### Uncertainties - NCSL International

```An Examination of the Uncertainty in
Testers Used For Pressure Calibrations in
Different Environments
Michael Bair
Director of Pressure Metrology
Fluke Calibration
Introduction - Learning Objectives
• What is an Industrial Dead Weight Tester (IDWT) and why is it being
treated differently from a piston gauge?
• What is the design of an IDWT? Need to know this for method and
uncertainty.
• What are the three methods of use and environmental limits?
• What are the uncertainties? Note the uncertainties are not FC
product uncertainties but something close to be able to express the
concepts.
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What is an IDWT (DWT)?
• What’s in a name? A DWT works the same by any other name.
• A DWT works under the same exact theory as what one might call a
Dead Weight Pressure Gauge, Piston Gauge or a Pressure
Balance.
• Those devices are defined in existing technical references including
– NCSLI RISP4
– OIML’s R110 Pressure Balances
– EA 10/03 Calibration of Pressure Balances
– The Pressure Balance, Theory and Practice by NPL
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What is a DWT?
• The difference is that a DWT is designed in such a way that it can
be used with reasonable uncertainty with out use of the pressure
equation described in the documents just mentioned.
• The reason for this design is to simplify its operation for industrial
applications, primarily industrial calibration of pressure gauges.
• Because of a recently acquired responsibility of a DWT line, we
decided to quantify product uncertainties for three different methods
of use in an industrial environmental limit. The methods we decided
to call…
– Full correction
– Partial correction
– No correction
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DWT Design
Mass x Gravity
Masses are rotated
EQUILIBRIUM!
PRESSURE
Pressure x
Area
Pressure = (Mass x Gravity)/
Effective Area
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DWT Design
• The full correction method is what is referenced in the technical
documents mentioned.
• For partial and no correction methods, it is easier to understand if
you understand the design.
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DWT Design
To create a DWT, we manufacture masses (weights) that will account
for as many variables in the equation as possible. We start by
removing the constants; surface tension and head correction; and
assume no correction for piston-cylinder temperature, calculate a mid
pressure effective area; and use what is left over.
   air  air  
m  gml  1g l  1 
  D 

 mass mass
 
 
P 
P 
   fluid   air   h  g l
 P 23
  1   P 
A 23 , 0  1  Ap 23, 0 c1


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DWT Design
Then we plug in the variables to determine what
pressure we will get for 1 kg.
 air


m  g l 1 


mass 

P 
A 23 , 0  1   P 
P 

1  9 . 80665 1  1 . 2
4 . 03155  10
6

7920
1  1 .3  10
6
 35

 2431997 Pa/kg
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DWT Design
It then has to be converted to the requested pressure unit. In this
example we will use psi. We then divide the Kl into the nominal
weights we want.
P 

1  9 . 80665 1  1 . 2
4 . 03155  10
6

7920
1  1 .3  10
Amount
4 ea
1 ea
4 ea
1 ea
4 ea
1 ea
2 ea
1 ea
psi
2000
1000
200
100
20
10
4
2
6
 35

 352 . 7313 psi/kg
kg
5.67004
2.83502
0.56700
0.28350
0.05670
0.02835
0.01134
0.00567
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DWT Design
For the first pressure the same calculation is made for the carrier, then
the piston mass is subtracted and corrections for surface tension, fluid
head correction is applied to a convenient location such as the test port
on the DWT.
Amount
4 ea
1 ea
4 ea
1 ea
4 ea
1 ea
2 ea
1 ea
Carrier
psi
2000
1000
200
100
20
10
4
2
200
kg
5.67004
2.83502
0.56700
0.28350
0.05670
0.02835
0.01134
0.00567
0.54300
Reference level at
Test port
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DWT Design
For DWTs that go to high pressure (20000 to 60000 psi), where
deformation can be as high as 0.05%, the main masses are manufactured
to be used in sequence to greatly reduce the uncertainty from the
deformation of the piston-cylinder.
