Lecture 11: Spreadsheets for Engineering Applications – part 1 BJ Furman 16APR2012.
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Transcript of Lecture 11: Spreadsheets for Engineering Applications – part 1 BJ Furman 16APR2012.
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Lecture 11: Spreadsheets for Engineering Applications – part 1
BJ Furman
16APR2012
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The Plan for Today
Spreadsheets for engineering applications - part 1 Charting and data presentation Example: LVDT calibration Adding a trend line to data Numerical integration Numerical differentiation
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Learning Objectives
Create effective charts and graphs Explain the difference between a line chart
and a scatter plot
Add and format secondary axes
Annotate and format a chart for presentation in a written report
Find the area under a curve using trapezoidal integration
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Graphical Presentation in Engineering
Presenting data in graphical form is extremely important! A picture really is worth a thousand words!
Especially for engineering!
Excel (or other spreadsheet program) offers very powerful, easy to use graphical presentation tools. Get good at using it!
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LVDT Sensor Linear Variable
Differential Transformer non-contact, friction-free
position sensor infinite resolution absolute position
measurement robust
Need to calibrate Measure output voltage
as the core is moved known amounts
Plot voltage vs. displacement
http://www.transtekinc.com/assets/images/240ACTION.gif
http://www.macrosensors.com/images/tutorial_page_images/images/fig1.jpg
http://www.rdpe.com/us/hiw-lvdt.htm
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LVDT application – Road Simulator
http://www.swenox.com/gtc/images/4-axis-durability-rig.jpg
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Calibration of LVDT Sensor
Method used by Leroy-Crandall Geotechnical Laboratory
http://gees.usc.edu/soilab/Photos/Calibration%20Pictures/mvc-159f.jpg
http://gees.usc.edu/soilab/Calibration.htm
Micrometer head
LVDT core
LVDT body
core motion
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XY Scatter vs. Line Chart
What is the difference? Different treatment of the x-axis data
XY Scatter Chart: for x data that varies continuously Interpolating between points makes sense Ex. temperature vs. time over 24 hrs
Line Chart: for x data that is categorical or equally spaced Interpolating between points may not make sense Ex. average lab report score for Tues, Wed, Thurs sections
XY Scatter Charto x-axis data varies continuouslyo Actual x-axis data that is unequally
spaced will be plotted properlyo good for analyzing trend in datao most often used for engineering
analysis
Line Charto x-axis data will be equally spaced on
the chart (beware!). If the actual x data is not equally spaced, the plot will be misleading.
See: XY Scatter vs. Line Chart.xls
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XY Scatter vs. Line Chart, cont.
Smoothed line or not? Generally, not
Smoothed line can be misleading unless generating function is a good representation of actual behavior of the data
Better to leave as points or fit a regression line/curve that is a likely candidate to describe the underlying behavior
right-click | Format Data Series | smoothed line check-box
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Analyze LVDT Calibration Data curve fit.xls
Plot data Add trend line with the
wizard Get the trend line using
SLOPE(), INTERCEPT(), OR LINEST( ) returns an array formula must be entered
as an array cntrl+shift+enter output array is 5 x
nindep_var +1 data sets
Displ. (mm) A/D signal (V)5.08 8.01884.572 7.50034.064 6.7563.556 5.92773.048 5.10862.54 4.27062.032 3.41.524 2.55621.016 1.68950.508 0.83190 -0.0256-0.508 -0.9036-1.016 -1.752-1.524 -2.6273-2.032 -3.4366-2.54 -4.3106-3.048 -5.1587-3.556 -5.976-4.064 -6.7865-4.572 -7.4911-5.08 -8.0548
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LINEST() statistics
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Adding Data Series
Cases where you might have additional data to add to a chart Calculations on a data set Multiple data sets
Right-click in the plot region ‘Select Data’ (2007) or ‘Source data’ (2003) Add a data series
Name X values Y values If x values are the same as previous, can just cut-and-paste
Example: LVDT_dataset_for_lecture.txt
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Adding a Secondary Y-axis
Sometimes it is useful to plot multiple data sets on the same graph that have the same x-values, but vastly different y-values. Example: voltage divider.xls
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Adding Names to RangesHighlight names and values
2003: Insert / Name / Create / Left column2007: Formulas / Defined Names tab / Create from Selection / Left column
Result
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Formatting Your Chart Default is probably not the best! Publication or presentation?
Publication No fill of chart background No fill of data point markers B&W markers, lines, annotation Use line types that can be differentiated in a B&W photocopy Maximize chart area For landscape orientation, title goes closest to the spine
Annotate well Descriptive title Labeled axes with units!! Error bars with measured data
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Creating a Figure
Maximize the information transfer What will the busy (or lazy) reader actually
read of your report? Structure of figure annotation:
Figure number Figure title Figure caption
Really important and often overlooked!
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Figure number must be
referred to in the report
Figure title Descriptive
Figure caption The key
information you want the reader to understand from the figure
Note inset figure and additional annotation for clarity
Figure Example
(Furman, 1991)
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Numerical Integration
Trapezoidal integration Ex. area under a
curve
Area Under ( 3+2cos(px/10) )
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
)10
cos(23 xyp
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Numerical Integration, cont. Divide into trapezoids Calculate the area of the
trapezoids
Sum areas Voila! Results
Exact 21.3661977
Numerical 21.3137515
)(2 1
1ii
iii xx
yyA
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Numerical Integration (recap)
Can think of integration as finding the area under a curve Break area
up into trapezoids
http://people.oregonstate.edu/~haggertr/487/integrate.htm
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Numerical Integration Example
http://www.onid.orst.edu/~haggertr/487/integrate.xls
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Numerical Differentiation
(Larsen, 2009)
First derivatives
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Numerical Differentiation, cont.
Second derivatives
(Larsen, 2009)
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Prose vs. a Figure
Tube wall and reflector pin temperatures vs. time during the radiative heating
feasibility test.The focus of the concentrator was brought into axial alignment with the tube bore at about t=1.4 s and re-adjusted at about t=5 s. The radiant flux impinging on the bore of the tube was estimated to be about 1.65 MW/m^2 from measurements made after the test. The tube wall temperature rises rapidly to about 275 ºC in comparison to the reflector pin, confirming predictions that non-contact heating using a radiant source and an internal conical reflector is indeed feasible.
Which would you rather look at?
Or
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References Furman, B. (June, 1991). A new, thermally
controlled, non-contact rotor balancing method (Doctoral dissertation). Available from University Microfilms International (UMI No. 9205634). p. 227
Larsen, R. W. (2009). Engineering with Excel, Pearson Prentice Hall, New Jersey. ISBN 0-13-601775-4
Engineering with Excel companion website: http://www.chbe.montana.edu/excel/EngExcel3.htm. Visited 25OCT2009.