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Add link to centrifugal forces study

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<?xml version="1.0" encoding="utf-8"?>
<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-05-05 mar. 10:34 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Centrifugal Forces</title>
<meta name="generator" content="Org mode" />
<meta name="author" content="Dehaeze Thomas" />
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<a accesskey="h" href="./index.html"> UP </a>
|
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</div><div id="content">
<h1 class="title">Centrifugal Forces</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org49834ed">1. Parameters</a></li>
<li><a href="#org4b7747e">2. Centrifugal forces for light and heavy sample</a></li>
<li><a href="#org92c9f54">3. Centrifugal forces as a function of the rotation speed</a></li>
<li><a href="#orgb7f1acf">4. Maximum rotation speed as a function of the mass</a></li>
</ul>
</div>
</div>
<p>
In this document, we wish to estimate the centrifugal forces due to the spindle&rsquo;s rotation when the sample&rsquo;s center of mass is off-centered with respect to the rotation axis.
</p>
<p>
This is the case then the sample is moved by the micro-hexapod.
</p>
<p>
The centrifugal forces are defined as represented Figure <a href="#orgd84fe6e">1</a> where:
</p>
<ul class="org-ul">
<li>\(M\) is the total mass of the rotating elements in \([kg]\)</li>
<li>\(\omega\) is the rotation speed in \([rad/s]\)</li>
<li>\(r\) is the distance to the rotation axis in \([m]\)</li>
</ul>
<div id="orgd84fe6e" class="figure">
<p><img src="./figs/centrifugal.png" alt="centrifugal.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Centrifugal forces</p>
</div>
<div id="outline-container-org49834ed" class="outline-2">
<h2 id="org49834ed"><span class="section-number-2">1</span> Parameters</h2>
<div class="outline-text-2" id="text-1">
<p>
We define some parameters for the computation.
</p>
<p>
The mass of the sample can vary from \(1\,kg\) to \(50\,kg\) to which is added to mass of the metrology reflector and the nano-hexapod&rsquo;s top platform (here set to \(15\,kg\)).
</p>
<div class="org-src-container">
<pre class="src src-matlab">M_light = 16; % mass of excentred parts mooving [kg]
M_heavy = 65; % [kg]
</pre>
</div>
<p>
For the light mass, the rotation speed is 60rpm whereas for the heavy mass, it is equal to 1rpm.
</p>
<div class="org-src-container">
<pre class="src src-matlab">w_light = 2*pi; % rotational speed [rad/s]
w_heavy = 2*pi/60; % rotational speed [rad/s]
</pre>
</div>
<p>
Finally, we consider a mass eccentricity of \(10\,mm\).
</p>
<div class="org-src-container">
<pre class="src src-matlab">R = 0.1; % Excentricity [m]
</pre>
</div>
</div>
</div>
<div id="outline-container-org4b7747e" class="outline-2">
<h2 id="org4b7747e"><span class="section-number-2">2</span> Centrifugal forces for light and heavy sample</h2>
<div class="outline-text-2" id="text-2">
<p>
From the formula \(F_c = m \omega^2 r\), we obtain the values shown below.
</p>
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">&#xa0;</th>
<th scope="col" class="org-right">Force [N]</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">light</td>
<td class="org-right">63.2</td>
</tr>
<tr>
<td class="org-left">heavy</td>
<td class="org-right">0.1</td>
</tr>
</tbody>
</table>
</div>
</div>
<div id="outline-container-org92c9f54" class="outline-2">
<h2 id="org92c9f54"><span class="section-number-2">3</span> Centrifugal forces as a function of the rotation speed</h2>
<div class="outline-text-2" id="text-3">
<p>
The centrifugal forces as a function of the rotation speed for light and heavy sample is shown on Figure <a href="#orgfaf795f">2</a>.
</p>
<div id="orgfaf795f" class="figure">
<p><img src="figs/centrifugal_forces_rpm.png" alt="centrifugal_forces_rpm.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Centrifugal forces function of the rotation speed</p>
</div>
</div>
</div>
<div id="outline-container-orgb7f1acf" class="outline-2">
<h2 id="orgb7f1acf"><span class="section-number-2">4</span> Maximum rotation speed as a function of the mass</h2>
<div class="outline-text-2" id="text-4">
<p>
We plot the maximum rotation speed as a function of the mass for different maximum force that we can use to counteract the centrifugal forces (Figure <a href="#org6ee8f38">3</a>).
</p>
<p>
From a specified maximum allowed centrifugal force (here set to \(100\,[N]\)), the maximum rotation speed as a function of the sample&rsquo;s mass is shown in Figure <a href="#org6ee8f38">3</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">F_max = 100; % Maximum accepted centrifugal forces [N]
R = 0.1;
M_sample = 0:1:100;
M_reflector = 15;
</pre>
</div>
<div id="org6ee8f38" class="figure">
<p><img src="figs/max_force_rpm.png" alt="max_force_rpm.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Maximum rotation speed as a function of the sample mass for an allowed centrifugal force of \(100\,[N]\)</p>
</div>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-05-05 mar. 10:34</p>
</div>
</body>
</html>

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<head> <head>
<!-- 2020-05-05 mar. 10:44 --> <!-- 2020-05-05 mar. 11:38 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> <meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Simscape Model of the Nano-Active-Stabilization-System</title> <title>Simscape Model of the Nano-Active-Stabilization-System</title>
<meta name="generator" content="Org mode" /> <meta name="generator" content="Org mode" />
@ -152,6 +152,11 @@ This is discussed <a href="./disturbances.html">here</a>.
<p> <p>
We also discuss how the disturbances are implemented in the model. We also discuss how the disturbances are implemented in the model.
</p> </p>
<p>
Centrifugal forces can be viewed as a constant force disturbance in the frame of the nano-hexapod.
Some numerical analysis of such forces are done <a href="centrifugal_forces.html">here</a>.
</p>
</div> </div>
</div> </div>
@ -244,7 +249,7 @@ These functions are all defined <a href="./functions.html">here</a>.
</div> </div>
<div id="postamble" class="status"> <div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p> <p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-05-05 mar. 10:44</p> <p class="date">Created: 2020-05-05 mar. 11:38</p>
</div> </div>
</body> </body>
</html> </html>

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@ -47,6 +47,9 @@ This is discussed [[./disturbances.org][here]].
We also discuss how the disturbances are implemented in the model. We also discuss how the disturbances are implemented in the model.
Centrifugal forces can be viewed as a constant force disturbance in the frame of the nano-hexapod.
Some numerical analysis of such forces are done [[file:centrifugal_forces.org][here]].
* Simulation of Experiment ([[./experiments.org][link]]) * Simulation of Experiment ([[./experiments.org][link]])
Now that the dynamics of the Model have been tuned and the Disturbances have included, we can simulate experiments. Now that the dynamics of the Model have been tuned and the Disturbances have included, we can simulate experiments.