801 lines
63 KiB
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801 lines
63 KiB
HTML
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<title>Vibrations induced by the Slip-Ring and the Spindle</title>
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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">Vibrations induced by the Slip-Ring and the Spindle</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="#orga44a9d5">1. Experimental Setup</a></li>
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<li><a href="#orgb5a2f1a">2. Data Analysis</a>
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<ul>
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<li><a href="#org239b200">2.1. Load data</a></li>
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<li><a href="#org66889bf">2.2. Voltage to Velocity</a></li>
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<li><a href="#orgd049ddc">2.3. Time domain plots</a></li>
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<li><a href="#orgfee57e5">2.4. Frequency Domain</a></li>
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<li><a href="#org7d3ac71">2.5. Relative Motion</a></li>
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<li><a href="#org1464a72">2.6. Conclusion</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orga44a9d5" class="outline-2">
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<h2 id="orga44a9d5"><span class="section-number-2">1</span> Experimental Setup</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<b>Setup</b>:
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All the stages are OFF.
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</p>
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<p>
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Two geophone are use:
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</p>
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<ul class="org-ul">
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<li>One on the marble (corresponding to the first column in the data)</li>
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<li>One at the sample location (corresponding to the second column in the data)</li>
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</ul>
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<p>
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Two voltage amplifiers are used, their setup is:
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</p>
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<ul class="org-ul">
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<li>gain of 60dB</li>
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<li>AC/DC switch on AC</li>
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<li>Low pass filter at 1kHz</li>
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</ul>
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<p>
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A first order low pass filter is also added at the input of the voltage amplifiers.
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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>Identify the vibrations induced by the rotation of the Slip-Ring and Spindle</li>
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</ul>
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<p>
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<b>Measurements</b>:
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Three measurements are done:
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</p>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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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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<thead>
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<tr>
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<th scope="col" class="org-left">Measurement File</th>
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<th scope="col" class="org-left">Description</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left"><code>mat/data_024.mat</code></td>
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<td class="org-left">All the stages are OFF</td>
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</tr>
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<tr>
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<td class="org-left"><code>mat/data_025.mat</code></td>
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<td class="org-left">The slip-ring is ON and rotates at 6rpm. The spindle is OFF</td>
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</tr>
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<tr>
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<td class="org-left"><code>mat/data_026.mat</code></td>
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<td class="org-left">The slip-ring and spindle are both ON. They are both turning at 6rpm</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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Each of the measurement <code>mat</code> file contains one <code>data</code> array with 3 columns:
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</p>
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-right" />
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<col class="org-left" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-right">Column number</th>
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<th scope="col" class="org-left">Description</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-right">1</td>
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<td class="org-left">Geophone - Marble</td>
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</tr>
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<tr>
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<td class="org-right">2</td>
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<td class="org-left">Geophone - Sample</td>
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</tr>
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<tr>
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<td class="org-right">3</td>
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<td class="org-left">Time</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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A movie showing the experiment is shown on figure <a href="#org1669ed1">1</a>.
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</p>
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<div id="org1669ed1" class="figure">
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<p><img src="./img/VID_20190510_155655.gif" alt="VID_20190510_155655.gif" width="300px" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Movie of the experiment, rotation speed is 6rpm</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgb5a2f1a" class="outline-2">
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<h2 id="orgb5a2f1a"><span class="section-number-2">2</span> Data Analysis</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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<a id="org73b6124"></a>
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</p>
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<div class="note">
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<p>
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All the files (data and Matlab scripts) are accessible <a href="data/spindle_slip_ring_vibrations.zip">here</a>.
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</p>
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</div>
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</div>
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<div id="outline-container-org239b200" class="outline-3">
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<h3 id="org239b200"><span class="section-number-3">2.1</span> Load data</h3>
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<div class="outline-text-3" id="text-2-1">
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<div class="org-src-container">
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<pre class="src src-matlab">of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_024.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; of = of.data;
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sr = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_025.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr = sr.data;
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sp = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_026.mat'</span>, <span class="org-string">'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sp = sp.data;
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</pre>
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</div>
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<div class="warning">
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<p>
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There is a sign error for the Geophone located on top of the Hexapod.
