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<body>
<div id="content">
<h1 class="title">Measurements</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgd454c8a">1. Experimental conditions</a></li>
<li><a href="#orgb822802">2. Measurements procedure</a></li>
<li><a href="#org99e9d56">3. Measurement Files</a></li>
<li><a href="#orgc95ce23">4. Data Analysis</a>
<ul>
<li><a href="#orga76b51e">4.1. Loading of the data</a></li>
<li><a href="#org820ac4d">4.2. Pre-processing of the data</a></li>
<li><a href="#org4e99f9f">4.3. X-direction FRF</a></li>
<li><a href="#orgda268c3">4.4. Y-direction FRF</a></li>
<li><a href="#org13db41d">4.5. Z-direction FRF</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgd454c8a" class="outline-2">
<h2 id="orgd454c8a"><span class="section-number-2">1</span> Experimental conditions</h2>
<div class="outline-text-2" id="text-1">
<ul class="org-ul">
<li>Measurement made in a metrology lab</li>
<li>The granite is not glued to the floor</li>
<li>The Y-Translation stage is powered and in closed-loop</li>
<li>The spindle is not powered</li>
<li>Mass is placed on top of the Hexapod (<b>how much?</b>) (figure <a href="#org977fe1e">1</a>).</li>
<li>Made by Marc Lesourd on the 17th of November 2017</li>
</ul>
<div id="org977fe1e" class="figure">
<p><img src="./figs/accelerometers.png" alt="accelerometers.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Accelerometers position</p>
</div>
<div id="orgbf23216" class="figure">
<p><img src="./figs/instrumented_hammer.png" alt="instrumented_hammer.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Instrumented Hammer used</p>
</div>
</div>
</div>
<div id="outline-container-orgb822802" class="outline-2">
<h2 id="orgb822802"><span class="section-number-2">2</span> Measurements procedure</h2>
<div class="outline-text-2" id="text-2">
<p>
<b>3-axis Accelerometers</b> (specifications table <a href="#orgd6d0454">1</a>) are glued on (see figure <a href="#org977fe1e">1</a>):
</p>
<ul class="org-ul">
<li>Marble</li>
<li>Y-Translation stage</li>
<li>Tilt stage</li>
<li>top of Hexapod</li>
</ul>
<table id="orgd6d0454" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Pieozoelectric acc. 356b18 - 3 axis</caption>
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left">Sensitivity</td>
<td class="org-left">0.102 V/(m/s2)</td>
</tr>
<tr>
<td class="org-left">Measurement Range</td>
<td class="org-left">4.9 m/s2 pk</td>
</tr>
<tr>
<td class="org-left">Frequency Range</td>
<td class="org-left">0.5 to 3000 Hz</td>
</tr>
<tr>
<td class="org-left">resonant frequency</td>
<td class="org-left">&gt;20000 Hz</td>
</tr>
<tr>
<td class="org-left">broadband resolution</td>
<td class="org-left">0.0005 m/s2 rms</td>
</tr>
</tbody>
</table>
<p>
The structure is excited using an <b>instrumented hammer</b> with impacts on (see figure <a href="#orgbf23216">2</a>):
</p>
<ul class="org-ul">
<li>Marble</li>
<li>Hexapod</li>
</ul>
</div>
</div>
<div id="outline-container-org99e9d56" class="outline-2">
<h2 id="org99e9d56"><span class="section-number-2">3</span> Measurement Files</h2>
<div class="outline-text-2" id="text-3">
<p>
Two measurements files are:
</p>
<ul class="org-ul">
<li><code>id31_microstation_2017_11_17_frf.mat</code> that contains:
<ul class="org-ul">
<li><code>freq_frf</code> the frequency vector in Hz</li>
<li>Computed frequency response functions (see table <a href="#orgdcce96c">2</a>)</li>
</ul></li>
<li><code>id31_microstation_2017_11_17_coh.mat</code>
<ul class="org-ul">
<li>Computed coherence</li>
</ul></li>
</ul>
<p>
For each of the measurement, the measured channels are shown on table <a href="#org8bc7496">3</a>.
