359 lines
12 KiB
HTML
359 lines
12 KiB
HTML
<?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>
|
||
<!-- 2021-02-02 mar. 19:29 -->
|
||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||
<title>Amplifier Piezoelectric Actuator APA300ML - Test Bench</title>
|
||
<meta name="generator" content="Org mode" />
|
||
<meta name="author" content="Dehaeze Thomas" />
|
||
<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
|
||
<script type="text/javascript" src="https://research.tdehaeze.xyz/js/script.js"></script>
|
||
<script>
|
||
MathJax = {
|
||
svg: {
|
||
scale: 1,
|
||
fontCache: "global"
|
||
},
|
||
tex: {
|
||
tags: "ams",
|
||
multlineWidth: "%MULTLINEWIDTH",
|
||
tagSide: "right",
|
||
macros: {bm: ["\\boldsymbol{#1}",1],},
|
||
tagIndent: ".8em"
|
||
}
|
||
};
|
||
</script>
|
||
<script id="MathJax-script" async
|
||
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js"></script>
|
||
</head>
|
||
<body>
|
||
<div id="org-div-home-and-up">
|
||
<a accesskey="h" href="../index.html"> UP </a>
|
||
|
|
||
<a accesskey="H" href="../index.html"> HOME </a>
|
||
</div><div id="content">
|
||
<h1 class="title">Amplifier Piezoelectric Actuator APA300ML - Test Bench</h1>
|
||
<div id="table-of-contents">
|
||
<h2>Table of Contents</h2>
|
||
<div id="text-table-of-contents">
|
||
<ul>
|
||
<li><a href="#org3671a24">1. Model of an Amplified Piezoelectric Actuator and Sensor</a></li>
|
||
<li><a href="#org83e51bc">2. Test-Bench Description</a></li>
|
||
<li><a href="#orgb8f415f">3. Measurement Procedure</a>
|
||
<ul>
|
||
<li><a href="#org6a1e417">3.1. Stroke Measurement</a></li>
|
||
<li><a href="#org96ea50c">3.2. Stiffness Measurement</a></li>
|
||
<li><a href="#orgd47f2df">3.3. Hysteresis measurement</a></li>
|
||
<li><a href="#orgf91088f">3.4. Piezoelectric Actuator Constant</a></li>
|
||
<li><a href="#org8d23151">3.5. Piezoelectric Sensor Constant</a></li>
|
||
<li><a href="#org3560597">3.6. Capacitance Measurement</a></li>
|
||
<li><a href="#org8113f87">3.7. Dynamical Behavior</a></li>
|
||
<li><a href="#org25802eb">3.8. Compare the results obtained for all 7 APA300ML</a></li>
|
||
</ul>
|
||
</li>
|
||
<li><a href="#org1f490aa">4. Measurement Results</a></li>
|
||
</ul>
|
||
</div>
|
||
</div>
|
||
<hr>
|
||
<p>This report is also available as a <a href="./test-bench-apa300ml.pdf">pdf</a>.</p>
|
||
<hr>
|
||
|
||
<p>
|
||
The goal of this test bench is to extract all the important parameters of the Amplified Piezoelectric Actuator APA300ML.
|
||
</p>
|
||
|
||
<p>
|
||
This include:
|
||
</p>
|
||
<ul class="org-ul">
|
||
<li>Stroke</li>
|
||
<li>Stiffness</li>
|
||
<li>Hysteresis</li>
|
||
<li>Gain from the applied voltage \(V_a\) to the generated Force \(F_a\)</li>
|
||
<li>Gain from the sensor stack strain \(\delta L\) to the generated voltage \(V_s\)</li>
|
||
<li>Dynamical behavior</li>
|
||
</ul>
|
||
|
||
|
||
<div id="orgb0d5679" 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-org3671a24" class="outline-2">
|
||
<h2 id="org3671a24"><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="#org3bbcf6a">2</a>.
