft feedthroughs are sealed by two oil sealed radial shaft seals running on a wear resistant bushing in order to protect the drive shaft. Flange motors of any protection class, voltage or frequency may be used. 

Integral leak tightness of this version is < 10-4 mbar  · l  · s-1.  

In the case of better leak tightness requirements of < 10-5 mbar  · l  · s-1 the Roots pump is equipped with a canned motor. The rotor is seated in the vacuum on the drive shaft of the pump and is separated from the stator by a vacuum- tight non- magnetic tube. The stator coils are cooled by a fan having its own drive motor. Thus shaft seals which might be subject to wear are no longer required. The use of Roots pumps equipped with canned motors is especially recommended when pumping high purity-, toxic- or radioactive gases and vapors. 

Maintaining the allowed pressure difference

 In the case of standard Roots pumps, measures must be introduced to ensure that the maximum permissible pressure difference between intake and exhaust port due to design constraints is not exceeded. This is done either by a pressure switch, which cuts the Roots pump in and out depending on the intake pressure, or by using a pressure difference or overflow valve in the bypass of the Roots pumps (Fig. 2.20 and 2.21). The use of an overflow valve in the bypass of the Roots pump is the better and more reliable solution. The weight and spring loaded valve is set to the maximum permissible pressure difference of the particular pump. This ensures that the Roots pump is not overloaded and that it may be operated in any pressure range. In practice this means that the Roots pump can be switched on, together with the backing pump, at atmospheric pressure. In the process any pressure increases will not adversely affect combined operation, i.e. the Roots pump is not switched off in such circumstances. 

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Fig. 2.20 Cross section of a Roots pumps with bypass line

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Fig. 2.21 Vacuum diagram – Roots pump with integrated bypass line and backing pump

Pre-admission cooling 

In the case of Roots pumps with pre-admission cooling (Fig. 2.22), the compression process basically is the same as that of a normal Roots pump. Since greater pressure differences are allowed more installed power is needed, which at the given speed and the pressure difference between inlet and discharge port is directly proportional and is composed of the theoretical work done on compression and various power losses. The compression process ends normally after opening of the pumping chamber in the direction of the discharge port. At this moment warmed gas at higher pressure flows into the pumping chamber and compresses the transported volume of gas. This compression process is performed in advance in the case of pre-admission cooling. Before the rotor opens the pumping chamber in the direction of the discharge port, compressed and cooled gas flows into the pumping chamber via the pre-admission channel. Finally, the rotors eject the pumped medium via the discharge port. The cooled gas, which in the case of single- stage compression is taken from the atmosphere and admitted from the pre-admission cooler, and which in the case of multi-stage pump systems is taken from downstream gas coolers, performs a pre-compression and removes by “inner cooling” the heat of compression at the point of time it occurs. 

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Fig 2.22 Diagram of a Roots pump with pre-admission cooling

  1. Intake port 
  2. Discharge port 
  3. Gas cooler 
  4. Flow of cold gas
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