359 lines
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359 lines
12 KiB
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<title>Amplifier Piezoelectric Actuator APA300ML - Test Bench</title>
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<div id="org-div-home-and-up">
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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="#org3671a24">1. Model of an Amplified Piezoelectric Actuator and Sensor</a></li>
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<li><a href="#org83e51bc">2. Test-Bench Description</a></li>
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<li><a href="#orgb8f415f">3. Measurement Procedure</a>
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<ul>
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<li><a href="#org6a1e417">3.1. Stroke Measurement</a></li>
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<li><a href="#org96ea50c">3.2. Stiffness Measurement</a></li>
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<li><a href="#orgd47f2df">3.3. Hysteresis measurement</a></li>
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<li><a href="#orgf91088f">3.4. Piezoelectric Actuator Constant</a></li>
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<li><a href="#org8d23151">3.5. Piezoelectric Sensor Constant</a></li>
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<li><a href="#org3560597">3.6. Capacitance Measurement</a></li>
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<li><a href="#org8113f87">3.7. Dynamical Behavior</a></li>
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<li><a href="#org25802eb">3.8. 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="#org1f490aa">4. 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="orgb0d5679" 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-org3671a24" class="outline-2">
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<h2 id="org3671a24"><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="#org3bbcf6a">2</a>.
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</p>
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<div id="org3bbcf6a" 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="#org12e874e">3</a>.
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</p>
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<div id="org12e874e" 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-org83e51bc" class="outline-2">
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<h2 id="org83e51bc"><span class="section-number-2">2</span> Test-Bench Description</h2>
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<div class="outline-text-2" id="text-2">
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<div class="note" id="orgdde2181">
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<p>
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Here are the documentation of the equipment used for this test bench:
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</p>
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<ul class="org-ul">
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<li>Voltage Amplifier: <a href="doc/PD200-V7-R1.pdf">PD200</a></li>
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<li>Amplified Piezoelectric Actuator: <a href="doc/APA300ML.pdf">APA300ML</a></li>
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<li>DAC/ADC: Speedgoat <a href="doc/IO131-OEM-Datasheet.pdf">IO313</a></li>
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<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>
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<li>Interferometer: <a href="https://www.attocube.com/en/products/laser-displacement-sensor/displacement-measuring-interferometer">Attocube IDS3010</a></li>
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</ul>
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</div>
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<div id="org2ca856d" class="figure">
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<p><img src="figs/test_bench_apa_alone.png" alt="test_bench_apa_alone.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Schematic of the Test Bench</p>
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</div>
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</div>
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</div>
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<div id="outline-container-orgb8f415f" class="outline-2">
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<h2 id="orgb8f415f"><span class="section-number-2">3</span> Measurement Procedure</h2>
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<div class="outline-text-2" id="text-3">
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</div>
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<div id="outline-container-org6a1e417" class="outline-3">
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<h3 id="org6a1e417"><span class="section-number-3">3.1</span> Stroke Measurement</h3>
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<div class="outline-text-3" id="text-3-1">
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<p>
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Using the PD200 amplifier, output a voltage:
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\[ V_a = 65 + 85 \sin(2\pi \cdot t) \]
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To have a quasi-static excitation between -20 and 150V.
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</p>
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<p>
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As the gain of the PD200 amplifier is 20, the DAC output voltage should be:
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\[ V_{dac}(t) = 3.25 + 4.25\sin(2\pi \cdot t) \]
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</p>
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<p>
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Verify that the voltage offset of the PD200 is zero!
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</p>
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<p>
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Measure the output vertical displacement \(d\) using the interferometer.
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</p>
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<p>
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Then, plot \(d\) as a function of \(V_a\), and perform a linear regression.
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Conclude on the obtained stroke.
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</p>
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</div>
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</div>
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<div id="outline-container-org96ea50c" class="outline-3">
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<h3 id="org96ea50c"><span class="section-number-3">3.2</span> Stiffness Measurement</h3>
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<div class="outline-text-3" id="text-3-2">
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<p>
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Add some (known) weight \(\delta m g\) on the suspended mass and measure the deflection \(\delta d\).
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This can be tested when the piezoelectric stacks are open-circuit.
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</p>
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<p>
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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.
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</p>
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<p>
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Then the obtained stiffness is:
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</p>
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\begin{equation}
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k = \frac{\delta m g}{\delta d}
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\end{equation}
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</div>
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</div>
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<div id="outline-container-orgd47f2df" class="outline-3">
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<h3 id="orgd47f2df"><span class="section-number-3">3.3</span> Hysteresis measurement</h3>
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<div class="outline-text-3" id="text-3-3">
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<p>
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Supply a quasi static sinusoidal excitation \(V_a\) at different voltages.
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</p>
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<p>
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The offset should be 65V, and the sin amplitude can range from 1V up to 85V.
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</p>
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<p>
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For each excitation amplitude, the vertical displacement \(d\) of the mass is measured.
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</p>
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<p>
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Then, \(d\) is plotted as a function of \(V_a\) for all the amplitudes.
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</p>
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<div id="orgab4aadf" class="figure">
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<p><img src="figs/expected_hysteresis.png" alt="expected_hysteresis.png" />
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</p>
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<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>
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</div>
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</div>
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</div>
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<div id="outline-container-orgf91088f" class="outline-3">
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<h3 id="orgf91088f"><span class="section-number-3">3.4</span> Piezoelectric Actuator Constant</h3>
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<div class="outline-text-3" id="text-3-4">
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<p>
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Using the measurement test-bench, it is rather easy the determine the static gain between the applied voltage \(V_a\) to the induced displacement \(d\).
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Use a quasi static (1Hz) excitation signal \(V_a\) on the piezoelectric stack and measure the vertical displacement \(d\).
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Perform a linear regression to obtain:
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</p>
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\begin{equation}
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d = g_{d/V_a} \cdot V_a
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\end{equation}
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<p>
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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 \(d\):
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</p>
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\begin{equation}
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d = g_{d/F_a} \cdot F_a
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\end{equation}
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<p>
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From the two gains, it is then easy to determine \(g_a\):
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</p>
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\begin{equation}
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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}}
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\end{equation}
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</div>
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</div>
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<div id="outline-container-org8d23151" class="outline-3">
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<h3 id="org8d23151"><span class="section-number-3">3.5</span> Piezoelectric Sensor Constant</h3>
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<div class="outline-text-3" id="text-3-5">
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<p>
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From a quasi static excitation of the piezoelectric stack, measure the gain from \(V_a\) to \(V_s\):
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</p>
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\begin{equation}
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V_s = g_{V_s/V_a} V_a
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\end{equation}
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<p>
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Note here that there is an high pass filter formed by the piezo capacitor and parallel resistor.
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The excitation frequency should then be in between the cut-off frequency of this high pass filter and the first resonance.
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</p>
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<p>
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Alternatively, the gain can be computed from the dynamical identification and taking the gain at the wanted frequency.
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</p>
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<p>
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Using the simscape model, compute the static gain from the actuator force \(F_a\) to the strain of the sensor stack \(dl\):
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</p>
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\begin{equation}
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dl = g_{dl/F_a} F_a
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\end{equation}
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<p>
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Then, the static gain from the sensor stack strain \(dl\) to the general voltage \(V_s\) is:
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</p>
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\begin{equation}
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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}}
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\end{equation}
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<p>
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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.
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This external force can be some weight added, or a piezo in parallel.
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</p>
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</div>
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</div>
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<div id="outline-container-org3560597" class="outline-3">
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<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>
|
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|
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</html>
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