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ME 322: Instrumentation Lecture 8

ME 322: Instrumentation Lecture 8. February 5, 2014 Professor Miles Greiner. Extra Credit Opportunity. http:// wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/SeviceLearningExtraCredit/2014LetterToStudents.pdf

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ME 322: Instrumentation Lecture 8

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  1. ME 322: InstrumentationLecture 8 February 5, 2014 Professor Miles Greiner

  2. Extra Credit Opportunity • http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/SeviceLearningExtraCredit/2014LetterToStudents.pdf • This Saturday, February 8, 8 AM to 4 PM, UNR is will host the Regional Science Olympiad in SEM. • A competition which tests middle and high school teams on various science topics and engineering abilities. • ME 322r students who participate in observing and judging the events for at least two hours (as reported by Shanelle Davis) will earn 1% extra credit in ME 322r. • Contact Ms. Davis, shanelles@unr.edu, (775) 682-7741 by Wednesday, February 5 to sign up. • If you sign-up but don’t show-up you will loose1%! • You cannot get extra-credit in two courses for the same work.

  3. Strain Gages • Their electrical resistance changes by small amounts when • They are strained (desired sensitivity) or • Their temperature changes (undesired sensitivity) • Solution: • Subject “identical” gages to the same environment so they experience the same temperature change and the same temperature-associated resistance change. • Incorporate them in a circuit that cancels-out the temperature effect

  4. Strain Gage Wheatstone Bridge • If initially, R1I= R2I = R3I= R4I • Then VOI ~ 0 + - • Bridge output voltage VO will exhibit large changes compared to VOI when Ri’s changes by small amounts • Incorporate strain gages in the bridge - R3 +

  5. Quarter Bridge + - Only one leg (R3) has a strain gauge. Other legs are fixed resistors, so there resistances don’t change Undesired sensitivity - + R3

  6. Half Bridge + - • Wire gages at R2 (-) and R3 (+) • Place R3 on deform specimen; ε3, ΔT3 • Place R2 on identical but un-deformed; ε2=0, ΔT2=ΔT3 Automatic temperature compensation - + R3

  7. Beam in Bending: Half Bridge ε3 • Twice the output amplitude as quarter bring, with temperature compensation ε2 = -ε3 ε2 = -ε3

  8. Full Bridge + - • If all four legs are stain gages, with nearly identical characteristics, then • Ri, Siand STi are same for all i, so • and • Provides automatic temperature compensation • Use of additional gages, at locations where the stain can be related to the needed strain, can increase output voltage. - + R3

  9. Beam in Bending: Full Bridge 3 1 + - • V0 is 4 times larger than quarter bridge • And has temperature compensation. - + R3 2 4 = -e3 = e3 = -e3 = DT3 = DT3 = DT3

  10. Tension Configuration (HW) ε1 = ε3 ε4 = ε2 = -υ ε3 + - 2 3 R3 - + 4 1

  11. Lab 4 Install Strain Gages on Aluminum or Steel Beams (next week) W T • Install two gage on a Steel or Aluminum beam • Top and bottom • Video Instructions: http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Labs/Lab%2004%20Install_Strain_Gage/Lab%2004%20Index.htm • Measure gage electrical resistance • Un-deformed, under tension, compression, and when cold • Measure beam thickness T, width W, and distance between centers of gage and pin, L • Partners use Vernier calipers, micrometer, and a ruler. • Calculate mean • Use standard deviation to estimate uncertainty • WL, WW, & WT • Use those values and uncertainties in Lab 5 L

  12. Lab 5 Measure Elastic Modulus of Steel and Aluminum Beams (week after next) • Incorporate top and bottom gages into a half bridge of a Strain Indicator • Power supply, Wheatstone bridge connections, voltmeter, scaled output • Measure micro-strain for a range of end weights • Knowing geometry, and strain versus weight, find Elastic Modulus E (of either Steel or Aluminum) • Compare to textbook values

  13. Set-Up e3 W e2 = -e3 T • Wire gages into positions 3 and 2 of a half bridge • e2 = -e3 • Adjust R4 so make V0I ~ 0 L From Manufacturer, i.e. 2.07 ± 1% SINPUT ≠ SREAL Strain Indicator meR R3

  14. Procedure E2 < E1 E1 • Record meRfor a range of beam end-masses, m • Fit to a straight line meR,Fit = a m + b • Slope a = fn(E, T, W, L, SREAL/ SINPUT =1)

  15. Bridge Output • How does indicator interpret VO? • It assumes a quarter bridge and the Inputted S • Transfer Function = 1 ± 0.01

  16. How to relate μεR to m, L, T, W, and E? y g W Neutral Axis m T • Stress: • M = bending moment = FL = mgL • Beam cross section moment of inertia • Rectangle: • Measure strain at upper surface, y = T/2 • Strain: σ L

  17. Indicated Reading • Units • Best estimate of modulus, E • = best estimate of measured or calculated value Slope, a

  18. Will everyone in the class get the same value as • A textbook? • Each other? • Why not? • Different samples have different moduli • Experimental errors in measuring lengths and masses (due to calibration errors and imprecision) • How can we estimate the uncertainty in (wE) from uncertainties in (wL), (wT), (wW), (wS), and (wa)? • How do we even find these uncertainties?

  19. Propagation of Uncertainty • A calculation based on uncertain inputs • R = fn(x1, x2, x3, …, xn) • For each input xi find (measure, calculate) the best estimate for its value , its uncertainty with a certainty level (probability) pi • The best estimate for the results is: • …,) • Find the confidence interval for the result • Find

  20. Concept • Vary one input xi by a small amount (wi) while holding all the others inputs constant (linear analysis) • Uncertainty in due to wi alone is

  21. All the ’s contribute to wR • How to combine them? • Two ideas: • If all the wi’s are the maximum possible uncertainty in xi (100% confident the true value is within ± wi) • Then the maximum possible uncertainty in is: • Use absolute values because it’s not likely that all of the derivatives will be positive

  22. Likely Uncertainty • Maximum possible error is overly pessimistic and not useful since it’s not likely • that all the actual measured values will be the maximum possible distance from the best estimate, or • that they will all push the result in the same direction • A “Likely” estimate (p < 100%) would be more realistic and useful uncertainty estimate • (p < 100%) < (p = 100%)

  23. Statistical Analysis Shows(meaning: take my word for it) • In this expression • Confidence level for all the wi’s, pi (i = 1, 2,…, n) must be the same • Confidence level of wR,Likely, pR = pi is the same at the wi’s • All errors must be uncorrelated • Not biased by the same calibration error

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