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Analyze stroke measurements

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Thomas Dehaeze
2021-03-16 14:31:01 +01:00
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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>
<!-- 2021-03-15 lun. 11:35 -->
<!-- 2021-03-16 mar. 14:30 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Amplifier Piezoelectric Actuator APA300ML - Test Bench</title>
<meta name="author" content="Dehaeze Thomas" />
@@ -39,33 +39,40 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#org0eb094b">1. Model of an Amplified Piezoelectric Actuator and Sensor</a></li>
<li><a href="#org6f9ba21">2. Geometrical Measurements</a>
<li><a href="#orgeae854b">1. Model of an Amplified Piezoelectric Actuator and Sensor</a></li>
<li><a href="#org5126568">2. Geometrical Measurements</a>
<ul>
<li><a href="#org8044086">2.1. Measurement Setup</a></li>
<li><a href="#org4293145">2.2. Measurement Results</a></li>
<li><a href="#orge477895">2.1. Measurement Setup</a></li>
<li><a href="#orgf6e38fd">2.2. Measurement Results</a></li>
</ul>
</li>
<li><a href="#org50d4352">3. Electrical Measurements</a></li>
<li><a href="#orgb8a1481">4. Stiffness measurement</a>
<li><a href="#org3da2e64">3. Electrical Measurements</a></li>
<li><a href="#orgcd8f0b8">4. Stiffness measurement</a>
<ul>
<li><a href="#org21bc9b2">4.1. APA test</a></li>
<li><a href="#org20509de">4.1. APA test</a></li>
</ul>
</li>
<li><a href="#orgb3154e0">5. Test-Bench Description</a></li>
<li><a href="#orgac581ad">6. Measurement Procedure</a>
<li><a href="#orgc5606b4">5. Stroke measurement</a>
<ul>
<li><a href="#orge00396f">6.1. Stroke Measurement</a></li>
<li><a href="#org66ac5bb">6.2. Stiffness Measurement</a></li>
<li><a href="#orgee2d3e8">6.3. Hysteresis measurement</a></li>
<li><a href="#orge6e89ca">6.4. Piezoelectric Actuator Constant</a></li>
<li><a href="#orge970d07">6.5. Piezoelectric Sensor Constant</a></li>
<li><a href="#org86b3954">6.6. Capacitance Measurement</a></li>
<li><a href="#orgc5205df">6.7. Dynamical Behavior</a></li>
<li><a href="#org2f73a1b">6.8. Compare the results obtained for all 7 APA300ML</a></li>
<li><a href="#org676705f">5.1. Voltage applied on one stack</a></li>
<li><a href="#orgf6d51af">5.2. Voltage applied on two stacks</a></li>
<li><a href="#org5fada7f">5.3. Voltage applied on all three stacks</a></li>
</ul>
</li>
<li><a href="#org175e8d0">7. Measurement Results</a></li>
<li><a href="#org3248c3e">6. Test-Bench Description</a></li>
<li><a href="#orgabbb81c">7. Measurement Procedure</a>
<ul>
<li><a href="#orge3152f8">7.1. Stroke Measurement</a></li>
<li><a href="#orgc1cf00d">7.2. Stiffness Measurement</a></li>
<li><a href="#org61adc4b">7.3. Hysteresis measurement</a></li>
<li><a href="#org3c6cfed">7.4. Piezoelectric Actuator Constant</a></li>
<li><a href="#org9c52d3c">7.5. Piezoelectric Sensor Constant</a></li>
<li><a href="#org30f8839">7.6. Capacitance Measurement</a></li>
<li><a href="#org7549456">7.7. Dynamical Behavior</a></li>
<li><a href="#org51816a1">7.8. Compare the results obtained for all 7 APA300ML</a></li>
</ul>
</li>
<li><a href="#org0b4e69a">8. Measurement Results</a></li>
</ul>
</div>
</div>
@@ -90,21 +97,21 @@ This include:
</ul>
<div id="org664d1fb" class="figure">
<div id="org6bbfe2e" class="figure">
<p><img src="figs/apa300ML.png" alt="apa300ML.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Picture of the APA300ML</p>
</div>
<div id="outline-container-org0eb094b" class="outline-2">
<h2 id="org0eb094b"><span class="section-number-2">1</span> Model of an Amplified Piezoelectric Actuator and Sensor</h2>
<div id="outline-container-orgeae854b" class="outline-2">
<h2 id="orgeae854b"><span class="section-number-2">1</span> Model of an Amplified Piezoelectric Actuator and Sensor</h2>
<div class="outline-text-2" id="text-1">
<p>
Consider a schematic of the Amplified Piezoelectric Actuator in Figure <a href="#orgc9df44d">2</a>.
