Beam Dynamics + Laser Micro Vibrometry 1

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1 ENMF 529 INTRODUCTION TO MICROELECTROMECHANICAL SYSTEMS p. 1 DATE:... Note: Print this document at Scale (Page Setup) = 75% LAB #4 ( VIL #7 ) Beam Dynamics + Laser Micro Vibrometry 1 SAFETY and instrument protection: Not applicable in this teleoperated experiment SCORE AND GRADER S REMARKS: REPORT DUE:..., 1 week after the experiment Team #: Contents: 1. Generating translational meso scale displacements with a piezoelectric bender PL112 (Physik Instrumente) 2. Measuring the generated displacements by Michelson and Doppler laser interferometers 3. Investigating responses of the bender to sinusoidal excitations with different frequencies 4. Investigating a response of the bender to a sharp impulse excitation 5. Investigating a response of the bender to a white noise excitation and identification of its resonance frequency 6. Analysis of the results. THE EXPERIMENT - NOTE: EXCEPT FOR THE TESTED OBJECT AND MOTION SENSING (LASERS) THIS LAB IS AMOST IDENTICAL WITH LAB 2 Part 1: Getting acquainted with the experimental setup and needed software 1. Follow instructions on the VIL web pages ( Laboratory Page > Lab #7 > Setup link) to learn about the experimental setup. More information will be provided verbally during the laboratory. 2. Throughout the experiment the assignment of channels at the front end of the data acquisition system (Analog-to-Digital Converter) is as follows: 0 The Command excitation signal generated by the computer and passed to the E Piezo Driver (V) command 1 V/V 1 The actual Excitation signal provided by the E Piezo Driver (V) excitation 6 V/V Note: The sensitivity of the velocity channel (#2) needs to be adjusted as we proceed through the steps of the experiment (2-3, 4-5, and 6-7). Part 2: Capturing responses to sinusoidal excitation from the investigated bender and from the lasers - Follow verbal instructions on how to download and install the required software. - Use the virtual instrument (VI) DAQ-02 to collect 1 set of 32k measurements. Set up the instrument according to verbal instructions given ii. set data size to 32 k iii. set sampling frequency to (100) khz according to the table (next page) continued... Instructor: S. Spiewak, sspiewak@ucalgary.ca October 14, 2012 Department of Mechanical and Manufacturing Engineering, University of Calgary

2 ENMF 529 INTRODUCTION TO MICROELECTROMECHANICAL SYSTEMS p. 2 i. set Amplitude to 8 V ii. set Noise to 0 % iii. set Function to Sine iv. set Shaping to Hanning v. set Freq to AS INSTRUCTED (e.g., 50, 730, 1000,... Hz). - Capture and store the signals. Sample signals posted on the web were collected with the following settings: Signal frequency, [Hz] Amplitude of excitation (generator), [V] Sampling frequency, [khz] Remarks (or 100, not possible in 10) Near resonance (below) (or 100, not possible in 10) Near resonance (above) (or 100, not possible in 10) (or 100, not possible in 10) Near 2nd resonance (below) (or 100, not possible in 10) Near 2nd resonance (above) impulse 4 50 (or 100, not possible in 10) impulse (2) 8 50 (or 100, not possible in 10) White Noise 2 20 Broadband Part 3: not, ask the instructor/ta for assistance. Inspect the data over the entire length of the sample and next zoom in on 5-7 periods of the signals at the centre of the sample. Part 4: Capturing responses to a sharp impulse excitation from the investigated bender and the lasers - Use the virtual instrument (VI) DAQ-02 to collect 1 set of 16 k measurements. Set up the instrument according to verbal instructions given ii. set data size to 16 k iii. set sampling frequency to 50,000 Hz i. set Amplitude to 4 or 8 V ii. set Noise to 0 % iii. set Function to Impulse iv. set Shaping to None v. set Duration to 0.1 (Hz) vi. set Duty cycle to 50 (%) vii. set Shape to Rectangular viii. set Centered : Horiz. to On and Vert. to Off - Capture and store the signals. Part 5: not, ask the instructor/ta for assistance. Inspect the data over the entire length of the sample and next zoom in on its center part, in the vicinity of the recorded impulse.

3 ENMF 529 INTRODUCTION TO MICROELECTROMECHANICAL SYSTEMS p. 3 Part 6: Capturing responses to a white noise excitation from the investigated bender and the lasers - Use the virtual instrument (VI) DAQ-02 to collect 1 set of 128 k measurements. Set up the instrument according to verbal instructions given ii. set data size to 128 k iii. set sampling frequency to 20,000 Hz i. set Amplitude to 2 V ii. set Function to None iii. set Shaping to None iv. set the Noise slider to such level that the displayed (in the window right) amplitude of the signal reaches the level ±2 - Capture and store the signals. Part 7: not, ask the instructor/ta for assistance. THE ASSIGNMENT Part A1: Analysis of the recorded signals - Parts 2, 3 of the lab - Sinusoidal excitation NOTE: Perform all following procedures for one sinusoidal signal out of the 2 assigned (to most teams) in class. It is your choice which signal to analyze thoroughly. In addition, perform step j. for both assigned sinusoidal signals. a. Open the recorded signals in the Convert-Decimate-01 virtual instrument. Select a portion of recorded signals stretching 5 periods of the excitation at the center of the recorded period. Select these periods as accurately as possible. Save the selected portion as a text file (e.g., signals_5periods.txt ) b. Plot samples of the following signals as recorded (i.e., in V). These signals can be plotted directly from the just created text file with, e.g., Excel. A demo in Mathematica is posted on the website. 0 The Command excitation signal generated by the computer and passed to the E Piezo Driver (V) command 1 The actual Excitation signal provided by the E Piezo Driver (V) excitation 6 V/V 1 V/V c. Briefly discuss the plotted signals (of interest are the amplitudes and phase shifts) d. Convert (use the Signal-Analysis-01 instrument) the following signals in the subset to displacement and save them in separate text files Plot in one graph: (1) the displacement measured by the laser interferometer in the Michelson mode and (2) the displacement measured by the laser interferometer in the Doppler mode. e. Briefly discuss the plotted signals.

