1. ME 322: Instrumentation Lecture 8 February 3, 2016 Professor Miles Greiner Lab 4, Propagation of Uncertainty, Maximum and likely, Power Product, Examples

2. Announcements/Reminders All future HW: all plots must be generated and clearly formatted by Excel, MatLab, or… – No hand-drawn plots This week in lab – Lab 3 Pressure Transmitter Calibration – Please bring you Excel from L3PP, and the instructions. For the rest of the week, groups will move to pressure standards instead of moving standards to pairs of groups. – Should be faster for everyone. We will purchase more standards before next year.

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 R3R3 + + - -

5. Beam in Bending: Half Bridge ε3ε3 ε 2 = -ε 3 R3R3 + + - -

6. Lab 4 Install Strain Gages on Aluminum and Steel Beams (next week) Install two gage on a Steel or Aluminum beams – Top and bottom – Video Instructions: http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/L abs/Lab%2004%20Install_Strain_Gage/Lab%2004%20Index.htm http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/L abs/Lab%2004%20Install_Strain_Gage/Lab%2004%20Index.htm Measure gage electrical resistance – Checks whether wire we connected correctly – Un-deformed, under tension, compression, and when cold W L T LTLT

7. Lab 4 Install Strain Gages on Aluminum and Steel Beams (next week) W L T LTLT

8. Calculate Beam Density

9. Propagation of Uncertainty

10. Concept

12. Likely Uncertainty

13. Statistical Analysis Shows (meaning: take my word for it)

14. Rectangle Example

15. Work on the white board Identify: – Are we trying to find the Maximum or Likely Uncertainty? – Are all the certainty levels the same? – n = ?

16. A Simple method to propagate uncertainties in Power Product calculations

17. Fractional Uncertainty

18. General Power Product Uncertainty

19. Repeat Rectangle Example using Power Product Rule

20. Lab 4: Calculate Beam Density W L T LTLT