### 4.7.1 Design / Operating principle

The principle of operation of single-stage Roots pumps corresponds to the operating principle of multi-stage pumps as described in Chapter 4.5. In the Roots vacuum pump, two synchronously counter-rotating rotors (4) rotate contactlessly in a housing (Figure 4.16). The rotors have a figure-eight configuration and are separated from one another and from the stator by a narrow gap. Their operating principle is analogous to that of a gear pump having one two-tooth gear each that pumps the gas from the inlet port (3) to the outlet port (12). One shaft is driven by a motor (1). The other shaft is synchronized by means of a pair of gears (6) in the gear chamber. Lubrication is limited to the two bearing and gear chambers, which are sealed off from the suction chamber (8) by labyrinth seals (5) with compression rings. Because there is no friction in the suction chamber, a Roots vacuum pump can be operated at high rotation speeds (1,500 – 3,000 rpm ). The absence of reciprocating masses also affords trouble-free dynamic balancing, which means that Roots vacuum pumps operate extremely quietly in spite of their high speeds.

### Design

The rotor shaft bearings are arranged in the two side covers. They are designed as fixed bearings on one side and as movable (loose) bearings on the other to enable unequal thermal expansion between housing and rotor. The bearings are lubricated with oil that is displaced to the bearings and gears by splash disks. The driveshaft feedthrough to the outside on standard versions is sealed with radial shaft seal rings made of FPM that are immersed in sealing oil. To protect the shaft, the sealing rings run on a protective sleeve that can be replaced when worn. If a hermetic seal to the outside is required, the pump can also be driven by means of a permanent-magnet coupling with a can. This design affords leakage rates $Q_I$ of less than 10-6 Pa m3 s-1.

### Pump properties, heat-up

Since Roots pumps do not have internal compression or an outlet valve, when the suction chamber is opened its gas volume surges back into the suction chamber and must then be re-discharged against the outlet pressure. As a result of this effect, particularly in the presence of a high pressure differential between inlet and outlet, a high level of energy dissipation is generated, which results in significant heat-up of the pump at low gas flows that only transport low quantities of heat. The rotating Roots pistons are relatively difficult to cool compared to the housing, as they are practically vacuum-insulated. Consequently, they expand more than the housing. To prevent contact or seizure, the maximum possible pressure differential, and so also the dissipated energy, is limited by an overflow valve (7). It is connected to the inlet side and the pressure side of the pump-through channels. A weight-loaded valve plate opens when the maximum pressure differential is exceeded and allows a greater or lesser portion of the intake gas to flow back from the pressure side to the inlet side, depending on the throughput. Due to the limited pressure differential, standard Roots pumps cannot discharge against atmospheric pressure and require a backing pump. However Roots vacuum pumps with overflow valves can be switched on together with the backing pump even at atmospheric pressure, thus increasing their pumping speed right from the start. This shortens evacuation times.

Figure 4.16: Operating principle of a Roots pump

### Backing pumps

Single-stage or two-stage rotary vane pumps or external vane pumps are used as oil-lubricated backing pumps. Screw pumps or multi-stage Roots pumps can be used as dry backing pumps. Pump combinations such as these can be used for all applications with a high pumping speed in the low and medium vacuum range. Liquid ring pumps can also be used as backing pumps.

### Gas-circulation-cooled Roots pumps

To allow Roots vacuum pumps to work against atmospheric pressure, some models are gas-cooled and do not have overflow valves (Figure 4.17). In this case, the gas that flows from the outlet flange (6) through a cooler (7) is re-admitted into the middle of the suction chamber (4). This artificially generated gas flow cools the pump, enabling it to compress against atmospheric pressure. Gas entry is controlled by the Roots pistons, thus eliminating the need for any additional valves. There is no possibility of thermal overload, even when operating at ultimate pressure.

Figure 4.17: Operating principle of a gas-cooled Roots pump

Figure 4.17 shows a cross-section of a gas-circulation-cooled Roots vacuum pump. The direction of gas flow is vertical from top to bottom, enabling the liquid or solid particles entrained in the inlet stream to flow off downward. In phase I, the chamber (3) is opened by the rotation of the pistons (1) and (2). Gas flows into the chamber through the inlet flange (5) at pressure $p_1$. In phase II, the chamber (3) is sealed off against both the inlet flange and the pressure flange. The inlet opening (4) for the cooling gas is opened by the rotation of the pistons in phase III. The chamber (3) is filled to the outlet pressure $p_2$, and the gas is advanced toward the pressure flange. Initially, the suction volume does not change with the rotary movement of the Roots pistons. The gas is compressed by the inflowing cooling gas. The Roots piston now continues to rotate (phase IV), and this movement pushes the now compressed gas over the cooler (7) to the discharge side (Phase V) at pressure $p_2$.

Gas-cooled Roots pumps can be used in the inlet pressure range of 130 to 1,013 hPa. Because there is no lubricant in the suction chamber, they do not discharge any mist or contaminate the medium that is being pumped. Connecting two of these pumps in series enables the ultimate pressure to be reduced to 20 to 30 hPa. In combination with additional Roots vacuum pumps, the ultimate pressure can be reduced to the medium vacuum range.

### Pumping speed and compression ratio

The characteristic performance data of Roots pumps are the pumping speed and compression ratio. The theoretical pumping speed $S_{th}=S_0$ is the volume flow rate which the pump displaces without counterpressure. The compression ratio $K_0$ when operated without gas displacement (inlet flange closed) depends on the outlet pressure $p_2$. Pumping speeds range from 200 m3 · h-1 to several thousand m3 · h-1. Typical $K_0$ values are between 10 and 75.

Figure 4.18: No-load compression ratio for air for Roots pumps

The compression ratio is negatively impacted by two effects:

• By the backflow into the gaps between the piston and housing
• By the gas that is deposited by adsorbtion on the surfaces of the piston on the outlet side and re-desorbs after rotating toward the suction side.

In the case of outlet pressures of 10-2 to 1 hPa, molecular flow prevails in the seal gaps,which results in less backflow due to their low conductivities. However the volume of gas that is pumped back through adsorption, which is relatively high by comparison with the pumped gas volume, reduces the compression ratio.

$K_0$ is highest in the 1 to 10 hPa range, since molecular flow still prevails due to the low inlet pressure in the pump’s sealing gaps, and backflow is therefore low. Since gas transport through adsorption is not a function of pressure, it is less important than the pressure-proportional gas flow that is transported by the pumping speed.

At pressures in excess of 10 hPa, laminar flow occurs in the gaps and the conductivities of the gaps increase significantly, which results in declining compression ratios. This effect is particularly noticeable in gas-cooled Roots pumps that achieve a compression ratio of only approximately $K_0$ = 10.

The gap widths have a major influence on the compression ratio. Due to the different thermal expansion of the pistons and the housing, they must not, however, fall below certain minimum values in order to avoid rotor-stator-contact.