Vacuum~volume 41/numbers 7-9/pages 2070 to 2072/1990 0042-207X/9053.00 + .00 Printed in Great Britain © 1990 Pergamon Press plc

The optimization design for turbo blades of a hybrid-type molecular pump J Y Tu, Y Zhu, X Z Wang and S J Pang, Beijing Laboratory of Vacuum Physics, Chinese Academy of Sciences; Department of Physics, Fudan University, Shanghai, PR China

It is important to make an optimized design of turbo blades by considering the correction factor on designing a hybrid molecular pump which combines a turbomolecular pump with a drag molecular pump. A computer program has been developed in which an optimized design of the pumping characteristics of turbo blades can be made automatically by an IBM PC/XT microcomputer after taking the correction of multi-stage turbo blades into account.

Introduction

Attention has been given to a new hybrid-type molecular pump which combines a turbomolecular pump with a drag molecular pump by many researchers I 4. The hybrid molecular pump can not only reach an ultrahigh vacuum of 10- t°mbar , but has a rather high pumping speed at an inlet pressure of 10 -2 mbar. The applications of hybrid pumps in some particular scientific and technical fields, such as ion etching, sputtering deposition and fusion technology, are growing increasingly. In order to obtain a high enough pumping speed with a hybrid pump, the present problem is that both maximum attainable pumping speed for the turbo stages, and a high enough compression ratio produced by the turbo stages are needed in order to ensure that gases are pumped by the drag pump. Thus it is necessary that a better design and more accurate calculation for the compres- sion ratio of turbo stages of hybrid-type molecular pumps be done.

A computation program for an IBM PC/XT microcomputer has been developed in which an optimized design of the pumping characteristics of turbo stages can be made automatically on taking the correction of multi-stage turbo blades into account 5.

Correction theory and computer program

It is well known that the theoretical pumping characteristics for a turbomolecular pump are calculated according to the trans- mission probability of the single stage, and can be calculated by the Monte Carlo method, the integral equation method or the transmission matrix method. Since the transmission matrix method 6, 7 has faster computing speed than the others it has been used in our computer program for optimized design. A data base of the transmission probability that molecules will pass directly through channels of single blade without collision with any blade surface and that those molecules will pass ultimately through single blade channels, has been set up to enable the computer to make the design automatically.

As pointed out in a previous paper 5, some of the molecules

may be reflected directly from one moving blade to another, or from one stationary blade to another, because some of the molecules transmitted through a blade will have passed directly through the blade channel without collision with either upper or lower blade surfaces. Thus the blade velocity ratio relative to these pumped molecules is equal to zero. It is clear that the practical pumping capability of the multi-stage blades in which the above phenomenon exists will be worse than the ideal theoretical result in which the blade velocity ratio of each stage blade relative to all molecules pumped was assummed not to equal zero. Therefore, when the result of single stage is used in the calculation of the pumping characteristics of multi-stage blades 8, 9, a correction of the transmission probability should be made by considering the above factor.

The corrected transmission probability of a single stage blade is calculated from the equations shown as follows:

M;~j+ 1) = Mj(j+ 1)(1 - - P j ) -]- M ° ( j + 1)Pj,

M~:+ l)s M ( j + l)j(l QJ) o (1) = - + M<j+ I)jQJ,

in which M c, M and M ° indicate the transmission probability of a single stage blade with the correction, without the correction and when the blade velocity ratio c is equal to zero. P j and Qj are the correction factors to the probability of transmission in forward and backward directions. Subscripts J (J = 0, I , . . . , J ) a n d j ( j = 1, 2 . . . . . j , j + 1) represent the number of blades and regions between the blades, respectively.

A computer program compiled in the BASIC language has been developed in our laboratory's microcomputer (IBM PC/ XT) for the optimized design of turbo blades of hybrid molecular pumps. A flowchart of the program is given in Figure 1. In Figure 1 So is the spacing-chord ratio of a blade, and z is the blade angle. The pumping speed (in I s - t ) may be calculated from:

S = 62.31 . A • Wmax/(m) 1/2 (2)

in which A is the effective pumping area and Wm,x is the maximum H o coefficient.

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J Y Tu et al: Molecular pump: optimized turbo blade design

Data input : Rotating speed n. Gas mass m Outer and inner diameter of disc D1 a D2 Desired compression rat io K d - .9 Desired pumping speed Sd = ? Minimum number of stages N - ?

-T I The computer selects automaticaLLy blade ]

parameters So, a and their arrangements.

CaLcuLation of compression rat io K and pumping speed S on considering correct ion fac tors .

1 No / If K :>K d and S>S d 9 / : /

Yes

I s, K, So,~ and form of blade arrangement I wiLL be stored in computer. I

Hove aLL possible arrangements been considered ?

Yes

Worker begins a dialogue with computer to select several bet ter r esu l t s , inc luding arrangements and pumping character is t ics~ from those which satisfy the design demands.

No / Is there any satisfactory result ? / /

I Yes

I Print results I

Figure 1. Flowchart of the optimization program.

/

Results and discussion

It can be found from the present results that there exist large differences in the selection of blade parameters between those with and without the correction. Some discussion for selecting blade parameters follows.

