a method for verifying traceability in effective area for high pressure oil piston-cylinders michael...
TRANSCRIPT
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.
2011 NCSL International Workshop & Symposium 4
Calibration Chain
24 Aug 2011
2011 NCSL International Workshop & Symposium 5
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
Hydraulic - free deformation: 2 to 200 MPa
Hydraulic - free deformation: 5 to 500 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.
2011 NCSL International Workshop & Symposium 6
Calibration Chain Verification
24 Aug 2011
• Comparison with Houston facility primary to 280 MPa (40,000 psi)
2011 NCSL International Workshop & Symposium 7
Calibration Chain Verification
-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).
2011 NCSL International Workshop & Symposium 8
Calibration Chain Verification
-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).
2011 NCSL International Workshop & Symposium 9
Calibration Chain Verification
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.
2011 NCSL International Workshop & Symposium 10
Single Piston Method Procedure
24 Aug 2011
2011 NCSL International Workshop & Symposium 11
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
2011 NCSL International Workshop & Symposium 12
Single Piston Method
24 Aug 2011
2011 NCSL International Workshop & Symposium 13
Single Piston Method
-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
Single Piston Method - Gap Determination
• 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
2011 NCSLI Workshop & Symposium 1524 Aug 2011
31
6
gauge
fl
P
VRLh
Single Piston Method - Gap Determination
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
Single Piston Method - Gap Determination
• 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.
2011 NCSLI Workshop & Symposium 1724 Aug 2011
Single Piston Method - Gap Determination
2011 NCSLI Workshop & Symposium 18
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
Single Piston Method - Gap Determination
• Result was actually much better than the uncertainty analysis.
2011 NCSLI Workshop & Symposium 19
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.
2011 NCSLI Workshop & Symposium 2024 Aug 2011