733 lines
26 KiB
HTML
733 lines
26 KiB
HTML
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Measurements</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgb9e4bbf">1. Experimental conditions</a></li>
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<li><a href="#orgbe7bf59">2. Measurements procedure</a></li>
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<li><a href="#org3337380">3. Measurement Files</a></li>
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<li><a href="#orgc59cdd1">4. Data Analysis</a>
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<ul>
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<li><a href="#org97ea2b9">4.1. Loading of the data</a></li>
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<li><a href="#org55d35ad">4.2. Pre-processing of the data</a></li>
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<li><a href="#org409f95e">4.3. X-direction FRF</a></li>
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<li><a href="#org5ca4365">4.4. Y-direction FRF</a></li>
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<li><a href="#org491a242">4.5. Z-direction FRF</a></li>
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</ul>
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</li>
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<li><a href="#orgf03bfb4">5. Results</a></li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgb9e4bbf" class="outline-2">
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<h2 id="orgb9e4bbf"><span class="section-number-2">1</span> Experimental conditions</h2>
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<div class="outline-text-2" id="text-1">
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<col class="org-left" />
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<tbody>
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<tr>
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<td class="org-left"><b>Date</b></td>
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<td class="org-left">2017-11-17</td>
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</tr>
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<tr>
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<td class="org-left"><b>Sensors</b></td>
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<td class="org-left">Accelerometers</td>
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</tr>
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<tr>
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<td class="org-left"><b>Excitation</b></td>
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<td class="org-left">Instrumented Hammer</td>
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</tr>
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<tr>
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<td class="org-left"><b>Location</b></td>
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<td class="org-left">Laboratory</td>
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</tr>
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</tbody>
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</table>
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<p>
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Dynamics of the station is evaluated using instrumented hammer and accelerometers fixed on each stage.
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</p>
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<p>
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<b>Goal</b>:
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</p>
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<ul class="org-ul">
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<li>Obtain a first estimation of resonance frequencies</li>
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</ul>
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<ul class="org-ul">
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<li>Measurement made in a metrology lab</li>
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<li>The granite is not glued to the floor</li>
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<li>The Y-Translation stage is powered and in closed-loop</li>
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<li>The spindle is not powered</li>
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<li>Mass is placed on top of the Hexapod (<b>how much?</b>) (figure <a href="#orgb5022d9">1</a>).</li>
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<li>Made by Marc Lesourd on the 17th of November 2017</li>
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</ul>
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<div id="orgb5022d9" class="figure">
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<p><img src="./figs/accelerometers.png" alt="accelerometers.png" width="500px" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Accelerometers position</p>
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</div>
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<div id="orgaaf63dd" class="figure">
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<p><img src="./figs/instrumented_hammer.png" alt="instrumented_hammer.png" width="500px" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Instrumented Hammer used</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgbe7bf59" class="outline-2">
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<h2 id="orgbe7bf59"><span class="section-number-2">2</span> Measurements procedure</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<b>3-axis Accelerometers</b> (specifications table <a href="#org2f4877d">1</a>) are glued on (see figure <a href="#orgb5022d9">1</a>):
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</p>
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<ul class="org-ul">
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<li>Marble</li>
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<li>Y-Translation stage</li>
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<li>Tilt stage</li>
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<li>top of Hexapod</li>
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</ul>
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<table id="org2f4877d" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Pieozoelectric acc. 356b18 - 3 axis</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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</colgroup>
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<tbody>
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<tr>
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<td class="org-left">Sensitivity</td>
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<td class="org-left">0.102 V/(m/s2)</td>
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</tr>
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<tr>
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<td class="org-left">Measurement Range</td>
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<td class="org-left">4.9 m/s2 pk</td>
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</tr>
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<tr>
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<td class="org-left">Frequency Range</td>
