Scholarly article on topic 'Development and Uncertainty Analysis of an Automatic Testing System for Diffusion Pump Performance'

Development and Uncertainty Analysis of an Automatic Testing System for Diffusion Pump Performance Academic research paper on "Materials engineering"

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Abstract of research paper on Materials engineering, author of scientific article — S.W. Zhang, W.S. Liang, Z.J. Zhang

Abstract A newly developed automatic testing system used in laboratory for diffusion pump performance measurement is introduced in this paper. By using two optical fiber sensors to indicate the oil level in glass-buret and a needle valve driven by a stepper motor to regulate the pressure in the test dome, the system can automatically test the ultimate pressure and pumping speed of a diffusion pump in accordance with ISO 1608. The uncertainty analysis theory is applied to analyze pumping speed measurement results. Based on the test principle and system structure, it is studied how much influence each component and test step contributes to the final uncertainty. According to differential method, the mathematical model for systematic uncertainty transfer function is established. Finally, by case study, combined uncertainties of manual operation and automatic operation are compared with each other (6.11% and 5.87% respectively). The reasonableness and practicality of this newly developed automatic testing system is proved.

Academic research paper on topic "Development and Uncertainty Analysis of an Automatic Testing System for Diffusion Pump Performance"

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Physics Procedía 32 (2012) 255 - 264

Conference Title

Development and Uncertainty Analysis of an Automatic Testing System for Diffusion Pump Performance

S.W. Zhang*, W.S. Liang, Z.J. Zhang

School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China

Abstract

A newly developed automatic testing system used in laboratory for diffusion pump performance measurement is introduced in this paper. By using two optical fiber sensors to indicate the oil level in glass-buret and a needle valve driven by a stepper motor to regulate the pressure in the test dome, the system can automatically test the ultimate pressure and pumping speed of a diffusion pump in accordance with ISO 1608. The uncertainty analysis theory is applied to analyze pumping speed measurement results. Based on the test principle and system structure, it is studied how much influence each component and test step contributes to the final uncertainty. According to differential method, the mathematical model for systematic uncertainty transfer function is established. Finally, by case study, combined uncertainties of manual operation and automatic operation are compared with each other (6.11% and 5.87% respectively). The reasonableness and practicality of this newly developed automatic testing system is proved.

© 2012 Published by Elsevier B.V. Selection and/or peer review under responsibility of Chinese Vacuum Society (CVS). PACS: Type pacs here, separated by semicolons ;

Keywords: diffusion pump, performance measurement, pumping speed, uncertainty analysis

1. Introduction

The diffusion pump is one traditional kind of the high vacuum pumps, which is most commonly used and plays important role in the vacuum science and technology field. However, the measurement technique of performance characteristics of the diffusion pump has still been backward and difficult to automatize[1]. The reasons are as follow: The measuring processes are quite complex according to the international standard [2]. All measuring operations are the manual skill, it means that the testing operators must be specially trained and have to master the professional theory and testing craftsmanship. The precision of measuring results is poor and seriously affected by many artificial factors. As a consequence, it is very difficult for the manufacturers to measure the performance characteristics of the diffusion pumps by themselves. Therefore, most of diffusion pumps were not tested for their performance before leaving factory.

* Corresponding author. Tel.:+86-024-83679926; fax: +86-024-83679926. E-mail address:shwzhang@mail.neu.edu.cn.

1875-3892 © 2012 Published by Elsevier B.V. Selection and/or peer review under responsibility of Chinese Vacuum Society (CVS). doi:10.1016/j.phpro.2012.03.552

To solve this problem, a set of full-automatic testing system for the performance of diffusion pump was developed by the authors. The equipment can automatically perform the measuring performance characteristics of diffusion vacuum pumps according to relative international standards [3]. The equipment can meet the practical needs of manufacturers and promote the measurement technique of the diffusion pumps.

