Characterization of quartz Bourdon-type high-pressure transducers

Abstract

The characteristics of commercially available pressure monitors were evaluated. The pressure range of these pressure monitors is up to 100 MPa and the resolution of the transducer is 0.1 kPa. The pressure monitor includes a quartz Bourdon-type high-precision electronic pressure transducer inside the body. The sensing element of the transducer is a precision quartz crystal resonator and the frequency of oscillation varies with pressure-induced stress. In total, six pressure monitors were prepared for this study. During 15 months, the six monitors were calibrated simultaneously using a hydraulic pressure balance 11 times in total. The effects on the readings of the monitors by setting parameters and environmental conditions were evaluated. The important characteristics for the pressure transducer such as the temperature coefficient of the span reading and long-term stability were also evaluated quantitatively. From the evaluation results, the behaviours of the transducers during the period were well characterized. The standard deviation of the relative deviations from the least-squares best-fitting function for each pressure transducer was less than 6 × 10−6 in the pressure range of 30 MPa to 100 MPa and had a maximum of 11 × 10−6 at 10 MPa. In this article, the details of the characterization are described.

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Characterization of quartz Bourdon-type high-pressure transducers
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2005 Metrologia 42 S235
(http://iopscience.iop.org/0026-1394/42/6/S20)
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INSTITUTE OF PHYSICS PUBLISHING METROLOGIA
Metrologia 42 (2005) S235–S238 doi:10.1088/0026-1394/42/6/S20
Characterization of quartz Bourdon-type
high-pressure transducers
Tokihiko Kobata
National Metrology Institute of Japan, National Institute of Advanced Industrial Science and
Technology (NMIJ/AIST), AIST Tsukuba Central 3, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8563,
Japan
Received 18 October 2005
Published 28 November 2005
Online at stacks.iop.org/Met/42/S235
Abstract
The characteristics of commercially available pressure monitors were evaluated. The
pressure range of these pressure monitors is up to 100 MPa and the resolution of the
transducer is 0.1 kPa. The pressure monitor includes a quartz Bourdon-type
high-precision electronic pressure transducer inside the body. The sensing element of
the transducer is a precision quartz crystal resonator and the frequency of oscillation
varies with pressure-induced stress. In total, six pressure monitors were prepared for
this study. During 15 months, the six monitors were calibrated simultaneously using
a hydraulic pressure balance 11 times in total. The effects on the readings of the
monitors by setting parameters and environmental conditions were evaluated. The
important characteristics for the pressure transducer such as the temperature
coefficient of the span reading and long-term stability were also evaluated
quantitatively. From the evaluation results, the behaviours of the transducers during
the period were well characterized. The standard deviation of the relative deviations
from the least-squares best-fitting function for each pressure transducer was less than
6×10−6in the pressure range of 30 MPa to 100 MPa and had a maximum of
11 ×10−6at 10 MPa. In this article, the details of the characterization are described.
1. Introduction
Many interlaboratory comparisons have been carried out at
different pressure ranges using different types of transfer
standards all over the world [1]. For a pressure in the
range of 10 MPa to 100 MPa for the hydraulic gauge mode,
commercially available pressure monitors were prepared as
transfer standards [2]. Each pressure monitor includes a quartz
Bourdon-type high-precision electronic pressure transducer
inside the body. The same type of transducer has been
used as a transfer standard in pressure comparisons, for
example [3]. During 15 months, the pressure transducers were
calibrated simultaneously at National Metrology Institute of
Japan, National Institute of Advanced Industrial Science and
Technology 11 times in total. From the measurement results,
the behaviours of the pressure transducers during the period
were well characterized.
2. Pressure transducers
Commercially available pressure monitors were used. One
type (a) is RPM3 A15000 from DH Instruments, Inc. and
another type (b) is 785 A15000 from Paroscientific, Inc. (in
alphabetical order) [4,5]. In total six pressure monitors
were prepared and were identified as m=1,3,5 (RPM3)
and m=2,4,6 (785) in this characterization. Each
pressure monitor includes a high-precision electronic pressure
transducer. The sensing element of the transducer is a precision
quartz crystal resonator and the frequency of oscillation varies
with pressure-induced stress. The pressure range of these
pressure transducers is 0 MPa to 100 MPa. The parameters
of each pressure monitor were set as follows: range of 0 MPa
to 100 MPa, kilopascal units, the gauge mode, the average
measurement mode for 20 readings each 20 s and 0.1 kPa
resolution. First, the effects on the readings of the monitors
by setting parameters and environmental conditions were
evaluated and the following results were obtained. (i) No
systematic effect on the reading by the voltage and frequency
of the power source was found. (ii) The levelling effect could
be reduced to be less than the resolution of the monitor by
adjusting the water level of the monitor within 0.1˚ using
a sensitive bubble level. (iii) The effect on the reading by
a transient response was investigated by generating pressure
change (a) from 0 MPa to 100 MPa and (b) from 100MPa
to 0 MPa as a step function. After the change, the reading
0026-1394/05/060235+04$30.00 © 2005 BIPM and IOP Publishing Ltd Printed in the UK S235