</p>
<table id="orgdcce96c" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Description of the location of direction of the excitation for each measurement</caption>
<colgroup>
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Object name</th>
<th scope="col" class="org-left">Location</th>
<th scope="col" class="org-left">Direction</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">frf<sub>hexa</sub><sub>x</sub></td>
<td class="org-left">Hexapod</td>
<td class="org-left">X</td>
</tr>
<tr>
<td class="org-left">frf<sub>hexa</sub><sub>y</sub></td>
<td class="org-left">Hexapod</td>
<td class="org-left">Y</td>
</tr>
<tr>
<td class="org-left">frf<sub>hexa</sub><sub>z</sub></td>
<td class="org-left">Hexapod</td>
<td class="org-left">Z</td>
</tr>
<tr>
<td class="org-left">frf<sub>marble</sub><sub>x</sub></td>
<td class="org-left">Marble</td>
<td class="org-left">X</td>
</tr>
<tr>
<td class="org-left">frf<sub>marble</sub><sub>y</sub></td>
<td class="org-left">Marble</td>
<td class="org-left">Y</td>
</tr>
<tr>
<td class="org-left">frf<sub>marble</sub><sub>z</sub></td>
<td class="org-left">Marble</td>
<td class="org-left">Z</td>
</tr>
</tbody>
</table>
<table id="org8bc7496" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 3:</span> Description of each measurement channel</caption>
<colgroup>
<col class="org-right" />
<col class="org-left" />
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Ch. nb</th>
<th scope="col" class="org-left">Element</th>
<th scope="col" class="org-left">Location</th>
<th scope="col" class="org-left">Direction</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">Not wired</td>
<td class="org-left">na</td>
<td class="org-left">na</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Marble</td>
<td class="org-left">X</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Marble</td>
<td class="org-left">Y</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Marble</td>
<td class="org-left">Z</td>
</tr>
<tr>
<td class="org-right">5</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Ty</td>
<td class="org-left">X</td>
</tr>
<tr>
<td class="org-right">6</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Ty</td>
<td class="org-left">Y</td>
</tr>
<tr>
<td class="org-right">7</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Ty</td>
<td class="org-left">Z</td>
</tr>
<tr>
<td class="org-right">8</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Tilt</td>
<td class="org-left">X</td>
</tr>
<tr>
<td class="org-right">9</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Tilt</td>
<td class="org-left">Y</td>
</tr>
<tr>
<td class="org-right">10</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Tilt</td>
<td class="org-left">Z</td>
</tr>
<tr>
<td class="org-right">11</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Hexapod</td>
<td class="org-left">X</td>
</tr>
<tr>
<td class="org-right">12</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Hexapod</td>
<td class="org-left">Y</td>
</tr>
<tr>
<td class="org-right">13</td>
<td class="org-left">Accelerometer</td>
<td class="org-left">Hexapod</td>
<td class="org-left">Z</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-orgc95ce23" class="outline-2">
<h2 id="orgc95ce23"><span class="section-number-2">4</span> Data Analysis</h2>
<div class="outline-text-2" id="text-4">
</div>
<div id="outline-container-orga76b51e" class="outline-3">
<h3 id="orga76b51e"><span class="section-number-3">4.1</span> Loading of the data</h3>
<div class="outline-text-3" id="text-4-1">
<div class="org-src-container">
<pre class="src src-matlab">load<span style="color: #707183;">(</span><span style="color: #008000;">'./raw_data/id31_microstation_2017_11_17_coh.mat'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'coh_hexa_x'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'coh_hexa_y'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'coh_hexa_z'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'coh_marble_x'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'coh_marble_y'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'coh_marble_z'</span><span style="color: #707183;">)</span>;
load<span style="color: #707183;">(</span><span style="color: #008000;">'./raw_data/id31_microstation_2017_11_17_frf.mat'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'freq_frf'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'frf_hexa_x'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'frf_hexa_y'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'frf_hexa_z'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'frf_marble_x'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'frf_marble_y'</span>,<span style="text-decoration: underline;">...</span>
<span style="color: #008000;">'frf_marble_z'</span><span style="color: #707183;">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org820ac4d" class="outline-3">
<h3 id="org820ac4d"><span class="section-number-3">4.2</span> Pre-processing of the data</h3>
<div class="outline-text-3" id="text-4-2">
<p>
The FRF data are scaled with the sensitivity of the accelerometer and integrated two times to have the displacement instead of the acceleration.
