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871 lines
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<!-- 2021-03-16 mar. 14:30 -->
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<title>Amplifier Piezoelectric Actuator APA300ML - Test Bench</title>
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<a accesskey="h" href="../index.html"> UP </a>
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<a accesskey="H" href="../index.html"> HOME </a>
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</div><div id="content">
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<h1 class="title">Amplifier Piezoelectric Actuator APA300ML - Test Bench</h1>
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgeae854b">1. Model of an Amplified Piezoelectric Actuator and Sensor</a></li>
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<li><a href="#org5126568">2. Geometrical Measurements</a>
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<ul>
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<li><a href="#orge477895">2.1. Measurement Setup</a></li>
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<li><a href="#orgf6e38fd">2.2. Measurement Results</a></li>
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</ul>
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</li>
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<li><a href="#org3da2e64">3. Electrical Measurements</a></li>
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<li><a href="#orgcd8f0b8">4. Stiffness measurement</a>
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<ul>
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<li><a href="#org20509de">4.1. APA test</a></li>
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</ul>
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</li>
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<li><a href="#orgc5606b4">5. Stroke measurement</a>
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<ul>
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<li><a href="#org676705f">5.1. Voltage applied on one stack</a></li>
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<li><a href="#orgf6d51af">5.2. Voltage applied on two stacks</a></li>
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<li><a href="#org5fada7f">5.3. Voltage applied on all three stacks</a></li>
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</ul>
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</li>
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<li><a href="#org3248c3e">6. Test-Bench Description</a></li>
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<li><a href="#orgabbb81c">7. Measurement Procedure</a>
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<ul>
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<li><a href="#orge3152f8">7.1. Stroke Measurement</a></li>
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<li><a href="#orgc1cf00d">7.2. Stiffness Measurement</a></li>
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<li><a href="#org61adc4b">7.3. Hysteresis measurement</a></li>
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<li><a href="#org3c6cfed">7.4. Piezoelectric Actuator Constant</a></li>
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<li><a href="#org9c52d3c">7.5. Piezoelectric Sensor Constant</a></li>
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<li><a href="#org30f8839">7.6. Capacitance Measurement</a></li>
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<li><a href="#org7549456">7.7. Dynamical Behavior</a></li>
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<li><a href="#org51816a1">7.8. Compare the results obtained for all 7 APA300ML</a></li>
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</ul>
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</li>
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<li><a href="#org0b4e69a">8. Measurement Results</a></li>
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</ul>
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</div>
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</div>
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<hr>
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<p>This report is also available as a <a href="./test-bench-apa300ml.pdf">pdf</a>.</p>
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<hr>
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<p>
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The goal of this test bench is to extract all the important parameters of the Amplified Piezoelectric Actuator APA300ML.
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</p>
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<p>
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This include:
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</p>
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<ul class="org-ul">
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<li>Stroke</li>
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<li>Stiffness</li>
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<li>Hysteresis</li>
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<li>Gain from the applied voltage \(V_a\) to the generated Force \(F_a\)</li>
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<li>Gain from the sensor stack strain \(\delta L\) to the generated voltage \(V_s\)</li>
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<li>Dynamical behavior</li>
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</ul>
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<div id="org6bbfe2e" class="figure">
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<p><img src="figs/apa300ML.png" alt="apa300ML.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Picture of the APA300ML</p>
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</div>
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<div id="outline-container-orgeae854b" class="outline-2">
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<h2 id="orgeae854b"><span class="section-number-2">1</span> Model of an Amplified Piezoelectric Actuator and Sensor</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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Consider a schematic of the Amplified Piezoelectric Actuator in Figure <a href="#org2844129">2</a>.
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</p>
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<div id="org2844129" class="figure">
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<p><img src="figs/apa_model_schematic.png" alt="apa_model_schematic.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Amplified Piezoelectric Actuator Schematic</p>
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</div>
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<p>
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A voltage \(V_a\) applied to the actuator stacks will induce an actuator force \(F_a\):
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</p>
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\begin{equation}
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F_a = g_a \cdot V_a
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\end{equation}
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<p>
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A change of length \(dl\) of the sensor stack will induce a voltage \(V_s\):
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</p>
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\begin{equation}
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V_s = g_s \cdot dl
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\end{equation}
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<p>
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We wish here to experimental measure \(g_a\) and \(g_s\).
