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< title > Amplifier Piezoelectric Actuator APA300ML - Test Bench< / title >
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< h1 class = "title" > Amplifier Piezoelectric Actuator APA300ML - Test Bench< / h1 >
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< h2 > Table of Contents< / h2 >
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< li > < a href = "#org678b530" > 1. Model of an Amplified Piezoelectric Actuator and Sensor< / a > < / li >
< li > < a href = "#orgb60d741" > 2. Test-Bench Description< / a > < / li >
< li > < a href = "#orgf881aa5" > 3. Measurement Procedure< / a >
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< li > < a href = "#orgd3519e0" > 3.1. Stroke Measurement< / a > < / li >
< li > < a href = "#org6844a7e" > 3.2. Stiffness Measurement< / a > < / li >
< li > < a href = "#org9b16fa0" > 3.3. Hysteresis measurement< / a > < / li >
< li > < a href = "#orgbfe1da1" > 3.4. Piezoelectric Actuator Constant< / a > < / li >
< li > < a href = "#orgb1792b1" > 3.5. Piezoelectric Sensor Constant< / a > < / li >
< li > < a href = "#orgd76cbb5" > 3.6. Capacitance Measurement< / a > < / li >
< li > < a href = "#orgbfe739f" > 3.7. Dynamical Behavior< / a > < / li >
< li > < a href = "#org007452b" > 3.8. Compare the results obtained for all 7 APA300ML< / a > < / li >
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< li > < a href = "#org7bda022" > 4. Measurement Results< / a > < / li >
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< p >
The goal of this test bench is to extract all the important parameters of the Amplified Piezoelectric Actuator APA300ML.
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This include:
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< li > Stroke< / li >
< li > Stiffness< / li >
< li > Hysteresis< / li >
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< 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 >
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< li > Dynamical behavior< / li >
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< h2 id = "org678b530" > < span class = "section-number-2" > 1< / span > Model of an Amplified Piezoelectric Actuator and Sensor< / h2 >
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Consider a schematic of the Amplified Piezoelectric Actuator in Figure < a href = "#orgf04d73b" > 1< / a > .
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< div id = "orgf04d73b" class = "figure" >
< p > < img src = "figs/apa_model_schematic.png" alt = "apa_model_schematic.png" / >
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< p > < span class = "figure-number" > Figure 1: < / span > Amplified Piezoelectric Actuator Schematic< / p >
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< p >
A voltage \(V_a\) applied to the actuator stacks will induce an actuator force \(F_a\):
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\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 \(V_s\):
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\begin{equation}
V_s = g_s \cdot dl
\end{equation}
< p >
We wish here to experimental measure \(g_a\) and \(g_s\).
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< p >
The block-diagram model of the piezoelectric actuator is then as shown in Figure < a href = "#org7ba9352" > 2< / a > .
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< p > < img src = "figs/apa-model-simscape-schematic.png" alt = "apa-model-simscape-schematic.png" / >
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< p > < span class = "figure-number" > Figure 2: < / span > Model of the APA with Simscape/Simulink< / p >
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< h2 id = "orgb60d741" > < span class = "section-number-2" > 2< / span > Test-Bench Description< / h2 >
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< p >
Here are the documentation of the equipment used for this test bench:
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< 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 >
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< div id = "orgfaaa568" 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 > < span class = "figure-number" > Figure 3: < / span > Schematic of the Test Bench< / p >
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< h2 id = "orgf881aa5" > < span class = "section-number-2" > 3< / span > Measurement Procedure< / h2 >
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< h3 id = "orgd3519e0" > < span class = "section-number-3" > 3.1< / span > Stroke Measurement< / h3 >
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< p >
Using the PD200 amplifier, output a voltage:
\[ V_a = 65 + 85 \sin(2\pi \cdot t) \]
To have a quasi-static excitation between -80 and 150V.
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< p >
As the gain of the PD200 amplifier is 20, the DAC output voltage should be:
\[ V_{dac}(t) = 3.25 + 4.25\sin(2\pi \cdot t) \]
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< p >
Verify that the voltage offset is zero!
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< p >
Measure the output vertical displacement \(d\) using the interferometer.
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< p >
Then, plot \(d\) as a function of \(V_a\), and perform a linear regression.
Conclude on the obtained stroke.
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< h3 id = "org6844a7e" > < span class = "section-number-3" > 3.2< / span > Stiffness Measurement< / h3 >
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< 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.
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< 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.
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Then the obtained stiffness is:
< / p >
\begin{equation}
k = \frac{\delta m g}{\delta d}
\end{equation}
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< h3 id = "org9b16fa0" > < span class = "section-number-3" > 3.3< / span > Hysteresis measurement< / h3 >
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< p >
Supply a quasi static sinusoidal excitation \(V_a\) at different voltages.
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< p >
The offset should be 65V, and the sin amplitude can range from 1V up to 85V.
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For each excitation amplitude, the vertical displacement \(d\) of the mass is measured.
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< p >
Then, \(d\) is plotted as a function of \(V_a\) for all the amplitudes.
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< h3 id = "orgbfe1da1" > < span class = "section-number-3" > 3.4< / span > Piezoelectric Actuator Constant< / h3 >
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< 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}
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< h3 id = "orgb1792b1" > < 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" >
< p >
From a quasi static (1Hz) 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 >
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.
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< h3 id = "orgd76cbb5" > < span class = "section-number-3" > 3.6< / span > Capacitance Measurement< / h3 >
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< p >
Measure the capacitance of the 3 stacks individually using a precise multi-meter.
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< h3 id = "orgbfe739f" > < span class = "section-number-3" > 3.7< / span > Dynamical Behavior< / h3 >
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< p >
Perform a system identification from \(V_a\) to the measured displacement \(d\) by the interferometer and by the encoder, and to the general voltage \(V_s\).
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< p >
This can be performed using different excitation signals.
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< p >
This can also be performed with and without the encoder fixed to the APA.
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< h3 id = "org007452b" > < span class = "section-number-3" > 3.8< / span > Compare the results obtained for all 7 APA300ML< / h3 >
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Compare all the obtained parameters for all the test APA.
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< h2 id = "org7bda022" > < span class = "section-number-2" > 4< / span > Measurement Results< / h2 >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
2020-12-17 14:55:18 +01:00
< p class = "date" > Created: 2020-12-17 jeu. 14:55< / p >
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