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EE13 Updating Selected Laboratories for Engineering Experimentation Course at Worcester Polytechnic Institute A Major Qualifying Project Report Su

3 2. Background 2.1 Contents and Implementation of the Course The Engineering Experimentation course at WPI is a junior-level compulsory course f

93 Figure 24 Neutral axis of a beam subjected to bending Euler—Bernoulli beam theory relates curvature of a bending beam to bending moment and rigid

94 distributed loads and uniformly varying loads over the span and a number of concentrated loads are conveniently handled using this technique. For

95      Figure 3 Deflection, Bending Moment and Shear Stress Recall Eq.2 and Eq.3, a

96   2.2 Dynamic Characteristics of a Cantilever Beam under Free Vibration Vibration is a mechanic

97   Solution for displacement is:    Where:  For a cantilev

98 A simple method of approximating the natural frequency of cantilever beams is shown below. The method also estimates equivalent stiffness and equi

99 The lumped load  at the end of beam has the kinetic energy:    The two kinetic energies of Eq. 29 and Eq.30 need to be e

100 underdamped cases, there exists a certain level of damping at which the system will just fail to overshoot and will not make a single oscillation

101   The critical damping factor of a cantilever beam is  = 2.3 Measurement Methods of Dynamic Ch

102  The three components are combined to form the Fourier series:   

4 Familiarity of computerized data acquisition system is cultivated in required courses in the majority of programs investigated, and a significant a

103 The components of the Fourier series are given by       

104 Figure 5 Fourier serious expansion of a periodic square wave (L=1). The number of terms in the series varies from one, three, to seven and 25.

105 Figure 26 Data input to Fourier analysis and results 0240 2 4 6 8 10 12 14 16 18 20Magnitude Frequency (Hz) FFT result: f=10.02Hz -2020 0.2

106 The result of FFT includes a real and an imaginary component. The magnitude (or power) and phase of the FFT data is computed by =

107 Figure 27 properties of Fourier Transformation This additivity can be understood in terms of how sinusoids behave. Consider adding two sinu

108 Time Domain: T=2 sec Magnitude in Frequency Domain Frequency: 0.5 Hz Phase (degrees) in Frequency Domain Figure 28 Fourier Transform of Peri

109 Phase (degrees) in Frequency Domain Figure 29 Fourier transformation of periodic sawtooth function without offset and time shift. Applying Fou

110 Time Domain: T=6 sec Magnitude in Frequency Domain First Frequency: 0.167 Hz Phase (degrees) in Frequency Domain Figure 31 Fourier transfor

111 2.3.3 Determining Vibration Amplitude, Velocity, and Acceleration Eq.28 shows the relationship between the deflection at the free end of the be

112 that defines the continuous waveform). In the case of a set of n values, the RMS is given by:      The R

5 acquire data in strains as the Strain and Pressure Measurement Laboratory, including strain gauges, a Wheatstone bridge, a signal condi

113 sensor is directly proportional to the change in resistance of the gauge used, as shown in Eq 7.When unstressed, usual strain gauge re

114 Figure 32 Temperature Effects on Thermal Output of Strain Gauges Strain gauge’s product name contains all critical information needed t

115 Figure 34 Crucial Information of Strain Gauge Selected 2.5 Basics of Wheatstone bridge A Wheatstone bridge is an electrical circuit used to me

116 Figure 10 circuit diagram of Wheatstone bridge When the bridge is unbalanced, equivalent resistance of the circuit is,  

117 3. PROCEDURES In order to determine the dynamic characteristics and elastic modulus of a vibrating cantilever beam, the procedure

118  The relationship between measured strain and change in output can be found as,  To achieve an output signal of 1mV per ,

119 3.2 Set-Up 3.2.1 Hardware Set-up Clamp the beam to the edge of the lab bench. Place a metal plate between the clamp and the beam for noise reduc

120 21) Mount on tape: secure strain gauge to the surface with tape, before applying adhesive. When mounting the gauge to the tape, make sure that t

121 Figure 37 Lift tape 24) Apply adhesive and attach: apply a drop of adhesive to the gage’s bonding side, attach the gauge and the surface by pr

122 3.2.3 Verify the Set-up Before starting the measurements, the strain gauge installations needs to be verified, the following steps should be fol

6 temperature and pressure vary, which unsettles the equilibrium of fluids and carbon dioxide in the can. For these stated sources or variab

