294 lines
11 KiB
Org Mode
294 lines
11 KiB
Org Mode
#+TITLE: Measurements
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:drawer:
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#+STARTUP: overview
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/htmlize.css"/>
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#+HTML_HEAD: <link rel="stylesheet" type="text/css" href="../css/readtheorg.css"/>
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#+HTML_HEAD: <script src="../js/jquery.min.js"></script>
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#+HTML_HEAD: <script src="../js/bootstrap.min.js"></script>
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#+HTML_HEAD: <script src="../js/jquery.stickytableheaders.min.js"></script>
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#+HTML_HEAD: <script src="../js/readtheorg.js"></script>
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#+LATEX_CLASS: cleanreport
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#+LaTeX_CLASS_OPTIONS: [tocnp, secbreak, minted]
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#+PROPERTY: header-args:matlab :session *MATLAB*
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#+PROPERTY: header-args:matlab+ :comments org
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#+PROPERTY: header-args:matlab+ :exports both
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#+PROPERTY: header-args:matlab+ :eval no-export
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#+PROPERTY: header-args:matlab+ :noweb yes
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#+PROPERTY: header-args:matlab+ :mkdirp yes
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#+PROPERTY: header-args:matlab+ :output-dir figs
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:end:
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* Experimental conditions
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- Measurement made in a metrology lab
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- The granite is not glued to the floor
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- The Y-Translation stage is powered and in closed-loop
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- The spindle is not powered
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- Mass is placed on top of the Hexapod (*how much?*) (figure [[fig:accelerometers]]).
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- Made by Marc Lesourd on the 17th of November 2017
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#+name: fig:accelerometers
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#+caption: Accelerometers position
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#+attr_latex: :width 0.5\linewidth
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file:./figs/accelerometers.png
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#+name: fig:instrumented_hammer
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#+caption: Instrumented Hammer used
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#+attr_latex: :width 0.5\linewidth
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file:./figs/instrumented_hammer.png
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* Measurements procedure
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*3-axis Accelerometers* (specifications table [[tab:accelerometer]]) are glued on (see figure [[fig:accelerometers]]):
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- Marble
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- Y-Translation stage
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- Tilt stage
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- top of Hexapod
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#+NAME: tab:accelerometer
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#+CAPTION: Pieozoelectric acc. 356b18 - 3 axis
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| Sensitivity | 0.102 V/(m/s2) |
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| Measurement Range | 4.9 m/s2 pk |
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| Frequency Range | 0.5 to 3000 Hz |
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| resonant frequency | >20000 Hz |
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| broadband resolution | 0.0005 m/s2 rms |
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The structure is excited using an *instrumented hammer* with impacts on (see figure [[fig:instrumented_hammer]]):
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- Marble
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- Hexapod
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* Measurement Files
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Two measurements files are:
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- =id31_microstation_2017_11_17_frf.mat= that contains:
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- =freq_frf= the frequency vector in Hz
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- Computed frequency response functions (see table [[tab:data_name]])
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- =id31_microstation_2017_11_17_coh.mat=
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- Computed coherence
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For each of the measurement, the measured channels are shown on table [[tab:meas_channels]].
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#+NAME: tab:data_name
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#+CAPTION: Description of the location of direction of the excitation for each measurement
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| Object name | Location | Direction |
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|--------------+----------+-----------|
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| frf_hexa_x | Hexapod | X |
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| frf_hexa_y | Hexapod | Y |
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| frf_hexa_z | Hexapod | Z |
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| frf_marble_x | Marble | X |
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| frf_marble_y | Marble | Y |
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| frf_marble_z | Marble | Z |
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#+NAME: tab:meas_channels
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#+CAPTION: Description of each measurement channel
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| Ch. nb | Element | Location | Direction |
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|--------+---------------+----------+-----------|
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| 1 | Not wired | na | na |
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| 2 | Accelerometer | Marble | X |
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| 3 | Accelerometer | Marble | Y |
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| 4 | Accelerometer | Marble | Z |
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| 5 | Accelerometer | Ty | X |
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| 6 | Accelerometer | Ty | Y |
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| 7 | Accelerometer | Ty | Z |
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| 8 | Accelerometer | Tilt | X |
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| 9 | Accelerometer | Tilt | Y |
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| 10 | Accelerometer | Tilt | Z |
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| 11 | Accelerometer | Hexapod | X |
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| 12 | Accelerometer | Hexapod | Y |
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| 13 | Accelerometer | Hexapod | Z |
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* Data Analysis
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** Loading of the data
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#+begin_src matlab :exports none :results silent
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<<matlab-init>>
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#+end_src
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#+begin_src matlab :exports code :results none
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load('./raw_data/id31_microstation_2017_11_17_coh.mat',...
