Characterization of spinning rotor gauge-3 using orific flow system and static expansion system


ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 325 

ACTA IMEKO 
ISSN: 2221-870X 
December 2020, Volume 9, Number 5, 325 - 328 

 
 

CHARACTERIZATION OF SPINNING ROTOR GAUGE-3 USING ORIFIC 

FLOW SYSTEM AND STATIC EXPANSION SYSTEM 
 

Ashok Kumar1,2,a, Vikas N. Thakur1,2b, Harish Kumar1,c  

 
1 CSIR-National Physical Laboratory, Dr. K. S. Krishnan Marg, Delhi 110012, India 
2 Academy of Scientific and Innovative Research (AcSIR), Ghaziabad-201002, India 

a ashok553@nplindia.org,  b vikasnthakur92@gmail.com,  c harish@nplindia.org 

 

Abstract:  

This article elucidates the calibration of newly 

procured spinning rotor gauge (SRG 3) from MKS 

Instruments, USA using primary vacuum standards: 

Orifice flow system (OFS) and Static expansion 

system (SES) established at National Physical 

Laboratory, India (NPLI) in the range of 10-4 Pa to 

1 Pa and further compared with manufacturer 

reported value which was calibrated by transfer 

standard of National Institute of Standards & 

Technology (NIST). The key parameters to 

calculate the pressure measured by SRG is the 

accommodation coefficients. The accommodation 

coefficients for N2 gas obtained using OFS, SES, 

and calibration report form NIST USA (SRG2) are 

0.957, 0.961, and 0.954 respectively. 

Keywords: Vacuum; orifice flow system; static 

expansion system; Pressure; spinning rotor gauge 

1. INTRODUCTION 

As a national metrology institute, NPLI has the 

responsibility of maintaining the various primary 

vacuum standards and disseminate the traceability 

down to secondary and reference standards. 

Barometric Pressure and Vacuum metrology section 

maintained the pressure standards in the range of 1 

micro Pa to 360 kPa. Among these standards, this 

section has two primary vacuum standards OFS and 

SES which measure the pressure in the range of 0.1 

Pa to 1 µPa and 0.05 Pa to 10 Pa, respectively with 

associate uncertainty 2% and 0.4% of the pressure 

reading at k=2.  The vacuum primary standards have 

participated in the international key comparisons 

[1,2] and found the reputations at the global level. 

There are many other transfer standards like 

resonant silicon gauge (RSG), old spinning rotor 

gauge (SRG 2), capacitance diaphragm gauge 

(CDGs), etc. which are frequently calibrated by SES 

and OFS. SES and OFS are two primary pressure 

standards which are used to generate pressures very 

accurately and sitting at the top of traceability chain 

in vacuum metrology in India. There are some 

defense laboratories, research institutions and 

accredited laboratories which also possess CDGs 

and SRGs as transfer or secondary standards which 

need to be calibrated time to time using NPLI 

primary vacuum standards. The low precision 

ionization gauges were used as transfer standard for 

inter-comparisons before high precision SRGs and 

CDGs came into the existence. Many inter-

comparisons were performed previously using these 

two vacuum standards i.e. OFS and SES [3,4]. 

Recently this section bought SRG 3 which has 

pressure measuring range of 1 Pa to 10-4 Pa. Comsa 

et. al first invented the spinning rotor gauge in 

vacuum and high vacuum range with unmatched 

accuracy among the existing transfer standards, 

almost similar to the uncertainty of OFS [5]. SRG is 

most commonly used as transfer vacuum standard 

since for the first time it was used as transfer 

standard by Messer et. al. [6]. In 1989 and 2014, the 

international key comparisons were performed 

using two SRGs [7]. MKS has designed and 

developed the third generation SRG and named it 

SRG3 which is more robust and stable in high 

vacuum range. The NPLI studied the 

accommodation factors of SRG3 in details. For the 

same purpose, NPLI has calibrated the SRG3 using 

both the primary standards (OFS and SES) and 

further compared with the value given by SRG2 

(transfer standard of NIST) 

2. APPARATUS WITH 
CHARACTERIZATION DETAILS 

Static expansion system consists of two large 

chambers of different volumes of 𝑉𝑠 = 24 l and 
𝑉𝐿 = 72 l. The gauge under calibration (GUC) 
connected to the port of the chamber of volume 72 l. 

Schematic diagram of SES is shown in Figure 1. 