T Kobata
0.0
0.5
1.0
1.5
2.0
0102 0
Time / min
∆R / kPa
1
2
3
4
5 6
-3.0
-2.0
-1.0
0.0
1.0
0102 0
Time / min
∆
R / kPa
1
2
3
4
5 6
(a)
(b)
Figure 1. (a) Reading change after pressurizing from 0 MPa to
100 MPa, (b) Reading change after depressurizing from 100 MPa to
0MPa.
of each monitor was sampled every 2min until 30 min later.
Figure 1shows the results sampled. The corrected reading R
is obtained from R =R−R30, where Ris the raw reading
and R30 is the reading at 30 min. In the figures, measurement
points at 0 min are removed to keep the vertical axes narrow.
When the pressure change from 0 MPa to 100 MPa was applied,
the reading was immediately overshot and gradually decreased
with time exponentially as shown in figure 1(a). On the other
hand, when the pressure change from 100 MPa to 0 MPa was
applied, the reading was immediately undershot and gradually
increased with time exponentially as shown in figure 1(b).
Considering these results and the efficiency of calibration, it
was decided that each measurement should be performed from
10 min to 15 min after pressure change.
3. Calibration procedure
Clean di(2)-ethyl-hexyl sebacate (DHS) was used as a working
fluid. One complete calibration cycle consists of 23
measurements performed at 11 pressure points from 0 MPa
to 100 MPa in steps of 10 MPa in ascending order, then
one point at 0 MPa and eleven points from 100 MPa to
0 MPa in steps of 10 MPa in descending order. A total of
three cycles were performed for each calibration set, with
each cycle being on a separate day. The duration of one
calibration cycle was approximately 6 h. At each pressure,
the pressure generated by a standard pressure balance was
applied to the pressure transducers. The pressure balance
was equipped with a simple-type piston–cylinder assembly
whose effective area was approximately 9.8×10−6m2.
After waiting for 10 min, within 5 min, the readings of
each pressure monitor, which were the resulting averages
for the 20 measurements and their corresponding standard
deviations, were measured. The ambient temperature around
each pressure monitor, Tb, and environmental conditions such
as room temperature, humidity and atmospheric pressure were
also measured. Then, the applied pressure with the associated
standard uncertainty at the reference level was calculated.
The difference between the actual pressure realized by the
pressure standard and the target pressure was adjusted to
Table 1. Simultaneous calibrations performed by changing date and
averaged room temperature of laboratory.
Room
Index Dates for calibrations temperature/˚C
1 9 10 11 October 2002 22.6
2 15 16 17 October 2002 20.7
3 18 21 22 October 2002 25.4
4 29 30 31 October 2002 22.6
5 11 12 13 November 2002 22.7
6 15 17 18 April 2003 22.3
7 16 20 22 May 2003 22.1
8 17 19 20 November 2003 22.4
9 24 25 26 November 2003 20.9
10 27 28 29 November 2003 25.8
11 1 2 3 December 2003 22.4
be within a thousandth of the target pressure by loading or
unloading fractional masses on the pressure balance. To apply
zero gauge pressure to the pressure transducers accurately,
a simple U-tube fabricated from a stainless pipe was used.
During 15 months, six pressure transducers were calibrated
simultaneously 11 times by changing the date and the room
temperature of the laboratory as shown in table 1. The
fluctuation of the room temperature was typically within
±0.2 ˚C during one day.
4. Analysis of data
The following data sets were obtained from the measurement
results
{R(m, y , w, i, n), P (m, y, w, i ), Tb(m, y, w , i)},
where the parameters are defined as follows: R: the raw reading
of each pressure monitor at the actual ambient condition in
kilopascals, P: the applied pressure at the reference level
by the standard pressure balance in kilopascals, Tb: the
ambient temperature around each pressure monitor measured
by platinum resistance thermometers, which slightly differs
from room temperature, m: the index for pressure monitor
identification, m=1–6, y: the index for calibration cycle,
y=1–3, w: the index for indicating ascending or descending
measurements, w=1or2,i: the index for indicating
pressure, i×10 MPa, i=0–10 and n: the number of days
from the beginning date, 1 October 2002, which was defined
for the purpose of evaluating the long-term shift with time, to
the date on which the calibration was performed.
The reduction and analysis of the data are performed as
described in the following subsections.
4.1. Correction for zero-pressure offsets
In one calibration cycle, 23 measurements were performed at
11 pressure points as explained in section 3. In the cycle, three
measurements were performed at 0 MPa, which were at the
beginning, the middle and the end of the cycle. From data
analysis, it turned out that the reproducibility of the reading
of the pressure monitor at the middle 0 MPa point was worse
than that at the beginning or the end 0 MPa points, and therefore
was not used for this correction. The readings for ascending
and descending pressure points of each cycle are offset by the
S236 Metrologia,42 (2005) S235–S238