</p>
<div class="org-src-container">
<pre class="src src-matlab">accel_sensitivity = <span style="color: #D0372D;">0</span>.<span style="color: #D0372D;">102</span>; <span style="color: #8D8D84; font-style: italic;">% [V/(m/s2)]</span>
w = <span style="color: #D0372D;">j</span><span style="color: #6434A3;">*</span><span style="color: #D0372D;">2</span><span style="color: #6434A3;">*</span><span style="color: #D0372D;">pi</span><span style="color: #6434A3;">*</span>freq_frf; <span style="color: #8D8D84; font-style: italic;">% j.omega in [rad/s]</span>
frf_hexa_x = <span style="color: #D0372D;">1</span><span style="color: #6434A3;">/</span>accel_sensitivity<span style="color: #6434A3;">*</span>frf_hexa_x<span style="color: #6434A3;">./</span><span style="color: #707183;">(</span>w<span style="color: #6434A3;">.^</span><span style="color: #D0372D;">2</span><span style="color: #707183;">)</span>;
frf_hexa_y = <span style="color: #6434A3;">-</span><span style="color: #D0372D;">1</span><span style="color: #6434A3;">/</span>accel_sensitivity<span style="color: #6434A3;">*</span>frf_hexa_y<span style="color: #6434A3;">./</span><span style="color: #707183;">(</span>w<span style="color: #6434A3;">.^</span><span style="color: #D0372D;">2</span><span style="color: #707183;">)</span>;
frf_hexa_z = <span style="color: #6434A3;">-</span><span style="color: #D0372D;">1</span><span style="color: #6434A3;">/</span>accel_sensitivity<span style="color: #6434A3;">*</span>frf_hexa_z<span style="color: #6434A3;">./</span><span style="color: #707183;">(</span>w<span style="color: #6434A3;">.^</span><span style="color: #D0372D;">2</span><span style="color: #707183;">)</span>;
frf_marble_x = <span style="color: #D0372D;">1</span><span style="color: #6434A3;">/</span>accel_sensitivity<span style="color: #6434A3;">*</span>frf_marble_x<span style="color: #6434A3;">./</span><span style="color: #707183;">(</span>w<span style="color: #6434A3;">.^</span><span style="color: #D0372D;">2</span><span style="color: #707183;">)</span>;
frf_marble_y = <span style="color: #D0372D;">1</span><span style="color: #6434A3;">/</span>accel_sensitivity<span style="color: #6434A3;">*</span>frf_marble_y<span style="color: #6434A3;">./</span><span style="color: #707183;">(</span>w<span style="color: #6434A3;">.^</span><span style="color: #D0372D;">2</span><span style="color: #707183;">)</span>;
frf_marble_z = <span style="color: #6434A3;">-</span><span style="color: #D0372D;">1</span><span style="color: #6434A3;">/</span>accel_sensitivity<span style="color: #6434A3;">*</span>frf_marble_z<span style="color: #6434A3;">./</span><span style="color: #707183;">(</span>w<span style="color: #6434A3;">.^</span><span style="color: #D0372D;">2</span><span style="color: #707183;">)</span>;
</pre>
</div>
</div>
</div>
<div id="outline-container-org4e99f9f" class="outline-3">
<h3 id="org4e99f9f"><span class="section-number-3">4.3</span> X-direction FRF</h3>