Weight
3000 psi 1
3000 psi 2
3000 psi 3
3000 psi 4
3000 psi 5
3000 psi 6
3000 psi 7
3000 psi 8
3000 psi 9
3000 psi 10
3000 psi 11
3000 psi 12
Mass
8505.184
8505.691
8506.197
8506.704
8507.210
8507.717
8508.223
8508.730
8509.236
8509.743
8510.249
8510.756
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DWT Design
And finally there are many DWTs where the same mass set is used for a
high and a low range piston-cylinder. The one mass set must be made to
work with both. This is called a ‘match’ and adds uncertainty.
High range
Low range
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DWT Design
• ‘No correction’ and ‘partial correction’ are similar in the sense that
they both depend on the nominal pressure values.
• ‘No correction’ is just as it sounds, there is complete dependency on
the nominal pressures.
• ‘Partial correction’ depends on the nominal pressure values but
includes a simple correction for gravity and piston-cylinder
temperature.
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DWT Design
• The calculation for ‘partial correction’ is as follows…
gl is where the DWT is going to be
used.
Pcorr g  Pnom 
and
Pcorr  Pcorr
g

gl
gc
gc is the gravity the

 1   p   c  23   
Thermal expansion of the piston-cylinder effective
area times the difference between the reference
temperature and the presumed piston-cylinder
temperature.
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Uncertainties
• The uncertainties listed in the paper are minimized for simplicity and
include those that are significant. They are…
–
–
–
–
–
–
–
–
Gravity
Mass
Air buoyancy
Effective Area
P-C temperature
Level
Performance
Deviations (uncorrected bias)
• Can’t go into detail in this presentation, but will hit the highlights.
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Uncertainties
• Gravity can vary as much as 0.4% in the normal industrial world.
Gravity needs to be determined for all of these types of devices.
• The difference is how we get it and the uncertainty.
• For DWT it was decided to use an uncertainty of ±20 ppm primarily
because of PTB’s gravity prediction web site and the fact it was
international.
• Other sources of gravity include National Geodetic Survey and the
WGS84 gravity calculation.
• A study was performed to look at uncertainties contributed by
gravity.
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Uncertainties
Table 1. Examples of gravity predictions and associated uncertainty predictions.
PTB
Difference
Difference
Location PTB
Ugl(95) NGS
NGS Ugl(95) from PTB
WGS84
from PTB
m/s2
[ppm]
m/s2
[ppm]
[ppm]
m/s2
[ppm]
US 1
9.79705
3.2
9.79708
4.1
-2.7
9.79774
70.4
US 2
9.79473
1.4
9.79474
2.0
-0.8
9.79481
8.3
US 3
9.81905
3.2
9.81921
4.1
-16.3
9.82008
104.6
INT 1
9.78981 20.0
---------9.78945
-36.9
INT 2
9.80261
1.0
---------9.80273
11.8
INT 3
9.81920 11.0
---------9.81909
-11.1
=  × 4.047 + 2 × −0.0456 × 0.009 ×
where:
L
=
D
=
Absolute value of latitude
latitude change in distance
[degrees]
[km]
For changes in elevation the error is approximately 0.31 ppm per meter of elevation change
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Uncertainties
• There were two uncertainties for mass, one for the determination,
and one for manufacturing, for no or partial correction methods.
• Air buoyancy was only significant for high altitudes and for no or
partial correction.
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Uncertainties
• Piston-cylinder temperature is significant only due to the assumption
there was not a device to measure the piston-cylinder temperature
and either ambient temperature was used, or there was no
correction.
• Environmental limits chosen for temperature were 18 to 28 ˚C (64 to
82 ˚F). Because in no correction there is not a temperature
measurement the uncertainty was very significant.
• There were three temperature tests performed to help with
evaluating an estimation of using ambient air for the piston-cylinder
temperature measurement.
