ME 322: InstrumentationLecture 10

February 9, 20154Professor Miles Greiner

Lab 5 Summary and Calculations

Announcements/Reminders• HW 3 due now (use ME 322 ID number!)– HW 4 due Friday • Really could be turned in Wednesday

– HW 5 Due Wednesday 2/18/15• Review 2/18/15, –Midterm Friday 2/20/15

• This week: Lab 4 Strain Gage Installation – Everyone must wear safety glasses

UNR General Undergraduate Research Award

• Apply for up to $1,500 to perform 2015-6 academic-year-projects in close collaboration with a faculty mentor

• Application Deadline: April 6th, 2015• Application instructions are online:

– http://environment.unr.edu/undergraduateresearch/opportunities/gura.html

• I am interested in working with students who do very well in this class– Opportunities in Heat Transfer applied to Nuclear

Packaging safety

Lab 5 Measurement of Elastic Modulus of Steel and Aluminum Beams

• Find slope a of micro-strain reading meR versus end mass m • , where and = slope

• Find uncertainty wE – Power Product? (Yes or no?)– Fill in blank

• Need to find best-estimate and 95%-confidence-level uncertainties of all 5 inputs

Mass, m

Microstrain Reading, me

[kg] [μm/m]0.0000 -10.2181 2000.5252 4830.9006 8251.2602 11591.5698 14471.2602 11560.9006 8270.5252 5800.2181 1990.0000 -20.0000 -10.2181 1990.5252 4820.9006 8241.2602 11581.5698 14441.2602 11570.9006 8270.5252 4840.2181 1970.0000 -5

Aluminum BeamMass,

mMicrostrain Reading, me

[kg] [μm/m]0.0000 00.2181 1400.5252 3410.9006 5861.2602 8331.5698 10491.2602 8380.9006 6070.5252 3570.2181 1520.0000 70.0000 60.2181 1460.5252 3460.9006 5921.2602 8351.5698 10481.2602 8440.9006 6050.5252 3500.2181 1510.0000 7

Steel Beam

Strain Gage Factor Uncertainty• In L5PP, manufacturer states– S = 2.08 ± 1% (pS =?, not given) • In Lab 5, the values of and wS may be different!

• In L5PP and Lab 5, assume pS = 68% (1s)– So assume the 95%-confidence-level uncertainty is twice

the manufacturer stated uncertainty• S = 2.08 ± 2% (95%)• So (95%)

Beam Thickness T and Width W

• In Lab 4, both are measured multiple times using a caliper and micrometer– Use sample means for the best value, – Use sample standard deviations and for the 68%-

confidence-level uncertainty• The 95%-confidence-level uncertainties are– = 2– = 2

Distance between Gage to Mass Centers, L

• Measure using a ruler– In L5PP, ruler’s smallest increment is 1/16 inch

• Uncertainty is 1/32 inch (half smallest increment)– Lab 5 – depends on the ruler you are issued

• may be different

• Assume the confidence-level for this uncertainty is 99.7% (3s)– The uncertainty with a 68% (1s) confidence level

• (1/3)(1/32) inch– The uncertainty with a 95% (2s) confidence level

• (2/3)(1/32) = 1/48 inch

Uncertainty of the Slope, a

• Fit data to yFit = ax + b using least-squares method• Uncertainty in a and b increases with standard error

of the estimate (scatter of date from line)–

Uncertainty of Slope and Intercept

• = (68%)• = (68%)

– Not in the textbook

• = ?sa (95%)

Summary• , where

• ; • ; =; • = 2; = mean• = 2; = mean

Lab 5 Sample Calculations

• http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Labs/Lab%2005%20Elastic%20Modulus/Lab%20Index.htm

• Slope uncertainty calculation, sa • 95%-confidence-level uncertainties for each

input• Relative contribution to the uncertainty in the

result from the uncertainty in each input • Comparison of a result to reference value– Reference citation format