In the actual testing process, due to the influence of various uncertainties, there is an error between measured value and true value for the measurand. In order to assess the reliability of testing results of this newly developed system, we need to analyze the uncertainty of this testing system. the International Standardization Organization (ISO) drafted a "Evaluation of measurement data—Guide to the expression of uncertainty in measurement" (the GUM) to guide the specific analysis of uncertainty[4]. Uncertainty analysis has been widely applied to many fields, such as, vacuum science and technology[5], mechanical precision machining[6], engineering thermal physics[7], biomedical [8], demographic analysis in sociology [9]. Through uncertainty analysis, we can not only obtain the measurement precision of the measurand, but also get how much influence each input quantity contributes to the final uncertainty, accordingly, propose specific improvement opinions.

2. The structure and the characteristics of the testing equipment

The major structure of the automatic testing equipment was designed completely based on the international standard [2]. Its structural drawing is shown as Fig. 1, mainly including the test dome, the elevating device, the vacuum system, the gas throughput adjusting system, the gas throughput measuring system by gage glass tube, the pressure measuring system, the trolley, the electrical and control system, etc.

Comparing with the traditional manual test equipments, the characteristics and advancement of the automatic test equipment are as follow: The liquid level heights in gage glass tube are automatically detected by two optical fiber liquid level sensors instead of by the testing operators' naked eyes. The test time is recorded by the computer instead of the manual stopwatch. The gas throughput and pressure in the test dome are regulated with the needle adjusting valve driven by a stepper motor, instead of by manual turning along with naked eye observation of pressure meters.

8 9 10 11 12 1:! 14 1: 16

1- trolley; 2- oil sink; 3- transformer oil; 4-optical fiber liquid level sensor; 5- gage glass tube holder; 6- test valve; 7- glass buret; 8- gas inlet pipe; 9- needle adjusting valve; 10- elevating device; 11- stepper motor; 12- test dome; 13- charge valve; 14-ionization vacuum gauge; 15- thermal conductivity gauge; 16- by-pass valve; 17-corrugated pipe; 18- cone transition pipe; 19- gate valve; 20- backing valve; 21-diffusion vacuum pump; 22- break valve with charging; 23- sliding vane rotary vacuum pump.

Fig. 1 Diagram of the automatic testing equipment for diffusion pump performances

As shown in Fig.2, the whole testing system and measuring process are automatically controlled by a two-stage control system with upper PC and lower PLC. As a consequence, requirement for the professional theory and testing craftsmanship of the test operators is independent and depressed.

(Data shortage]) ( Data.....Display ^(Graphic drawing]^(Report printing)

t í t t

j^X PC/PPI

-{ RS-232^4,—C

Controller

24V Relay fl-

optical Fiber Sensor

(Liquid Le^ei^

-^{220V Relay ]j-

Stepper Motor Driver}

^Motor Driver)-Needle Waive

-f Ionization gauge

„/Thermal condul I -ctivity gauged

Diffusionpump^

w ^Sliding vane rotary fr vacuum pump \

»^►(Backing valve J

■^►(By-pass valve^ Break valve^^ ^^(Test valve ^

Fig.2 Control flow diagram of automatic testing system for diffusion pump performances

The control system contains two operation modes: manual operation and automatic operation. The purpose of manual operation mode is practical training for students in college and measurement staffs in enterprise. By operating the system personally, they can deeply understand the composition of vacuum system and the performance testing principle of vacuum pumps. While automatic operation mode is mainly serves he request of manufacturers and try to achieve automatic control to improve test efficiency and accuracy.

3. Basic analysis approach for the evaluation of uncertainty

Frequently, the result of an experiment will not be obtained directly. Rather, the measuraned Y depends upon a number of input quantitiesX1, X2 ,•••, XN according to the functional relationship f [10]:

Y - f (X15 X2 ' ' XN )

Let be the measured values of X1, X2 XN . Substitutingx1

in Eq. (1), it is possible to

obtain an estimation y of the measurand Y. The combined standard uncertainty associated to the evaluation of y can be calculated as the root-sum-squared combination of the single uncertainty associated to the evaluation of xx, x2 ,••• xN , if u (x), u (x2) ,••• u (xN) are independent and casual, so that:

Áy KE

N (f ^

\dxi y

where f /dxt is called sensitivity coefficient or propagation coefficient. And Eq. (2) is known as the general formula for the propagation of uncertainty.