Consider a schematic of the Amplified Piezoelectric Actuator in Figure <a href="#org2844129">2</a>.
</p>
<div id="orgc9df44d" class="figure">
<div id="org2844129" class="figure">
<p><img src="figs/apa_model_schematic.png" alt="apa_model_schematic.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Amplified Piezoelectric Actuator Schematic</p>
@@ -129,11 +136,11 @@ We wish here to experimental measure \(g_a\) and \(g_s\).
</p>
<p>
The block-diagram model of the piezoelectric actuator is then as shown in Figure <a href="#orgc4bba98">3</a>.
The block-diagram model of the piezoelectric actuator is then as shown in Figure <a href="#org5ba1265">3</a>.
</p>
<div id="orgc4bba98" class="figure">
<div id="org5ba1265" class="figure">
<p><img src="figs/apa-model-simscape-schematic.png" alt="apa-model-simscape-schematic.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Model of the APA with Simscape/Simulink</p>
@@ -141,22 +148,30 @@ The block-diagram model of the piezoelectric actuator is then as shown in Figure
</div>
</div>
<div id="outline-container-org6f9ba21" class="outline-2">
<h2 id="org6f9ba21"><span class="section-number-2">2</span> Geometrical Measurements</h2>
<div id="outline-container-org5126568" class="outline-2">
<h2 id="org5126568"><span class="section-number-2">2</span> Geometrical Measurements</h2>
<div class="outline-text-2" id="text-2">
<p>
The received APA are shown in Figure <a href="#org1895ec7">4</a>.
</p>
<div id="org939ac64" class="figure">
<div id="org1895ec7" class="figure">
<p><img src="figs/IMG_20210224_143500.jpg" alt="IMG_20210224_143500.jpg" />
</p>
<p><span class="figure-number">Figure 4: </span>Received APA</p>
</div>
</div>
<div id="outline-container-org8044086" class="outline-3">
<h3 id="org8044086"><span class="section-number-3">2.1</span> Measurement Setup</h3>
<div id="outline-container-orge477895" class="outline-3">
<h3 id="orge477895"><span class="section-number-3">2.1</span> Measurement Setup</h3>
<div class="outline-text-3" id="text-2-1">
<p>
The flatness corresponding to the two interface planes are measured as shown in Figure <a href="#org9fff0ac">5</a>.
</p>
<div id="org43d857b" class="figure">
<div id="org9fff0ac" class="figure">
<p><img src="figs/IMG_20210224_143809.jpg" alt="IMG_20210224_143809.jpg" />
</p>
<p><span class="figure-number">Figure 5: </span>Measurement Setup</p>
@@ -164,11 +179,11 @@ The block-diagram model of the piezoelectric actuator is then as shown in Figure
</div>
</div>
<div id="outline-container-org4293145" class="outline-3">
<h3 id="org4293145"><span class="section-number-3">2.2</span> Measurement Results</h3>
<div id="outline-container-orgf6e38fd" class="outline-3">
<h3 id="orgf6e38fd"><span class="section-number-3">2.2</span> Measurement Results</h3>
<div class="outline-text-3" id="text-2-2">
<p>
Height (Z) measurements:
The height (Z) measurements at the 8 locations (4 points by plane) are defined below.
</p>
<div class="org-src-container">
<pre class="src src-matlab">apa1 = 1e<span class="org-type">-</span>6<span class="org-type">*</span>[0, <span class="org-type">-</span>0.5 , 3.5 , 3.5 , 42 , 45.5, 52.5 , 46];
@@ -184,7 +199,7 @@ apa = {apa1, apa2, apa3, apa4, apa5, apa6, apa7b};
</div>
<p>
X/Y Positions of the 8 measurement points:
The X/Y Positions of the 8 measurement points are defined below.
