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<title>Vibrations induced by the Slip-Ring and the Spindle</title>
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<h1 class="title">Vibrations induced by the Slip-Ring and the Spindle</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org2422081">1. Experimental Setup</a></li>
<li><a href="#org6220fc6">2. Data Analysis</a>
<ul>
<li><a href="#org122f0e9">2.1. Load data</a></li>
<li><a href="#orgaea71b5">2.2. Voltage to Velocity</a></li>
<li><a href="#org485d23f">2.3. Time domain plots</a></li>
<li><a href="#org38cf97f">2.4. Frequency Domain</a></li>
<li><a href="#orgbaa08aa">2.5. Relative Motion</a></li>
<li><a href="#orgad3b42a">2.6. Save</a></li>
<li><a href="#org0a44924">2.7. Conclusion</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-org2422081" class="outline-2">
<h2 id="org2422081"><span class="section-number-2">1</span> Experimental Setup</h2>
<div class="outline-text-2" id="text-1">
<p>
<b>Setup</b>:
All the stages are OFF.
</p>
<p>
Two geophone are use:
</p>
<ul class="org-ul">
<li>One on the marble (corresponding to the first column in the data)</li>
<li>One at the sample location (corresponding to the second column in the data)</li>
</ul>
<p>
Two voltage amplifiers are used, their setup is:
</p>
<ul class="org-ul">
<li>gain of 60dB</li>
<li>AC/DC switch on AC</li>
<li>Low pass filter at 1kHz</li>
</ul>
<p>
A first order low pass filter is also added at the input of the voltage amplifiers.
</p>
<p>
<b>Goal</b>:
</p>
<ul class="org-ul">
<li>Identify the vibrations induced by the rotation of the Slip-Ring and Spindle</li>
</ul>
<p>
<b>Measurements</b>:
Three measurements are done:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Measurement File</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left"><code>mat/data_024.mat</code></td>
<td class="org-left">All the stages are OFF</td>
</tr>
<tr>
<td class="org-left"><code>mat/data_025.mat</code></td>
<td class="org-left">The slip-ring is ON and rotates at 6rpm. The spindle is OFF</td>
</tr>
<tr>
<td class="org-left"><code>mat/data_026.mat</code></td>
<td class="org-left">The slip-ring and spindle are both ON. They are both turning at 6rpm</td>
</tr>
</tbody>
</table>
<p>
Each of the measurement <code>mat</code> file contains one <code>data</code> array with 3 columns:
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-right" />
<col class="org-left" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Column number</th>
<th scope="col" class="org-left">Description</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">Geophone - Marble</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">Geophone - Sample</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">Time</td>
</tr>
</tbody>
</table>
<p>
A movie showing the experiment is shown on figure <a href="#orgc1e7286">1</a>.
</p>
<div id="orgc1e7286" 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>
</div>
<div id="outline-container-org6220fc6" class="outline-2">
<h2 id="org6220fc6"><span class="section-number-2">2</span> Data Analysis</h2>
<div class="outline-text-2" id="text-2">
<p>
<a id="org8446070"></a>
</p>
<div class="note" id="orga7b7a45">
<p>
All the files (data and Matlab scripts) are accessible <a href="data/spindle_slip_ring_vibrations.zip">here</a>.