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</p>
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<p>
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The block-diagram model of the piezoelectric actuator is then as shown in Figure <a href="#org5ba1265">3</a>.
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</p>
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<div id="org5ba1265" class="figure">
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<p><img src="figs/apa-model-simscape-schematic.png" alt="apa-model-simscape-schematic.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Model of the APA with Simscape/Simulink</p>
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</div>
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</div>
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</div>
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<div id="outline-container-org5126568" class="outline-2">
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<h2 id="org5126568"><span class="section-number-2">2</span> Geometrical Measurements</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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The received APA are shown in Figure <a href="#org1895ec7">4</a>.
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</p>
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<div id="org1895ec7" class="figure">
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<p><img src="figs/IMG_20210224_143500.jpg" alt="IMG_20210224_143500.jpg" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Received APA</p>
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</div>
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</div>
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<div id="outline-container-orge477895" class="outline-3">
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<h3 id="orge477895"><span class="section-number-3">2.1</span> Measurement Setup</h3>
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<div class="outline-text-3" id="text-2-1">
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<p>
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The flatness corresponding to the two interface planes are measured as shown in Figure <a href="#org9fff0ac">5</a>.
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</p>
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<div id="org9fff0ac" class="figure">
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<p><img src="figs/IMG_20210224_143809.jpg" alt="IMG_20210224_143809.jpg" />
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</p>
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<p><span class="figure-number">Figure 5: </span>Measurement Setup</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgf6e38fd" class="outline-3">
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<h3 id="orgf6e38fd"><span class="section-number-3">2.2</span> Measurement Results</h3>
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<div class="outline-text-3" id="text-2-2">
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<p>
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The height (Z) measurements at the 8 locations (4 points by plane) are defined below.
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</p>
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<div class="org-src-container">
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<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];
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apa2 = 1e<span class="org-type">-</span>6<span class="org-type">*</span>[0, <span class="org-type">-</span>2.5 , <span class="org-type">-</span>3 , 0 , <span class="org-type">-</span>1.5 , 1 , <span class="org-type">-</span>2 , <span class="org-type">-</span>4];
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apa3 = 1e<span class="org-type">-</span>6<span class="org-type">*</span>[0, <span class="org-type">-</span>1.5 , 15 , 17.5 , 6.5 , 6.5 , 21 , 23];
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apa4 = 1e<span class="org-type">-</span>6<span class="org-type">*</span>[0, 6.5 , 14.5 , 9 , 16 , 22 , 29.5 , 21];
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apa5 = 1e<span class="org-type">-</span>6<span class="org-type">*</span>[0, <span class="org-type">-</span>12.5, 16.5 , 28.5 , <span class="org-type">-</span>43 , <span class="org-type">-</span>52 , <span class="org-type">-</span>22.5, <span class="org-type">-</span>13.5];
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apa6 = 1e<span class="org-type">-</span>6<span class="org-type">*</span>[0, <span class="org-type">-</span>8 , <span class="org-type">-</span>2 , 5 , <span class="org-type">-</span>57.5, <span class="org-type">-</span>62 , <span class="org-type">-</span>55.5, <span class="org-type">-</span>52.5];
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apa7 = 1e<span class="org-type">-</span>6<span class="org-type">*</span>[0, 19.5 , <span class="org-type">-</span>8 , <span class="org-type">-</span>29.5, 75 , 97.5, 70 , 48];
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apa7b = 1e<span class="org-type">-</span>6<span class="org-type">*</span>[0, 9 , <span class="org-type">-</span>18.5, <span class="org-type">-</span>30 , 31 , 46.5, 16.5 , 7.5];
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apa = {apa1, apa2, apa3, apa4, apa5, apa6, apa7b};
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</pre>
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</div>
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<p>
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The X/Y Positions of the 8 measurement points are defined below.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">W = 20e<span class="org-type">-</span>3; <span class="org-comment">% Width [m]</span>
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L = 61e<span class="org-type">-</span>3; <span class="org-comment">% Length [m]</span>
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d = 1e<span class="org-type">-</span>3; <span class="org-comment">% Distance from border [m]</span>
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l = 15.5e<span class="org-type">-</span>3; <span class="org-comment">% [m]</span>