</p>
<div class="org-src-container">
<pre class="src src-matlab">W = 20e<span class="org-type">-</span>3; <span class="org-comment">% Width [m]</span>
@@ -196,6 +211,9 @@ pos = [[<span class="org-type">-</span>L<span class="org-type">/</span>2 <span c
</pre>
</div>
<p>
Finally, the flatness is estimated by fitting a plane through the 8 points using the <code>fminsearch</code> command.
</p>
<div class="org-src-container">
<pre class="src src-matlab">apa_d = zeros(1, 7);
<span class="org-keyword">for</span> <span class="org-variable-name"><span class="org-constant">i</span></span> = <span class="org-constant">1:7</span>
@@ -207,43 +225,57 @@ pos = [[<span class="org-type">-</span>L<span class="org-type">/</span>2 <span c
</pre>
</div>
<table id="org2443ab1" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<p>
The obtained flatness are shown in Table <a href="#org36f0e82">1</a>.
</p>
<table id="org36f0e82" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 1:</span> Estimated flatness</caption>
<colgroup>
<col class="org-left" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right">Flatness [um]</th>
<th scope="col" class="org-left">&#xa0;</th>
<th scope="col" class="org-right"><b>Flatness</b> \([\mu m]\)</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">APA 1</td>
<td class="org-right">8.9</td>
</tr>
<tr>
<td class="org-left">APA 2</td>
<td class="org-right">3.1</td>
</tr>
<tr>
<td class="org-left">APA 3</td>
<td class="org-right">9.1</td>
</tr>
<tr>
<td class="org-left">APA 4</td>
<td class="org-right">3.0</td>
</tr>
<tr>
<td class="org-left">APA 5</td>
<td class="org-right">1.9</td>
</tr>
<tr>
<td class="org-left">APA 6</td>
<td class="org-right">7.1</td>
</tr>
<tr>
<td class="org-left">APA 7</td>
<td class="org-right">18.7</td>
</tr>
</tbody>
@@ -252,10 +284,10 @@ pos = [[<span class="org-type">-</span>L<span class="org-type">/</span>2 <span c
</div>
</div>
<div id="outline-container-org50d4352" class="outline-2">
<h2 id="org50d4352"><span class="section-number-2">3</span> Electrical Measurements</h2>
<div id="outline-container-org3da2e64" class="outline-2">
<h2 id="org3da2e64"><span class="section-number-2">3</span> Electrical Measurements</h2>
<div class="outline-text-2" id="text-3">
<div class="note" id="org262a984">
<div class="note" id="org7758b1f">
<p>
The capacitance of the stacks is measure with the <a href="https://www.gwinstek.com/en-global/products/detail/LCR-800">LCR-800 Meter</a> (<a href="doc/DS_LCR-800_Series_V2_E.pdf">doc</a>)
</p>
@@ -263,7 +295,7 @@ The capacitance of the stacks is measure with the <a href="https://www.gwinstek.
</div>
<div id="orgdaa55e5" class="figure">
<div id="org66db1d7" class="figure">
<p><img src="figs/IMG_20210312_120337.jpg" alt="IMG_20210312_120337.jpg" />
</p>
<p><span class="figure-number">Figure 6: </span>LCR Meter used for the measurements</p>
@@ -273,11 +305,11 @@ The capacitance of the stacks is measure with the <a href="https://www.gwinstek.
The excitation frequency is set to be 1kHz.
</p>
<table id="org9d7793d" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<table id="org2ae85fd" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 2:</span> Capacitance measured with the LCR meter. The excitation signal is a sinus at 1kHz</caption>
<colgroup>
<col class="org-right" />
<col class="org-left" />
<col class="org-right" />
@@ -285,57 +317,57 @@ The excitation frequency is set to be 1kHz.