<div class="outline-text-3" id="text-4-3">
<div id="org276857f" class="figure">
<p><img src="figs/marble_x_frf.png" alt="marble_x_frf.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Response to a force applied on the marble in the X direction</p>
</div>
<div id="orgf0e10a5" class="figure">
<p><img src="figs/hexa_x_frf.png" alt="hexa_x_frf.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Response to a force applied on the hexa in the X direction</p>
</div>
</div>
</div>
<div id="outline-container-orgda268c3" class="outline-3">
<h3 id="orgda268c3"><span class="section-number-3">4.4</span> Y-direction FRF</h3>
<div class="outline-text-3" id="text-4-4">
<div id="org236241c" class="figure">
<p><img src="figs/marble_y_frf.png" alt="marble_y_frf.png" />
</p>
<p><span class="figure-number">Figure 5: </span>Response to a force applied on the marble in the Y direction</p>
</div>
<div id="org82af17e" class="figure">
<p><img src="figs/hexa_y_frf.png" alt="hexa_y_frf.png" />
</p>
<p><span class="figure-number">Figure 6: </span>Response to a force applied on the hexa in the Y direction</p>
</div>
</div>
</div>
<div id="outline-container-org13db41d" class="outline-3">
<h3 id="org13db41d"><span class="section-number-3">4.5</span> Z-direction FRF</h3>
<div class="outline-text-3" id="text-4-5">
<div id="org59429a8" class="figure">
<p><img src="figs/marble_z_frf.png" alt="marble_z_frf.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Response to a force applied on the marble in the Z direction</p>
</div>
<div id="org74da9a0" class="figure">
<p><img src="figs/hexa_z_frf.png" alt="hexa_z_frf.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Response to a force applied on the hexa in the Z direction</p>
</div>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Thomas Dehaeze</p>
<p class="date">Created: 2019-03-14 jeu. 11:54</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>

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

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#+TITLE: Measurements made by Marc Lessourd on the 17th of November 2017 - Matlab
:drawer:
#+LATEX_CLASS: cleanreport
#+LaTeX_CLASS_OPTIONS: [tocnp, secbreak, minted]
#+STARTUP: overview
#+PROPERTY: header-args:matlab :session *MATLAB*
#+PROPERTY: header-args:matlab+ :comments org
#+PROPERTY: header-args:matlab+ :exports both
#+PROPERTY: header-args:matlab+ :eval no-export
#+PROPERTY: header-args:matlab+ :noweb yes
#+PROPERTY: header-args:matlab+ :mkdirp yes
#+PROPERTY: header-args:matlab+ :output-dir figs
:end:
* Load the data
#+begin_src matlab :exports code :results none
load('./raw_data/id31_microstation_2017_11_17_coh.mat',...
'coh_hexa_x',...
'coh_hexa_y',...
'coh_hexa_z',...
'coh_marble_x',...
'coh_marble_y',...
'coh_marble_z');
load('./raw_data/id31_microstation_2017_11_17_frf.mat',...
'freq_frf',...
'frf_hexa_x',...
'frf_hexa_y',...
'frf_hexa_z',...
'frf_marble_x',...
'frf_marble_y',...
'frf_marble_z');
#+end_src
Measurement is in V?