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pos = [[<span class="org-type">-</span>L<span class="org-type">/</span>2 <span class="org-type">+</span> d; W<span class="org-type">/</span>2 <span class="org-type">-</span> d], [<span class="org-type">-</span>L<span class="org-type">/</span>2 <span class="org-type">+</span> l <span class="org-type">-</span> d; W<span class="org-type">/</span>2 <span class="org-type">-</span> d], [<span class="org-type">-</span>L<span class="org-type">/</span>2 <span class="org-type">+</span> l <span class="org-type">-</span> d; <span class="org-type">-</span>W<span class="org-type">/</span>2 <span class="org-type">+</span> d], [<span class="org-type">-</span>L<span class="org-type">/</span>2 <span class="org-type">+</span> d; <span class="org-type">-</span>W<span class="org-type">/</span>2 <span class="org-type">+</span> d], [L<span class="org-type">/</span>2 <span class="org-type">-</span> l <span class="org-type">+</span> d; W<span class="org-type">/</span>2 <span class="org-type">-</span> d], [L<span class="org-type">/</span>2 <span class="org-type">-</span> d; W<span class="org-type">/</span>2 <span class="org-type">-</span> d], [L<span class="org-type">/</span>2 <span class="org-type">-</span> d; <span class="org-type">-</span>W<span class="org-type">/</span>2 <span class="org-type">+</span> d], [L<span class="org-type">/</span>2 <span class="org-type">-</span> l <span class="org-type">+</span> d; <span class="org-type">-</span>W<span class="org-type">/</span>2 <span class="org-type">+</span> d]];
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</pre>
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</div>
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<p>
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Finally, the flatness is estimated by fitting a plane through the 8 points using the <code>fminsearch</code> command.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab">apa_d = zeros(1, 7);
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<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>
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fun = @(x)max(abs(([pos; apa{<span class="org-constant">i</span>}]<span class="org-type">-</span>[0;0;x(1)])<span class="org-type">'*</span>([x(2<span class="org-type">:</span>3);1]<span class="org-type">/</span>norm([x(2<span class="org-type">:</span>3);1]))));
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x0 = [0;0;0];
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[x, min_d] = fminsearch(fun,x0);
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apa_d(<span class="org-constant">i</span>) = min_d;
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<span class="org-keyword">end</span>
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</pre>
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</div>
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<p>
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The obtained flatness are shown in Table <a href="#org36f0e82">1</a>.
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</p>
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<table id="org36f0e82" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<caption class="t-above"><span class="table-number">Table 1:</span> Estimated flatness</caption>
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<colgroup>
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<col class="org-left" />
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<col class="org-right" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left"> </th>
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<th scope="col" class="org-right"><b>Flatness</b> \([\mu m]\)</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">APA 1</td>
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<td class="org-right">8.9</td>
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</tr>
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<tr>
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<td class="org-left">APA 2</td>
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<td class="org-right">3.1</td>
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</tr>
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<tr>
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<td class="org-left">APA 3</td>
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<td class="org-right">9.1</td>
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</tr>
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<tr>
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<td class="org-left">APA 4</td>
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<td class="org-right">3.0</td>
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</tr>
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<tr>
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<td class="org-left">APA 5</td>
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<td class="org-right">1.9</td>
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</tr>
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<tr>
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<td class="org-left">APA 6</td>
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<td class="org-right">7.1</td>
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</tr>
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<tr>
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<td class="org-left">APA 7</td>
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<td class="org-right">18.7</td>
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</tr>
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</tbody>
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</table>
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</div>
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</div>
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</div>
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<div id="outline-container-org3da2e64" class="outline-2">
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<h2 id="org3da2e64"><span class="section-number-2">3</span> Electrical Measurements</h2>
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<div class="outline-text-2" id="text-3">
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<div class="note" id="org7758b1f">
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<p>
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||
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>)
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</p>
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</div>
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<div id="org66db1d7" class="figure">
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<p><img src="figs/IMG_20210312_120337.jpg" alt="IMG_20210312_120337.jpg" />
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</p>
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<p><span class="figure-number">Figure 6: </span>LCR Meter used for the measurements</p>
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</div>
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<p>
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The excitation frequency is set to be 1kHz.