4 ENMF 529 INTRODUCTION TO MICROELECTROMECHANICAL SYSTEMS p. 4 f. Plot the displacement measured by the Michelson mode interferometer (Y axis) versus the actual Excitation signal (Ch #1). Briefly discuss the plot. g. Estimate a sensitivity of the bender, i.e., the deflection/excitation ratio in µm/v. h. Plot the actual Excitation signal in Ch #1 (Y axis) versus the Command signal (Ch #0). Briefly discuss the plot. i. Estimate a sensitivity of the bender driver, i.e., the Excitation/Command ratio in V/V. j. Estimate the gain, k b, and phase shift, φ, between the bender displacement measured by Michelson laser and the actual Excitation signal in Ch #1 of ADC. Show result in the report. Use the gainphase-measure virtual instrument or the cursors and their displays in the Signal- Analysis-01 instrument. Note: The gainphase-measure instrument gives more accurate results. To use it, proceed as follows: (1) Convert and save the actual Excitation signal (Ch#1), entire length, to a text file. (2) Convert the Michelson laser signal (Ch#3), entire length, to displacement. Estimate its component which represents an undistorted response to the Excitation (note that the recorded signal can be strongly distorted). Save the actual estimate (the residual generated by Signal-Analysis instrument - remember to choose the residual to be saved), its entire length, to a text file. (3) Combine both text files into one, with 3 columns containing: Time, Excitation and Displacement. This file with gainphase-measure. Part A2: Analysis of the recorded signals - Parts 4, 5 of the lab - Sharp impulse excitation a. Open the recorded signals in the Convert-Decimate-01 virtual instrument. Select a portion of recorded signals around the impulse (e.g., the total width about 0.2 sec). Save the selected portion as a text file (e.g., impulse_math ) b. Plot samples of the following signals as recorded (i.e., in V). c. Briefly discuss the plotted signals (of particular interest are their shapes), qualitatively d. With the Signal-Analysis-01 instrument convert the following signals in the subset to displacement and save them in separate text files. For the actual Excitation signal use the sensitivity obtained in A.1.g. 2 Output of the OVF-5000 laser controller ( Doppler mode) - velocity Steps 4 and 5: velocity 50 (mm/s)/v Plot in one graph the bender s displacement measured by (1) the laser interferometer in the Michelson mode, and (2) the laser interferometer in the Doppler mode. e. Briefly discuss the plotted signals. f. Plot in one graph: (1) the displacement measured by the Michelson mode interferometer and (2) the Excitation signal (use the sensitivity obtained in A.1.g). Briefly discuss the plotted signals. Part A3: Spectral analysis of the recorded signals - Parts 6, 7 of the lab - White noise excitation a. With the Spectral-Analysis instrument open the data recorded in Parts 6, 7 of the lab. During opening, set correct sensitivities for the recorded signals. Specifically, we are interested in

5 ENMF 529 INTRODUCTION TO MICROELECTROMECHANICAL SYSTEMS p. 5 NOTE: In the Spectral-Analysis instrument channel numbers are incremented by 1. Thus Ch #1 in the above table becomes Ch #2 in the Spectral-Analysis instrument. b. Perform spectral analysis of the actual Excitation signal. In all displayed windows select the frequency range (X axis) axis from 0 to about 8,000 (Hz). c. Save the result, e.g. as a fft_excitation.txt file. Choose the frequency range 0-7,000 Hz. d. Perform spectral analysis of the beam velocity measured by the Doppler laser and save the result, e.g. as a fft_doppler.txt file. e. Perform spectral analysis of the beam displacement measured by the Michelson laser and save the result, e.g. as a fft_michelson.txt file. f. Perform simultaneous analysis of the Excitation and Michelson signals. Visually inspect the results (no need to write anything in the report, but this step will be helpful in the following analysis). g. With the Signal-Analysis-01 instrument convert the Michelson signal to displacement (µm) and save it, e.g. as a MichelsonVsTime.txt file. Convert the Doppler signal to velocity (mm/s) and save it, e.g. as a DopplerVsTime.txt file Part A4: Open the spectra of the Excitation, Doppler, and Michelson signals obtained in Part A3 in a software of your choice to perform further analysis. See e.g., the Mathematica demo program in Lab_4_signalProc_1.zip. Note: All files generated by Spectral-Analysis contain the so-called Power Spectra in their second columns. You need to convert these power spectra into the Magnitude Spectra (intuitively more meaningful) before processing them as asked below. To convert the Power Spectra into the Magnitude Spectra take square root of the former. So, for example if you are using Excel, load the files generated by Spectral-Analysis and take SQRT of each element in the 2nd column. The first column, frequency, does not require any modification. a. Convert the velocity spectrum ( Doppler ) to displacement by dividing its elements (magnitudes in the 2nd column) by 2πf where f is the frequency automatically generated in the 1st column. b. Plot the converted spectrum of Doppler (displacement) and the spectrum of Michelson (displacement) on the same graph. Show the plot in the report. Briefly discuss. c. Plot the Excitation spectrum in one graph together with one of the graphs from the step above (if the graphs above are significantly different select the one which is better in your opinion). Show the plot in the report. Briefly discuss, in particular if you can see any feature in the spectrum of the actual beam motion (Michelson) that can reveal its resonance frequency.

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