analysis of beam dynamics - part...

ENMF 529 – INTRODUCTION TO MICROELECTROMECHANICAL SYSTEMS p. 1

DATE: ...............

Instructor: S. Spiewak, [email protected] November 1, 2012 Department of Mechanical and Manufacturing Engineering, University of Calgary

Note: Print this document at Scale (Page Setup) = 75%

LAB #7 (VIL #9)

Analysis of Beam Dynamics - Part II

(REPORT DUE: . . . . . . . . . . . – 1 week after the experiment)

✰ SAFETY and instrument protection:

Not applicable in this teleoperated experiment ✰ SCORE AND GRADER’S REMARKS:

✰ Team #: 1. ............. 2. ............. 3. ............. 4. .............

✰ Contents: 1. Generating translational micro scale displacements with microelectromechanical beams 2. Measuring the generated displacements by the Doppler laser interferometer 3. Investigating responses of the beams to sinusoidal, square and white noise excitations 4. Analysis of the results.

✰ THE EXPERIMENT

Part 1: Getting acquainted with the experimental setup and needed software

1. 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 fol-

lows:

Ch # Signal Code Sensitivity

0 The actual “Excitation” signal, computer generated excitation 1 V/V

1 Output of the OVF-5000 laser controller (“Doppler” mode) - velocity velocity 2 (mm/s)/V

Part 2: Capturing responses to a Biased (+5V) Sinusoidal Excitation from the investigated 100 µm and 200 µm long beams. These responses are measured by the laser

- If needed, download and install the required software (follow verbal instructions)

- Use the virtual instrument (VI) “DAQ-02” to collect 1 set of 128k measurements. Set up the “instrument” according to verbal instructions given

during the lab execution. In particular:

in the “Arm System” dialog box

i. “arm” channels 0 and 1

ii. set data size to 128 k

iii. set the “Fixed” button (left of the “Sampling Freq.” to “OFF”

iv. set sampling frequency to 200,000 Hz (do not enter the “,” )

in the “Set Excitation” dialog box

i. set “Amplitude” to 4.5 V

ii. set “Noise” to 0 %

iii. set “Function” to “Sine”

iv. set “Shaping” to “None”

v. set “Freq” to “AS INSTRUCTED” (e.g., 1,000 Hz, 3,000 Hz, etc.)

vi. set the knob “Gain in Ch 1 ....” to 5 (actually this knob adds an offset, 5V in this case, to the generated Excitation signal)

- Capture and store the signals.


Part 3: Preliminary visual inspection of the recorded signals

- With the “Signal_Analysis_01” virtual instrument open the recorded file and check that the signals (2 recorded channels) “make sense”. If 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. In the case of velocity (the 2nd channel) consider integrating the signal before inspecting it.

Part 4: Capturing responses to a Zero-centered (unbiased) Sinusoidal Excitation from the investigated 100 µm and 200 µm long beams. These re-sponses are measured by the laser



in the “Arm System” dialog box <= All lines identical with Part 2 i. “arm” channels 0 and 1





i. set “Amplitude” to 9 V <= This line is different as compared with Part 2


iii. set “Function” to “Sine”



vi. set the knob “Gain in Ch 1 ....” to 0 (actually this knob adds an offset, 0V in this case to the generated Excitation signal) <= This line is dif-ferent as compared with Part 2





centre of the sample. In the case of velocity (the 2nd channel) consider integrating the signal before inspecting it. Can you see anything un-usual, which is a specific feature of the electrostatic actuator ?

- If you can not see this “unusual” phenomenon, analyze the Excitation and Velocity (Doppler) signals with the Spectral-Analysis instrument. This

should help.

Part 6: Capturing responses to a Biased (+5V) Square Excitation from the investigated 100 µm and 200 µm long beams. These responses are meas-ured by the laser








i. set “Amplitude” to 4.5 V <= This line is the same as in Part 2


iii. set “Function” to “Square”




vi. set the knob “Gain in Ch 1 ....” to 5 (actually this knob adds an offset, 5V in this case to the generated Excitation signal) <= This line is the same as in Part 2, but different than in Part 4





centre of the sample. In the case of velocity (the 2nd channel) consider integrating the signal before inspecting it.