Uncertainty analysis includes the following steps[10]: 1) Establish a mathematical model Eq. (1) to describe the

relationship between the measurand Y and input quantities X1, X2 , •••, measurand Y , denoted by y , from Eq (1) using input estimates x1, x2

XN ; 2) Calculate an estimate of the • • • xN for the values of the N quantities X1, X2,•••, XN 3) List the source of uncertainty and categorize them into different groups; 4) Calculate the individual uncertainties and corresponding sensitivity coefficients of various uncertainty sources; 5) Obtain the combined standard uncertainty from Eq. (2) using former calculated individual uncertainties and sensitivity coefficients; 6) Uncertainty analysis and evaluation.

4. Individual uncertainty analysis for pumping speed measurement

As testing the pumping speed of a diffusion pump is the basic and most significant function for the automatic testing system introduced in this paper, the uncertainty analysis of pumping speed measurement is carried out in the

flowing parts. In accordance with the uncertainty analysis steps given in Part 3, mathematical model of pumping speed is shown in the flowing equation:

h[pat -AY + pg(V0-2h0-AY-AY-h)]

Eq. (3) is derived in ISO 1608-1. The automatic testing system developed in this paper follows this formula as

4.1 Uncertainty sources

Actually, many elements from the components of testing system influence the reading of pumping speed, such as variations of test dome design[11], location of vacuum gauge[12]. But we do not consider the error from system structure; instead, focus on the error from the input quantities of the pumping speed calculation formula.

The sources of uncertainties in the testing system for pumping speed of diffusion pump can be divided into two groups: 1)Uncertainties resulting from the difference between actual environment temperature and the standard one, and uncertainty caused by temperature instability; 2) Systematic uncertainties resulting from the error propagation of the measured values of X1, X2 ,•••, XN .

Environment temperature will definitely affect the testing results. Because pumping speed measurement is a complex process with multi-input quantities and the impact to testing results from environment temperature comes up during each testing session, it is difficult to directly use a mathematical formula to illustrate the measurement error caused by environment temperature. In view of this, ISO 1608-1 clearly claim that the range of environment temperature during the testing process is 20 ± 5°C . The testing process described in this paper is carried out under 20 ± 1 °C; therefore, uncertainty caused by environment temperature is omitted in this paper.

Only systematic uncertainties caused by listed sources are considered in the following analysis, shown in Table 1.

Table 1 Description of systematic uncertainties sources

Uncertainty

Quantity descriptions

Unites

Pat AY

local atmospheric pressure (Pa)

volume increment of the oil in the glass buret after rising by 1 mm along plumb line (L/mm ) density of oil in the glass buret

the total volume trapped between the oil and the needle valve before the oil begins to move

oil-level rising height (from the surface of oil outside the glass-buret) before time recording

time-consuming of oil column in the buret after rising by a height of h oil-level net rising height in time t

the equilibrium pressure at a specified position in the test dome

(g/cm3) (L)

sources

4.2 Evaluation of individual uncertainties

Since the individual uncertainties are from different sources, the corresponding evaluation methods of uncertainties are various. Uncertainty quantities are divided into flowing three groups:

1. Quantities measured directly

Direct measurement are those physical quantities can be read directly through corresponding instruments. The equilibrium pressure at a specified position in the test dome p and local atmospheric pressure pat belong to this group, so we take p as an example to calculate its uncertainty u (p) .

The uncertainty from direct measurement includes two parts. Firstly, uncertainty arising from variations in repeated observations of the measurand under apparently identical conditions. This type of uncertainty is obtained through statistical analysis method, which is given by.

u (pX = s(p)/Vn Pa (4)

where s(p) is the experimental standard deviation, n is times of independent observation.