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'coh_hexa_x',...
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'coh_hexa_y',...
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'coh_hexa_z',...
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'coh_marble_x',...
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'coh_marble_y',...
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'coh_marble_z');
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load('./raw_data/id31_microstation_2017_11_17_frf.mat',...
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'freq_frf',...
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'frf_hexa_x',...
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'frf_hexa_y',...
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'frf_hexa_z',...
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'frf_marble_x',...
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'frf_marble_y',...
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'frf_marble_z');
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#+end_src
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** Pre-processing of the data
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The FRF data are scaled with the sensitivity of the accelerometer and integrated two times to have the displacement instead of the acceleration.
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#+begin_src matlab :results none
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accel_sensitivity = 0.102; % [V/(m/s2)]
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w = j*2*pi*freq_frf; % j.omega in [rad/s]
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frf_hexa_x = 1/accel_sensitivity*frf_hexa_x./(w.^2);
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frf_hexa_y = -1/accel_sensitivity*frf_hexa_y./(w.^2);
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frf_hexa_z = -1/accel_sensitivity*frf_hexa_z./(w.^2);
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frf_marble_x = 1/accel_sensitivity*frf_marble_x./(w.^2);
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frf_marble_y = 1/accel_sensitivity*frf_marble_y./(w.^2);
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frf_marble_z = -1/accel_sensitivity*frf_marble_z./(w.^2);
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#+end_src
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** X-direction FRF
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#+begin_src matlab :exports none :results none
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figure;
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hold on;
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plot(freq_frf, abs(frf_marble_x(:, 2)), 'DisplayName', 'Marble - X');
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plot(freq_frf, abs(frf_marble_x(:, 5)), 'DisplayName', 'Ty - X');
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plot(freq_frf, abs(frf_marble_x(:, 8)), 'DisplayName', 'Ry - X');
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plot(freq_frf, abs(frf_marble_x(:, 11)), 'DisplayName', 'Hexa - X');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
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xlim([20, 200]); xticks([20, 50, 100, 200]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:marble_x_frf
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#+HEADER: :tangle no :exports results :results raw :noweb yes
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#+begin_src matlab :var filepath="figs/marble_x_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:marble_x_frf
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#+CAPTION: Response to a force applied on the marble in the X direction
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#+RESULTS: fig:marble_x_frf
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[[file:figs/marble_x_frf.png]]
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#+begin_src matlab :exports none :results none
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figure;
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hold on;
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plot(freq_frf, abs(frf_hexa_x(:, 2)), 'DisplayName', 'Marble - X');
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plot(freq_frf, abs(frf_hexa_x(:, 5)), 'DisplayName', 'Ty - X');
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plot(freq_frf, abs(frf_hexa_x(:, 8)), 'DisplayName', 'Ry - X');
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plot(freq_frf, abs(frf_hexa_x(:, 11)), 'DisplayName', 'Hexa - X');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
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xlim([20, 200]); xticks([20, 50, 100, 200]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:hexa_x_frf
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#+HEADER: :tangle no :exports results :results raw :noweb yes
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#+begin_src matlab :var filepath="figs/hexa_x_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:hexa_x_frf
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#+CAPTION: Response to a force applied on the hexa in the X direction
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#+RESULTS: fig:hexa_x_frf
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[[file:figs/hexa_x_frf.png]]
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** Y-direction FRF
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#+begin_src matlab :exports none :results none
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figure;
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hold on;
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plot(freq_frf, abs(frf_marble_y(:, 3)), 'DisplayName', 'Marble - Y');
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plot(freq_frf, abs(frf_marble_y(:, 6)), 'DisplayName', 'Ty - Y');