– Heating or cooling due to pressurizing or depressurizing
– Fluctuations in an air conditioner
– No air conditioning
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Uncertainties
Upper MP
Lower MP
Low Range MP
Extra MP
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Uncertainties
23.75
23.25
˚C
Ambient
Temperature
22.75
Mounting
Post
Temperature
22.25
21.75
0:43:12
1:55:12
3:07:12
Elapsed time
4:19:12
5:31:12
6:43:12
Figure 1. Simultaneous log of temperatures of an IDWT mounting post and
Ambient temperature in a controlled environment.
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Uncertainties
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26.5
26
25.5
Ambient
Temperature
˚C
25
24.5
Mounting Post
Temperature
24
23.5
23
22.5
22
0:00:00
2:24:00
4:48:00
7:12:00
Elapsed Time
9:36:00
12:00:00
14:24:00
Figure 2. Simultaneous log of temperatures of an IDWT mounting post and
ambient temperature in an uncontrolled environment.
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Uncertainties
• With these tests we felt comfortable using the following for the
uncertainties of the change in effective area due to piston-cylinder
temperature.
Application
( +  )
[1/˚C]
11 x 10-6
16 x 10-6
21 x 10-6
22 x 10-6
Table 4. Contributing temperature uncertainties
All Methods
Method 1,2
Method 1,2
Method 3
UT no
UTalpha
UTdevice
UTp-c
correction
[ppm]
2.8
4.0
5.0
5.5
[ppm]
11.0
16.0
20.0
22.0
[ppm]
11.0
16.0
20.0
22.0
[ppm]
55.0
80.0
100.0
110.0
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Uncertainties
• There are three uncertainties that ended up being evaluated as one.
• These are called deviations and only apply to no or partial correction
methods.
– Mass Manufacturing.
– Piston-cylinder deformation.
– Piston-cylinder matches.
• To determine this uncertainty the nominal pressures are compared
to the calculated pressures, as in the difference between no and full
correction methods.
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Uncertainties
Table 6. Deviations of a dual range hydraulic IDWT
Nominal
Measured
Pressure
Pressure
Difference
70 MPa (10000 psi) range
[psi]
[psi]
[ppm]
200
200.013
65
2000
2000.069
34
4000
3999.993
-2
6000
5999.692
-51
8000
7999.152
-106
10000
9998.39
-161
Maximum Deviation:
161
10
100
200
300
400
500
3.5 MPa (500 psi) range
10.0001
100.0067
200.0175
300.0278
400.0371
500.0463
Maximum Deviation:
10
67
88
93
93
93
93
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Conclusion
• The final uncertainty budget ended up looking something like this…
Table 7. Uncertainty Budget for a dual range hydraulic IDWT
Method
Influence
Section
Gravity
5.1
Mass
5.2
Air Buoyancy
5.3
Effective Area
5.4
P-C temperature 5.5a
P-C temperature 5.5b
Level
5.8
Performance
5.9
5.2,
5.6,
Deviations
5.10
Combined
Expanded
70 Mpa (10000 psi) range
1
2
3
[ppm]
[ppm]
[ppm]
10
10
10
10
10
10
1
8.5
8.5
50
50
50
8
8
40
8
8
0
8.5
8.5
8.5
15
15
15
3.5 Mpa (500 psi) range
1
2
3
[ppm]
[ppm]
[ppm]
10
10
10
10
10
10
1
8.5
8.5
50
50
50
8
8
40
8
8
0
8.5
8.5
8.5
15
15
15
0
[ppm]
55
80.5
[ppm]
98
80.5
[ppm]
101
0
[ppm]
56
46.5
[ppm]
73
46.5
[ppm]
83
112
197
211
112
146
165
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Conclusion
• Using a DWT in no or partial correction mode means that the entire
DWT should be calibrated as a whole. Adjustments can be made to
masses to account for changes in effective area.
• DWTs are very useful in an industrial environment. Ease of use is
important in this environment. Using the no correction method you
only need to know what the environmental temperature limits are
and to be able to add nominal values. They are very stable and
naturally control pressure to within their performance limits.
• This paper shows that uncertainties of the partial and no correction,
in which DWTs are designed for, are sufficient for the applications
with which they were intended to be used.
• Thank you!
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```