Secondly, uncertainties resulting from testing precision of the measurement device which can be taken from a manufacturer's specification, calibration certificate, handbook, or other source. When it is possible to assess only the upper and lower bounds of an error, a rectangular probability distribution should be assumed for the uncertainty associated with this error. Then, if Ap is the semi-range limit of testing accuracy of vacuum gauge and the assumed probability distribution is rectangular (k = V3 )[13], the standard uncertainty is given by

u (p )2 = Ap/k Pa (5)

The combined uncertainty u (p) for p is: u (p ) = >/ u2 (p )1 + u2 (p )2 Pa (6)

2. Quantities measured indirectly

This group contains four quantities p, t, h0, h, and they are obtained using simple indirectly method. Take p for example to show the evaluation process. The density of oil in the glass-buret p is measured through MassVolume method, with calculation formula:

p = (M - m )/V (7)

The combined uncertainty u (p) for p is given by:

2 / „ \2 / _ \ 2

u W'iemu (m) J +(i|„(M)) + u (V)) g/cm3 (8)

where u(m) , u(M) , u(V) are uncertainties of quantities measured directly and their calculation means are introduced before.

3. Calibrated quantities

Some physical quantities value can not be obtained by direct measurement, and they should be calibrated with some standard methods or rules. In this testing system, AV and V0 are both calibrated by classical liquid injection method, and the calibration error is given based on the value of the calibrated quantity and calibration environment.

Uncertainty from AV is caused by the error of glass-buret manufacturing craft. There is cylindrical error along the inner face of glass-buret, in this case, the inner volume of glass-buret of 1 mm height is discrepant. Because of this, we assign the total volume calibration error of glass-buret to every unit millimetre, which is shown by Eq. (9). Illustrated by latter analysis, the uncertainty of AV is not dominant, thus this assumption is reasonable.

u (AV )=S(AV} L/mm (9)

V ' H xV3

where S(AV) is the total volume calibration error of glass-buret, H is the height of glass-buret.

The uncertainty sources of V0 include three parts: volume calibration error of glass-buret, volume calibration error of vacuum tube and shape deformation of vacuum tube. V0 is composed of inner total volume V0' of glass-buret and inner volume V0" of vacuum tube between the top of glass-buret and the needle of needle valve. S(V0' )1

is the volume calibration error of glass-buret. S(V0" X is the volume calibration error of V0". As the vacuum tube is quite soft, its inner volume is quite susceptible to external factor, e.g. temperature, pressure. Especially, when the tube is bent and straight, it exists apparent volume difference. For these reasons, we find the difference of vacuum tube volume is 2% in bent and straight case and the error from shape deformation of vacuum tube is written as S(V0" )2 = V/ x 2%. The combined uncertainty u (V0) for V0 is given by:

u(V0) = .

s(V: x

sy )2 V3

5. Total uncertainty of this calibrator

From Eqs. (2) and (3), using the general formula for the combined uncertainty, it is possible to express the relative combined uncertainty of the pumping speed of diffusion pump as a function of the relative uncertainty in terms of pat, A V , p , V0, h0, h , t, p as follows:

Uc (s )

i ds u (pat )Y , f df u (AVf 2 ( ds u(p)^ 2 ( ds u (Vo )"ï

l^Pat s ^ [ôAV s j [ô^ s y Wo s )

ds u(ho)) (dsn(h)) (dsn(t)

ydho s

where expression of sensitivity coefficient df /dxi of every uncertainty u (xt ) is shown in Table 2. Table2 The sensitivity coefficients corresponding to the single sources of uncertainties

Uncertainty

Sensitivity coefficients

1 u (Pa, ) ds C>Pat AV ■ h Pt

2 u (AV ) ds pat ■h -pgh - 2Pëhho

dAV pt

3 u (P) N gh (V0 -AV ■ h - 2h0 AV ) pt

4 u(Vo) ds dVÔ" Pgh pt

5 u ( ho ) ds dho 2pghAV pt

6 u (h ) ds Pat, -AV + pg(Vo -2hoAV-2hAV)

7 u (t ) ds h [ Pat -AV + pg (V, -2ho AV -AV -h )]

dt pt2

8 u (p ) ds h [ Pat -AV + pg (Vo -2ho AV -AV -h )]

dp p 2t

6. Case study

Since, at different measurement pressure point, the pumping speeds of diffusion pump fluctuate seriously and the size of glass-buret is discrepant, the uncertainty of pumping speed is not the same. Take measurement pressure point p = 6.3 x10-3 Pa for example to show the calculate result of uncertainty.

