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Thomas Dehaeze
" /><meta name="description" content="Tags Vibration Isolation Reference (Christophe Collette {\it et al.}, 2011) Author(s) Collette, C., Janssens, S., &amp;amp; Artoos, K. Year 2011 Background and Motivations Passive Isolation Tradeoffs \[ X(s) = \underbrace{\frac{cs &#43; k}{ms^2 &#43; cs &#43; k}}_{T_{wx}(s)} W(s) &#43; \underbrace{\frac{1}{ms^2 &#43; cs &#43; k}}_{T_{Fx}(s)} F(s) \]
\(T_{wx}(s)\) is called the transmissibility of the isolator. It characterize the way seismic vibrations \(w\) are transmitted to the equipment. \(T_{Fx}(s)\) is called the compliance." />
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<h1 class="post-title">Review of active vibration isolation strategies</h1>
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<h2 class="post-toc-title">Contents</h2>
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<ul>
<li><a href="#background-and-motivations">Background and Motivations</a>
<ul>
<li><a href="#passive-isolation-tradeoffs">Passive Isolation Tradeoffs</a></li>
<li><a href="#active-isolation">Active Isolation</a></li>
</ul>
</li>
<li><a href="#practical-realizations">Practical Realizations</a></li>
<li><a href="#sensor-limitations">Sensor Limitations</a></li>
<li><a href="#conclusions">Conclusions</a></li>
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<dl>
<dt>Tags</dt>
<dd><a href="/zettels/vibration_isolation/">Vibration Isolation</a></dd>
<dt>Reference</dt>
<dd><sup id="2d69d483f210ca387ca8061596ec27ea"><a href="#collette11_review_activ_vibrat_isolat_strat" title="Christophe Collette, Stef Janssens \&amp; Kurt Artoos, Review of Active Vibration Isolation Strategies, {Recent Patents on Mechanical Engineeringe}, v(3), 212-219 (2011).">(Christophe Collette {\it et al.}, 2011)</a></sup></dd>
<dt>Author(s)</dt>
<dd>Collette, C., Janssens, S., &amp; Artoos, K.</dd>
<dt>Year</dt>
<dd>2011</dd>
</dl>
<h2 id="background-and-motivations">Background and Motivations</h2>
<h3 id="passive-isolation-tradeoffs">Passive Isolation Tradeoffs</h3>
<div class="cbox">
<div></div>
<p>\[ X(s) = \underbrace{\frac{cs + k}{ms^2 + cs + k}}_{T_{wx}(s)} W(s) + \underbrace{\frac{1}{ms^2 + cs + k}}_{T_{Fx}(s)} F(s) \]</p>
</div>
<ul>
<li>\(T_{wx}(s)\) is called the <strong>transmissibility</strong> of the isolator. It characterize the way seismic vibrations \(w\) are transmitted to the equipment.</li>
<li>\(T_{Fx}(s)\) is called the <strong>compliance</strong>. It characterize the capacity of disturbing forces \(F\) to create motion \(x\) of the equipment.</li>
</ul>
<p>In order to minimize the vibrations of a sensitive equipment, a general objective to design a good isolator is to minimize both \(\abs{T_{wx}}\) and \(\abs{T_{Fx}}\) in the frequency range of interest.</p>
<p>To decrease the amplitude of the overshoot at the resonance frequency, <strong>damping</strong> can be increased.
The price to pay is degradation of the isolation at high frequency (the roll off becomes \(-1\) instead of \(-2\)).</p>
<p><strong>First Trade-off</strong>: Trade-off between damping and isolation.</p>
<p>To improve the transmissibility, the resonance frequency can be decreased.
However, the systems becomes more sensitive to external force \(F\) applied on the equipment.</p>
<p><strong>Second trade-off</strong>: Trade-off between isolation and robustness to external force</p>
<h3 id="active-isolation">Active Isolation</h3>
<p>We apply a feedback control.
The general expression of the force delivered by the actuator is \(f = g_a \ddot{x} + g_v \dot{x} + g_p x\). \(g_a\), \(g_v\) and \(g_p\) are constant gains.</p>
<p><a id="table--table:active-isolation"></a></p>
<div class="table-caption">
<span class="table-number"><a href="#table--table:active-isolation">Table 1</a></span>:
Active isolation techniques
</div>
<table>
<thead>
<tr>
<th><strong>Feedback Signal</strong></th>
<th><strong>Effect</strong></th>
<th><strong>Applications</strong></th>
</tr>
</thead>
<tbody>
<tr>
<td>Acceleration</td>
<td>Add virtual mass</td>
<td>Few</td>
</tr>
<tr>
<td>Velocity</td>
<td>Add virtual dashpot connected to the sky</td>
<td>Sky-Hook Damping</td>
</tr>
<tr>
<td>Position</td>
<td>Add virtual spring connected to the sky</td>
<td>Sky-Hook Spring</td>
</tr>
</tbody>
</table>
<h2 id="practical-realizations">Practical Realizations</h2>
<h2 id="sensor-limitations">Sensor Limitations</h2>
<h2 id="conclusions">Conclusions</h2>
<p><a id="orgef29aaf"></a></p>
<figure>
<img src="/ox-hugo/collette11_comp_isolation_strategies.png"
alt="Figure 1: Comparison of Active Vibration Isolation Strategies"/> <figcaption>
<p>Figure 1: Comparison of Active Vibration Isolation Strategies</p>
</figcaption>
</figure>
<h1 id="bibliography">Bibliography</h1>
<p><a id="collette11_review_activ_vibrat_isolat_strat"></a>Collette, C., Janssens, S., &amp; Artoos, K., <em>Review of active vibration isolation strategies</em>, Recent Patents on Mechanical Engineeringe, <em>4(3)</em>, 212–219 (2011). <a href="http://dx.doi.org/10.2174/2212797611104030212">http://dx.doi.org/10.2174/2212797611104030212</a> <a href="#2d69d483f210ca387ca8061596ec27ea">↩</a></p>
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