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Thomas Dehaeze
2020-04-27 11:35:57 +02:00
parent dbd4320349
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@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2019-05-14 mar. 10:53 -->
<!-- 2019-10-31 jeu. 16:19 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<title>Vibrations induced by the Slip-Ring and the Spindle</title>
@@ -258,27 +258,26 @@ for the JavaScript code in this tag.
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgae707b1">1. Experimental Setup</a></li>
<li><a href="#org78dded5">2. Data Analysis</a>
<li><a href="#orga44a9d5">1. Experimental Setup</a></li>
<li><a href="#orgb5a2f1a">2. Data Analysis</a>
<ul>
<li><a href="#orgaf48712">2.1. Load data</a></li>
<li><a href="#orga3184c9">2.2. Time domain plots</a></li>
<li><a href="#org66e3cd4">2.3. Frequency Domain</a></li>
<li><a href="#orgbe56ee4">2.4. Conclusion</a></li>
<li><a href="#org239b200">2.1. Load data</a></li>
<li><a href="#org66889bf">2.2. Voltage to Velocity</a></li>
<li><a href="#orgd049ddc">2.3. Time domain plots</a></li>
<li><a href="#orgfee57e5">2.4. Frequency Domain</a></li>
<li><a href="#org7d3ac71">2.5. Relative Motion</a></li>
<li><a href="#org1464a72">2.6. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orgae707b1" class="outline-2">
<h2 id="orgae707b1"><span class="section-number-2">1</span> Experimental Setup</h2>
<div id="outline-container-orga44a9d5" class="outline-2">
<h2 id="orga44a9d5"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1">
</div>
<ol class="org-ol">
<li><a id="orgd4a8f25"></a>Setup<br />
<div class="outline-text-6" id="text-1-0-0-0-1">
<p>
<b>Setup</b>:
All the stages are OFF.
</p>
@@ -303,6 +302,7 @@ Two voltage amplifiers are used, their setup is:
A first order low pass filter is also added at the input of the voltage amplifiers.
</p>
<p>
<b>Goal</b>:
</p>
@@ -383,27 +383,24 @@ Each of the measurement <code>mat</code> file contains one <code>data</code> arr
</table>
<p>
A movie showing the experiment is shown on figure <a href="#orgb52ab90">1</a>.
A movie showing the experiment is shown on figure <a href="#org1669ed1">1</a>.
</p>
<div id="orgb52ab90" class="figure">
<div id="org1669ed1" class="figure">
<p><img src="./img/VID_20190510_155655.gif" alt="VID_20190510_155655.gif" width="300px" />
</p>
<p><span class="figure-number">Figure 1: </span>Movie of the experiment, rotation speed is 6rpm</p>
</div>
</div>
</li>
</ol>
</div>
<div id="outline-container-org78dded5" class="outline-2">
<h2 id="org78dded5"><span class="section-number-2">2</span> Data Analysis</h2>
<div id="outline-container-orgb5a2f1a" class="outline-2">
<h2 id="orgb5a2f1a"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org66307ff"></a>
<a id="org73b6124"></a>
</p>
<div class="note">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/spindle_slip_ring_vibrations.zip">here</a>.
@@ -412,75 +409,119 @@ All the files (data and Matlab scripts) are accessible <a href="data/spindle_sli
</div>
</div>
<div id="outline-container-orgaf48712" class="outline-3">
<h3 id="orgaf48712"><span class="section-number-3">2.1</span> Load data</h3>
<div id="outline-container-org239b200" class="outline-3">
<h3 id="org239b200"><span class="section-number-3">2.1</span> Load data</h3>
<div class="outline-text-3" id="text-2-1">
<div class="org-src-container">
<pre class="src src-matlab">of = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_024.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; of = of.data;
sr = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_025.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sr = sr.data;
sp = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_026.mat', 'data'</span><span class="org-rainbow-delimiters-depth-1">)</span>; sp = sp.data;
<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;
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;
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;
</pre>
</div>
<div class="warning">
<p>
There is a sign error for the Geophone located on top of the Hexapod.
The problem probably comes from the wiring in the Slip-Ring.