In this case, we choose a glass-buret with inner diameter of 3.0mm , the calculated result of pumping speed is s = 1234.5L/s. Measured Value, uncertainty, sensitivity coefficients and relative uncertainty of every source are listed in Tables 3 and Fig. 4.

Using relative combined uncertainty formula Eq. (11), the relative combined uncertainty of pumping speed at the pressure of 6.3x10~3 Pa is 6.11%» As can be seen from the Fig.3, the contribution from each uncertainty source to the total combined uncertainty is different, and top three are uncertainty of the equilibrium pressure in the test dome (u (p) =5.78%), uncertainty of AV with 1.51% and uncertainty of liquid level raising time t (u (t) =1.06%). Therefore, during actual system design and value testing process, we should lower the measurement error from them in priority, especially the measurement precision of vacuum gauge.

Table 3 Calculation result of uncertainty analysis at the testing pressure point p = 6.3 x 10 3 Pa

Uncertainty sources Measured value Uncertainty value u (x ) Sensitivity ds/dx coefficients Relative uncertainty ds u ( x ) dx s

1 Pat 10076Pa 115.47 6.548 x10~3 0.0612%

2 AV 8.0 x10~6 L 2.31 x10-7 8.11 x 107 1.51%

3 P 0.839 g/ml 4.16 x10-3 685.02 0.23%

4 V 0.08708L 1.27 x10~3 6729.85 0.69%

5 h0 35mm 0.245 0.108 0.002%

6 t 27.15s 0.287 45.47 1.06%

7 h 140mm 0.245 8.76 0.17%

8 P 6.3 x10~3 Pa 3.64 X10"4 195953.10 5.78%

Sg 10E-1-J

<û ¡t=

^ 10E-3

f 10E-4

■è 10E-5

V0 AV h h0 Different uncertainty sources

Fig.3 The contribution from each uncertainty source to the combined uncertainty at the testing pressure point p = 6.3 x1Q 3Pa

Fig. 4 shows the uncertainty of different uncertainty sources (pat, A V , p , V0, h0, h, t, p) and total combined relative uncertainty at different measurement pressure points from 8.0 xlO-4 to 1.5 x10~'Pa. We can see obviously that the broken line of total combined uncertainty nearly overlaps with the one of pat, which proves that u (p) is the main contribution to the total combined uncertainty uc (s). Actually, the measurement precision of vacuum gauge used in this newly developed system is 10%, so we should choose vacuum gauges with better measurement precision. By observing each uncertainty broke line, though the uncertainties fluctuates from 8.0xlO-4 to 1.5 x10_1 Pa, they keep stable around a fix value.

Pumping speed of diffusin pump

Fig.4 An example of the uncertainty of different uncertainty sources ( pat, AV , p , V0 , h0, h , t, p ) and combined relative uncertainty at different measurement pressure points from 8.0x10 4 to 1.5 x 10 1 Pa.

7 Uncertainty comparison of manual operation with automation operation

The calculation case of uncertainty in preceding three parts is based on manual operation, while in automatic testing process, measurement method of three physical quantities (h , h0, t) have changed. Accordingly, the uncertainty value caused by these three sources is different.

During automatic testing process, the height of oil column in galss-buret is indicated by two optical fiber sensors. Before the test, adjust the vertical height of galss-buret to make the bottom scale line on galss-buret is flush with the level of oil in the oil sink. After that, adjust the height of two optical fiber sensors to make the height difference between lower optical fiber sensor and oil level is h0 , and the height difference between upper optical fiber sensor and lower optical fiber sensor is h . As a consequence, for all testing pressure points, the value of h0 and h are the same. The uncertainties from them are caused by installation error of optical fiber sensors in vertical direction which is 0.1mm.