Part 8: Capturing responses to a Biased (+5V) “White Noise” excitation from the investigated beams. These responses are measured by the laser

- Use the virtual instrument (VI) “DAQ-02” to collect 1 set of 128 k measurements. Set up the “instrument” according to verbal instructions given





iv. set sampling frequency to 200,000 Hz


i. set “Amplitude” to 4.5 V <= This line is the same as in Part 6


iii. set “Function” to “None”


v. If needed, adjust the “Noise level” slider until the displayed signal (right) reaches the amplitude 4.5 V

vi. set the knob “Gain in Ch 1 ....” to 5 (actually this knob adds an offset, 5V in this case to the generated Excitation signal) <= This line is the same as in Part 6



- With the “Signal_Analysis_01” virtual instrument open the recorded file and check that the signals (all 4 recorded channels) “make sense”. If

not, ask the instructor/TA for assistance.

✰ THE ASSIGNMENT - wherever applicable below, the excitation frequency used in the experiments was 3,000 Hz Part A1: Computations based on the analytical model of the investigated microbeam

Consider a 100 µm long microbeam fabricated with Sandia’s SUMMiT surface micromachining technology. We investigated such beams, focus-

ing the attention on a 200 µm long one. A simplified model of the beam is shown in Figure 1a on the next page (see also lecture units 19-21).

Dimensions of the beam, which are defined mainly by the thickness of SUMMiT layers shown in Figure 1b, are as follows:

Length: LB = 100 µm ; width: WB = 20 µm ; thickness: TB = 2.5 µm ; air gap: d = 2 µm

The microbeam is made of polysilicon SUMMiT layers “poly1” and “poly2”, with ρ = 2330 kg/m3 and EY = 180 109 Pa. The laser spot (light) is

positioned at a distance LL µm from the fixed end of the beam. Figure 2 shows a picture of the microbeams taken by a CCD camera mounted on

the microscope. The laser spot is clearly visible.

continued ...


(a) (b)

Figure 1. The investigated beam (a) and cross-section through SUMMiT’s structural and sacrificial layers (b).

Figure 2. A photo of the investigated microbeams as seen by the CCD camera on the microscope (larger version on the web site, Lab. 10).

a. Estimate from the photograph the distance LL of the laser spot from the fixed end of the microbeam. Show the result in the report. NOTE: Team #1 is responsible for the spot at the end of the beam, which is shown above. Enlarged image, “100um_end”, is on the web site in the Lab 10 section. Team #2-3 is responsible for the spot in mid-point (approx.) of the beam. The needed image, “100um_midPoint“, is on the web site.

b. Compute a deflection of this microbeam due to its weight at the point LL (laser spot). Show the result in the report. c. Compute a deflection of this microbeam at LL due to the electrostatic excitation with a constant level voltages Va0 = 0.5 V and Va1 = 9.5 V.

Note that these are the extreme levels of the voltage in Part 2 and Part 6 of the performed experiments (sine and square waveforms with 4.5 V amplitude centered around 5 V). The actuator is 82 µm long (shorter than the beam), and begins at the fixed end of the beam.

d. Compute the difference of deflections for the above voltages. This is a value we expect to confirm with the laser measurements. Note that,

since the laser measures velocity, we can not compute the absolute position of the beam (e.g., from the substrate), but only its displacement. Show the result in the report.

e. Plot a deflection of the beam versus time, when the beam is excited by a sinusoidal waveform with 4.5 V amplitude centered around 5 V. For

convenience assume Va(t) = 4.5 sin( 2 π t ) + 5 , and t ∈ {0,2}. Show the result in the report. f. Plot in the same graph a deflection of the beam versus time, when the beam is excited by a sinusoidal “0 centered” waveform with 9 V ampli-

tude. In this case Va(t) = 9 sin( 2 π t ) , and t ∈ {0,2}. Show the result in the report. g. Briefly discuss the plots in the report.


continued ...

