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<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="#org20cd7af">1. Experimental conditions</a></li>
<li><a href="#org4b136ea">2. Measurements procedure</a></li>
<li><a href="#org7a4e10c">3. Measurement Files</a></li>
<li><a href="#orgc4e4e05">4. Data Analysis</a>
<ul>
<li><a href="#org8e48582">4.1. Loading of the data</a></li>
<li><a href="#orgdef23af">4.2. Pre-processing of the data</a></li>
<li><a href="#org9329022">4.3. X-direction FRF</a></li>
<li><a href="#orgf143ff0">4.4. Y-direction FRF</a></li>
<li><a href="#org69dd2ae">4.5. Z-direction FRF</a></li>
</ul>
</li>
<li><a href="#orgdfa9254">5. Results</a></li>
</ul>
</div>
</div>
<div id="outline-container-org20cd7af" class="outline-2">
<h2 id="org20cd7af"><span class="section-number-2">1</span> Experimental conditions</h2>
<div class="outline-text-2" id="text-1">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<tbody>
<tr>
<td class="org-left"><b>Date</b></td>
<td class="org-left">2017-11-17</td>
</tr>
<tr>
<td class="org-left"><b>Sensors</b></td>
<td class="org-left">Accelerometers</td>
</tr>
<tr>
<td class="org-left"><b>Excitation</b></td>
<td class="org-left">Instrumented Hammer</td>
</tr>
<tr>
<td class="org-left"><b>Location</b></td>
<td class="org-left">Laboratory</td>
</tr>
</tbody>
</table>
<p>
Dynamics of the station is evaluated using instrumented hammer and accelerometers fixed on each stage.
</p>
<p>
<b>Goal</b>:
</p>
<ul class="org-ul">
<li>Obtain a first estimation of resonance frequencies</li>
</ul>
<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="#orge99c284">1</a>).</li>
<li>Made by Marc Lesourd on the 17th of November 2017</li>
</ul>
<div id="orge99c284" class="figure">
<p><img src="./figs/accelerometers.png" alt="accelerometers.png" width="500px" />
</p>
<p><span class="figure-number">Figure 1: </span>Accelerometers position</p>
</div>
<div id="org363f97a" class="figure">
<p><img src="./figs/instrumented_hammer.png" alt="instrumented_hammer.png" width="500px" />
</p>
<p><span class="figure-number">Figure 2: </span>Instrumented Hammer used</p>
</div>
</div>
</div>
<div id="outline-container-org4b136ea" class="outline-2">
<h2 id="org4b136ea"><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="#org3aa8e2c">1</a>) are glued on (see figure <a href="#orge99c284">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="org3aa8e2c" 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="#org363f97a">2</a>):
</p>
<ul class="org-ul">
<li>Marble</li>
<li>Hexapod</li>
</ul>
</div>
</div>
<div id="outline-container-org7a4e10c" class="outline-2">
<h2 id="org7a4e10c"><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="#org2cde1ca">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="#org6601586">3</a>.
</p>
<table id="org2cde1ca" 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_hexa_x</td>
<td class="org-left">Hexapod</td>
<td class="org-left">X</td>
</tr>
<tr>
<td class="org-left">frf_hexa_y</td>
<td class="org-left">Hexapod</td>
<td class="org-left">Y</td>
</tr>
<tr>
<td class="org-left">frf_hexa_z</td>
<td class="org-left">Hexapod</td>
<td class="org-left">Z</td>
</tr>
<tr>
<td class="org-left">frf_marble_x</td>
<td class="org-left">Marble</td>
<td class="org-left">X</td>
</tr>
<tr>
<td class="org-left">frf_marble_y</td>
<td class="org-left">Marble</td>
<td class="org-left">Y</td>
</tr>
<tr>
<td class="org-left">frf_marble_z</td>
<td class="org-left">Marble</td>
<td class="org-left">Z</td>
</tr>
</tbody>
</table>
<table id="org6601586" 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-orgc4e4e05" class="outline-2">
<h2 id="orgc4e4e05"><span class="section-number-2">4</span> Data Analysis</h2>
<div class="outline-text-2" id="text-4">
</div>
<div id="outline-container-org8e48582" class="outline-3">
<h3 id="org8e48582"><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 class="org-string">'./raw_data/id31_microstation_2017_11_17_coh.mat'</span>,...
<span class="org-string">'coh_hexa_x'</span>,...
<span class="org-string">'coh_hexa_y'</span>,...
<span class="org-string">'coh_hexa_z'</span>,...
<span class="org-string">'coh_marble_x'</span>,...
<span class="org-string">'coh_marble_y'</span>,...
<span class="org-string">'coh_marble_z'</span>);
load(<span class="org-string">'./raw_data/id31_microstation_2017_11_17_frf.mat'</span>,...
<span class="org-string">'freq_frf'</span>,...
<span class="org-string">'frf_hexa_x'</span>,...
<span class="org-string">'frf_hexa_y'</span>,...
<span class="org-string">'frf_hexa_z'</span>,...
<span class="org-string">'frf_marble_x'</span>,...
<span class="org-string">'frf_marble_y'</span>,...
<span class="org-string">'frf_marble_z'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-orgdef23af" class="outline-3">
<h3 id="orgdef23af"><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 = 0.102; <span class="org-comment">% [V/(m/s2)]</span>
w = <span class="org-constant">j</span><span class="org-type">*</span>2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>freq_frf; <span class="org-comment">% j.omega in [rad/s]</span>
frf_hexa_x = 1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_x<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
frf_hexa_y = <span class="org-type">-</span>1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_y<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
frf_hexa_z = <span class="org-type">-</span>1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_z<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
frf_marble_x = 1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_x<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
frf_marble_y = 1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_y<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
frf_marble_z = <span class="org-type">-</span>1<span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_z<span class="org-type">./</span>(w<span class="org-type">.^</span>2);
</pre>
</div>
</div>
</div>
<div id="outline-container-org9329022" class="outline-3">
<h3 id="org9329022"><span class="section-number-3">4.3</span> X-direction FRF</h3>
<div class="outline-text-3" id="text-4-3">
<div id="orgc62d27f" 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="org6bfc7a4" 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-orgf143ff0" class="outline-3">
<h3 id="orgf143ff0"><span class="section-number-3">4.4</span> Y-direction FRF</h3>
<div class="outline-text-3" id="text-4-4">
<div id="org1460e50" 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="org50bc3da" 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-org69dd2ae" class="outline-3">
<h3 id="org69dd2ae"><span class="section-number-3">4.5</span> Z-direction FRF</h3>
<div class="outline-text-3" id="text-4-5">
<div id="orga24d122" 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="orge608125" 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 id="outline-container-orgdfa9254" class="outline-2">
<h2 id="orgdfa9254"><span class="section-number-2">5</span> Results</h2>
<div class="outline-text-2" id="text-5">
<div class="important" id="orgbd89935">
<ul class="org-ul">
<li>Resonances have been identified at 45Hz and 75Hz</li>
<li>However, the quality of the measurements are bad at low frequency</li>
<li>New measurements should be done with Geophones</li>
</ul>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-11-12 jeu. 10:26</p>
</div>
</body>
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