The uncertainty u(h) from h is given by

u(h) = V2x= 8.16x10~2 mm (12)

For h0, we should also consider the error brought by operator's naked observation when adjust the height of galss-buret to make the bottom scale line on galss-buret is flush with the level of oil, and the error is Ah0. The uncertainty u (h0) from h0 is given by

i{h0 ) = ^(a HJ43 )2 )2

During automatic testing process, the liquid level rising time t is recorded automatically. Uncertainty is mainly caused by time loss in the data communication between PC and PLC, and the running process of software. Without consider the complicated analysis, the total time error is 40ms which is apparently accurate than manual operation. The uncertainty u (t) from t is given by

u (t) = 40ms/43 = 2.31 x!0~2 s

Using combined uncertainty calculation formula Eq. (11), the relative combined uncertainty under automatic testing process at the pressure of 6.3 x10~3Pa is 5.87%, and the combined uncertainties at other testing pressure points are shown in Fig. 5 by the broken line signed with square.

20% -r

18% ■: 16%-j 14%-j 12% -Ï 10% -j 8%-j 6%-i 4%-i 2%-i 0%J

■ Manual testinc if Automatic tes } ting /*

-1 > g

1x10-2

Measurement pressure point (Pa)

Fig.5 Comparison of uncertainties of manual/auto testing modes

Fig. 5 shows the uncertainty distribution of automatic and manual testing modes at different testing pressure

points. Some analysis is listed below:

1) The uncertainties of automatic and manual testing modes are nearly the same, and the automatic testing mode does not bring out obvious advantage in accuracy. The main reason is that, in all uncertainty sources, the uncertainty from equilibrium pressure in the test dome p takes the largest proportion (nearly 93%). And under both operation modes, the measurement precision of vacuum gauge is the same. Choosing advanced vacuum gauge with higher measurement precision is necessary for this testing system. Otherwise, it will become the bottleneck to the whole system.

2) The pumping speed of diffusion pump with 200mm inlet is stable at 1100L/s, which is lower than the pumping speed of 1500L/s given in products brochure. Because there is a transition interface between the test dome with inner diameter of 400mm and the diffusion pump with 200mm inlet, which is not inconsistent with the provisions in ISO standard. The transition interface results in an additional flow conductance, reducing the pumping speed.

3) The uncertainty surges from 6% to about 16% after 6.3 x 10~2 Pa. This is because the diffusion pump can not work efficiently under such large pressure and the pressure in the test dome fluctuates sharply, as a consequence, the A type uncertainty u (p )1 calculated according to Eq. (4) is quite large. In fact, the value of u (p )1 at the other testing pressure (from 8 x 10-4 to 6.3 x 10~2 Pa) is quite small and even can be omitted.

8. Conclusion

A newly developed automatic testing system used in laboratory for diffusion pump performances is introduced in this paper. The key techniques for the automation are as follow: The liquid level of the oil column in gage-glass tube is automatically detected by two optical fiber sensors instead of by the testing operators' naked eyes. The liquid level rising time is recorded by the computer instead of the manual stopwatch. We try to regulate the pressure in the test dome and the gas throughout with the needle adjusting valve driven by a stepper motor, instead of by manual turning along with naked eye observation of pressure meters. The whole testing system and measuring process are automatically controlled by a two-stage control system with an upper PC and a lower PLC.

The uncertainty analysis theory is applied to the performance analysis of this newly developed automatic testing system, and established the mathematical model for systematic uncertainty transfer function known as Eq. (11). Some main results are given:

1) At the testing pressure 6.3x 10~3 Pa, the relative combined uncertainty is 5.87% for automatic testing mode, while it is 6.11% for manual testing mode.

2) Under manual testing mode, the top three contributions to total relative uncertainty are: uncertainty of the equilibrium pressure in the test dome (u (p)=5.78%), uncertainty of AV with (1.51%) and uncertainty of liquid level raising time t (u (t) =1.06%).

3) When the pressure in test dome is larger than 6.3 x 10~2 Pa, the uncertainty surges from around 6% to about 16% . And the uncertainty analysis method and accuracy calculation results in this paper also provide the theory basis

and an instance to the uncertainty analysis for other types of vacuum pump performance testing systems.

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