Part A2: Visual inspection of the signals recorded in Part 2 - Sinusoidal excitation, 5 V centered signal

a. Open the record from Part 2 with the “Convert-Decimate-01” virtual instrument. Select a portion of recorded signals stretching 4 periods of the

excitation near the center of the recorded period. Select these periods as accurately as possible. Save the selected portion as a binary file

(e.g., “sine_5V_center.bin”)

b. Open the above subset with “Signal-Analysis-01”. Attempt to estimate the amplitude of beam deflections in Ch 1 (integrate the Doppler veloc-

ity). Recall that the laser sensitivity is 2 (mm/s)/V. Due to distortions, this task may not be easy - use your engineering intuition and results

from Part A1 of this assignment. I will provide more explanation and a demo in class.

c. Show the result - a representative screen print from part “b” - in the report.

Part A3: Visual inspection of the signals recorded in Part 4 - Sinusoidal excitation, zero-centered signal



(e.g., “sine_0_center.bin”)

b. Open the above subset with “Signal-Analysis-01”. Attempt to estimate the amplitude of beam deflections in Ch 1. Due to distortions, this task

may not be easy.


Part A4: Visual inspection of the signals recorded in Part 6 - Square wave excitation, 5 V centered signal



(e.g., “square_5V_center.bin”)

b. Open the above subset with “Signal-Analysis-01”. Attempt to estimate the amplitude of beam deflections in Ch 1. Due to distortions, this task

may not be easy.


Part A5: Spectral analysis of the recorded signals

Note 1: If needed, refer to the guided tour “Spectral Analysis of selected signals: Step-by-step instruction”, a link to which is in the Lab #8 “contents box” on the Laboratory web site.

Note 2: In the Spectral-Analysis program (v15) use the “Hanning” window. It is recommended that you test the program using the “FFT Calibra-

tion.bin” signal provided in Lab 8. Recall that the strong sinusoid in this file has amplitude 1 and frequency 10 Hz.

Note 3: Since the investigated beam deflection measured by the Doppler laser is velocity (in Channel 2 of the Spectral-Analysis program), you need to convert this velocity to displacement. It is done conveniently in the “2nd layer window” opened by pressing the “Enlarged Dis-plays” button.

a. Perform spectral analysis of the microbeam deflection (i.e., displacement at the laser spot) measured by the Doppler laser in Part 2 of this

laboratory (i.e., for the Biased Sinusoidal Excitation). From the obtained spectrum estimate the amplitude of this deflection at 3,000 Hz, which

is the excitation frequency used in all tests conducted in this laboratory. Show the result in the report.

b. Estimate the amplitude of the 2nd and 3rd harmonics of this deflection. Show the result in the report.

c. Perform spectral analysis of the microbeam deflection measured by the Doppler laser in Part 4 (i.e., for the Zero-centered Sinusoidal Excita-

tion). From the obtained spectrum estimate the amplitude of this deflection at 3,000 Hz. Show the result in the report.


d. Estimate the amplitude of the 2nd and 3rd harmonics of the excitation signal (i.e., 3,000 kHz). Show the result in the report.

e. Perform spectral analysis of the microbeam deflection measured by the Doppler laser in Part 8 (i.e., for the Biased White Noise Excitation).

Based on the obtained spectrum, does the tested microbeam feature any resonance frequency in the frequency range between 1000 - 1000

Hz? Briefly justify the answer in the report. Results of testing the piezoelectric macrobeam in Laboratory #5 (VIL #4) may provide a hint.

f. Compute the first resonance frequency of this microbeam using its “analytical” properties given in Part A1. Show the result in the report.

Part A6: Tabulate the following maximum deflections (peak-to-peak) of the microbeam at the laser spot obtained analytically and experimentally.

Excitation → Source ↓

Biased sine wave (Part 2) Zero-centered sine (Part 4) Units

Computed in Part A1 pm

Obtained experimentally 1) pm

1) Estimated in Parts A2 and A3

analysis of beam dynamics - part...

Documents