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

• 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.

2

Introduction - Learning Objectives

July 30, 2012 2012 NCSLI Workshop & Symposium

3

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

4

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

5

DWT Design


Mass x Gravity

Pressure = (Mass x Gravity)/ Effective Area

EQUILIBRIUM!

Masses are rotated

Pressure xArea

PRESSURE

6

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.

7

DWT Design

lairfluidcp

mass

airl

ghPA

DgmP

1231

1

0,23

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.

PA

gmP mass

airl

1

1

0,23


8

DWT Design

Then we plug in the variables to determine what pressure we will get for 1 kg.

Pa/kg 2431997

35103.111003155.47920

2.1180665.9166

P

PA

gmP mass

airl

1

1

0,23


9

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.

psi/kg 7313.352

35103.111003155.47920

2.1180665.9166

P

Amount psi kg4 ea 2000 5.670041 ea 1000 2.835024 ea 200 0.567001 ea 100 0.283504 ea 20 0.056701 ea 10 0.028352 ea 4 0.011341 ea 2 0.00567


10

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.

Amount psi kg4 ea 2000 5.670041 ea 1000 2.835024 ea 200 0.567001 ea 100 0.283504 ea 20 0.056701 ea 10 0.028352 ea 4 0.011341 ea 2 0.00567Carrier 200 0.54300

Reference level at Test port


11

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 Mass3000 psi 1 8505.1843000 psi 2 8505.6913000 psi 3 8506.1973000 psi 4 8506.7043000 psi 5 8507.2103000 psi 6 8507.7173000 psi 7 8508.2233000 psi 8 8508.7303000 psi 9 8509.2363000 psi 10 8509.7433000 psi 11 8510.2493000 psi 12 8510.756


12

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.

Low range

High range


13

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.


14

DWT Design

• The calculation for ‘partial correction’ is as follows…

andc

lnomgcorr g

gPP

231 cpgcorrcorr PP

gc is the gravity the DWT was made for.

gl is where the DWT is going to be used.

Thermal expansion of the piston-cylinder effective area times the difference between the reference temperature and the presumed piston-cylinder temperature.

15

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.


16

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.


17

Uncertainties


Table 1. Examples of gravity predictions and associated uncertainty predictions.

Location PTB PTB Ugl(95) NGS NGS Ugl(95)

Difference from PTB WGS84

Difference 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

𝐸𝑟𝑟𝑜𝑟 𝑝𝑝𝑚 = ሺ𝐿× 4.047+ 𝐿2 × −0.0456ሻ× 0.009× 𝐷 where:

L = Absolute value of latitude [degrees] D = latitude change in distance [km]

For changes in elevation the error is approximately 0.31 ppm per meter of elevation change

18

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.


19

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


20

Uncertainties


Piston Head

Upper MP Lower MP

Low Range MP Extra MP

21

Uncertainties


Figure 1. Simultaneous log of temperatures of an IDWT mounting post and

Ambient temperature in a controlled environment.

21.75

22.25

22.75

23.25

23.75

0:43:12 1:55:12 3:07:12 4:19:12 5:31:12 6:43:12

˚ C

Elapsed time

Ambient Temperature

Mounting Post Temperature

22

Uncertainties


Figure 2. Simultaneous log of temperatures of an IDWT mounting post and

ambient temperature in an uncontrolled environment.

22

22.5

23

23.5

24

24.5

25

25.5

26

26.5

27

0:00:00 2:24:00 4:48:00 7:12:00 9:36:00 12:00:00 14:24:00

˚ C

Elapsed Time

Ambient Temperature

Mounting Post Temperature

23

Uncertainties

• With these tests we felt comfortable using the following for the uncertainties of the change in effective area due to piston-cylinder temperature.


Table 4. Contributing temperature uncertainties

Application All Methods Method 1,2 Method 1,2 Method 3

(𝛼𝑝 + 𝛼𝑐)

UTalpha

UTdevice

UTp-c UT no

correction [1/˚C] [ppm] [ppm] [ppm] [ppm]

11 x 10-6 2.8 11.0 11.0 55.0 16 x 10-6 4.0 16.0 16.0 80.0 21 x 10-6 5.0 20.0 20.0 100.0 22 x 10-6 5.5 22.0 22.0 110.0

24

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.


25

Uncertainties


Table 6. Deviations of a dual range hydraulic IDWT

Nominal Pressure

Measured 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

3.5 MPa (500 psi) range 10 10.0001 10 100 100.0067 67 200 200.0175 88 300 300.0278 93 400 400.0371 93 500 500.0463 93

Maximum Deviation: 93

26

Conclusion

• The final uncertainty budget ended up looking something like this…


Table 7. Uncertainty Budget for a dual range hydraulic IDWT

70 Mpa (10000 psi) range 3.5 Mpa (500 psi) range

Method 1 2 3 1 2 3

Influence Section [ppm] [ppm] [ppm] [ppm] [ppm] [ppm] Gravity 5.1 10 10 10 10 10 10 Mass 5.2 10 10 10 10 10 10 Air Buoyancy 5.3 1 8.5 8.5 1 8.5 8.5 Effective Area 5.4 50 50 50 50 50 50 P-C temperature 5.5a 8 8 40 8 8 40 P-C temperature 5.5b 8 8 0 8 8 0 Level 5.8 8.5 8.5 8.5 8.5 8.5 8.5 Performance 5.9 15 15 15 15 15 15

Deviations

5.2, 5.6, 5.10 0 80.5 80.5 0 46.5 46.5

[ppm] [ppm] [ppm] [ppm] [ppm] [ppm]

Combined

55 98 101 56 73 83 Expanded

112 197 211 112 146 165

27

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!


michael bair director of pressure metrology fluke calibration

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