1. Michael Bair Director of Pressure Metrology Fluke Calibration
An Examination of the Uncertainty in Pressure of Industrial Dead-Weight Testers Used For Pressure Calibrations in Different Environments
Michael Bair
Director of Pressure Metrology
Fluke Calibration

2. 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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2012 NCSLI Workshop & Symposium

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DWT Design
Mass x Gravity
Masses are rotated
EQUILIBRIUM!
Pressure x
Area
PRESSURE
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.
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DWT Design
Then we plug in the variables to determine what pressure we will get for 1 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.
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2012 NCSLI Workshop & Symposium

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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 buoyancy and head correction are applied by adjusting the mass. The head correction is applied to a convenient location such as the test port on the DWT.
Reference level at
Test port
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DWT Design
For DWTs that go to high pressure (20000 to 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.
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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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2012 NCSLI Workshop & Symposium

14. DWT Design The calculation for ‘partial correction’ is as follows…
and
gl is where the DWT is going to be used.
gc is the gravity the DWT was made for.
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
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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
Piston Head
Upper MP
Lower MP
Low Range MP
Extra MP
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Uncertainties
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Uncertainties
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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.
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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
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Conclusion
The final uncertainty budget ended up looking something like this…
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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!
July 30, 2012
2012 NCSLI Workshop & Symposium