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</p>
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<table id="org2ae85fd" border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<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>
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<colgroup>
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<col class="org-left" />
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||
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||
<col class="org-right" />
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||
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||
<col class="org-right" />
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</colgroup>
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<thead>
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<tr>
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<th scope="col" class="org-left"> </th>
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<th scope="col" class="org-right"><b>Sensor Stack</b></th>
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<th scope="col" class="org-right"><b>Actuator Stacks</b></th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">APA 1</td>
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<td class="org-right">5.10</td>
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<td class="org-right">10.03</td>
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</tr>
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<tr>
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<td class="org-left">APA 2</td>
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<td class="org-right">4.99</td>
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<td class="org-right">9.85</td>
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</tr>
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<tr>
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<td class="org-left">APA 3</td>
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<td class="org-right">1.72</td>
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<td class="org-right">5.18</td>
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</tr>
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<tr>
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<td class="org-left">APA 4</td>
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<td class="org-right">4.94</td>
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<td class="org-right">9.82</td>
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</tr>
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<tr>
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<td class="org-left">APA 5</td>
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<td class="org-right">4.90</td>
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<td class="org-right">9.66</td>
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</tr>
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<tr>
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<td class="org-left">APA 6</td>
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<td class="org-right">4.99</td>
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<td class="org-right">9.91</td>
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||
</tr>
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||
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<tr>
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<td class="org-left">APA 7</td>
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<td class="org-right">4.85</td>
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<td class="org-right">9.85</td>
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||
</tr>
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||
</tbody>
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||
</table>
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<div class="warning" id="org7282231">
|
||
<p>
|
||
There is clearly a problem with APA300ML number 3
|
||
</p>
|
||
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
<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-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>);
|
||
</pre>
|
||
</div>
|
||
|
||
<div class="org-src-container">
|
||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||
plot(t, F)
|
||
</pre>
|
||
</div>
|
||
|
||
<div class="org-src-container">
|
||
<pre class="src src-matlab"><span class="org-matlab-cellbreak"><span class="org-comment">%% Automatic Zero of the force</span></span>
|
||
