ME 322: Instrumentation Lecture 5

1. ME 322: InstrumentationLecture 5 January 29, 2014 Professor Miles Greiner

2. Announcements • Do you know anyone who took ME 322 and would like to get paid to help in Lab? • If so, please ask them to contact me. • greiner@unr.edu

3. Lab 3 Pressure Transmitter Calibrations (or proximity Sensor) IT • Dwyer Series 616 Pressure Transmitter • Measurand: Pressure difference between HI and LO ports, DP = PHI – PLO. • The Output or “Reading” is current, IT [mA], measured by a Digital Multimeter (DMM) • Power must be supplied to pins 1 and 2 (0-35 VDC) • Diaphragm with starin or proximity gage • Output may be affected by orientation wrt gravity (undesired) PLO PHI

4. Transmitter Characteristics • See Lab 3 website, ~$150 • Use different diaphragm thickness or flexibilities to get different sensitivities to vary Full Scale (FS) range and resolution • Accuracy: 616: ±0.25% F.S. • Stability: ±1% F.S./yr. • Two models in lab: • 616-1: FS = 3 in WC; Accuracy = 0.0025*3 = ±0.0075 in WC • 616-4: FS = 40in WC; Accuracy = 0.0025*40 = ±0.1 in WC • What does this accuracy mean (what is its confidence level)? • Manufacturer’s Inverted Transfer Function (M vs R) • Pressure head: h = FS(I – 4mA)/16mA • IT = 4 to 20 mA • What is the confidence level (probability) that the real pressure head is within the interval h ± Accuracy? • Pressure Difference: DP = PHI – PLO = rWgh • rW = 998.7 kg/m3 g = 9.81 m/s2

5. Pressure Standard Characteristics • Martel BetaGage Model 321A, ~$2000 • More stable (less calibration drift) than Dwyer 616’s (More expensive) • Each has two pressure gages, • FS = 25 mBar (10 in WC); ±0.1% FS: • Accuracy = 10*0.001= 0.01 in WC • Use this to calibrate 3 in WC transmitter (±0.0075 in WC) • FS = 350 mBar (141 in WC), ±0.035% FS • Accuracy = 141*0.00035=0.05 in WC • Use this to calibrate 40 in WC transmitter (±0.1 in WC) • In Lab 3, one gage will be shared by two stations

6. Lab 3 Set-up and Procedure • Transmitter LO port open to atmosphere • Bulb and valve to standard, HI transmitter port, and high pressure port of manometer • Allow high tube pressure to reach atmospheric • Set IT = 4.00 mA, and “zero” the Pressure Standard • At each pressure level record hS (from Standard) and IT (from DMM) • Record data from two ascending and descending pressure cycles, with at least 6 measurements in each direction

7. Gage Characteristic • High pressure transmitters will be connected to high pressure calibrator port • Low pressure transmitters to low calibrator port • One calibrator will be shared by two groups • Accuracy of the transmitter and Standard are roughly the same, but Standard drifts less

8. Plot Manufacturer’s and Measured Transfer Functions • Fit a line IT,F = ahS+ b to the data • Measured transfer function (How to find a & b?) • The data does not all fall along one thin line due to gage imprecision (more like a “cloud” than a line) • The measured current for this gage is systematically larger than predicted by the Manufacturer

9. Error of Manufacturer’s Transfer Function • Error plot e = IT – IM makes it easier to see • Increases with hS reaches ~0.35 mV (out of 20 mV)

10. Deviation of Data form Fit Line • Deviation plot d= IT – IT,F makes it easier to see • ~Equally scatter above and below • Same for ascending and descending data (no hysteresis) • No systematic deviations (linear response)

11. Example of Non-Linear Behavior • Deviation plot makes it easier to see

12. How to use the Calibration? • Measure gage current, I • Algebraically invert the transfer function (I = ah + b) to find h • h = (I – b)/a • If we did not calibrate, then we would assume the dotted line, which systematically give higher pressures than actually applied • How to find a and b and the uncertainty in h? Manufacturer Prediction Measured

13. Least Squares Linear Fit di = yi – yF,i y or R • Two Unknowns: a and b • Define deviation of data from best fit line for each data point • di = yi – yF,i = yi – (axi – b) • Minimize: E = yF= ax + b x or M

14. Find a & b that minimize E • Two constraints: E: and • Solve simultaneously … and get Hint: You may use your calculator to find a & b – unless told otherwise. Learn how.

15. How well does Best Fit Line fit the data? • Best fit line • yF = ax + b • Deviation of each estimate • di = yi - yF,i = yi – axi - b • Define Standard Error of the estimate, of y given x • Note: if n = 2, the di = 0 (a line will pass through both points • Only has meaning if n > 2

16. Standard Error of the Estimate of y given x sy,x • Characterizes the vertical spread of the data • 68% of all yi will be within ±sx,y of yF(x) • 95% is within ±2sx,y • Assuming the error is the same for all x y x

17. Standard Error of the Estimate of x given y sy,x • Characterizes the horizontal spread that contains 68% of the data • sx,y= sy,x/a, a = slope of best fit line sx,y y x

19. Transfer Function Hint: You may use your calculator to find a & b – unless told otherwise. Learn how. How well does Yfit = aX + b fit the data? Deviation of the output Standard error of the estimate.

20. Equipment for Lab 6 What is the confidence level?

21. Equipment for Lab 6 How confident that the actual pressure is within this range? How many standard deviations is W?

22. Transfer Function Plot Best fit line R = a*hT+ b