123 4. DATA ANALYSIS AND DISCUSSIONS Determine the vibration amplitude, velocity, and acceleration in various units of measure; determine natural

124 Document 1: Bending Stress and Strain in Cantilever Beam Recall, the definition of normal strain is  Using the line segments shown in Fig

125  This relationship between radius of curvature and the bending moment can be determined by summing the moment due to the normal stresses on

126 Document 2: Set-up Procedure for the Signal Conditioner (Tacuna) d. Connection Connect the wires as indicated in Figure 3. Figure 1 Connecti

127 It is required to open the enclosure to adjust the gain switches but not the offset potentiometer. The wire connections are locate

128 Document 3: LabVIEW Construction Tutorial This sample LabVIEW program for the Vibration Laboratory acquires the voltage input from connected NI D

129

130 Add a While Loop and connect the (already created) Stop Button with the Loop Condition icon. (Functions Palette  Programming  Structures Whi

131 select “Power spectrum” as measurement. Change the labels of the Graphical Indicators into “Frequency Domain – Linear” and “Frequency

132 Go to Front Panel and configure the three Waveform Graphs. Replace the default axis labels with appropriate names (left clicking on the l

7 error in finding the “effective length” adds uncertainty to the elastic modulus estimation. The boundary condition created by the fixt

133 The Write to Measurement File should be configured as shown below. The filename in this wizard will be overwritten by the input; it should “

134 Rearrange the objects for a desirable layout. Drag the icon and drop them at appropriate locations. The objects can be arranged with the tools o

135 When the run button appears as a rightward arrow, enter appropriate parameters on the Front Panel, connect a BNC cable to AI0 of the D

136 Document 4: Optional Activities 1. Create a shared data file for the class; consolidate measured internal pressure from all the students. What i

8 Finite Element simulation (Kargar, S; Bardot, D.M. ., 2010) to simplified method of drawing a smooth curve to connect the data points on a plot wit

9 2.2.2.5 Software The course requires no previous experience of programming in LabVIEW, therefore, the instructive materials need to guide the

10 3. Methodology 3.1 Selection of Alternative Signal Conditioners 3.1.1 Selection of Potential Alternative Signal Conditioners for In-Lab Testin

11 In the case of the current set-up, the range can be set to 5V. Thus, the resolution is 0.22mV. Amplifier gain determines the tr

12 Table 1 Parameters for Testing Strain load can be simulated when a shunt resistor is connected to the Wheatstone bridge in parallel to the a

Abstract This project aimed at updating two existing laboratories in Engineering Experiment course at Worcester Polytechnic Institute:

13 The Error is the percentage difference between measured strain and simulated strain. The Maximum Error is the largest observed error in the five s

14 3.1.4 Test Run of the Laboratories with Selected Signal Conditioners Test run of the laboratories are performed with selected signal conditioner

15 4. Results This project recommended two alternative signal conditioners for use in Strain and Pressure Measurement Laboratory and

16 Vishay 2310 Omega DMD-465WB Honeywell UV-10 DATAQ DI5B38-041 Tacuna Supply Voltage 115VAC 115VAC 18 - 32 VDC 5VDC 6-16VDC Excitation Voltage 0

17 4.1.2 Output Testing With the method described in section 3.1.2 of this report, the noise, accuracy, and precision of measurements a

18 Figure 2 DATAQ’s Signal Response to Shunt Resistor With the method described in section 3.1.2 of this report, the noise, accuracy, and are evalu

19 As shown in the test results, the current system, Vishay 2310, outperforms all other system in all measured aspects. It is, however,

20 Figure 4 Location of Gain select switch and offset potentiometer G0 G1 G2 ON OFF OFF Table 7 Switch settings for Tacuna for 220 Gain 3. Bridge B

21 Figure 5 Connections for Honeywell UV-10 In-line Amplifier 2. Gain setting While excitation jumper is set to 5V, in order to get a gain of 200

22 Figure 6 Connections for Omega DMD 465-WB 2. Set excitation voltage Connect a multi-meter to terminal 2 and 4; adjust potentiometer B+

2 Acknowledgements I am grateful for all the help received during the process of this project. I thank my advisor Professor Cosme Fu

23 4. Adjust gain Connect the shunt resistor simulating strain desired for full scale. Adjust the COARSE GAIN and FINE gain potentiometers for the d