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plot(freq_frf, abs(frf_marble_y(:, 9)), 'DisplayName', 'Ry - Y');
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plot(freq_frf, abs(frf_marble_y(:, 12)), 'DisplayName', 'Hexa - Y');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
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xlim([20, 200]); xticks([20, 50, 100, 200]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:marble_y_frf
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#+HEADER: :tangle no :exports results :results raw :noweb yes
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#+begin_src matlab :var filepath="figs/marble_y_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:marble_y_frf
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#+CAPTION: Response to a force applied on the marble in the Y direction
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#+RESULTS: fig:marble_y_frf
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[[file:figs/marble_y_frf.png]]
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#+begin_src matlab :exports none :results none
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figure;
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hold on;
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plot(freq_frf, abs(frf_hexa_y(:, 3)), 'DisplayName', 'Marble - Y');
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plot(freq_frf, abs(frf_hexa_y(:, 6)), 'DisplayName', 'Ty - Y');
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plot(freq_frf, abs(frf_hexa_y(:, 9)), 'DisplayName', 'Ry - Y');
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plot(freq_frf, abs(frf_hexa_y(:, 12)), 'DisplayName', 'Hexa - Y');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
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xlim([20, 200]); xticks([20, 50, 100, 200]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:hexa_y_frf
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#+HEADER: :tangle no :exports results :results raw :noweb yes
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#+begin_src matlab :var filepath="figs/hexa_y_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:hexa_y_frf
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#+CAPTION: Response to a force applied on the hexa in the Y direction
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#+RESULTS: fig:hexa_y_frf
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[[file:figs/hexa_y_frf.png]]
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** Z-direction FRF
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#+begin_src matlab :exports none :results none
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figure;
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hold on;
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plot(freq_frf, abs(frf_marble_z(:, 4)), 'DisplayName', 'Marble - Z');
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plot(freq_frf, abs(frf_marble_z(:, 7)), 'DisplayName', 'Ty - Z');
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plot(freq_frf, abs(frf_marble_z(:, 10)), 'DisplayName', 'Ry - Z');
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plot(freq_frf, abs(frf_marble_z(:, 13)), 'DisplayName', 'Hexa - Z');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
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xlim([20, 200]); xticks([20, 50, 100, 200]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:marble_z_frf
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#+HEADER: :tangle no :exports results :results raw :noweb yes
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#+begin_src matlab :var filepath="figs/marble_z_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:marble_z_frf
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#+CAPTION: Response to a force applied on the marble in the Z direction
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#+RESULTS: fig:marble_z_frf
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[[file:figs/marble_z_frf.png]]
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#+begin_src matlab :exports none :results none
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figure;
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hold on;
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plot(freq_frf, abs(frf_hexa_z(:, 4)), 'DisplayName', 'Marble - Z');
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plot(freq_frf, abs(frf_hexa_z(:, 7)), 'DisplayName', 'Ty - Z');
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plot(freq_frf, abs(frf_hexa_z(:, 10)), 'DisplayName', 'Ry - Z');
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plot(freq_frf, abs(frf_hexa_z(:, 13)), 'DisplayName', 'Hexa - Z');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('Displacement/Force [m/N]');
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xlim([20, 200]); xticks([20, 50, 100, 200]);
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legend('Location', 'southwest');
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#+end_src
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#+NAME: fig:hexa_z_frf
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#+HEADER: :tangle no :exports results :results raw :noweb yes
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#+begin_src matlab :var filepath="figs/hexa_z_frf.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
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<<plt-matlab>>
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#+end_src
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#+NAME: fig:hexa_z_frf
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#+CAPTION: Response to a force applied on the hexa in the Z direction
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#+RESULTS: fig:hexa_z_frf
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[[file:figs/hexa_z_frf.png]]
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