</colgroup>
<thead>
<tr>
<th scope="col" class="org-right"><b>APA Number</b></th>
<th scope="col" class="org-left">&#xa0;</th>
<th scope="col" class="org-right"><b>Sensor Stack</b></th>
<th scope="col" class="org-right"><b>Actuator Stacks</b></th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-right">1</td>
<td class="org-left">APA 1</td>
<td class="org-right">5.10</td>
<td class="org-right">10.03</td>
</tr>
<tr>
<td class="org-right">2</td>
<td class="org-left">APA 2</td>
<td class="org-right">4.99</td>
<td class="org-right">9.85</td>
</tr>
<tr>
<td class="org-right">3</td>
<td class="org-left">APA 3</td>
<td class="org-right">1.72</td>
<td class="org-right">5.18</td>
</tr>
<tr>
<td class="org-right">4</td>
<td class="org-left">APA 4</td>
<td class="org-right">4.94</td>
<td class="org-right">9.82</td>
</tr>
<tr>
<td class="org-right">5</td>
<td class="org-left">APA 5</td>
<td class="org-right">4.90</td>
<td class="org-right">9.66</td>
</tr>
<tr>
<td class="org-right">6</td>
<td class="org-left">APA 6</td>
<td class="org-right">4.99</td>
<td class="org-right">9.91</td>
</tr>
<tr>
<td class="org-right">7</td>
<td class="org-left">APA 7</td>
<td class="org-right">4.85</td>
<td class="org-right">9.85</td>
</tr>
</tbody>
</table>
<div class="warning" id="org5042148">
<div class="warning" id="org7282231">
<p>
There is clearly a problem with APA300ML number 3
</p>
@@ -344,12 +376,12 @@ There is clearly a problem with APA300ML number 3
</div>
</div>
<div id="outline-container-orgb8a1481" class="outline-2">
<h2 id="orgb8a1481"><span class="section-number-2">4</span> Stiffness measurement</h2>
<div id="outline-container-orgcd8f0b8" class="outline-2">
<h2 id="orgcd8f0b8"><span class="section-number-2">4</span> Stiffness measurement</h2>
<div class="outline-text-2" id="text-4">
</div>
<div id="outline-container-org21bc9b2" class="outline-3">
<h3 id="org21bc9b2"><span class="section-number-3">4.1</span> APA test</h3>
<div id="outline-container-org20509de" class="outline-3">
<h3 id="org20509de"><span class="section-number-3">4.1</span> APA test</h3>
<div class="outline-text-3" id="text-4-1">
<div class="org-src-container">
<pre class="src src-matlab">load(<span class="org-string">'meas_stiff_apa_1_x.mat'</span>, <span class="org-string">'t'</span>, <span class="org-string">'F'</span>, <span class="org-string">'d'</span>);
@@ -415,10 +447,204 @@ plot(F_l, F_l<span class="org-type">*</span>fit_l(1) <span class="org-type">+</s
</div>
</div>
</div>
<div id="outline-container-orgb3154e0" class="outline-2">
<h2 id="orgb3154e0"><span class="section-number-2">5</span> Test-Bench Description</h2>
<div id="outline-container-orgc5606b4" class="outline-2">
<h2 id="orgc5606b4"><span class="section-number-2">5</span> Stroke measurement</h2>
<div class="outline-text-2" id="text-5">
<div class="note" id="orgc87eff8">
<p>
We here wish to estimate the stroke of the APA.
</p>
<p>
To do so, one side of the APA is fixed, and a displacement probe is located on the other side as shown in Figure <a href="#org51f6741">7</a>.
</p>
<p>
Then, a voltage is applied on either one or two stacks using a DAC and a voltage amplifier.
</p>
<div class="note" id="orgef58353">
<p>
Here are the documentation of the equipment used for this test bench:
</p>
<ul class="org-ul">
<li><b>Voltage Amplifier</b>: <a href="doc/PD200-V7-R1.pdf">PD200</a> with a gain of 20</li>
<li><b>16bits DAC</b>: <a href="doc/IO131-OEM-Datasheet.pdf">IO313 Speedgoat card</a></li>
<li><b>Displacement Probe</b>: <a href="doc/Millimar--3723046--BA--C1208-C1216-C1240--FR--2016-11-08.pdf">Millimar C1216 electronics</a> and <a href="doc/tmp3m0cvmue_7888038c-cdc8-48d8-a837-35de02760685.pdf">Millimar 1318 probe</a></li>
</ul>
</div>
<div id="org51f6741" class="figure">
<p><img src="figs/CE0EF55E-07B7-461B-8CDB-98590F68D15B.jpeg" alt="CE0EF55E-07B7-461B-8CDB-98590F68D15B.jpeg" />
</p>
<p><span class="figure-number">Figure 7: </span>Bench to measured the APA stroke</p>
</div>
</div>
<div id="outline-container-org676705f" class="outline-3">
<h3 id="org676705f"><span class="section-number-3">5.1</span> Voltage applied on one stack</h3>
<div class="outline-text-3" id="text-5-1">
<p>
Let&rsquo;s first look at the relation between the voltage applied to <b>one</b> stack to the displacement of the APA as measured by the displacement probe.
