ME 322: Instrumentation Lecture 4

1. ME 322: InstrumentationLecture 4 January 27, 2014 Professor Miles Greiner

2. Announcements • Turn in HW 1 now (use ME 322 student number, not name) • HW 2 due Monday 2/3/2014 (assignment and reading on Web) • Go to PE 113 for lab this week • Lab 2 - Statistical Analysis of UNR Quad Measurements • Download and read instructions Lab 2 Instructions and Lab Guidelines

3. In Lab • Please • Work in 2-person lab groups (assigned in lab) • Be on time (responsibility to lab partner) • Be prepared (read lab instructions) • Be professional and patient (treat the TA’s well) • Lab Participation Points are assigned by Lab TA

4. Pressure • Can’t see it • Need gages (gauges) to • Qualitatively know when it changes • Quantitativelymeasure it • Units • [Pa] = [N/m2]; [kPa] = [1000 Pa]; [MPa] = [106 Pa] • [psi] = [lbf/in2] • Gage Pressure • Amount a vessel’s pressure is above its surrounding’s • PGAGE = P – PATM P PATM

5. Some Gages • Bourdon Tube • Diaphragm • Manometers • Vertical • Inclined • Water Head, h

6. Instrument Transfer Function • Relationship between the instrument reading R and its measurand M (quantity being measured) • May not be linear

7. U-Tube Manometer • The reading can be given in units of inches or cm of water column [in WC] or [cm WC] • Or inches or cm of mercury or alcohol • What is the transfer function (Reading versus Measurand)? Measurand Reading DP = 0 Fluid Air (1 ATM, 27°C) Water (30°C) Hg (27°C) 1.774 995.7 13,565

8. Transfer Function Low rm (alcohol) High rm (mercury)

9. Inclined-Well Manometer AW P1 P2 AT h1 q h2 DP = 0 R

10. Transfer Function R If And

11. Transfer Function Small q Large q

12. General “Linear” Instrument Characteristics RMAX DRMIN MMAX DMMIN (smallest change in reading that can be detected, i.e. tick mark, digit) )

13. Sensitivity affects both Resolution and Range • In general, it is not hard to change sensitivity • Increasing S improves resolution • but decreases range • Resolution as a fraction of Range

14. Instrument Repeatability • Will an instrument give the same reading every time it is exposed to the same Measurand? • Why not? • Transfer function may drift with time. So at a later time the readings may shift to consistently higher (or lower) values than before. • Referred to as Systematic or Calibration Error • Random variations of uncontrolled inputs (such as RF (radio frequency) noise, orientation of instrument, humidity, may lead to Random variations of the Reading. • Referred to as Random Errors or Imprecision

15. General Instrument Desired Input (Measurand M) i.e. length, pressure temperature Instrument Output Reading R (deflection, number of steps, needle angle) Controlled (i.e. temperature, orientation) Uncontrolled (i.e. RF frequency, walking stride length Undesired Inputs x1, x2, x3, x4, x5,…

16. General Transfer Function • Reading R = fn(M, x1, x2,…, xn) • How to find the Transfer Function? • Theory: • good for simple device (manometer) • Done in other classes • Only includes the effects you model (at best)! • Calibration: • controlled measurement process • Measure reading (R) while exposing instrument to a range of measurands (M) that are being measured by a reliable standard (used to determine M).

17. Calibration Correlation Instrument Under Test Standard • Correlate Reading R with Measurand M (least squares fit) • May not be linear • Uncontrolled inputs can cause R to have undesired variations of the same M! • The sized of the variation is a measure of the instrument impression (random, inconsistent output) • Systematic errors can be removed using calibration, but random errors cannot!

18. How to reduce Measurement Imprecision? • Improve the control of undesired inputs, and/or • Use a different instrument that is less sensitive to uncontrolled inputs

19. Calibration Transfer Function Data Correlate Scatter – Uncontrolled inputs instrument