</p>
</div>
<div class="org-src-container">
<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-orga3184c9" class="outline-3">
<h3 id="orga3184c9"><span class="section-number-3">2.2</span> Time domain plots</h3>
<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>, 'DisplayName', 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</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>, 'DisplayName', 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</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', 'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</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>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">10</span> <span class="org-highlight-numbers-number">10</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', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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="orga435a98" class="figure">
<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>Measurement of the geophone located on the marble - Time domain</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', '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', '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', 'OFF'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'Voltage </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">V</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>; ylim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">-</span><span class="org-highlight-numbers-number">10</span> <span class="org-highlight-numbers-number">10</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', 'northeast'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
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="org2bafcfa" class="figure">
<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>Measurement of the geophone at the sample location - Time domain</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-org66e3cd4" class="outline-3">
<h3 id="org66e3cd4"><span class="section-number-3">2.3</span> Frequency Domain</h3>
<div class="outline-text-3" id="text-2-3">
<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>;
<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>;
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>
@@ -502,79 +543,249 @@ First for the geophone located on the marble
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, 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">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 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 signals:
And we plot the ASD of the measured velocities:
</p>
<ul class="org-ul">
<li>figure <a href="#org3fb6d61">4</a> for the geophone located on the marble</li>
<li>figure <a href="#orge9619ee">5</a> for the geophone at the sample position</li>
<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>, 'DisplayName', 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</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>, 'DisplayName', 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</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', 'OFF'</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>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', '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', '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-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', '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">0</span>.<span class="org-highlight-numbers-number">1</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>;
<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="org3fb6d61" class="figure">
<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 4: </span>Comparison of the ASD of the measured voltage from the Geophone on the marble</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>, 'DisplayName', 'Spindle <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</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>, 'DisplayName', 'Slip<span class="org-type">-</span>Ring <span class="org-type">-</span> <span class="org-highlight-numbers-number">6rpm</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', 'OFF'</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>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', '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', '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-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>ASD of the measured Voltage $<span class="org-type">\</span>left<span class="org-rainbow-delimiters-depth-2">[</span><span class="org-type">\</span>frac<span class="org-rainbow-delimiters-depth-3">{</span>V<span class="org-rainbow-delimiters-depth-3">}{</span><span class="org-type">\</span>sqrt<span class="org-rainbow-delimiters-depth-4">{</span>Hz<span class="org-rainbow-delimiters-depth-4">}</span><span class="org-rainbow-delimiters-depth-3">}</span><span class="org-type">\</span>right<span class="org-rainbow-delimiters-depth-2">]</span>$'<span class="org-rainbow-delimiters-depth-1">)</span>
legend<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Location', '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">0</span>.<span class="org-highlight-numbers-number">1</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>;
<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="orge9619ee" class="figure">
<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 5: </span>Comparison of the ASD of the measured voltage from the Geophone at the sample location</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-orgbe56ee4" class="outline-3">
<h3 id="orgbe56ee4"><span class="section-number-3">2.4</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-4">
<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" />
</p>
<p><span class="figure-number">Figure 11: </span>Comparison of the ASD of the relative velocity</p>
</div>
<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>
<div id="org76a9b23" class="figure">
<p><img src="figs/dist_rz_cps.png" alt="dist_rz_cps.png" />
</p>
<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>
</div>
<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>
</div>
<p>
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 slip-ring rotation induces almost no vibrations on the marble, and only a little vibrations on the sample above 100Hz.
The relative motion below 20Hz is dominated by another effect than the rotation of the Spindle (probably ground motion).
</p>
<p>
The spindle rotation induces a lot of vibrations of the sample as well as on the granite.
There is a huge peak at 24Hz on the sample vibration but not on the granite vibration.
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>
@@ -582,7 +793,7 @@ There is a huge peak at 24Hz on the sample vibration but not on the granite vibr
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2019-05-14 mar. 10:53</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>
</body>

236
disturbance-sr-rz/index.org
View File

@@ -98,22 +98,36 @@ A movie showing the experiment is shown on figure [[fig:exp_sl_sp_gif]].
