a method for verifying traceability in effective area for high pressure oil piston-cylinders michael...

A Method for Verifying Traceability in Effective Area for High Pressure

Oil Piston-Cylinders

Michael Bair

Director of Metrology-Pressure

Fluke 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

P

VRLh

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

P

VRLh


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 0.00009

P 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 michael...

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