Characterization of Bourdon-type high-pressure transducers
readings at the beginning or the end 0 MPa points of each cycle,
respectively. By subtracting the offset from the raw reading,
R, the corrected reading, Rc0, is obtained as follows:
Rc0(m, y , w, i, n) =R (m, y, w, i, n) −R (m, y, w, 0,n).
(1)
4.2. Correction for difference between nominal pressure and
actual pressure
Rc0 is the reading of the pressure monitor when the actual
pressure realized by the pressure standard, P, is applied. Since
the readings are nominally linear and the ratios of the readings
to the actual pressure are generally independent of pressure for
the pressure range where the deviation of the actual pressure
from the nominal target pressure is small, the ratios can be used
to correct the readings for deviations of the pressure standard
from the nominal pressure. When the nominal pressure, Pn,is
applied to the pressure transducer, the predicted reading, Rc1,
is calculated as
Rc1(m, y , w, i, n) =Rc0 (m, y, w , i, n)
P (m, y, w, i ) ·Pn(i ). (2)
4.3. Correction to reference temperature
Rc1 is the reading of each pressure monitor when the ambient
temperature around the pressure monitor is Tb. Since the
reading is affected by the temperature, the reading should
be corrected. The temperature coefficient of each pressure
transducer at each target nominal pressure, β(m, i ) kPa ˚C−1,
was calculated using the following equation from measurement
results:
β(m, i ) =1
12
×
2

q=1
2

w=1
3

y=1
Rq
c1(m, y , w, i, n) −R0
c1(m, y , w, i, n)
Tq
b(m, y, w , i) −T0
b(m, y, w , i) .
(3)
Here, Tq
bis the temperature measured at approximately 23 ˚C
for q=0, at 20 ˚C for q=1 and at 26 ˚C for q=
2, and Rq
c1 is the corresponding reading of each pressure
monitor. The temperature coefficient, β(m, i ), was evaluated
at intervals of one year. From the reproducibility, the standard
uncertainty of each coefficient was estimated as 0.03 kPa ˚C−1.
Figure 2presents the calculated temperature coefficients of
each pressure transducer for nominal target pressures. Some
discontinuous deviations shown in figure 2may be caused by
the actual characteristics of the pressure transducers evaluated
since it has been confirmed that the reading of the pressure
monitor at the deviated temperature can be corrected to
the reading at the reference temperature appropriately using
the temperature coefficient. The reading corrected to the
reference temperature, Rc2, can be calculated as
Rc2(m, y , w, i, n) =Rc1 (m, y, w , i, n)
−β(m, i ) ·[Tb(m, y, w , i) −Tr].(4)
Here, Tris the reference temperature which was determined as
Tr=21.5 ˚C in this characterization so that the maximum
temperature deviation from the reference temperature was
minimized when the transducer was used in the temperature
range of 20 ˚C to 23 ˚C.
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0 20406080100
Pressure / MPa
β
/ (kPa/
°
C)
1 2 3 4 5 6
Figure 2. Calculated temperature coefficient βof each pressure
transducer.
-3
0
3
6
9
12
15
18
21
24
0 100 200 300 400
Number of da
y
s n
Difference in R
c2
/ kPa
0 MPa
10 MPa
20 MPa
30 MPa
40 MPa
50 MPa
60 MPa
70 MPa
80 MPa
90 MPa
100 MPa
Figure 3. Example of long-term shift obtained from pressure
monitor m=2.
4.4. Correction for long-term shift in characteristics of
transducer
The calibration set from three cycle measurements was
repeated 11 times. In the successive calibration results, a
clear long-term shift in the characteristics of each transducer
was observed as a monotonic drift with time. Figure 3
shows an example of the long-term shift obtained from
the pressure monitor m=2. The averaged differences
between Rc2(m, y , w, i, n) and Rc2 (m, y, w, i, 0)are plotted
as functions of the number of days, n. It has been confirmed
that the shifts were due to the characteristics of the transducers
and were not due to the pressure standard used. The stability
of the pressure balance used as the pressure standard had been
evaluated by cross-float comparison against other standard
pressure balances in the period of this characterization and it
was confirmed that there was no systematic shift in the pressure
balance used and the relative instability was of the order of
less than 2 ×10−6. In this analysis, the long-term shift of the
transducer was fitted by a least-squares best-fitting straight line
using Rc2 taken during simultaneous calibrations.
Re(m, w, i, n) =α0(m, w, i ) ·n+α1(m, w, i ). (5)
Here, Reis the predicted reading on the date the calibration
cycle was performed: ndays after the beginning date. The
coefficients α0and α1were calculated with the least-squares
fit for the long-term shift obtained from 11 simultaneous
Metrologia,42 (2005) S235–S238 S237