There are two larger chambers as discussed above 

are mechanically connected with three small 

chambers of volume 𝑣1 = 25 ml, 𝑣2 = 25 ml and 
𝑣 = 343 ml between the valves 1 and 2, 4 and 5 and 

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ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 326 

2 and 3, respectively as shown in Figure 1. The large 

chamber 𝑉𝐿  connected to a turbomolecular pump 
having automated pneumatic gate valve to control 

and release the generate pressure. The chamber 𝑉𝑠 
was pumped through a separate pumping system. 

Prior to any measurement, the whole system was 

backed at 200 ℃ and minimum 10-8 Pa for several 
days while system connected to pumping 

stations/systems. The pressures were generated by 

following the expansion equation: 𝑣2 → 𝑣2 + 𝑉𝐿 . 
The principle of working of SES is the static 

expansion of gas. The gas is first enclosed in the 

smaller volume i.e. 25 ml, then it is allowed to enter 

the larger volume i.e. 72 l to expand under nearly 

perfect isothermal conditions. The pressure in the 

larger volume was calculated using the gas equation 

given by equation (1), 

𝑃𝐿 =
𝑃𝑠 𝑇𝐿

𝑅𝑇𝑠(1 + 𝑃𝑠𝐵
′′)

 (1) 

where 𝑅 =
𝑉𝑠+𝑉𝐿

𝑉𝑠
 is the ratio of final volume to 

initial volume, 𝑃𝑠  and 𝑃𝐿  are the initial and final 
pressure in smaller volume and larger volume 

respectively, 𝑉𝑠  and 𝑉𝐿  are the volumes of smaller 
and larger chambers respectively, 𝑇𝑠 and 𝑇𝐿 are the 
temperature values in the smaller and larger 

chambers respectively and 𝐵′′ = 𝐵/𝑇𝑅𝑚  is the 
second virial coefficient, 𝑅𝑚  is the molar gas 
constant. SES has the pressure measuring range of 

0.05 Pa to 10 Pa with the expanded uncertainty of 

0.4% of pressure reading at k = 2. 

Orifice flow system is another vacuums standard 

which is used to calibrate the vacuum gauges in the 

molecular flow region i.e. the molecular mean free 

path is larger than the dimension of the vessel. OFS 

consists of two chambers of equal volume 

connected by a cylindrical path. The schematic 

diagram of the OFS is shown in Figure 2(a). Both 

the chambers are of equal diameter of 30 cm. The 

gauges under test are to be connected to the upper 

chamber. The residual gas analyzer was connected 

to the upper chamber to check the purity of the gas 

in the chamber. The configuration of the 

experimental setup consists of two spheres to have 

the maximum isotropy of the molecular distribution 

of Maxwellian velocity distribution. The chambers 

were pumped out by following the same procedure 

as used explained by Hojo et. al [9]. The 

turbomolecular pump is used for pumping the gas 

inside the chamber. A titanium sublimation pump 

(TSP) was also connected to the lower chamber. 

Before the calibration start, the chambers were 

baked for several days by heating tapes and an 

ultimum vacuum of 10-10 Pa was maintained. The 

temperatures were measured by the platinum 

resistance thermometers (PRTs) connected five 

different points in the system. The average of the 

temperatures in the calibration sphere was used as 

the reference temperature. 

At the centre of the cylinder path a disk is placed 

made up of copper known as orifice denoted by ‘C’. 

The magnified view of orifice is shown in Figure 

2(b). The orifice has the diameter of 10 mm. The 

edges of the aperture are prepared  

 

 

 

Figure 1: Schematic of static expansion system having chambers of volume 72 l and 24 l. [8]. 

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ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 327 

 

Figure 2: (a) Schematic diagram of the orifice flow system [8], TSP – titanium sublimation pump, BAG – nude Bayard 

Alpert gauges, MS – mass spectrometer, C- orifice (b) magnified view of the orifice. 

 

in such a manner that the thickness of the disk at the 

periphery of the orifice nearly approached to zero. 

The working principle of the OFS is based on the 

flow of gas in molecular flow regions through the 

orifice of known conductance (C) connected across 

two chambers [10]. If Q is the flow rate of the gas 

throughout then the pressure upstream is given by 

equation (2) 

𝑃 =
𝑄

𝐶
(1 +  

𝐶

𝑆𝑃
) , (2) 

where P is the pressure upstream of the orifice or 

the pressure in the calibration chamber and Sp is the 

pumping speed available in the chamber below the 

orifice.  