</p>
<p>
The applied voltage is shown in Figure <a href="#org46608eb">8</a>.
</p>
<div id="org46608eb" class="figure">
<p><img src="figs/apa_stroke_voltage_time.png" alt="apa_stroke_voltage_time.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Applied voltage as a function of time</p>
</div>
<p>
The obtained displacement is shown in Figure <a href="#org14e1b3b">9</a>.
The displacement is set to zero at initial time when the voltage applied is -20V.
</p>
<div id="org14e1b3b" class="figure">
<p><img src="figs/apa_stroke_time_1s.png" alt="apa_stroke_time_1s.png" />
</p>
<p><span class="figure-number">Figure 9: </span>Displacement as a function of time for all the APA300ML</p>
</div>
<p>
Finally, the displacement is shown as a function of the applied voltage in Figure <a href="#org18bcdf6">10</a>.
We can clearly see that there is a problem with the APA 3.
Also, there is a large hysteresis.
</p>
<div id="org18bcdf6" class="figure">
<p><img src="figs/apa_d_vs_V_1s.png" alt="apa_d_vs_V_1s.png" />
</p>
<p><span class="figure-number">Figure 10: </span>Displacement as a function of the applied voltage</p>
</div>
<div class="important" id="orgb2961f0">
<p>
We can clearly see from Figure <a href="#org18bcdf6">10</a> that there is a problem with the APA number 3.
</p>
</div>
</div>
</div>
<div id="outline-container-orgf6d51af" class="outline-3">
<h3 id="orgf6d51af"><span class="section-number-3">5.2</span> Voltage applied on two stacks</h3>
<div class="outline-text-3" id="text-5-2">
<p>
Now look at the relation between the voltage applied to the <b>two</b> other stacks to the displacement of the APA as measured by the displacement probe.
</p>
<p>
The obtained displacement is shown in Figure <a href="#org6aae24c">11</a>.
The displacement is set to zero at initial time when the voltage applied is -20V.
</p>
<div id="org6aae24c" class="figure">
<p><img src="figs/apa_stroke_time_2s.png" alt="apa_stroke_time_2s.png" />
</p>
<p><span class="figure-number">Figure 11: </span>Displacement as a function of time for all the APA300ML</p>
</div>
<p>
Finally, the displacement is shown as a function of the applied voltage in Figure <a href="#orgdf848b0">12</a>.
We can clearly see that there is a problem with the APA 3.
Also, there is a large hysteresis.
</p>
<div id="orgdf848b0" class="figure">
<p><img src="figs/apa_d_vs_V_2s.png" alt="apa_d_vs_V_2s.png" />
</p>
<p><span class="figure-number">Figure 12: </span>Displacement as a function of the applied voltage</p>
</div>
</div>
</div>
<div id="outline-container-org5fada7f" class="outline-3">
<h3 id="org5fada7f"><span class="section-number-3">5.3</span> Voltage applied on all three stacks</h3>
<div class="outline-text-3" id="text-5-3">
<p>
Finally, we can combine the two measurements to estimate the relation between the displacement and the voltage applied to the <b>three</b> stacks (Figure <a href="#orge301ee3">13</a>).
</p>
<div id="orge301ee3" class="figure">
<p><img src="figs/apa_d_vs_V_3s.png" alt="apa_d_vs_V_3s.png" />
</p>
<p><span class="figure-number">Figure 13: </span>Displacement as a function of the applied voltage</p>
</div>
<p>
The obtained maximum stroke for all the APA are summarized in Table <a href="#org0ae8a54">3</a>.