24 4.1.4 Selection of Alternative Signal Conditioner Tacuna Systems Strain Gauge or Load Cell Amplifier/Conditioner Interface Manual (Tac

25 Node requires dynamic data to be converted to numerical data. This enables the program to process and record all acquired data point

26 o Mode shapes of a cantilever beam under free vibration o Damping factor of a cantilever beam under free vibration  Measurement methods of dyn

27 5. Conclusions and Future Work This project examined two existing laboratories in WPI’s Engineering Experiment course and made a series of recomm

28 Works Cited Poisson's Ratio. (2003). Retrieved December 2012, from Fulton School of Engineering, Arizona State University: http://enpub.fulto

29 Mostic, K. (1990). Lab: Calibration of and Measurement with Strain Gages. Retrieved Dec 2012, from Northen Illinois University: http://www.kostic.

30 Appendix 1: Sample Laboratory Report for Strain and Pressure Measurement Laboratory Abstract In this experiment, characterization of internal pre

31 Experimental Procedures In order to understand the errors in this experiment, the procedure is repeated on three soda cans of the same product. P

32 Bridge Balancing and Verification Make sure then NI DAQ box is turned on before starting the VI. Adjust the measurement time to 0.01 second on th

3 Table of Contents Abstract ...

33 Key Equations The expression for internal pressure of a thin-wall vessel can be given by:    where E is Elastic Modulus of the m

34 Results and Conclusions The results of the characterization are listed in Table 1. The parameters are calculated by taking the differences of the

35 Uncertainty Analysis The parameters in Table 2 are used to perform uncertainty analysis for characterized internal pressure. The detai

36 Supplemental Materials LabVIEW Programming Figure 8 Front Panel of LabVIEW Program Figure 9 Block Diagram of LabVIEW Program

37 Uncertainty Analysis

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39

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41 Appendix 2: Sample Laboratory Report for Strain and Pressure Measurement Laboratory Abstract In this experiment, strain gauges are used to measur

42 Description Purpose of the Experiment The purpose of the vibration measurement experiment is to use strain gauges to measure the dynamic characte

4 4.2.2 Updated Instruction Materials for Strain and Pressure Measurement Laboratory 25 4.2.3 Updated Instruction Materials for Vibration Measur

43 Experimental Procedures In order to understand the errors in this experiment, the procedure is repeated on two similar cantilever beams. Preparat

44 Bridge Balancing and Verification Make sure then NI DAQ box is turned on before starting the VI. Adjust the measurement time to 0.01 second on t

45 Key Equations Strain in a Cantilever under Known Load The strain in a cantilever beam under a known load applied at the free end is given by: 

46 The altitude is equivalent to maximum deflection at vibration peaks. The amplitude can be given by:  Therefore, the maximum ve

47 Equipment List  National Instruments USB-6229 DAQ  Tacuna Systems Strain Gauge or Load Cell Amplifier/Conditioner Interface Manual  Wheatst

48 Results and Conclusions Initial Measurements and Research The beams used in this experiment are made with 6061 Aluminum. The Modulus of Elasticity

49 Verification of Correct Installation To verify the correct installation, a weight attached close to the free end on the beam. The analytical stra

50 Theoretical Natural Frequency (Hz) Measured Natural Frequency (Hz) 35.5 35.3 Table 4 Comparison of Measured Fundamental Frequency and Theoretical

51 Acceleration (g) Acceleration  Velocity (m/s) Amplitude (m) Peak 6.6 64.7 1.84 0.052 Peak-To-Peak 13.2 129.4 3.67 0.104 RMS 4.7 45.8 1.

52 Uncertainty Analysis The uncertainty of natural frequency is 0.05 Hz, which is limited by the resolution of spectral analyzer in LabVIEW p

5 Table of Tables Table 1 Parameters for Testing ...

53 Supplemental Materials LabVIEW Program Figure 3 shows the front panel of the LabVIEW program used in this experiment. Figure 4 shows the block dia

54 Uncertainty Analysis

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59 Appendix 3: Instructions for Strain and Pressure Measurement Laboratory Laboratory: Strain and Pressure Measurement 1. OBJECTIVES The objectives

60 2. BACKGROUND A thin walled cylinder has a wall thickness smaller than 1/10 of the cylinder’s radius. In this case, only the membrane stresses ar

61 Figure 1b Top View of a Pressure Transducer Figure 1c Circuit Diagram of a Wheat Stone Bridge 2.2 Stress and Strai

62 Similarly, in the axial direction, the pressure acts to push the two halves apart, while axial stress balances the effects, as shown in figure 3.

