Transcript Lecture Slides

ME 322: Instrumentation
Lecture 10
February 8, 2016
Professor Miles Greiner
Lab 5 Summary and Calculations
Announcements/Reminders
• HW 3 due now
– use ME 322 ID number and lab day
• HW 4 Due Wednesday 2/10/16
– Joseph Young and Marissa will hold office hours
tomorrow (email)
– Will accept Friday without penalty
• HW 5 Due Wednesday 2/17/16
• Midterm Friday 2/19/16
– Review 2/17/16
• This week: Lab 4 Strain Gage Installation
– Everyone must wear safety glasses
Lab 5 Measurement of Elastic Modulus of
Steel and Aluminum Beams (next week)
Aluminum Beam
Mass, Microstrain
m
Reading, me
[kg]
[μm/m]
0.0000
-1
0.2181
200
0.5252
483
0.9006
825
1.2602
1159
1.5698
1447
1.2602
1156
0.9006
827
0.5252
580
0.2181
199
0.0000
-2
0.0000
-1
0.2181
199
0.5252
482
0.9006
824
1.2602
1158
1.5698
1444
1.2602
1157
0.9006
827
0.5252
484
0.2181
197
0.0000
-5
Steel Beam
Mass, Microstrain
m
Reading, me
[kg]
[μm/m]
0.0000
0
0.2181
140
0.5252
341
0.9006
586
1.2602
833
1.5698
1049
1.2602
838
0.9006
607
0.5252
357
0.2181
152
0.0000
7
0.0000
6
0.2181
146
0.5252
346
0.9006
592
1.2602
835
1.5698
1048
1.2602
844
0.9006
605
0.5252
350
0.2181
151
0.0000
7
•
Find slope a of micro-strain reading meR versus end mass m
•
•
Last lecture: 𝐸 = 12 × 106
Find uncertainty 𝑤𝐸 (95%)
𝜇𝑚
𝑚
𝑔𝐿 𝑅𝑆
𝑎𝑇 2 𝑊
, where 𝑅𝑆 =
𝑆real
𝑆input
𝜇𝑚
and 𝑎 = slope, 𝑎 = 𝑚 𝑘𝑔
– Power Product? (Yes or no?)
–
•
𝑤𝐸 2
𝐸
= Fill in blank
Need to find best-estimate and 95%-confidence-level uncertainties of all 5 inputs (including 𝑎)
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)
–
𝑠𝑦,𝑥 =
𝑛 (𝑦 −𝑎𝑥 −𝑏)2
𝑖
𝑖=1 𝑖
𝑛−2
Uncertainty of Slope and Intercept
• 𝑠𝑎 = 𝑠𝑦,𝑥
𝑛
𝐷𝑒𝑛𝑜
(68%)
• 𝑠𝑏 = 𝑠𝑦,𝑥
( 𝑥𝑖 )2
𝐷𝑒𝑛𝑜
(68%)
– Where Deno = 𝑛 𝑥𝑖2 −
– Not in the textbook
𝑥𝑖
• Hint: Write this into book for test
• 𝑤𝑎 = ?sa (95%)
2
Summary
• 𝐸 = 12
𝑤𝐸 2
𝐸
=
6 𝜇𝑚
× 10
𝑚
𝑤𝐿 2
1
𝐿
+ 1
𝑔𝐿 𝑅𝑆
𝑎𝑇 2 𝑊
𝑤𝑅𝑆 2
𝑅𝑆
+
𝑆real
𝑆input
, where 𝑅𝑆 =
𝑤𝑎 2
−1
𝑎
+
𝑤𝑇 2
−2
𝑇
+
𝑤𝑊 2
𝑊
𝑥𝑖2 −
𝑥𝑖
• 𝑤𝑇 = 2𝑠𝑇 ; 𝑇 = mean
• 𝑤𝑊 = 2𝑠𝑊 ; 𝑊 = mean
• 𝑤𝐿 =
1
2
𝑖𝑛𝑐ℎ
32
3
=
1
48
𝑖𝑛𝑐ℎ 95%
• 𝑤𝑅𝑆 = 0.02 95% ; 𝑅𝑆 = 1
• 𝑤𝑎 = 2𝑠𝑎 ; 𝑠𝑎 = 𝑠𝑦,𝑥
𝑛
𝐷𝑒𝑛𝑜
; Deno = 𝑛
2
Lab 5 Sample Calculations
• http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentati
on/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
Strain Gage Factor Uncertainty
• In L5PP, manufacturer states
– S = 2.08 ± 1% (pS =?, not given)
• In Lab 5, the values of 𝑆 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 𝑅𝑆 =
𝑆𝑅𝑒𝑎𝑙
𝑆𝐼𝑛𝑝𝑢𝑡
= 1 ± 0.02 (95%)
• 𝑤𝑅𝑆 = 0.02 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, 𝑇 𝑎𝑛𝑑 𝑊
– Use sample standard deviations 𝑠𝑇 and 𝑠𝑊 for the 68%confidence-level uncertainty
• The 95%-confidence-level uncertainties are
– 𝑤𝑇 = 2𝑠𝑇
– 𝑤𝑊 = 2𝑠𝑊
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
• 𝑤𝐿 = (2/3)(1/32) = 1/48 inch
UNR General Undergraduate Research Award
• Apply for up to $1,500 to perform 2015-6 academicyear-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