|
||
</p>
|
||
|
||
|
||
<div id="org3bbcf6a" 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>
|
||
</div>
|
||
|
||
<p>
|
||
A voltage \(V_a\) applied to the actuator stacks will induce an actuator force \(F_a\):
|
||
</p>
|
||
\begin{equation}
|
||
F_a = g_a \cdot V_a
|
||
\end{equation}
|
||
|
||
<p>
|
||
A change of length \(dl\) of the sensor stack will induce a voltage \(V_s\):
|
||
</p>
|
||
\begin{equation}
|
||
V_s = g_s \cdot dl
|
||
\end{equation}
|
||
|
||
<p>
|
||
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="#org12e874e">3</a>.
|
||
</p>
|
||
|
||
|
||
<div id="org12e874e" 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>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
<div id="outline-container-org83e51bc" class="outline-2">
|
||
<h2 id="org83e51bc"><span class="section-number-2">2</span> Test-Bench Description</h2>
|
||
<div class="outline-text-2" id="text-2">
|
||
<div class="note" id="orgdde2181">
|
||
<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="org2ca856d" class="figure">
|
||
<p><img src="figs/test_bench_apa_alone.png" alt="test_bench_apa_alone.png" />
|
||
</p>
|
||
<p><span class="figure-number">Figure 4: </span>Schematic of the Test Bench</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
<div id="outline-container-orgb8f415f" class="outline-2">
|
||
<h2 id="orgb8f415f"><span class="section-number-2">3</span> Measurement Procedure</h2>
|
||
<div class="outline-text-2" id="text-3">
|
||
</div>
|
||
<div id="outline-container-org6a1e417" class="outline-3">
|
||
<h3 id="org6a1e417"><span class="section-number-3">3.1</span> Stroke Measurement</h3>
|
||
<div class="outline-text-3" id="text-3-1">
|
||
<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-org96ea50c" class="outline-3">
|
||
<h3 id="org96ea50c"><span class="section-number-3">3.2</span> Stiffness Measurement</h3>
|
||
<div class="outline-text-3" id="text-3-2">
|
||
<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-orgd47f2df" class="outline-3">
|
||
<h3 id="orgd47f2df"><span class="section-number-3">3.3</span> Hysteresis measurement</h3>
|
||
<div class="outline-text-3" id="text-3-3">
|
||
<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="orgab4aadf" class="figure">
|
||
<p><img src="figs/expected_hysteresis.png" alt="expected_hysteresis.png" />
|
||
</p>
|
||
<p><span class="figure-number">Figure 5: </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-orgf91088f" class="outline-3">
|
||
<h3 id="orgf91088f"><span class="section-number-3">3.4</span> Piezoelectric Actuator Constant</h3>
|
||
<div class="outline-text-3" id="text-3-4">
|
||
<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-org8d23151" class="outline-3">
|
||
<h3 id="org8d23151"><span class="section-number-3">3.5</span> Piezoelectric Sensor Constant</h3>
|
||
<div class="outline-text-3" id="text-3-5">
|
||
<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-org3560597" class="outline-3">
|
||
<h3 id="org3560597"><span class="section-number-3">3.6</span> Capacitance Measurement</h3>
|
||
<div class="outline-text-3" id="text-3-6">
|
||
<p>
|
||
Measure the capacitance of the 3 stacks individually using a precise multi-meter.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
|
||
<div id="outline-container-org8113f87" class="outline-3">
|
||
<h3 id="org8113f87"><span class="section-number-3">3.7</span> Dynamical Behavior</h3>
|
||
<div class="outline-text-3" id="text-3-7">
|
||
<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-org25802eb" class="outline-3">
|
||
<h3 id="org25802eb"><span class="section-number-3">3.8</span> Compare the results obtained for all 7 APA300ML</h3>
|
||
<div class="outline-text-3" id="text-3-8">
|
||
<p>
|
||
Compare all the obtained parameters for all the test APA.
|
||
</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
|
||
<div id="outline-container-org1f490aa" class="outline-2">
|
||
<h2 id="org1f490aa"><span class="section-number-2">4</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: 2021-02-02 mar. 19:29</p>
|
||
</div>
|
||
</body>
|
||
</html>
|