#+begin_src matlab :results none
accel_sensitivity = 0.102; % [V/(m/s2)]
w = j*2*pi*freq_frf;
frf_hexa_x = 1/accel_sensitivity*frf_hexa_x./(w.^2);
frf_hexa_y = -1/accel_sensitivity*frf_hexa_y./(w.^2);
frf_hexa_z = -1/accel_sensitivity*frf_hexa_z./(w.^2);
frf_marble_x = 1/accel_sensitivity*frf_marble_x./(w.^2);
frf_marble_y = 1/accel_sensitivity*frf_marble_y./(w.^2);
frf_marble_z = -1/accel_sensitivity*frf_marble_z./(w.^2);
#+end_src
* Plots
#+begin_src matlab :exports none :results none
figure;
hold on;
plot(freq_frf, abs(frf_hexa_x(:, 2)), 'DisplayName', 'Marble - X');
plot(freq_frf, abs(frf_hexa_x(:, 5)), 'DisplayName', 'Ty - X');
plot(freq_frf, abs(frf_hexa_x(:, 8)), 'DisplayName', 'Ry - X');
plot(freq_frf, abs(frf_hexa_x(:, 11)), 'DisplayName', 'Hexa - X');
hold off;
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
xlim([20, 200]);
legend('Location', 'northeast');
#+end_src
#+begin_src matlab :exports none :results none
figure;
hold on;
plot(freq_frf, abs(frf_hexa_x(:, 2)), 'DisplayName', 'Marble - X');
plot(freq_frf, abs(frf_hexa_x(:, 5)), 'DisplayName', 'Ty - X');
plot(freq_frf, abs(frf_hexa_x(:, 8)), 'DisplayName', 'Ry - X');
plot(freq_frf, abs(frf_hexa_x(:, 11)), 'DisplayName', 'Hexa - X');
hold off;
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
xlim([20, 200]);
legend('Location', 'northeast');
#+end_src
#+begin_src matlab :exports none :results none
channel = 12;
figure;
ax1 = subaxis(3,1,1);
plot(freq_frf, abs(frf_hexa_y(:, channel)))
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
ax2 = subaxis(3,1,2);
plot(freq_frf, mod(180/pi*phase(frf_hexa_y(:, channel))+180, 360)-180)
set(gca, 'Xscale', 'log');
ylim([-180 180]);
yticks([-180:90:180]);
ax3 = subaxis(3,1,3);
plot(freq_frf, coh_hexa_y(:, channel))
set(gca, 'Xscale', 'log');
linkaxes([ax1,ax2,ax3],'x');
xlim([20, 200]);
#+end_src
#+begin_src matlab :exports none :results none
figure;
ax1 = subaxis(2,1,1);
plot(freq_frf, abs(frf_marble_z(:, 4)))
set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log')
ax2 = subaxis(2,1,2);
plot(freq_frf, mod(180/pi*phase(frf_marble_z(:, 4))+180, 360)-180)
linkaxes([ax1,ax2],'x');
ylim([-180 180]);
yticks([-180:90:180]);
set(gca, 'Xscale', 'log')
xlim([20, 200])
#+end_src

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%%
clear;
close all;
clc
%% Coherence
load('../raw_data/id31_microstation_2017_11_17_coh.mat', 'coh_hexa_x',...
'coh_hexa_y',...
'coh_hexa_z',...
'coh_marble_x',...
'coh_marble_y',...
'coh_marble_z');
%% Save Coherence data
save('../data/id31_microstation_2017_11_17_coh.mat', ...
'coh_marble_x', ...
'coh_hexa_x', ...
'coh_marble_y', ...
'coh_hexa_y', ...
'coh_marble_z', ...
'coh_hexa_z');
%% Frequency Response
load('../raw_data/id31_microstation_2017_11_17_frf.mat', 'freq_frf', ...
'frf_hexa_x',...
'frf_hexa_y',...
'frf_hexa_z',...
'frf_marble_x',...
'frf_marble_y',...
'frf_marble_z');
force_factor = 1;
accel_factor = 1000;
scale_factor = accel_factor/force_factor;
frf_hexa_x = scale_factor*frf_hexa_x;
frf_hexa_y = -scale_factor*frf_hexa_y;
frf_hexa_z = -scale_factor*frf_hexa_z;
frf_marble_x = scale_factor*frf_marble_x;
frf_marble_y = scale_factor*frf_marble_y;
frf_marble_z = -scale_factor*frf_marble_z;
%% Save Frequency Response Data
save('../data/id31_microstation_2017_11_17_frf.mat', ...
'freq_frf', ...
'frf_marble_x', ...
'frf_hexa_x', ...
'frf_marble_y', ...
'frf_hexa_y', ...
'frf_marble_z', ...
'frf_hexa_z');

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ground = struct(...
'full_name', 'Ground',...
'short_name', 'ground',...
'letter', 'g',...
'above_of', '',...
'bellow_of', 'marble',...
'tx', struct(...
'isMeasured', false, ...
'isExcited', false, ...
'id', 0 ...
),...
'ty', struct(...
'isMeasured', false, ...
'isExcited', false, ...
'id', 0 ...
),...
'tz', struct(...