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The problem probably comes from the wiring in the Slip-Ring.
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</p>
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</div>
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<div class="org-src-container">
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<pre class="src src-matlab">of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = <span class="org-type">-</span>sp<span class="org-rainbow-delimiters-depth-1">(</span><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-org66889bf" class="outline-3">
|
|
<h3 id="org66889bf"><span class="section-number-3">2.2</span> Voltage to Velocity</h3>
|
|
<div class="outline-text-3" id="text-2-2">
|
|
<p>
|
|
We convert the measured voltage to velocity using the function <code>voltageToVelocityL22</code> (accessible <a href="../src/index.html">here</a>).
|
|
</p>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">gain = <span class="org-highlight-numbers-number">60</span>; <span class="org-comment">% [dB]</span>
|
|
|
|
of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
|
|
of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
sr<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
sp<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-1">)</span> = voltageToVelocityL22<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, gain<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgd049ddc" class="outline-3">
|
|
<h3 id="orgd049ddc"><span class="section-number-3">2.3</span> Time domain plots</h3>
|
|
<div class="outline-text-3" id="text-2-3">
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org4e9bed0" class="figure">
|
|
<p><img src="figs/slip_ring_spindle_marble_time.png" alt="slip_ring_spindle_marble_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 2: </span>Velocity as measured by the geophone located on the marble - Time domain</p>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle and Slip-Ring'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Only Slip-Ring'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-2">)</span>, of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Time </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Velocity </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>, <span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org8be7963" class="figure">
|
|
<p><img src="figs/slip_ring_spindle_sample_time.png" alt="slip_ring_spindle_sample_time.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 3: </span>Velocity as measured by the geophone at the sample location - Time domain</p>
|
|
</div>
|
|
|
|
|
|
<div id="orgfc19876" class="figure">
|
|
<p><img src="figs/slip_ring_spindle_sample_zoom.png" alt="slip_ring_spindle_sample_zoom.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 4: </span>Velocity as measured by the geophone at the sample location - Time domain</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-orgfee57e5" class="outline-3">
|
|
<h3 id="orgfee57e5"><span class="section-number-3">2.4</span> Frequency Domain</h3>
|
|
<div class="outline-text-3" id="text-2-4">
|
|
<p>
|
|
We first compute some parameters that will be used for the PSD computation.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">dt = of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span><span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">3</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% [s]</span>
|
|
|
|
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
|
|
|
|
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-comment">% Window used</span>
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
Then we compute the Power Spectral Density using <code>pwelch</code> function.
|
|
</p>
|
|
|
|
<p>
|
|
First for the geophone located on the marble
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_m, f<span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxsp_m, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And for the geophone located at the sample position.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxsp_s, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
And we plot the ASD of the measured velocities:
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>figure <a href="#org704b4b4">5</a> for the geophone located on the marble</li>
|
|
<li>figure <a href="#orga078b66">6</a> for the geophone at the sample position</li>
|
|
</ul>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org704b4b4" class="figure">
|
|
<p><img src="figs/sr_sp_psd_marble_compare.png" alt="sr_sp_psd_marble_compare.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 5: </span>Comparison of the ASD of the measured velocities from the Geophone on the marble</p>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_s<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="orga078b66" class="figure">
|
|
<p><img src="figs/sr_sp_psd_sample_compare.png" alt="sr_sp_psd_sample_compare.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 6: </span>Comparison of the ASD of the measured velocities from the Geophone at the sample location</p>
|
|
</div>
|
|
|
|
<p>
|
|
We load the ground motion to compare with the measurements (Fig. <a href="#org71cc947">7</a>).