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<td class="org-left">0.5 to 3000 Hz</td>
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</tr>
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|
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<tr>
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<td class="org-left">resonant frequency</td>
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<td class="org-left">>20000 Hz</td>
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</tr>
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<tr>
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<td class="org-left">broadband resolution</td>
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<td class="org-left">0.0005 m/s2 rms</td>
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</tr>
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</tbody>
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</table>
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<p>
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The structure is excited using an <b>instrumented hammer</b> with impacts on (see figure <a href="#orgaaf63dd">2</a>):
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</p>
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<ul class="org-ul">
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<li>Marble</li>
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<li>Hexapod</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org3337380" class="outline-2">
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<h2 id="org3337380"><span class="section-number-2">3</span> Measurement Files</h2>
|
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<div class="outline-text-2" id="text-3">
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<p>
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Two measurements files are:
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</p>
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<ul class="org-ul">
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<li><code>id31_microstation_2017_11_17_frf.mat</code> that contains:
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<ul class="org-ul">
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<li><code>freq_frf</code> the frequency vector in Hz</li>
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<li>Computed frequency response functions (see table <a href="#org71ee83c">2</a>)</li>
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</ul></li>
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<li><code>id31_microstation_2017_11_17_coh.mat</code>
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<ul class="org-ul">
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<li>Computed coherence</li>
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</ul></li>
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</ul>
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<p>
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For each of the measurement, the measured channels are shown on table <a href="#org1bf8383">3</a>.
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</p>
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<table id="org71ee83c" 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="org1bf8383" 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-orgc59cdd1" class="outline-2">
|
|
<h2 id="orgc59cdd1"><span class="section-number-2">4</span> Data Analysis</h2>
|
|
<div class="outline-text-2" id="text-4">
|
|
</div>
|
|
<div id="outline-container-org97ea2b9" class="outline-3">
|
|
<h3 id="org97ea2b9"><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-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/id31_microstation_2017_11_17_coh.mat'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'coh_hexa_x'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'coh_hexa_y'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'coh_hexa_z'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'coh_marble_x'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'coh_marble_y'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'coh_marble_z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'./raw_data/id31_microstation_2017_11_17_frf.mat'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'freq_frf'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'frf_hexa_x'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'frf_hexa_y'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'frf_hexa_z'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'frf_marble_x'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'frf_marble_y'</span>,<span class="org-underline">...</span>
|
|
<span class="org-string">'frf_marble_z'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org55d35ad" class="outline-3">
|
|
<h3 id="org55d35ad"><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 class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">102</span>; <span class="org-comment">% [V/(m/s2)]</span>
|
|
w = <span class="org-constant">j</span><span class="org-type">*</span><span class="org-highlight-numbers-number">2</span><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 = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_x<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
frf_hexa_y = <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_y<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
frf_hexa_z = <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_hexa_z<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
frf_marble_x = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_x<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
frf_marble_y = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_y<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
frf_marble_z = <span class="org-type">-</span><span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>accel_sensitivity<span class="org-type">*</span>frf_marble_z<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-1">(</span>w<span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org409f95e" class="outline-3">
|
|
<h3 id="org409f95e"><span class="section-number-3">4.3</span> X-direction FRF</h3>
|
|
<div class="outline-text-3" id="text-4-3">
|
|
|
|
<div id="org5d69ec3" 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="orgf472153" 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-org5ca4365" class="outline-3">
|
|
<h3 id="org5ca4365"><span class="section-number-3">4.4</span> Y-direction FRF</h3>
|
|
<div class="outline-text-3" id="text-4-4">
|
|
|
|
<div id="org8581a20" 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="orgdea2e62" 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-org491a242" class="outline-3">
|
|
<h3 id="org491a242"><span class="section-number-3">4.5</span> Z-direction FRF</h3>
|
|
<div class="outline-text-3" id="text-4-5">
|
|
|
|
<div id="org525b297" 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="orgf376c05" 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-orgf03bfb4" class="outline-2">
|
|
<h2 id="orgf03bfb4"><span class="section-number-2">5</span> Results</h2>
|
|
<div class="outline-text-2" id="text-5">
|
|
<div class="important">
|
|
<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: 2019-05-14 mar. 23:06</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
|
|
</body>
|
|
</html>
|