** Matlab Init :noexport:ignore:
#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
<<matlab-dir>>
addpath('../src');
#+end_src
#+begin_src matlab :exports none :results silent :noweb yes
<<matlab-init>>
#+end_src
#+begin_src matlab
addpath('../src');
#+end_src
** Load data
#+begin_src matlab
of = load('mat/data_024.mat', 'data'); of = of.data;
sr = load('mat/data_025.mat', 'data'); sr = sr.data;
sp = load('mat/data_026.mat', 'data'); sp = sp.data;
of = load('mat/data_024.mat', 'data'); of = of.data; % OFF
sr = load('mat/data_025.mat', 'data'); sr = sr.data; % Slip Ring
sp = load('mat/data_026.mat', 'data'); sp = sp.data; % Spindle
#+end_src
#+begin_warning
There is a sign error for the Geophone located on top of the Hexapod.
The problem probably comes from the wiring in the Slip-Ring.
#+end_warning
#+begin_src matlab
of(:, 2) = -of(:, 2);
sr(:, 2) = -sr(:, 2);
sp(:, 2) = -sp(:, 2);
#+end_src
** Voltage to Velocity
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:~/Cloud/These/meas/src/index.org][here]]).
We convert the measured voltage to velocity using the function =voltageToVelocityL22= (accessible [[file:../src/index.org][here]]).
#+begin_src matlab
gain = 60; % [dB]
@@ -192,11 +206,11 @@ We convert the measured voltage to velocity using the function =voltageToVelocit
** Frequency Domain
We first compute some parameters that will be used for the PSD computation.
#+begin_src matlab :results none
dt = of(2, 3)-of(1, 3);
dt = of(2, 3)-of(1, 3); % [s]
Fs = 1/dt; % [Hz]
win = hanning(ceil(10*Fs));
win = hanning(ceil(10*Fs)); % Window used
#+end_src
Then we compute the Power Spectral Density using =pwelch= function.
@@ -215,13 +229,6 @@ And for the geophone located at the sample position.
[pxsp_s, ~] = pwelch(sp(:, 2), win, [], [], Fs);
#+end_src
And finally for the relative velocity between the sample and the marble.
#+begin_src matlab
[pxof_r, ~] = pwelch(of(:, 2)-of(:, 1), win, [], [], Fs);
[pxsr_r, ~] = pwelch(sr(:, 2)-sr(:, 1), win, [], [], Fs);
[pxsp_r, ~] = pwelch(sp(:, 2)-sp(:, 1), win, [], [], Fs);
#+end_src
And we plot the ASD of the measured velocities:
- figure [[fig:sr_sp_psd_marble_compare]] for the geophone located on the marble
- figure [[fig:sr_sp_psd_sample_compare]] for the geophone at the sample position
@@ -276,6 +283,115 @@ And we plot the ASD of the measured velocities:
#+RESULTS: fig:sr_sp_psd_sample_compare
[[file:figs/sr_sp_psd_sample_compare.png]]
We load the ground motion to compare with the measurements (Fig. [[fig:ty_comp_gm]]).
We see that the motion is dominated by the ground motion below 20Hz.
#+begin_src matlab
gm = load('../ground-motion/mat/psd_gm.mat', 'f', 'psd_gv');
#+end_src
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(pxsp_m), 'DisplayName', 'Spindle - 6rpm');
plot(f, sqrt(pxsr_m), 'DisplayName', 'Slip-Ring - 6rpm');
plot(f, sqrt(pxof_m), 'DisplayName', 'OFF');
plot(gm.f, sqrt(gm.psd_gv), 'k-', 'DisplayName', 'Ground Motion');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/ty_comp_gm.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:ty_comp_gm
#+CAPTION: Comparison of the ground velocity with the measured velocity ([[./figs/ty_comp_gm.png][png]], [[./figs/ty_comp_gm.pdf][pdf]])
[[file:figs/ty_comp_gm.png]]
** Relative Motion
The relative velocity between the sample and the marble is shown in Fig. [[fig:rz_relative_velocity]].
The velocity is integrated to have the relative displacement in Fig. [[fig:rz_relative_motion]].