|
|
We see that the motion is dominated by the ground motion below 20Hz.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">gm = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gv'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_m<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>gm.f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>gm.psd_gv<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the measured velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org71cc947" class="figure">
|
|
<p><img src="figs/ty_comp_gm.png" alt="ty_comp_gm.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 7: </span>Comparison of the ground velocity with the measured velocity (<a href="./figs/ty_comp_gm.png">png</a>, <a href="./figs/ty_comp_gm.pdf">pdf</a>)</p>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<div id="outline-container-org7d3ac71" class="outline-3">
|
|
<h3 id="org7d3ac71"><span class="section-number-3">2.5</span> Relative Motion</h3>
|
|
<div class="outline-text-3" id="text-2-5">
|
|
<p>
|
|
The relative velocity between the sample and the marble is shown in Fig. <a href="#org21be4d0">8</a>.
|
|
The velocity is integrated to have the relative displacement in Fig. <a href="#org2d58d24">9</a>.
|
|
</p>
|
|
|
|
|
|
<div id="org21be4d0" class="figure">
|
|
<p><img src="figs/rz_relative_velocity.png" alt="rz_relative_velocity.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 8: </span>Relative velocity between the hexapod and the marble (<a href="./figs/rz_relative_velocity.png">png</a>, <a href="./figs/rz_relative_velocity.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
Time domain: Integration to have the displacement
|
|
</p>
|
|
|
|
<div id="org2d58d24" class="figure">
|
|
<p><img src="figs/rz_relative_motion.png" alt="rz_relative_motion.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 9: </span>Relative displacement between the Hexapod and the marble (<a href="./figs/rz_relative_motion.png">png</a>, <a href="./figs/rz_relative_motion.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
We compute the PSD of the relative velocity between the sample and the marble.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-rainbow-delimiters-depth-1">[</span>pxof_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>of<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxsr_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>sr<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-rainbow-delimiters-depth-1">[</span>pxsp_r, <span class="org-type">~</span><span class="org-rainbow-delimiters-depth-1">]</span> = pwelch<span class="org-rainbow-delimiters-depth-1">(</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-type">-</span>sp<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-type">:</span>, <span class="org-highlight-numbers-number">1</span><span class="org-rainbow-delimiters-depth-2">)</span>, win, <span class="org-rainbow-delimiters-depth-2">[]</span>, <span class="org-rainbow-delimiters-depth-2">[]</span>, Fs<span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
<p>
|
|
The Power Spectral Density of the Granite Velocity, Sample velocity and relative velocity are compare in Fig. <a href="#org0cfb4b3">10</a>.
|
|
</p>
|
|
|
|
<div id="org0cfb4b3" class="figure">
|
|
<p><img src="figs/rz_psd_sample_granite_relative_comp.png" alt="rz_psd_sample_granite_relative_comp.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 10: </span>Comparison of the PSD of the velocity of the Sample, Granite and relative velocity (<a href="./figs/rz_psd_sample_granite_relative_comp.png">png</a>, <a href="./figs/rz_psd_sample_granite_relative_comp.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
Then, we display the PSD of the relative velocity for all three cases in Fig. <a href="#org9d08176">11</a>.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsp_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxsr_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>pxof_r<span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'ASD of the relative velocity $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m/s</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org9d08176" class="figure">
|
|
<p><img src="figs/sr_sp_psd_relative_compare.png" alt="sr_sp_psd_relative_compare.png" />
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|
</p>
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|
<p><span class="figure-number">Figure 11: </span>Comparison of the ASD of the relative velocity</p>
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|
</div>
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|
|
|
<p>
|
|
The Cumulative Power Spectrum of the relative velocity is shown in Fig. <a href="#org76a9b23">12</a> and in Fig. <a href="#org61e2e4a">13</a> (integrated in reverse direction).
