1. ME 322: Instrumentation Lecture 6 January 30, 2015 Professor Miles Greiner Review Calibration, Lab 3 Calculations, Plots and Tables

2. Announcements/Reminders HW 2 due Monday – L3PP – Lab 3 preparation problem Create an Excel Spreadsheet to complete the tables, plots and question in the Lab 3 instructions, using the sample data on the Lab 3 website. Bring that spreadsheet to lab next week and use it for your data. You can sign up for Extra credit Science Olympiad until Wed, Feb 4, 2015 HW 1 Comments – Plot using Excel (not by hand) – Hint: Do some summation calculations by hand to be sure you know how it is done

3. Instrument Calibration (review)

4. How to Use the Calibration

5. What does Calibration do? Removes systematic bias (calibration) error Quantifies random errors – imprecision, non-repeatability errors – But does not remove them Quantifies user’s level of confidence in the instrument

6. Manufacturers often state “accuracy” May include both imprecision and calibration drift – Often not clearly defined This is one of the objectives of Lab 3

7. Table 1 Equipment Specifications In your report you will use the first column, and only one from the second and third columns The confidence levels for the transmitter accuracy is not given by the manufacturer –We will determine it in this experiment.

8. Table 2 Calibration Data This table shows two cycles of ascending and descending pressure calibration data. The transmitter current did not return to 4.00 mA at the end of the descending cycles.

9. Fig. 1 Measured Transfer Function For the sample data – The measured transmitter current is consistently higher than that predicted by the manufacturer- specified transfer function. – Standard errors of the estimates for the transmitter current for a given pressure heat is S I,h = 0.035 mA, and S h,I = 0.0065 in-WC. – The manufacturer-stated accuracy (0.0075 in-WC) for the transmitter is 1.15 times larger than S h,I, corresponding to a 75% confidence level. Your data may be different!

10. Fig. 2 Error in Manufacturer’s Transfer Function Error in the manufacturer-specified transfer function increases with pressure Maximum error magnitude is 0.35 mA.

11. Fig. 3 Deviation from Linear Fit S I,h characterizes the deviations over the full range of h S Neither the ascending nor the deviations are generally positive or negative, which suggests that hysteresis does not play a strong role in these measurements. There are no systematic deviations form the fit correlation, indicating the instrument response is essentially linear.

12. This lecture demonstrates how to Format plot labels, borders, fonts,.. – Different symbols for ascending and descending data Calculate standard error of estimate, confidence level Write abstract last: Objective, methods, results Sample Data http://wolfweb.unr.edu/homepage/greiner/teaching/MECH3 22Instrumentation/Labs/Lab%2003%20PressureCalibration /Lab%20Index.htm http://wolfweb.unr.edu/homepage/greiner/teaching/MECH3 22Instrumentation/Labs/Lab%2003%20PressureCalibration /Lab%20Index.htm

13. Confidence Level of Manufacture-Stated Uncertainty Find the probability a measurement is within 1.15 standard deviations of the mean Identify: Symmetric problem z 1 = -1.15, z 2 = 1.15 Your confidence level may be different

15. Interpretation of Measurement Question

16. Abstract In this lab, a 3-inch-WC pressure transmitter was calibrated using a pressure standard. – The transmitter current I T was measured for a range of pressure heads h, as measured by a pressure standard. The measured inverted-transfer-function was – h = (0.1838 in-WC/mA)I T – (0.7335 in-WC), – The 68%-confidence-level confidence-interval for this function is ± 0.0064 in-WC The manufacturer’s stated uncertainty is 0.0075 in-WC – This is 1.15 time larger than the 68%-confidence-level interval, which corresponds to a 75%-confidence-level

17. Lab 3 Static Calibration of Electronic Pressure Transmitters February 3, 2014 Group 0 Miles Greiner Lab Instructors: Josh McGuire, Şevki Çeşmeci, and Roberto Bejarano

19. S xy = Standard error in X given Y S yx S xy

20. Example of Hysteresis