#+begin_src matlab :exports results
figure;
hold on;
plot(sp(:, 3), sp(:, 2)-sp(:, 1), 'DisplayName', 'Spindle - 6rpm');
plot(sr(:, 3), sr(:, 2)-sr(:, 1), 'DisplayName', 'Slip-Ring - 6rpm');
plot(of(:, 3), of(:, 2)-of(:, 1), 'DisplayName', 'OFF');
hold off;
xlabel('Time [s]'); ylabel('Velocity [m/s]');
xlim([0, 100]); ylim([-1e-4, 1e-4]);
legend('Location', 'northeast');
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/rz_relative_velocity.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:rz_relative_velocity
#+CAPTION: Relative velocity between the hexapod and the marble ([[./figs/rz_relative_velocity.png][png]], [[./figs/rz_relative_velocity.pdf][pdf]])
[[file:figs/rz_relative_velocity.png]]
Time domain: Integration to have the displacement
#+begin_src matlab :exports results
figure;
hold on;
plot(sp(:, 3), lsim(1/s, sp(:, 2)-sp(:, 1), sp(:, 3)), 'DisplayName', 'Spindle - 6rpm');
plot(sr(:, 3), lsim(1/s, sr(:, 2)-sr(:, 1), sr(:, 3)), 'DisplayName', 'Slip-Ring - 6rpm');
plot(of(:, 3), lsim(1/s, of(:, 2)-of(:, 1), of(:, 3)), 'DisplayName', 'OFF');
hold off;
xlabel('Time [s]'); ylabel('Displacement [m]');
xlim([0, 100]);
legend('Location', 'northeast');
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/rz_relative_motion.pdf" :var figsize="wide-normal" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:rz_relative_motion
#+CAPTION: Relative displacement between the Hexapod and the marble ([[./figs/rz_relative_motion.png][png]], [[./figs/rz_relative_motion.pdf][pdf]])
[[file:figs/rz_relative_motion.png]]
We compute the PSD of the relative velocity between the sample and the marble.
#+begin_src matlab
[pxof_r, f] = pwelch(of(:, 2)-of(:, 1), win, [], [], Fs);
[pxsr_r, ~] = pwelch(sr(:, 2)-sr(:, 1), win, [], [], Fs);
[pxsp_r, ~] = pwelch(sp(:, 2)-sp(:, 1), win, [], [], Fs);
#+end_src
The Power Spectral Density of the Granite Velocity, Sample velocity and relative velocity are compare in Fig. [[fig:rz_psd_sample_granite_relative_comp]].
#+begin_src matlab :exports results
figure;
hold on;
plot(f, sqrt(pxof_m)./(2*pi*f), 'DisplayName', 'Granite');
plot(f, sqrt(pxof_s)./(2*pi*f), 'DisplayName', 'Sample');
plot(f, sqrt(pxof_r)./(2*pi*f), 'DisplayName', 'Diff');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('ASD of the relative velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/rz_psd_sample_granite_relative_comp.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:rz_psd_sample_granite_relative_comp
#+CAPTION: Comparison of the PSD of the velocity of the Sample, Granite and relative velocity ([[./figs/rz_psd_sample_granite_relative_comp.png][png]], [[./figs/rz_psd_sample_granite_relative_comp.pdf][pdf]])
[[file:figs/rz_psd_sample_granite_relative_comp.png]]
Then, we display the PSD of the relative velocity for all three cases in Fig. [[fig:sr_sp_psd_relative_compare]].
#+begin_src matlab :results none
figure;
hold on;
@@ -301,12 +417,94 @@ And we plot the ASD of the measured velocities:
#+RESULTS: fig:sr_sp_psd_relative_compare
[[file:figs/sr_sp_psd_relative_compare.png]]
The Cumulative Power Spectrum of the relative velocity is shown in Fig. [[fig:dist_rz_cps]] and in Fig. [[fig:dist_rz_cps_reverse]] (integrated in reverse direction).
