A Method for Verifying Traceability in Effective Area for High Pressure Oil Piston-Cylinders

A Method for Verifying Traceability in Effective Area for High Pressure

Oil Piston-CylindersMichael Bair

Director of Metrology-PressureFluke Calibration

• Traceability in pressure, like temperature, cannot be “built up” by measuring in parallel.

• Traceability in pressure is dependent upon effective area and the elastic properties of piston-cylinders used with pressure balances (piston gauges).

• Fluke Calibration’s reference (method) for effective area/ pressure is the Piston-Cylinder Pressure Calibration Chain.

• With this Fluke Calibration’s uncertainty in pressure is ±0.0028% at 200 MPa (30,000 psi) which is very low when reviewing NMI’s CMC uncertainties for that range.

• Because there is extrapolation of the effective area and elastic deformation coefficient verification is required at high pressure.

• Calibration chain was re-characterized in 2010. This paper shows 3 methods of verification, one being an attempt to use the Dadson single piston method.

2011 NCSL International Workshop & Symposium 2

Introduction

24 Aug 2011

3

One Minute Piston Gauge Primer

Mass x Gravity

Pressure = (Mass x Gravity)/ Effective Area

EQUILIBIUM!

Masses are rotated

Effective Area

Pressure xArea

Effective AreaChanges with Pressure

• Primary standard for effective area from 5 kPa to 500 MPa (<1 psi to 72500 psi).

• Re-characterized in 2009/2010. 4th modern re-characterization.

• Original traceability is defined using dimensional measurements and the Dadson method on a 50 mm diameter piston-cylinder.

• Traceability is transferred to higher pressures/ smaller effective areas using the “Base Ratio” crossfloat.

• Each level has some portion of the range that extrapolates elastic deformation to support the next higher range.

• Uncertainties increase as pressure gets higher.


Calibration Chain

24 Aug 2011


Calibration Chain

10 kPa/kg

5 kPa/kg

50 kPa/kg

200 kPa/kg

500 kPa/kg

335154

117 118

1 MPa/kg

2 MPa/kg

5 MPa/kg

512D 20D

22D 23D

24D 25D

397 742

468 405

Lines between piston-cylinders are the average of atleast two measured ratios between the two piston-cylinders.

Gas - controlled clearance: 5 to 175 kPa

Gas - free deformation: 13 to 1000 kPa

Gas - negative free deformation: 50 to 5000 kPa

Hydraulic - free deformation: 0.2 to 20 MPa

Hydraulic - free deformation: 0.5 to 50 MPa

Hydraulic - free deformation: 1 to 100 MPa



450 407

Hydraulic – Controlled Clearance (1488)And free deformation (27D)

1488 and 27D2 MPa/kg

PTB Comparison/ Dimensional Characterization

Gas - controlled clearance: 5 to 500 kPa

5 kPa/kg 1161

572Gas/Oil - negative free deformation: 0.1 to 10 MPa

624100 kPa/kg

24 Aug 2011

• Comparison with Houston facility primary to 280 MPa (40,000 psi)

• Comparison with SN 27D, an old/dormant 200 MPa range piston-cylinder with original traceability with NIST and LNE (France).

• A alternate method based on a basic principal discussed by Dadson called the single piston method.


Calibration Chain Verification

24 Aug 2011

• Comparison with Houston facility primary to 280 MPa (40,000 psi)



-70

-50

-30

-10

10

30

50

70

0 100 200 300

[par

ts in

106 ]

[MPa]

Phoenix k=2

Houston k=2

24 Aug 2011

• Comparison with SN 27D, an old/dormant 200 MPa range piston-cylinder with original traceability to NIST and LNE (France).



-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

0 50 100 150 200

[Par

ts in

106 ]

[MPa]

NIST 1993

LNE 1998

NIST 2004

Chain 2010

24 Aug 2011

• A alternate method based on a basic principal discussed by Dadson called the single piston method.

– Not used this time as a complete characterization of the pressure balance but just as a verification tool for the results of the CalChain.

– Attractive because of the equation used for an incompressible fluid to determine average gap and the fact a known viscosity characterization existed for the test fluid (Vergne).



31

6

gauge

fl

PVRL

h

24 Aug 2011

• Determine the effective area of SN 1488 controlled clearance piston gauge using the calibration chain and base ratio method.

• Dimensionally characterize SN 1488 2.5 mm piston at NIST.

• Perform drop rate tests to determine the average gaps at various pressures.

• Using the zero pressure gap and dimensioned piston, calculate the effective area at zero pressure and 20˚C and compare to what was determined from the crossfloats.


Single Piston Method Procedure

24 Aug 2011


Single Piston Method

Table 1. Results of Base Ratio crossfloats of SN 1488 at 0 controlled clearance pressure

Pressure Ratio from 742 at 0 MPa and 20˚C

Calculated Ae(20,0)

Ratio from 397 at 0 MPa and 20˚C

Calculated Ae(20,0)

[MPa] [---] [mm^2] [---] [mm^2]

40 0.9996962 4.9033917 0.9999149 4.9033921 80 0.9996991 4.9033772 0.9999150 4.9033920 120 0.9996994 4.9033759 0.9999143 4.9033950 160 0.9996986 4.9033797 0.9999113 4.9034097 200 0.9997013 4.9033667 0.9999119 4.9034069

Average Ae(20,0) 4.9033887 mm2 2 standard deviations of all Ae(20,0) 5.6 Parts in 106 Elastic Deformation 7.75 x 10-7 MPa-1 Uncertainty (k=2) 20 Parts in 106

24 Aug 2011

• Two pistons were sent to NIST for dimensioning, one was for SN 1488, the other a slightly smaller piston for future use.