</p>
<table id="org0ae8a54" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<caption class="t-above"><span class="table-number">Table 3:</span> Measured maximum stroke</caption>
<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"><b>Stroke</b> \([\mu m]\)</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">APA 1</td>
<td class="org-right">373.2</td>
</tr>
<tr>
<td class="org-left">APA 2</td>
<td class="org-right">365.5</td>
</tr>
<tr>
<td class="org-left">APA 3</td>
<td class="org-right">181.7</td>
</tr>
<tr>
<td class="org-left">APA 4</td>
<td class="org-right">359.7</td>
</tr>
<tr>
<td class="org-left">APA 5</td>
<td class="org-right">361.5</td>
</tr>
<tr>
<td class="org-left">APA 6</td>
<td class="org-right">363.9</td>
</tr>
<tr>
<td class="org-left">APA 7</td>
<td class="org-right">358.4</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<div id="outline-container-org3248c3e" class="outline-2">
<h2 id="org3248c3e"><span class="section-number-2">6</span> Test-Bench Description</h2>
<div class="outline-text-2" id="text-6">
<div class="note" id="org5db8c73">
<p>
Here are the documentation of the equipment used for this test bench:
</p>
@@ -433,21 +659,21 @@ Here are the documentation of the equipment used for this test bench:
</div>
<div id="orgfd15602" class="figure">
<div id="org0400f6b" class="figure">
<p><img src="figs/test_bench_apa_alone.png" alt="test_bench_apa_alone.png" />
</p>
<p><span class="figure-number">Figure 7: </span>Schematic of the Test Bench</p>
<p><span class="figure-number">Figure 14: </span>Schematic of the Test Bench</p>
</div>
</div>
</div>
<div id="outline-container-orgac581ad" class="outline-2">
<h2 id="orgac581ad"><span class="section-number-2">6</span> Measurement Procedure</h2>
<div class="outline-text-2" id="text-6">
<div id="outline-container-orgabbb81c" class="outline-2">
<h2 id="orgabbb81c"><span class="section-number-2">7</span> Measurement Procedure</h2>
<div class="outline-text-2" id="text-7">
</div>
<div id="outline-container-orge00396f" class="outline-3">
<h3 id="orge00396f"><span class="section-number-3">6.1</span> Stroke Measurement</h3>
<div class="outline-text-3" id="text-6-1">
<div id="outline-container-orge3152f8" class="outline-3">
<h3 id="orge3152f8"><span class="section-number-3">7.1</span> Stroke Measurement</h3>
<div class="outline-text-3" id="text-7-1">
<p>
Using the PD200 amplifier, output a voltage:
\[ V_a = 65 + 85 \sin(2\pi \cdot t) \]
@@ -474,9 +700,9 @@ Conclude on the obtained stroke.
</div>
</div>
<div id="outline-container-org66ac5bb" class="outline-3">
<h3 id="org66ac5bb"><span class="section-number-3">6.2</span> Stiffness Measurement</h3>
<div class="outline-text-3" id="text-6-2">
<div id="outline-container-orgc1cf00d" class="outline-3">
<h3 id="orgc1cf00d"><span class="section-number-3">7.2</span> Stiffness Measurement</h3>
<div class="outline-text-3" id="text-7-2">
<p>
Add some (known) weight \(\delta m g\) on the suspended mass and measure the deflection \(\delta d\).
This can be tested when the piezoelectric stacks are open-circuit.
@@ -495,9 +721,9 @@ Then the obtained stiffness is:
</div>
</div>
<div id="outline-container-orgee2d3e8" class="outline-3">
<h3 id="orgee2d3e8"><span class="section-number-3">6.3</span> Hysteresis measurement</h3>
<div class="outline-text-3" id="text-6-3">
<div id="outline-container-org61adc4b" class="outline-3">
<h3 id="org61adc4b"><span class="section-number-3">7.3</span> Hysteresis measurement</h3>
<div class="outline-text-3" id="text-7-3">
<p>
Supply a quasi static sinusoidal excitation \(V_a\) at different voltages.
</p>
@@ -515,17 +741,17 @@ Then, \(d\) is plotted as a function of \(V_a\) for all the amplitudes.