6 Table of Figures Figure 1 System Schematic of Strain Measurement Set-up ... 10 Figure 2 DATA

63 temperature, material properties, the adhesive that bonds the gage to the surface, and the stability of the metal. The strain sensitivity, which

64 Figure 17 Temperature Effects on Thermal Output of Strain Gauges Strain gauge’s product name contains all critical information needed to

65 Figure 19 Crucial Information of Strain Gauge Selected 2.4 Basics of Wheatstone bridge A Wheatstone bridge is an electrical circuit used to mea

66 Figure 6 circuit diagram of Wheatstone bridge When the bridge is unbalanced, equivalent resistance of the circuit is,  

67 3. PROCEDURES In order to estimate the internal pressure of soda cans, the procedures of this experiment include research for relevant data, h

68  To achieve an output signal of 1mV per , the gain (G) needs to satisfy:       Therefore,   

69 Besides strain gauge and the cans, material needed for attaching the gauge to a surface include: sand paper, degreaser/alcohol, conditioner, neut

70 7) Lift tape: prior to applying adhesive, lift the end of tape opposite the solder tabs at a shallow angle, until the gauge and terminal is fre

71 11) Protecting the gage: apply a protective coating over the entire gage and terminal area. 12) Measure the base resistance of the unstrained

72 b. Enter relevant information into VI’s front panel, use standard thickness obtain from research as initial value. Press the can or slightly shak

1 1. Introduction ABET accreditation criteria requires undergraduate engineering programs to prepare students with “an ability to design and

73 4. DATA ANALYSIS & DISCUSSION With the results acquired with three soda cans, estimate the range of internal pressure of similar soda cans. C

74 Document 1: Soda Can Parameters and Uncertainty Estimation as a Reference a. Standard dimension of the soda can (diameter and thickness) and the

75    The beverage can lids are usually made from AA5182 H48, while bodies are usually made from AA 3004

76 c. Common internal pressure range of soda cans Gases exert a pressure on any surface with which they are in contact. The amount of pressure exert

77 Document 2: Set-Up Procedure for Signal Conditioner (Tacuna) a. Connection Connect the wires as indicated in Figure 1. Figure 1 Connections fo

78 It is required to open the enclosure to adjust the gain switches but not the offset potentiometer. The wire connections are located

79 Document 3: Tutorial for LabVIEW Program This sample LabVIEW program for the Strain and Pressure Laboratory acquires the voltage inpu

80

81 On Front Panel, right click on a blank location and access the Controls Palette, under Express menu find Numeric Controls, then select a Num Ctrl

82 Add Numeric Indicator and Waveform Graph for Micro Strain readings. The path for Numeric Indicator is Control Palette  Express  Nume

2 techniques involved. The equipment should enable acceptable level of accuracy and resolution.  Student Experience. The instructive

83 Add a DAQ Assistant in the While Loop and configure the subVI with the wizard. (Functions Palette  Measurement I/O NI DAQ mx  DAQ

84 On the block diagram, drag down the arrow on the bottom of the Formula icon to expand the input/output menu. To change the order of the elements,

85 Calculated pressure, diameter and thickness are used to calculate circumferential stress and axial stress. The formulas are shown in the two fi

86 Dynamic data of micro strain, pressure, circumferential and axial stress are then combined with Merge Signal function and then writte

87 The Write to Measurement File should be configured as shown below. The filename in this wizard will be overwritten by the input; it should

88 Now we have completed constructing the VI. If there is any error in the program, the run button will appear “broken” as shown in the figure below.

89 Document 4: Optional Activities in this Laboratory 1. Create a shared data file for the class; consolidate measured internal pressure from all th

90 Appendix 4: Instructions for Vibration Measurement Laboratory Laboratory: Vibration Measurements 1. OBJECTIVES This laboratory uses strain gaug

91 2. BACKGROUND Health monitoring is the process of studying and assessing the integrity of structures, which is crucial for preventin

92 maximum tensile force occurs at the upper most edge. The equation for determining the bending stress is  where M is the applied moment, c is