• Two different orthogonal planes

• ±16.5 mm to cover float range

• 24 total diameter measurements



24 Aug 2011



-20

-15

-10

-5

0

5

10

15

20

-0.50 0.00 0.50

Table 2. Results of 1488 2.5 mm piston from NIST Z Position 0 deg 90 deg Average

[mm] [mm] [mm] [mm] 16.5 2.498181 2.498176 2.498179 13.5 2.498211 2.498203 2.498207 10.5 2.498183 2.498188 2.498186 7.5 2.498099 2.498126 2.498113 4.5 2.498146 2.498151 2.498149 1.5 2.498154 2.498169 2.498162 -1.5 2.498158 2.498193 2.498176 -4.5 2.498164 2.498179 2.498172 -7.5 2.498098 2.498114 2.498106

-10.5 2.497951 2.497988 2.497970 -13.5 2.497898 2.497903 2.497901 -16.5 2.497723 2.497763 2.497743

Average diameter = 2.4980883 mm

Diff of 90˚

[nm]

-5

-8

5

27

5

15

35

15

16

37

5

40

24 Aug 2011

Single Piston Method - Gap Determination

• Performed gap determinations for three different controlled clearance pressures, 0, 25 and 50% of measured pressure.

• For each CCP performed drop rates for at least 5 pressures.

• Tried to get 5 drop rates for each CCP/measured pressure combination. Performed 92 drop rate tests.

• Calculated gap for each drop rate test.

• Plotted gap to get zero pressure gap to be used with the diameter.

2011 NCSLI Workshop & Symposium 1424 Aug 2011


• Where– h = average gap between piston and cylinder.– L = engagement length of piston cylinder– R = radius of the piston– Vfl = volume flow calculated by piston drop rate– Pgauge = gauge pressure of the fluid


31

6

gauge

fl

PVRL

h


2011 NCSLI Workshop & Symposium 16

0.4000

0.5000

0.6000

0.7000

0.8000

0.9000

1.0000

0 50 100 150 200

gap

[um

]

[MPa]

0 % CCP

50% CCP

25% CCP

24 Aug 2011


• Keys to performing the drop rate tests.– Started with high end industrial drop indicator.

• Kept getting stuck.• Contact reduced rotation times.• Found out that the internal non-contact position sensor performed very well if

calibrated every day – 2 minute procedure.– It was essential to perform the tests from approximately +1.5 to -1.5 mm

to match the dimensional tests on the piston.– Could not have ANY air in the system, went through extensive purge

procedure.– Temperature had to be very stable. Used piston-cylinder temperature

for the temperature of the media.– Isolated pressure directly outside the piston gauge to reduce

environmental temperature influences on the fluid. (changes were usually less than 0.02 deg for each test)

– Leveled as best as possible for each test.




Table 3. Gap determinations for piston-cylinder SN 1488. Pressure 0% CCP 25% CCP 50% CCP [MPa] [um] [um] [um]

200 0.9482 0.6932 0.4756 160 0.8840 0.6681 0.4830 120 0.8126 0.6386 0.4994 80 0.7253 0.6221 0.5157 40 0.6240 0.5800 0.5321 12 0.5657 ---------- ---------- 0 0.5488 0.5587 0.5449

Using the average piston radius and the average of the gaps at zero pressure, the result effective area at 20˚C and zero pressure is 4.9033956 mm2.

+1.4 ppm from CalChain Determination24 Aug 2011


• Result was actually much better than the uncertainty analysis.


k=1 Sensitivity Unc (h) k=1

[% relative] [% of 0.550 µm] [µm]Vfl 0.234% 0.33 0.00043

R 0.034% 0.33 0.00006

L 0.050% 0.33 0.00009P gauge 0.250% 0.33 0.00046

η 3.000% 0.33 0.00549

h Combined 0.0055

k=1 Sensitivity U radius k=1

[µm] [µm/µm] [µm]

Piston Diameter 0.0215 0.5 0.0108

h (from above) 0.0055 0.5 0.0028

h std error of fit 0.0076 0.5 0.0038

Combined 0.0117

Expanded (k=2) 0.0235

Radius 0.0019%

effective area 0.0038%

24 Aug 2011

Conclusion

• Results are good due to the keys described earlier.

• All methods of validation show that the CalChain to 200 MPa is within stated uncertainties.

• Would like to move forward with FEM analysis, Heydemann and Welch model and also verify using a smaller piston in the same cylinder.

• The 100 – 500 MPa part of the CalChain will be re-characterized at the end of 2012. Will attempt to repeat this process.

• Thanks to Ken Kolb and NIST.


A Method for Verifying Traceability in Effective Area for High Pressure Oil Piston-Cylinders

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