# 2.8.1.1 Turbomolecular pump operating principle

The pumping effect of an arrangement consisting of rotor and stator blades is based upon the transfer of impulses from the rapidly rotating blades to the gas molecules being pumped. Molecules that collide with the blades are adsorbed there and leave the blades again after a certain length of time. In this process, blade speed is added to the thermal molecular speed. To ensure that the speed component that is transferred by the blades is not lost due to collisions with other molecules, molecular flow must prevail in the pump, i.e. the mean free path length must be greater than the blade spacing.

Figure 2.17: Operating principle of a turbomolecular pump

In the case of kinetic pumps, a counter-pressure occurs when pumping gas; this causes a backflow. The pumping speed is denoted by S0. The volume flow rate decreases as pressure increases and reaches a value of 0 at the maximum compression ratio K0.

## Compression ratio

The compression ratio, which is denoted K0, can be estimated according to Gaede's considerations [9]. The following applies for visually dense blade structure (Figure 2.17).

#### Formula 2-9:

Turbopump K0

The geometric ratios are taken from Figure 2.17. The factor g is between 1 and 3 [10]. From the equation, it is evident that K0 increases exponentially with blade velocity v as well as with √M because

.

Consequently, the compression ratio for nitrogen, for example, is significantly higher than for hydrogen.

## Pumping speed

Pumping speed S0 is proportional to the inlet area A and the mean circumferential velocity of the blades v, i.e. rotational speed [9]. Taking the blade angle α into account produces:

#### Formula 2-10:

Turbopump pumping speed

Taking the entry conductivity of the flange into account, as well as the optimal blade angle of 45°, produces the approximate effective pumping speed Seff of a turbopump for heavy gases (molecular weight > 20) in accordance with the following formula:

#### Formula 2-11:

Turbopump Seff

Dividing the effective pumping speed by the bladed entry surface of the uppermost disk and taking the area blocked by the blade thickness into consideration with factor df ≈ 0.9 provides the specific pumping speed of a turbopump for nitrogen, for example (curve in Figure 2.18):

#### Formula 2-12:

Specific pumping speed

In Figure 2.18, the specific pumping speed df = 1 in l / (s · cm2) is plotted on the ordinate and the mean blade speed on the abscissa v = π · f · (Ra + Ri ). Moving up vertically from this point, the point of intersection with the curve shows the pump's maximum specific pumping speed SA. Multiplying this value by the bladed surface area of the inlet disk: A = (Ra2 - Ri2) · π, yields the pumping speed of the pumps and enables it to be compared with the catalog information.

The points plotted in Figure 2.18 are determined by Pfeiffer Vacuum on the basis of the measured values of the indicated pumps. Points that are far above the curve are not realistic.

Figure 2.18: Specific turbopump pumping speeds

Figure 2.19: Pumping speed as a function of molecular weight

The pumping speeds (l / s) thus determined still tell nothing about the values for light gases, e.g. for hydrogen. Pump stages having differing blade angles are normally used in a turbopump to optimize the maximum pumping speed for hydrogen. This produces pumps with sufficient compression ratios for both hydrogen (approximately 1,000) and nitrogen, which should be 109 due to the high partial pressure in the air. In the case of pure turbomolecular pumps, backing-vacuum pressures of approximately 10-2 mbar are required due to their molecular flow.

Figure 2.20: Pumping speed as a function of inlet pressure

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