#+begin_src matlab :results none :exports results
figure;
hold on;
plot(f, cumtrapz(f,pxsp_r), 'DisplayName', 'Spindle - 6rpm');
plot(f, cumtrapz(f,pxsr_r), 'DisplayName', 'Slip-Ring - 6rpm');
plot(f, cumtrapz(f,pxof_r), 'DisplayName', 'OFF');
hold off;
set(gca, 'xscale', 'log');
set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('CPS of the relative velocity $\left[\frac{(m/s)^2}{Hz}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/dist_rz_cps.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:dist_rz_cps
#+CAPTION: Cumulative Power Spectrum of the relative velocity ([[./figs/dist_rz_cps.png][png]], [[./figs/dist_rz_cps.pdf][pdf]])
[[file:figs/dist_rz_cps.png]]
#+begin_src matlab :exports results
figure;
hold on;
plot(f, flip(-cumtrapz(flip(f), flip(pxsp_r))), 'DisplayName', 'Spindle - 6rpm');
plot(f, flip(-cumtrapz(flip(f), flip(pxsr_r))), 'DisplayName', 'Slip-Ring - 6rpm');
plot(f, flip(-cumtrapz(flip(f), flip(pxof_r))), 'DisplayName', 'OFF');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('CPS of the relative velocity $\left[\frac{(m/s)^2}{Hz}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/dist_rz_cps_reverse.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:dist_rz_cps_reverse
#+CAPTION: Cumulative Power Spectrum of the relative velocity (integrated from high to low frequencies) ([[./figs/dist_rz_cps_reverse.png][png]], [[./figs/dist_rz_cps_reverse.pdf][pdf]])
[[file:figs/dist_rz_cps_reverse.png]]
Finally, the Cumulative Amplitude Spectrum of the relative position between the hexapod and the marble is shown in Fig. [[fig:dist_rz_cas]].
#+begin_src matlab :results none
figure;
hold on;
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(pxsp_r./(2*pi*f).^2)))), 'DisplayName', 'Spindle - 6rpm');
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(pxsr_r./(2*pi*f).^2)))), 'DisplayName', 'Slip-Ring - 6rpm');
plot(f, sqrt(flip(-cumtrapz(flip(f), flip(pxof_r./(2*pi*f).^2)))), 'DisplayName', 'OFF');
hold off;
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
xlabel('Frequency [Hz]'); ylabel('CAS of the relative displacement $\left[\frac{m}{\sqrt{Hz}}\right]$')
legend('Location', 'southwest');
xlim([2, 500]);
#+end_src
#+HEADER: :tangle no :exports results :results none :noweb yes
#+begin_src matlab :var filepath="figs/dist_rz_cas.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
<<plt-matlab>>
#+end_src
#+NAME: fig:dist_rz_cas
#+CAPTION: Cumulative Amplitude Spectrum of the relative motion Hexapod/Granite ([[./figs/dist_rz_cas.png][png]], [[./figs/dist_rz_cas.pdf][pdf]])
[[file:figs/dist_rz_cas.png]]
** Save
The Power Spectral Density of the relative velocity and of the hexapod velocity is saved for further analysis.
#+begin_src matlab
save('mat/pxsp_r.mat', 'f', 'pxsp_r', 'pxsp_s');
#+end_src
** Conclusion
#+begin_important
- The slip-ring rotation induces almost no vibrations on the marble, and only a little vibrations on the sample above 100Hz.
The relative motion below 20Hz is dominated by another effect than the rotation of the Spindle (probably ground motion).
- The spindle rotation induces a lot of vibrations of the sample as well as on the granite.
- There is a huge peak at 24Hz on the sample vibration but not on the granite vibration
- The peak is really sharp, could this be due to magnetic effect?
- Should redo the measurement with piezo accelerometers.
The Slip-Ring rotation induce almost no relative motion of the hexapod with respect to the granite (only a little above 400Hz).
The Spindle rotation induces relative motion of the hexapod with respect to the granite above 20Hz.
#+end_important
#+begin_important
There is a huge peak at 24Hz on the sample vibration but not on the granite vibration
- The peak is really sharp, could this be due to magnetic effect?
- Should redo the measurement with piezo accelerometers.
#+end_important

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