ME 322: Instrumentation Lecture 7

1. ME 322: InstrumentationLecture 7 February 3, 2014 Strain Gage Introduction

2. Announcements/Reminders • HW 2 due now (before lecture starts) • PE 113, Lab 3 Pressure Transmitter Calibration

3. 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. • A competition which tests middle school 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%!)

4. General Guidelines for HWs • Use your Course ID numbers(which you can find in MyNevada), not your name or student ID number, when submitting your HWs • Units always! When giving your final answer, always include the units since the numbers itself does not mean anything without units. • No hand-drawn plots! Starting from HW3, whenever you are asked to plot your data, plot them using computer software, i.e. Excel, Matlab, Mathcad etc. • Include labels for both axes with the units. If necessary, include legends too. Make it look good! • Show you work! Do not skip the steps and just write your final answer. Whenever applicable, list your assumptions, write out your formulas and work through to your final answer. If you use a Table (or graph) on your solutions, give reference to that table in your book, i.e from Table 6.3, z=-1.28. • Be clear with your solutions and work neatly! If the grader needs to spend more than 3 minutes to figure out what you write, you may not get even partial credit.

5. Common Mistakes on HW1 • In Problem 6.7, when calculating S.D., a number of students had used the population standard deviation formula instead of sample standard deviation formula.

6. Pressure Gage • Measure • Pressure difference caused diaphragm deformation • elongation or compression • Deformation can be measured using a Strain Gage

7. Strain Gauge Construction • Thin substrate (0.0002”) • Firmly bounded to surface • Metal or Semiconductor foil on or within substrate • Surface deformation stretches the foil and changes its resistance. • Measure DR = R - Ri • However, are small • Demo: Gage resistance on an aluminum beam in bending

8. Other Stain Gage Applications • Measure • Strain of a deformed part (or elastic modulus) • Applied force or weight • Acceleration

9. What is Strain? • Unit strain • Microstrain • Caused by stress • For Linear Elements • E ≡ Elastic Modulus or Young's Modulus • Material property = fn(Temperature, material) • Describes material stiffness L δ F F

10. To use a Strain Gage, firmly bond it to Surface • The gage will experience nearly the same stain and the object’s (specimen’s) surface • eGAGE = eSURFACE • Does not measure internal stains • The gage deformation will affect the gage resistance, R • The initial (un-deformed) resistance is RI • How to predict DR = R – RI?

11. Wire Resistance L, R • r ≡ Electric Resistivity • Material property = fn(Temperature, Strain, …) • Stretching wire changes L, D & ρby small amounts, and results in small changes in R A D

12. Effect of Deformation • DR = R – RI For small changes DR = dR, use the chain rule: • dR= • Divide by R to get fractional change • Evaluate d( )/( ) terms

13. Evaluate Terms • axial strain • Tying to measure this! • Transverse strain = • ≡ Poisons Ratio • ~ 0 – 0.5 • ~ 0.3 for metals • Cstrain≡ Strain Coefficient of Resistivity • Material property = fn(Temperature, …) • Can be large, and > or < 0 for semiconductors

14. Combined Effects • = • Dimensionless • Metal Foils: S = 1.6 to 4 (typical 2.07) • Semiconductors: S = -140 to 175

15. L Example D • Apply 1000 lbf to diameter D = 0.25” steel rod. • E = 207 GPa = 30x106 psi • For a strain gage with: RI = 120 Ω, S = 2.07 • Find: R = RI + ∆R • R = 120 + 120(0.001406) = 120.17 W • Very small fractional change!

16. Undesired Temperature Sensitivity • Gauge resistivity is affected by temperature • Thermal expansion of specimen and gage may be different, which can stain the gage • Resistance is determined by measuring the voltage across the gage while passing a current though it, which can heat the gage! • Temperature factor ST: • Can a circuit “automatically” compensate? Gage Temperature Change - undesirable sensitivity Desired measurand

17. Wheatstone Bridge Circuit • Two voltage dividers • Use stain gages, whose resistances change by small amounts when they are deformed, for some of these resisters R3

18. Initial State • Choose initial resistances so that initial VO,I ~ 0 • R1R3~ R2R4 (For example, all could be ~equal) • Small changes in each Ri will cause a relatively large fractional change in VO (compared to VO,I ~ 0) R3

19. Effect of small resistance (dRi) changes on VO • Chain Rule: • ++ • Find partial derivatives, plug in and us R1R3= R2R4, = 0 = , ... • Opposite legs (1, 3) and (2, 4) reinforce • Adjacent legs (1, 2) and (3, 4) oppose R3

20. Full Bridge + - • If all four legs are stain gages, with nearly identical characteristics, then • Ri, Siand STi are same for all I, so • and - + R3

21. Quarter Bridge + - Only one leg (R3) has a strain gauge. Undesired sensitivity - + R3

22. Half Bridge + - • Wire gages at R2(-) and R3 (+) • Place R3on deform specimen; ε3, ΔT3 • Place R2on identical but un-deformed; ε2=0, ΔT2=ΔT3 Automatic temperature compensation - + R3

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

24. Beam in Bending: Full Bridge • All four legs. • V0is 4 times larger than quarter bridge • And has temperature compensation. + - 3 1 R3 - + 2 4

25. Tension ε4=υ ε3 ε2=υ ε3 ε4=ε3 2 3 R3 4 1

27. Other Applications of Stain Gages