'isMeasured', false, ...
'isExcited', false, ...
'id', 0 ...
)...
);
marble = struct(...
'full_name', 'Marble',...
'short_name', 'marble',...
'letter', 'm',...
'above_of', 'ground',...
'bellow_of', 'trans_stage',...
'tx', struct(...
'isMeasured', true, ...
'isExcited', true, ...
'id', 2 ...
),...
'ty', struct(...
'isMeasured', true, ...
'isExcited', true, ...
'id', 3 ...
),...
'tz', struct(...
'isMeasured', true, ...
'isExcited', true, ...
'id', 4 ...
)...
);
trans_stage = struct(...
'full_name', 'Translation Stage',...
'short_name', 'trans_stage',...
'letter', 't',...
'above_of', 'marble',...
'bellow_of', 'tilt_stage',...
'tx', struct(...
'isMeasured', true, ...
'isExcited', false, ...
'id', 5 ...
),...
'ty', struct(...
'isMeasured', true, ...
'isExcited', false, ...
'id', 6 ...
),...
'tz', struct(...
'isMeasured', true, ...
'isExcited', false, ...
'id', 7 ...
)...
);
tilt_stage = struct(...
'full_name', 'Tilt Stage',...
'short_name', 'tilt_stage',...
'letter', 'o',...
'above_of', 'trans_stage',...
'bellow_of', 'hexa',...
'tx', struct(...
'isMeasured', true, ...
'isExcited', false, ...
'id', 8 ...
),...
'ty', struct(...
'isMeasured', true, ...
'isExcited', false, ...
'id', 9 ...
),...
'tz', struct(...
'isMeasured', true, ...
'isExcited', false, ...
'id', 10 ...
)...
);
hexa = struct(...
'full_name', 'Hexapod',...
'short_name', 'hexa',...
'letter', 'h',...
'above_of', 'tilt_stage',...
'bellow_of', 'nano_stage',...
'tx', struct(...
'isMeasured', true, ...
'isExcited', true, ...
'id', 11 ...
),...
'ty', struct(...
'isMeasured', true, ...
'isExcited', true, ...
'id', 12 ...
),...
'tz', struct(...
'isMeasured', true, ...
'isExcited', true, ...
'id', 13 ...
)...
);
nano_stage = struct(...
'full_name', 'Nano Stage',...
'short_name', 'nano_stage',...
'letter', 'n',...
'above_of', 'hexa',...
'bellow_of', 'sample',...
'tx', struct(...
'isMeasured', false, ...
'isExcited', false, ...
'id', 0 ...
),...
'ty', struct(...
'isMeasured', false, ...
'isExcited', false, ...
'id', 0 ...
),...
'tz', struct(...
'isMeasured', false, ...
'isExcited', false, ...
'id', 0 ...
)...
);
sample = struct(...
'full_name', 'Sample',...
'short_name', 'sample',...
'letter', 's',...
'above_of', 'nano_stage',...
'bellow_of', '',...
'tx', struct(...
'isMeasured', false, ...
'isExcited', false, ...
'id', 0 ...
),...
'ty', struct(...
'isMeasured', false, ...
'isExcited', false, ...
'id', 0 ...
),...
'tz', struct(...
'isMeasured', false, ...
'isExcited', false, ...
'id', 0 ...
)...
);
%%
elements = struct(...
'ground', ground,...
'marble', marble,...
'trans_stage', trans_stage,...
'tilt_stage', tilt_stage,...
'hexa', hexa,...
'nano_stage', nano_stage,...
'sample', sample ...
);
%% Where is located the data files generated by export_measure_data script
files = struct(...
'frf', 'id31_microstation_2017_11_17_frf.mat',...
'coh', 'id31_microstation_2017_11_17_coh.mat' ...
);
%%
m_object = struct(...
'files', files,...
'elements', elements,...
'quantity', 'acceleration', ...
'notes', 'Mesures du 17/11/2017 par Marc Lessourd - Accelerometers' ...
);
%% Save m_object
save('../data/2017_11_17.mat', 'm_object')

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