F = F <span class="org-type">-</span> mean(F(t <span class="org-type">></span> 0.1 <span class="org-type">&</span> t <span class="org-type"><</span> 0.3));
|
||
|
||
<span class="org-matlab-cellbreak"><span class="org-comment">%% Start measurement at t = 0.2 s</span></span>
|
||
d = d(t <span class="org-type">></span> 0.2);
|
||
F = F(t <span class="org-type">></span> 0.2);
|
||
t = t(t <span class="org-type">></span> 0.2); t = t <span class="org-type">-</span> t(1);
|
||
</pre>
|
||
</div>
|
||
|
||
<div class="org-src-container">
|
||
<pre class="src src-matlab">i_l_start = find(F <span class="org-type">></span> 0.3, 1, <span class="org-string">'first'</span>);
|
||
[<span class="org-type">~</span>, i_l_stop] = max(F);
|
||
</pre>
|
||
</div>
|
||
|
||
<div class="org-src-container">
|
||
<pre class="src src-matlab">F_l = F(i_l_start<span class="org-type">:</span>i_l_stop);
|
||
d_l = d(i_l_start<span class="org-type">:</span>i_l_stop);
|
||
</pre>
|
||
</div>
|
||
|
||
<div class="org-src-container">
|
||
<pre class="src src-matlab">fit_l = polyfit(F_l, d_l, 1);
|
||
|
||
<span class="org-comment">% %% Reset displacement based on fit</span>
|
||
<span class="org-comment">% d = d - fit_l(2);</span>
|
||
<span class="org-comment">% fit_s(2) = fit_s(2) - fit_l(2);</span>
|
||
<span class="org-comment">% fit_l(2) = 0;</span>
|
||
|
||
<span class="org-comment">% %% Estimated Stroke</span>
|
||
<span class="org-comment">% F_max = fit_s(2)/(fit_l(1) - fit_s(1));</span>
|
||
<span class="org-comment">% d_max = fit_l(1)*F_max;</span>
|
||
</pre>
|
||
</div>
|
||
|
||
<div class="org-src-container">
|
||
<pre class="src src-matlab">h<span class="org-type">^</span>2<span class="org-type">/</span>fit_l(1)
|
||
</pre>
|
||
</div>
|
||
|
||
<div class="org-src-container">
|
||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||
hold on;
|
||
plot(F,d,<span class="org-string">'k'</span>)
|
||
plot(F_l, d_l)
|
||
plot(F_l, F_l<span class="org-type">*</span>fit_l(1) <span class="org-type">+</span> fit_l(2), <span class="org-string">'--'</span>)
|
||
</pre>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<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">
|
||
<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’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"> </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>
|
||
<ul class="org-ul">
|
||
<li>Voltage Amplifier: <a href="doc/PD200-V7-R1.pdf">PD200</a></li>
|
||
<li>Amplified Piezoelectric Actuator: <a href="doc/APA300ML.pdf">APA300ML</a></li>
|
||
<li>DAC/ADC: Speedgoat <a href="doc/IO131-OEM-Datasheet.pdf">IO313</a></li>
|
||
<li>Encoder: <a href="doc/L-9517-9678-05-A_Data_sheet_VIONiC_series_en.pdf">Renishaw Vionic</a> and used <a href="doc/L-9517-9862-01-C_Data_sheet_RKLC_EN.pdf">Ruler</a></li>
|
||
<li>Interferometer: <a href="https://www.attocube.com/en/products/laser-displacement-sensor/displacement-measuring-interferometer">Attocube IDS3010</a></li>
|
||
</ul>
|
||
|
||
</div>
|
||
|
||
|
||
<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 14: </span>Schematic of the Test Bench</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
<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-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:
|
||
\[ V_a = 65 + 85 \sin(2\pi \cdot t) \]
|
||
To have a quasi-static excitation between -20 and 150V.
|
||
</p>
|
||
|
||
<p>
|
||
As the gain of the PD200 amplifier is 20, the DAC output voltage should be:
|
||
\[ V_{dac}(t) = 3.25 + 4.25\sin(2\pi \cdot t) \]
|
||
</p>
|
||
|
||
<p>
|
||
Verify that the voltage offset of the PD200 is zero!
|
||
</p>
|
||
|
||
<p>
|
||
Measure the output vertical displacement \(d\) using the interferometer.
|
||
</p>
|
||
|
||
<p>
|
||
Then, plot \(d\) as a function of \(V_a\), and perform a linear regression.
|
||
Conclude on the obtained stroke.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
|
||
<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.
|
||
</p>
|
||
|
||
<p>
|
||
As the stiffness will be around \(k \approx 10^6 N/m\), an added mass of \(m \approx 100g\) will induce a static deflection of \(\approx 1\mu m\) which should be large enough for a precise measurement using the interferometer.
|
||
</p>
|
||
|
||
<p>
|
||
Then the obtained stiffness is:
|
||
</p>
|
||
\begin{equation}
|
||
k = \frac{\delta m g}{\delta d}
|
||
\end{equation}
|
||
</div>
|
||
</div>
|
||
|
||
<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>
|
||
|
||
<p>
|
||
The offset should be 65V, and the sin amplitude can range from 1V up to 85V.