The SRG 3 consists of ball–tube assembly using 

which vacuum is to be measured. The ball spins 

using a controlled electronics mechanism with the 

frequency of nearly 450 Hz. While spinning the ball 

slows down due to the gas friction and falls down 

with the gas pressure. A sensing head is mounted on 

the ball–tube housing to keep the ball immobilized 

and collect the deceleration of ball due to change in 

pressure inside the chamber. According to the basic 

pressure measurement method of SRG 3, the 

relation between gas pressure P and the speed of the 

ball is given by equation (3) [11] 

𝑃 = (−
𝑑𝜔

𝑑𝜔𝑡
)

𝑎𝜌

10𝜎
 √

8𝜋𝑅𝑚 𝑇

𝑀
− [𝑅𝐷] . (3) 

Here, 𝑎 and 𝜌 are the radius and density of the SRG 
rotor, respectively. M and T are the molecular mass 

of the gas and temperature inside the chamber, RD 

is the residual drag, i.e., the deceleration of the rotor, 

and −
𝑑𝜔

𝑑𝜔𝑡
  is the relative deceleration rate of the 

sphere per unit time and has units of s-1, σ is the 

accommodation coefficient, and Rm is molecular 

gas constant, 8.314x103 (Nm/kmol . K).  

3. RESULTS & DISCUSSION 

The SRG3 ball was placed in their respective 

tubular housing. Since the comparison did not 

involve transportation of the ball/tube assemblies to 

other laboratories, no need was felt of using the 

transport device for fixing the balls in the tubular 

housings during transportation. However, the 

ball/tube assembly was fitted with a mini ultra-high 

vacuum (UHV) right angle valve so that the rotors 

could be isolated from exposure to air during 

venting of the chamber for shifting the ball/tube 

assemblies from one calibration system to the other 

and back. Precautions were taken to keep the 

sensing head mounted on the tubular housing so as 

to keep the ball immobilized because of permanent 

magnets of the head, while transferring the ball/tube 

assembly from one system to the other.  

The SRG3 was first calibrated on the SES, in the 

pressure range of 0.1 – 1 Pa, by following the 

method of SES i.e. successive expansion of the gas 

from one chamber to another. Later, it was 

calibrated using OFS in the range of 0.001 – 0.01 

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ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 328 

Pa. The key parameter to compare, calibrate, and 

characterize any SRG is accommodation 

coefficients. The accommodation coefficient is 

obtained by the intercept of the plot of the 

calibration factor – pressure measured by the 

vacuum standards (i.e. SES and OFS), where 

calibration factor is given by the ratio of the 

pressures measured by gauge under calibration (i.e. 

SRG3) and vacuum standards. As SRG3 has 

measuring range of 10-4 Pa to 1 Pa, therefore, SRG3 

was calibrated by both SES and OFS for vacuum 

and high vacuum range, respectively. To calculate 

the value of accommodation coefficients, the 

calibration factor for SES and OFS are plotted as a 

function of pressure in Figure 3 and Figure 4, 

respectively. The y-intercept (at zero pressure) of 

the graphs in Fig. 3 and Fig. 4 give the 

accommodation coefficients of the SRG3 measured 

by SES and OFS, respectively. The values of 

accommodation coefficients calculated using SES, 

OFS and SRG2 (MKS, NIST) are given by Table 1. 

The values of accommodation coefficients given 

in Table 1 show the maximum standard deviation of 

≈0.003. 

 
Figure 3: Calibration factor of SRG3 as a function of 

pressure using the SES.  

 
Figure 4: Calibration factor of SRG3 as a function of 

pressure using the OFS. 

Table 1: Accommodation coefficients obtained by 

different vacuum standards. 

S. No. Standard Accommodation 

coefficient  

1 SES 0.961 

2 OFS 0.957 

3 SRG2 (MKS, NIST) 0.954 

4. SUMMARY 

The values of the accommodation coefficients 

were successfully calculated and the values 

obtained from SES and OFS were further compared 

with the value obtained from SRG3 (MKS, NIST). 

It is found that these three values of accommodation 

coefficients having the maximum standard 

deviation of   ≈ 0.003. 

5. REFERENCES 

[1] D.A. Olson, P.J. Abbott, K. Jousten, F.J. Redgrave, 

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