</p>
</div>
</div>
<div id="outline-container-org122f0e9" class="outline-3">
<h3 id="org122f0e9"><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-string">'mat/data_024.mat'</span>, <span class="org-string">'data'</span>); of = of.data; <span class="org-comment">% OFF</span>
sr = load(<span class="org-string">'mat/data_025.mat'</span>, <span class="org-string">'data'</span>); sr = sr.data; <span class="org-comment">% Slip Ring</span>
sp = load(<span class="org-string">'mat/data_026.mat'</span>, <span class="org-string">'data'</span>); sp = sp.data; <span class="org-comment">% Spindle</span>
</pre>
</div>
<div class="warning" id="orgb2b819c">
<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-type">:</span>, 2) = <span class="org-type">-</span>of(<span class="org-type">:</span>, 2);
sr(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>sr(<span class="org-type">:</span>, 2);
sp(<span class="org-type">:</span>, 2) = <span class="org-type">-</span>sp(<span class="org-type">:</span>, 2);
</pre>
</div>
</div>
</div>
<div id="outline-container-orgaea71b5" class="outline-3">
<h3 id="orgaea71b5"><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 = 60; <span class="org-comment">% [dB]</span>
of(<span class="org-type">:</span>, 1) = voltageToVelocityL22(of(<span class="org-type">:</span>, 1), of(<span class="org-type">:</span>, 3), gain);
sr(<span class="org-type">:</span>, 1) = voltageToVelocityL22(sr(<span class="org-type">:</span>, 1), sr(<span class="org-type">:</span>, 3), gain);
sp(<span class="org-type">:</span>, 1) = voltageToVelocityL22(sp(<span class="org-type">:</span>, 1), sp(<span class="org-type">:</span>, 3), gain);
of(<span class="org-type">:</span>, 2) = voltageToVelocityL22(of(<span class="org-type">:</span>, 2), of(<span class="org-type">:</span>, 3), gain);
sr(<span class="org-type">:</span>, 2) = voltageToVelocityL22(sr(<span class="org-type">:</span>, 2), sr(<span class="org-type">:</span>, 3), gain);
sp(<span class="org-type">:</span>, 2) = voltageToVelocityL22(sp(<span class="org-type">:</span>, 2), sp(<span class="org-type">:</span>, 3), gain);
</pre>
</div>
</div>
</div>
<div id="outline-container-org485d23f" class="outline-3">
<h3 id="org485d23f"><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(sp(<span class="org-type">:</span>, 3), sp(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(sr(<span class="org-type">:</span>, 3), sr(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(of(<span class="org-type">:</span>, 3), of(<span class="org-type">:</span>, 1), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Velocity [m/s]'</span>);
xlim([0, 100]);
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre>
</div>
<div id="org4a00ffe" 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(sp(<span class="org-type">:</span>, 3), sp(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle and Slip-Ring'</span>);
plot(sr(<span class="org-type">:</span>, 3), sr(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Only Slip-Ring'</span>);
plot(of(<span class="org-type">:</span>, 3), of(<span class="org-type">:</span>, 2), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
xlabel(<span class="org-string">'Time [s]'</span>); ylabel(<span class="org-string">'Velocity [m/s]'</span>);
xlim([0, 100]);
legend(<span class="org-string">'Location'</span>, <span class="org-string">'northeast'</span>);
</pre>
</div>
<div id="orgcea5a30" 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="org3c59dd5" 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-org38cf97f" class="outline-3">
<h3 id="org38cf97f"><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(2, 3)<span class="org-type">-</span>of(1, 3); <span class="org-comment">% [s]</span>
Fs = 1<span class="org-type">/</span>dt; <span class="org-comment">% [Hz]</span>
win = hanning(ceil(10<span class="org-type">*</span>Fs)); <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">[pxof_m, f] = pwelch(of(<span class="org-type">:</span>, 1), win, [], [], Fs);
[pxsr_m, <span class="org-type">~</span>] = pwelch(sr(<span class="org-type">:</span>, 1), win, [], [], Fs);
[pxsp_m, <span class="org-type">~</span>] = pwelch(sp(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre>
</div>
<p>
And for the geophone located at the sample position.
</p>
<div class="org-src-container">
<pre class="src src-matlab">[pxof_s, <span class="org-type">~</span>] = pwelch(of(<span class="org-type">:</span>, 2), win, [], [], Fs);
[pxsr_s, <span class="org-type">~</span>] = pwelch(sr(<span class="org-type">:</span>, 2), win, [], [], Fs);
[pxsp_s, <span class="org-type">~</span>] = pwelch(sp(<span class="org-type">:</span>, 2), win, [], [], Fs);
</pre>
</div>
<p>
And we plot the ASD of the measured velocities:
</p>
<ul class="org-ul">
<li>figure <a href="#orgf38cb1d">5</a> for the geophone located on the marble</li>
<li>figure <a href="#orgbe7eafc">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(f, sqrt(pxsp_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(f, sqrt(pxsr_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(f, sqrt(pxof_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim([2, 500]);
</pre>
</div>
<div id="orgf38cb1d" 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(f, sqrt(pxsp_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(f, sqrt(pxsr_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(f, sqrt(pxof_s), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim([2, 500]);
</pre>
</div>
<div id="orgbe7eafc" 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="#org71b3fba">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-string">'../ground-motion/mat/psd_gm.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'psd_gv'</span>);
</pre>
</div>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(f, sqrt(pxsp_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(f, sqrt(pxsr_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(f, sqrt(pxof_m), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
plot(gm.f, sqrt(gm.psd_gv), <span class="org-string">'k-'</span>, <span class="org-string">'DisplayName'</span>, <span class="org-string">'Ground Motion'</span>);
hold off;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the measured velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim([2, 500]);
</pre>
</div>
<div id="org71b3fba" 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-orgbaa08aa" class="outline-3">
<h3 id="orgbaa08aa"><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="#orgb098e37">8</a>.