(1) The larger and spacing-chord ratio S O of a blade (provided So > 1.5) the more serious the effect on the pumping character- istics in multi-stage turbo blades. If one wants to increase the H o coefficient and guarantee a certain compression ratio, it will be better to enlarge the blade angle ~t than to increase the

Table 1. Pumping characteristics of six stage blades

c = 0.4 Without correction With correction S o ¢X ° Kma x Wmax Kmax Wmax

1.5 35 16 0.403 7.5 0.322 1.0 40 27 0.383 15 0.326

Table 2. Pumping characteristics of six stage blades

c = 0.4 Without correction With correction S o ~=" Kma x Wmax Kma,, Wma,,

1.0 10 192 0.132 136 0.126 0.5 20 182 0.139 157 0.136

spacing-chord ratio So. Table 1 shows an example of pumping characteristics of six stage blades including three moving and stationary blades. (2) The effect on the pumping performance in multi-stage turbo blades is less when So = 0.5. If one wants to increase the compression ratio and guarantee a certain Ho coefficient, it will be better to decrease the spacing-chord ratio, So than to reduce the blade angle ~t. Table 2 is another example. (3) Table 3 shows several arrangements of multi-stage turbo blades. It can be seen from Table 4 that the H 0 coefficient without the correction in scheme A-I is larger than in A-2 and the compression correction in scheme A-1 is larger than in A-2 and the compression ratio without the correction in scheme B-1 is higher than in B-2, but those performance targets with the correction in scheme A-2 and B-2 are better than in A-I and B-l , respectively. Schemes C-1 and C-2 are selected from several thousand possibilities in which the demands of the compression ratio and the Ho coefficient for different gas masses (i.e. the different blade velocity ratio) have been simul- taneously satisfied. However, there will be other optimized arrangements when the design targets, the blade velocity ratio and the number of stages are changed.

In conclusion, it is most important in optimizing the design of turbo blades that one consider the correction factors when one wants to design a hybrid molecular pump by combining a turbomolecular pump with a drag molecular pump. This is so

Table 3. The arrangement of turbo stages

No A-I A-2 B-I B-2 C-I C-2 So ~" So ~" So ~ ° So ~ ° So • ° So • °

1 1.5 30 1.0 40 1.0 40 1.0 40 1.5 40 1.0 40 2 1.5 30 1.0 40 1.0 40 1.0 40 1.5 40 1.0 40 3 1.5 30 1.0 40 1.0 20 1.0 20 1.0 30 1.0 40 4 1.5 30 1.0 40 1.0 20 1.0 20 1.0 30 1.0 40 5 1.0 30 1.0 30 1.0 20 1.0 20 1.0 30 1.0 30 6 1.0 30 1.0 30 1.0 20 1.0 20 1.0 20 1.0 30 7 1.0 20 1.0 20 1.0 10 0.5 20 1.0 20 1.0 20 8 1.0 20 1.0 20 1.0 10 0.5 20 1.0 20 1.0 20 9 1.0 20 1.0 20 1.0 10 0.5 20 0.5 20 0.5 20

10 1.0 20 1.0 20 1.0 10 0.5 20 0.5 20 0.5 20 11 0.5 20 0.5 20 12 0.5 20 0.5 20

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d Y Tu et al: Molecular pump: optimized turbo blade design

~ b l e 4 . ~ m p i n g c h a r a c t e r i s t i c s o f m u l t i - s t a ~ b l a d e s

c = 0 . 4 A-I A-2 B-I B-2 C-1 C-2

I Kma x 586 740 2171 2100 6269 Wma x 0.3813 0.3767 0.3197 0.3200 0.3731

I1 Kma x 186 327 919 1005 2271 Wmax 0.3013 0.3088 0.2690 0.2703 0.2954

c = 0.2 I

II

5126 0.3740

1889 0.3139

Kma x 25.0 28.5 48.9 48.5 84.0 76.5 Wma x 0.1937 0.1939 0.1425 0.1438 0.1679 0.1788

Kmax 14.0 16.7 31.6 33.3 50.3 45.7 Wma x 0.1492 0.1578 0.1184 0.1207 0.1328 0.1435

Note: (I) without the correction, (II) with the correction.

because it is necessary to find the op t imum coefficient Ho, while ensuring a high enough compression rat io for a reasonable match of turbo stages to drag stages.

References

t L Maurice, Japan J Appl Phys, Suppl, 2, 17 (1974). 2 K R Shoulders, US Patent, No 3969039 (1976).

3 j G Chu, PhD Thesis, Fudan University (1985). 4 N H Yang, L G Yu, S J Pang and Y Zhu, J Vac Sci Technol, A5(7/8), 2594 (1987). 5j y Tu and N H Yang, Vacuum, 37, 831 (1987). 6 W Yu, J Scient Instrum, 42, 867 (1968). 7j y TR and N H Yang, Vacuum (China), 4, 2 (1986). s T Sawada, M Suzuki and O Tangiguchi, Symp Japan Mech Eng Soc, 36, 5 (1970). 9 j y Tu and N H Yang, Vacuum, 38, 13 (1988).

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