T Kobata
-10
0
10
20
30
40
50
60
0 20 40 60 80 100
Pressure / MPa
α
0
/ (Pa/day)
1 2 3 4 5 6
-150
-50
50
150
250
350
0 20406080100
Pressure / MPa
10
6
× (
α
1
−P
n
) / P
n
1 2 3 4 5 6
(a)
(b)
Figure 4. Coefficients α0and α1for long-term shifts calculated with
least-squares fit.
calibrations for the ascending and descending sequences,
respectively. Figure 4shows the coefficients α0and α1
obtained as functions of pressure.
4.5. Normalization of ratio of pressure transducer
By taking the ratios of Rc2 to Re, the normalized ratio for each
measurement point, s0, is calculated as
s0(m, y, w , i) =Rc2 (m, y , w, i, n)
Re(m, w, i, n) .(6)
By taking the average of s0for the ascending and descending
pressures of the three cycles, the normalized mean ratio of each
pressure transducer, s1, is calculated as
s1(m, i) =1
6·
2

w=1
3

y=1
s0(m, y, w , i). (7)
Figure 5shows the instabilities of the pressure transducers
expressed as the standard deviation, σ{sl
1(m, i)}, which is
calculated from 11 values of sl
1(m, i) about its mean, where
sl
1(m, i) is the normalized mean ratio obtained from the lth
calibration data set (11 sets in total) using equation (7). The
standard deviation obtained from each pressure transducer is
0
2
4
6
8
10
12
0 20406080100
Pressure / MPa
106× Standard deviations
.
1 2 3 4 5 6
Figure 5. Instabilities of pressure transducers expressed as standard
deviations.
less than 6 ×10−6in the pressure range of 30MPa to 100 MPa
and has a maximum of 11 ×10−6at 10 MPa.
5. Conclusions
High-precision quartz Bourdon-type electronic pressure
transducers were characterized. During 15 months, six
pressure transducers were calibrated simultaneously 11 times
in total. Important characteristics such as the temperature
coefficient of the span reading and the long-term stability
are evaluated quantitatively. From the measurement results,
the behaviours of the pressure transducers during the period
were well characterized. The standard deviation of the relative
deviations from the least-squares best-fitting function for each
pressure transducer was less than 6 ×10−6in the pressure
range of 30 MPa to 100 MPa and had a maximum of 11 ×10−6
at 10 MPa. From these results, it can be stated that the
capabilities of the pressure transducers to be used in a pressure
key comparison as the transfer standards are sufficient.
Acknowledgments
The author is grateful to DH Instruments, Inc. and
Paroscientific, Inc. for lending the pressure monitors.
Contributions of Mr K Ide and Mr S Kimura by way of their
assistance with multiple calibrations are also acknowledged.
References
[1] Legras J C 1994 Metrologia 30 701–4
[2] Kobata T et al 2005 Final Report on Key Comparison
APMP.M.P-K7 in hydraulic gauge pressure from 10 MPa to
100 MPa Metrologia 42 Tech. Suppl. 07006
[3] Fitzgerald M P et al 1999 Metrologia 36 669–72
[4] DH Instruments, Inc. 2000 RPM3 Operation and Maintenance
Manual
[5] Paroscientific, Inc. 2001 Model 785 Multi-Range Pressure
Standard Operation and Maintenance Manual
S238 Metrologia,42 (2005) S235–S238