|
||
</p>
|
||
|
||
<p>
|
||
For each excitation amplitude, the vertical displacement \(d\) of the mass is measured.
|
||
</p>
|
||
|
||
<p>
|
||
Then, \(d\) is plotted as a function of \(V_a\) for all the amplitudes.
|
||
</p>
|
||
|
||
|
||
<div id="org0fb5c18" class="figure">
|
||
<p><img src="figs/expected_hysteresis.png" alt="expected_hysteresis.png" />
|
||
</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-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 \(d\).
|
||
Perform a linear regression to obtain:
|
||
</p>
|
||
\begin{equation}
|
||
d = g_{d/V_a} \cdot V_a
|
||
\end{equation}
|
||
|
||
<p>
|
||
Using the Simscape model of the APA, it is possible to determine the static gain between the actuator force \(F_a\) to the induced displacement \(d\):
|
||
</p>
|
||
\begin{equation}
|
||
d = g_{d/F_a} \cdot F_a
|
||
\end{equation}
|
||
|
||
<p>
|
||
From the two gains, it is then easy to determine \(g_a\):
|
||
</p>
|
||
\begin{equation}
|
||
g_a = \frac{F_a}{V_a} = \frac{F_a}{d} \cdot \frac{d}{V_a} = \frac{g_{d/V_a}}{g_{d/F_a}}
|
||
\end{equation}
|
||
</div>
|
||
</div>
|
||
|
||
<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>
|
||
\begin{equation}
|
||
V_s = g_{V_s/V_a} V_a
|
||
\end{equation}
|
||
|
||
<p>
|
||
Note here that there is an high pass filter formed by the piezo capacitor and parallel resistor.
|
||
The excitation frequency should then be in between the cut-off frequency of this high pass filter and the first resonance.
|
||
</p>
|
||
|
||
<p>
|
||
Alternatively, the gain can be computed from the dynamical identification and taking the gain at the wanted frequency.
|
||
</p>
|
||
|
||
<p>
|
||
Using the simscape model, compute the static gain from the actuator force \(F_a\) to the strain of the sensor stack \(dl\):
|
||
</p>
|
||
\begin{equation}
|
||
dl = g_{dl/F_a} F_a
|
||
\end{equation}
|
||
|
||
<p>
|
||
Then, the static gain from the sensor stack strain \(dl\) to the general voltage \(V_s\) is:
|
||
</p>
|
||
\begin{equation}
|
||
g_s = \frac{V_s}{dl} = \frac{V_s}{V_a} \cdot \frac{V_a}{F_a} \cdot \frac{F_a}{dl} = \frac{g_{V_s/V_a}}{g_a \cdot g_{dl/F_a}}
|
||
\end{equation}
|
||
|
||
<p>
|
||
Alternatively, we could impose an external force to add strain in the APA that should be equally present in all the 3 stacks and equal to 1/5 of the vertical strain.
|
||
This external force can be some weight added, or a piezo in parallel.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
|
||
<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-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>
|
||
|
||
<p>
|
||
This can be performed using different excitation signals.
|
||
</p>
|
||
|
||
<p>
|
||
This can also be performed with and without the encoder fixed to the APA.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
|
||
<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>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
<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>
|
||
<div class="csl-bib-body">
|
||
<div class="csl-entry"><a name="citeproc_bib_item_1"></a>Souleille, Adrien, Thibault Lampert, V Lafarga, Sylvain Hellegouarch, Alan Rondineau, Gonçalo Rodrigues, and Christophe Collette. 2018. “A Concept of Active Mount for Space Applications.” <i>CEAS Space Journal</i> 10 (2). Springer:157–65.</div>
|
||
</div>
|
||
</div>
|
||
<div id="postamble" class="status">
|
||
<p class="author">Author: Dehaeze Thomas</p>
|
||
<p class="date">Created: 2021-03-16 mar. 14:30</p>
|
||
</div>
|
||
</body>
|
||
</html>
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