</p>
<div id="org7123135" class="figure">
<div id="org0fb5c18" class="figure">
<p><img src="figs/expected_hysteresis.png" alt="expected_hysteresis.png" />
</p>
<p><span class="figure-number">Figure 8: </span>Expected Hysteresis (<a class='org-ref-reference' href="#poel10_explor_activ_hard_mount_vibrat">poel10_explor_activ_hard_mount_vibrat</a>)</p>
<p><span class="figure-number">Figure 15: </span>Expected Hysteresis (<a class='org-ref-reference' href="#poel10_explor_activ_hard_mount_vibrat">poel10_explor_activ_hard_mount_vibrat</a>)</p>
</div>
</div>
</div>
<div id="outline-container-orge6e89ca" class="outline-3">
<h3 id="orge6e89ca"><span class="section-number-3">6.4</span> Piezoelectric Actuator Constant</h3>
<div class="outline-text-3" id="text-6-4">
<div id="outline-container-org3c6cfed" class="outline-3">
<h3 id="org3c6cfed"><span class="section-number-3">7.4</span> Piezoelectric Actuator Constant</h3>
<div class="outline-text-3" id="text-7-4">
<p>
Using the measurement test-bench, it is rather easy the determine the static gain between the applied voltage \(V_a\) to the induced displacement \(d\).
Use a quasi static (1Hz) excitation signal \(V_a\) on the piezoelectric stack and measure the vertical displacement \(d\).
@@ -551,9 +777,9 @@ From the two gains, it is then easy to determine \(g_a\):
</div>
</div>
<div id="outline-container-orge970d07" class="outline-3">
<h3 id="orge970d07"><span class="section-number-3">6.5</span> Piezoelectric Sensor Constant</h3>
<div class="outline-text-3" id="text-6-5">
<div id="outline-container-org9c52d3c" class="outline-3">
<h3 id="org9c52d3c"><span class="section-number-3">7.5</span> Piezoelectric Sensor Constant</h3>
<div class="outline-text-3" id="text-7-5">
<p>
From a quasi static excitation of the piezoelectric stack, measure the gain from \(V_a\) to \(V_s\):
</p>
@@ -591,18 +817,18 @@ This external force can be some weight added, or a piezo in parallel.
</div>
</div>
<div id="outline-container-org86b3954" class="outline-3">
<h3 id="org86b3954"><span class="section-number-3">6.6</span> Capacitance Measurement</h3>
<div class="outline-text-3" id="text-6-6">
<div id="outline-container-org30f8839" class="outline-3">
<h3 id="org30f8839"><span class="section-number-3">7.6</span> Capacitance Measurement</h3>
<div class="outline-text-3" id="text-7-6">
<p>
Measure the capacitance of the 3 stacks individually using a precise multi-meter.
</p>
</div>
</div>
<div id="outline-container-orgc5205df" class="outline-3">
<h3 id="orgc5205df"><span class="section-number-3">6.7</span> Dynamical Behavior</h3>
<div class="outline-text-3" id="text-6-7">
<div id="outline-container-org7549456" class="outline-3">
<h3 id="org7549456"><span class="section-number-3">7.7</span> Dynamical Behavior</h3>
<div class="outline-text-3" id="text-7-7">
<p>
Perform a system identification from \(V_a\) to the measured displacement \(d\) by the interferometer and by the encoder, and to the generated voltage \(V_s\).
</p>
@@ -617,9 +843,9 @@ This can also be performed with and without the encoder fixed to the APA.
</div>
</div>
<div id="outline-container-org2f73a1b" class="outline-3">
<h3 id="org2f73a1b"><span class="section-number-3">6.8</span> Compare the results obtained for all 7 APA300ML</h3>
<div class="outline-text-3" id="text-6-8">
<div id="outline-container-org51816a1" class="outline-3">
<h3 id="org51816a1"><span class="section-number-3">7.8</span> Compare the results obtained for all 7 APA300ML</h3>
<div class="outline-text-3" id="text-7-8">
<p>
Compare all the obtained parameters for all the test APA.
</p>
@@ -627,8 +853,8 @@ Compare all the obtained parameters for all the test APA.
</div>
</div>
<div id="outline-container-org175e8d0" class="outline-2">
<h2 id="org175e8d0"><span class="section-number-2">7</span> Measurement Results</h2>
<div id="outline-container-org0b4e69a" class="outline-2">
<h2 id="org0b4e69a"><span class="section-number-2">8</span> Measurement Results</h2>
</div>
<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><h2 class='citeproc-org-bib-h2'>Bibliography</h2>
@@ -638,7 +864,7 @@ Compare all the obtained parameters for all the test APA.
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2021-03-15 lun. 11:35</p>
<p class="date">Created: 2021-03-16 mar. 14:30</p>
</div>
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