<li><ahref="#org4b7747e">2. Centrifugal forces for light and heavy sample</a></li>
<li><ahref="#org92c9f54">3. Centrifugal forces as a function of the rotation speed</a></li>
<li><ahref="#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’s rotation when the sample’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 <ahref="#orgd84fe6e">1</a> where:
</p>
<ulclass="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>
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’s top platform (here set to \(15\,kg\)).
</p>
<divclass="org-src-container">
<preclass="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.
<h2id="orgb7f1acf"><spanclass="section-number-2">4</span> Maximum rotation speed as a function of the mass</h2>
<divclass="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 <ahref="#org6ee8f38">3</a>).
From a specified maximum allowed centrifugal force (here set to \(10\,[N]\)), the maximum rotation speed as a function of the sample’s mass is shown in Figure <ahref="#org6ee8f38">3</a>.
<p><spanclass="figure-number">Figure 3: </span>Maximum rotation speed as a function of the sample mass for an allowed centrifugal force of \(100\,[N]\)</p>