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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 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. July 30, 2012 2012 NCSLI Workshop & Symposium 2 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 July 30, 2012 2012 NCSLI Workshop & Symposium 3 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 July 30, 2012 2012 NCSLI Workshop & Symposium 4 DWT Design Mass x Gravity Masses are rotated EQUILIBRIUM! PRESSURE Pressure x Area Pressure = (Mass x Gravity)/ Effective Area July 30, 2012 2012 NCSLI Workshop & Symposium 5 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. July 30, 2012 2012 NCSLI Workshop & Symposium 6 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. air air m gml 1g l 1 D mass mass P P fluid air h g l P 23 1 P A 23 , 0 1 Ap 23, 0 c1 7 July 30, 2012 2012 NCSLI Workshop & Symposium DWT Design Then we plug in the variables to determine what pressure we will get for 1 kg. air m g l 1 mass P A 23 , 0 1 P P 1 9 . 80665 1 1 . 2 4 . 03155 10 6 7920 1 1 .3 10 6 35 2431997 Pa/kg 8 July 30, 2012 2012 NCSLI Workshop & Symposium 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. P 1 9 . 80665 1 1 . 2 4 . 03155 10 6 7920 1 1 .3 10 Amount 4 ea 1 ea 4 ea 1 ea 4 ea 1 ea 2 ea 1 ea psi 2000 1000 200 100 20 10 4 2 6 35 352 . 7313 psi/kg kg 5.67004 2.83502 0.56700 0.28350 0.05670 0.02835 0.01134 0.00567 9 July 30, 2012 2012 NCSLI Workshop & Symposium 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 4 ea 1 ea 4 ea 1 ea 4 ea 1 ea 2 ea 1 ea Carrier psi 2000 1000 200 100 20 10 4 2 200 kg 5.67004 2.83502 0.56700 0.28350 0.05670 0.02835 0.01134 0.00567 0.54300 Reference level at Test port 10 July 30, 2012 2012 NCSLI Workshop & Symposium 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 3000 psi 1 3000 psi 2 3000 psi 3 3000 psi 4 3000 psi 5 3000 psi 6 3000 psi 7 3000 psi 8 3000 psi 9 3000 psi 10 3000 psi 11 3000 psi 12 Mass 8505.184 8505.691 8506.197 8506.704 8507.210 8507.717 8508.223 8508.730 8509.236 8509.743 8510.249 8510.756 11 July 30, 2012 2012 NCSLI Workshop & Symposium 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 12 July 30, 2012 2012 NCSLI Workshop & Symposium 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. 13 July 30, 2012 2012 NCSLI Workshop & Symposium DWT Design • The calculation for ‘partial correction’ is as follows… gl is where the DWT is going to be used. Pcorr g Pnom and Pcorr Pcorr g gl gc gc is the gravity the DWT was made for. 1 p c 23 Thermal expansion of the piston-cylinder effective area times the difference between the reference temperature and the presumed piston-cylinder temperature. 14 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. 15 July 30, 2012 2012 NCSLI Workshop & Symposium 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. 16 July 30, 2012 2012 NCSLI Workshop & Symposium Uncertainties Table 1. Examples of gravity predictions and associated uncertainty predictions. PTB Difference Difference Location PTB Ugl(95) NGS NGS Ugl(95) from PTB WGS84 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 = × 4.047 + 2 × −0.0456 × 0.009 × where: L = D = Absolute value of latitude latitude change in distance [degrees] [km] For changes in elevation the error is approximately 0.31 ppm per meter of elevation change 17 July 30, 2012 2012 NCSLI Workshop & Symposium 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. 18 July 30, 2012 2012 NCSLI Workshop & Symposium 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 19 July 30, 2012 2012 NCSLI Workshop & Symposium Uncertainties Piston Head Upper MP Lower MP Low Range MP Extra MP 20 July 30, 2012 2012 NCSLI Workshop & Symposium Uncertainties 23.75 23.25 ˚C Ambient Temperature 22.75 Mounting Post Temperature 22.25 21.75 0:43:12 1:55:12 3:07:12 Elapsed time 4:19:12 5:31:12 6:43:12 Figure 1. Simultaneous log of temperatures of an IDWT mounting post and Ambient temperature in a controlled environment. 21 July 30, 2012 2012 NCSLI Workshop & Symposium Uncertainties 27 26.5 26 25.5 Ambient Temperature ˚C 25 24.5 Mounting Post Temperature 24 23.5 23 22.5 22 0:00:00 2:24:00 4:48:00 7:12:00 Elapsed Time 9:36:00 12:00:00 14:24:00 Figure 2. Simultaneous log of temperatures of an IDWT mounting post and ambient temperature in an uncontrolled environment. 22 July 30, 2012 2012 NCSLI Workshop & Symposium Uncertainties • With these tests we felt comfortable using the following for the uncertainties of the change in effective area due to piston-cylinder temperature. Application ( + ) [1/˚C] 11 x 10-6 16 x 10-6 21 x 10-6 22 x 10-6 Table 4. Contributing temperature uncertainties All Methods Method 1,2 Method 1,2 Method 3 UT no UTalpha UTdevice UTp-c correction [ppm] 2.8 4.0 5.0 5.5 [ppm] 11.0 16.0 20.0 22.0 [ppm] 11.0 16.0 20.0 22.0 [ppm] 55.0 80.0 100.0 110.0 23 July 30, 2012 2012 NCSLI Workshop & Symposium 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. 24 July 30, 2012 2012 NCSLI Workshop & Symposium Uncertainties Table 6. Deviations of a dual range hydraulic IDWT Nominal Measured Pressure 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 10 100 200 300 400 500 3.5 MPa (500 psi) range 10.0001 100.0067 200.0175 300.0278 400.0371 500.0463 Maximum Deviation: 10 67 88 93 93 93 93 25 July 30, 2012 2012 NCSLI Workshop & Symposium Conclusion • The final uncertainty budget ended up looking something like this… Table 7. Uncertainty Budget for a dual range hydraulic IDWT Method Influence Section Gravity 5.1 Mass 5.2 Air Buoyancy 5.3 Effective Area 5.4 P-C temperature 5.5a P-C temperature 5.5b Level 5.8 Performance 5.9 5.2, 5.6, Deviations 5.10 Combined Expanded 70 Mpa (10000 psi) range 1 2 3 [ppm] [ppm] [ppm] 10 10 10 10 10 10 1 8.5 8.5 50 50 50 8 8 40 8 8 0 8.5 8.5 8.5 15 15 15 3.5 Mpa (500 psi) range 1 2 3 [ppm] [ppm] [ppm] 10 10 10 10 10 10 1 8.5 8.5 50 50 50 8 8 40 8 8 0 8.5 8.5 8.5 15 15 15 0 [ppm] 55 80.5 [ppm] 98 80.5 [ppm] 101 0 [ppm] 56 46.5 [ppm] 73 46.5 [ppm] 83 112 197 211 112 146 165 26 July 30, 2012 2012 NCSLI Workshop & Symposium 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! 27 July 30, 2012 2012 NCSLI Workshop & Symposium