The velocity is integrated to have the relative displacement in Fig. <a href="#org3dac066">9</a>.
</p>
<div id="orgb098e37" 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="org3dac066" 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">[pxof_r, f] = pwelch(of(<span class="org-type">:</span>, 2)<span class="org-type">-</span>of(<span class="org-type">:</span>, 1), win, [], [], Fs);
[pxsr_r, <span class="org-type">~</span>] = pwelch(sr(<span class="org-type">:</span>, 2)<span class="org-type">-</span>sr(<span class="org-type">:</span>, 1), win, [], [], Fs);
[pxsp_r, <span class="org-type">~</span>] = pwelch(sp(<span class="org-type">:</span>, 2)<span class="org-type">-</span>sp(<span class="org-type">:</span>, 1), win, [], [], Fs);
</pre>
</div>
<p>
The Power Spectral Density of the Granite Velocity, Sample velocity and relative velocity are compare in Fig. <a href="#orga42fb07">10</a>.
</p>
<div id="orga42fb07" 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="#org1f1dfc7">11</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(f, sqrt(pxsp_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(f, sqrt(pxsr_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(f, sqrt(pxof_r), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>);
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'ASD of the relative velocity $\left[\frac{m/s}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim([2, 500]);
</pre>
</div>
<div id="org1f1dfc7" 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="#org11a9cb7">12</a> and in Fig. <a href="#orga256753">13</a> (integrated in reverse direction).
</p>
<div id="org11a9cb7" 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="orga256753" 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="#orgb16a9f7">14</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab"><span class="org-type">figure</span>;
hold on;
plot(f, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(f), flip(pxsp_r<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f)<span class="org-type">.^</span>2)))), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Spindle - 6rpm'</span>);
plot(f, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(f), flip(pxsr_r<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f)<span class="org-type">.^</span>2)))), <span class="org-string">'DisplayName'</span>, <span class="org-string">'Slip-Ring - 6rpm'</span>);
plot(f, sqrt(flip(<span class="org-type">-</span>cumtrapz(flip(f), flip(pxof_r<span class="org-type">./</span>(2<span class="org-type">*</span><span class="org-constant">pi</span><span class="org-type">*</span>f)<span class="org-type">.^</span>2)))), <span class="org-string">'DisplayName'</span>, <span class="org-string">'OFF'</span>);
hold off;
<span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'xscale'</span>, <span class="org-string">'log'</span>); <span class="org-type">set</span>(<span class="org-variable-name">gca</span>, <span class="org-string">'yscale'</span>, <span class="org-string">'log'</span>);
xlabel(<span class="org-string">'Frequency [Hz]'</span>); ylabel(<span class="org-string">'CAS of the relative displacement $\left[\frac{m}{\sqrt{Hz}}\right]$'</span>)
legend(<span class="org-string">'Location'</span>, <span class="org-string">'southwest'</span>);
xlim([2, 500]);
</pre>
</div>
<div id="orgb16a9f7" 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>
</div>
</div>
<div id="outline-container-orgad3b42a" class="outline-3">
<h3 id="orgad3b42a"><span class="section-number-3">2.6</span> Save</h3>
<div class="outline-text-3" id="text-2-6">
<p>
The Power Spectral Density of the relative velocity and of the hexapod velocity is saved for further analysis.
</p>
<div class="org-src-container">
<pre class="src src-matlab">save(<span class="org-string">'mat/pxsp_r.mat'</span>, <span class="org-string">'f'</span>, <span class="org-string">'pxsp_r'</span>, <span class="org-string">'pxsp_s'</span>);
</pre>
</div>
</div>
</div>
<div id="outline-container-org0a44924" class="outline-3">
<h3 id="org0a44924"><span class="section-number-3">2.7</span> Conclusion</h3>
<div class="outline-text-3" id="text-2-7">
<div class="important" id="orga7d722f">
<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" id="orga4c2e01">
<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: 2020-11-12 jeu. 10:27</p>
</div>
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