|
|
</p>
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|
|
|
<div id="org76a9b23" class="figure">
|
|
<p><img src="figs/dist_rz_cps.png" alt="dist_rz_cps.png" />
|
|
</p>
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|
<p><span class="figure-number">Figure 12: </span>Cumulative Power Spectrum of the relative velocity (<a href="./figs/dist_rz_cps.png">png</a>, <a href="./figs/dist_rz_cps.pdf">pdf</a>)</p>
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|
</div>
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|
|
|
|
|
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|
<div id="org61e2e4a" class="figure">
|
|
<p><img src="figs/dist_rz_cps_reverse.png" alt="dist_rz_cps_reverse.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 13: </span>Cumulative Power Spectrum of the relative velocity (integrated from high to low frequencies) (<a href="./figs/dist_rz_cps_reverse.png">png</a>, <a href="./figs/dist_rz_cps_reverse.pdf">pdf</a>)</p>
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|
</div>
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|
|
|
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<p>
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|
Finally, the Cumulative Amplitude Spectrum of the relative position between the hexapod and the marble is shown in Fig. <a href="#org454a2a7">14</a>.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
|
hold on;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxsp_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</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>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxsr_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</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>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</span><span class="org-type">'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org-rainbow-delimiters-depth-2">(</span>flip<span class="org-rainbow-delimiters-depth-3">(</span><span class="org-type">-</span>cumtrapz<span class="org-rainbow-delimiters-depth-4">(</span>flip<span class="org-rainbow-delimiters-depth-5">(</span>f<span class="org-rainbow-delimiters-depth-5">)</span>, flip<span class="org-rainbow-delimiters-depth-5">(</span>pxof_r<span class="org-type">./</span><span class="org-rainbow-delimiters-depth-6">(</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>f<span class="org-rainbow-delimiters-depth-6">)</span><span class="org-type">.^</span><span class="org-highlight-numbers-number">2</span><span class="org-rainbow-delimiters-depth-5">)</span><span class="org-rainbow-delimiters-depth-4">)</span><span class="org-rainbow-delimiters-depth-3">)</span><span class="org-rainbow-delimiters-depth-2">)</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
hold off;
|
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>; <span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'CAS of the relative displacement $\left</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">\frac</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">{</span></span><span class="org-string">m</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}{</span></span><span class="org-string">\sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">{</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-4">}</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">}</span></span><span class="org-string">\right</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">$'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
|
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
|
|
|
|
<div id="org454a2a7" class="figure">
|
|
<p><img src="figs/dist_rz_cas.png" alt="dist_rz_cas.png" />
|
|
</p>
|
|
<p><span class="figure-number">Figure 14: </span>Cumulative Amplitude Spectrum of the relative motion Hexapod/Granite (<a href="./figs/dist_rz_cas.png">png</a>, <a href="./figs/dist_rz_cas.pdf">pdf</a>)</p>
|
|
</div>
|
|
|
|
<p>
|
|
The Power Spectral Density of the relative velocity is saved for further analysis.
|
|
</p>
|
|
<div class="org-src-container">
|
|
<pre class="src src-matlab">save<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/pxsp_r.mat'</span>, <span class="org-string">'pxsp_r'</span>, <span class="org-string">'f'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
|
</pre>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
|
|
<div id="outline-container-org1464a72" class="outline-3">
|
|
<h3 id="org1464a72"><span class="section-number-3">2.6</span> Conclusion</h3>
|
|
<div class="outline-text-3" id="text-2-6">
|
|
<div class="important">
|
|
<p>
|
|
The relative motion below 20Hz is dominated by another effect than the rotation of the Spindle (probably ground motion).
|
|
</p>
|
|
|
|
<p>
|
|
The Slip-Ring rotation induce almost no relative motion of the hexapod with respect to the granite (only a little above 400Hz).
|
|
</p>
|
|
|
|
<p>
|
|
The Spindle rotation induces relative motion of the hexapod with respect to the granite above 20Hz.
|
|
</p>
|
|
|
|
</div>
|
|
|
|
<div class="important">
|
|
<p>
|
|
There is a huge peak at 24Hz on the sample vibration but not on the granite vibration
|
|
</p>
|
|
<ul class="org-ul">
|
|
<li>The peak is really sharp, could this be due to magnetic effect?</li>
|
|
<li>Should redo the measurement with piezo accelerometers.</li>
|
|
</ul>
|
|
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
</div>
|
|
<div id="postamble" class="status">
|
|
<p class="author">Author: Dehaeze Thomas</p>
|
|
<p class="date">Created: 2019-10-31 jeu. 16:19</p>
|
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
|
</div>
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</body>
|
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</html>
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