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< title > Amplifier Piezoelectric Actuator APA300ML - Test Bench< / title >
< meta name = "author" content = "Dehaeze Thomas" / >
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< 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 >
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< li > < a href = "#orgeae854b" > 1. Model of an Amplified Piezoelectric Actuator and Sensor< / a > < / li >
< 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 >
< li > < a href = "#orgf6e38fd" > 2.2. Measurement Results< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org3da2e64" > 3. Electrical Measurements< / a > < / li >
< 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 >
< / 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 >
< li > < a href = "#orgf6d51af" > 5.2. Voltage applied on two stacks< / a > < / li >
< li > < a href = "#org5fada7f" > 5.3. Voltage applied on all three stacks< / a > < / li >
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< / ul >
< / li >
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< li > < a href = "#org3248c3e" > 6. Test-Bench Description< / a > < / li >
< li > < a href = "#orgabbb81c" > 7. Measurement Procedure< / a >
< ul >
< li > < a href = "#orge3152f8" > 7.1. Stroke Measurement< / a > < / li >
< li > < a href = "#orgc1cf00d" > 7.2. Stiffness Measurement< / a > < / li >
< li > < a href = "#org61adc4b" > 7.3. Hysteresis measurement< / a > < / li >
< li > < a href = "#org3c6cfed" > 7.4. Piezoelectric Actuator Constant< / a > < / li >
< li > < a href = "#org9c52d3c" > 7.5. Piezoelectric Sensor Constant< / a > < / li >
< li > < a href = "#org30f8839" > 7.6. Capacitance Measurement< / a > < / li >
< li > < a href = "#org7549456" > 7.7. Dynamical Behavior< / a > < / li >
< li > < a href = "#org51816a1" > 7.8. Compare the results obtained for all 7 APA300ML< / a > < / li >
< / ul >
< / li >
< li > < a href = "#org0b4e69a" > 8. Measurement Results< / a > < / li >
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< / 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 >
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< div id = "org6bbfe2e" class = "figure" >
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< p > < img src = "figs/apa300ML.png" alt = "apa300ML.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Picture of the APA300ML< / p >
< / div >
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< div id = "outline-container-orgeae854b" class = "outline-2" >
< h2 id = "orgeae854b" > < span class = "section-number-2" > 1< / span > Model of an Amplified Piezoelectric Actuator and Sensor< / h2 >
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< div class = "outline-text-2" id = "text-1" >
< 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" / >
< / 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 >
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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" / >
< / p >
< p > < span class = "figure-number" > Figure 3: < / span > Model of the APA with Simscape/Simulink< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-org5126568" class = "outline-2" >
< 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 >
The received APA are shown in Figure < a href = "#org1895ec7" > 4< / a > .
< / 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" / >
< / p >
< p > < span class = "figure-number" > Figure 4: < / span > Received APA< / p >
< / div >
< / div >
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< div id = "outline-container-orge477895" class = "outline-3" >
< 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 >
The flatness corresponding to the two interface planes are measured as shown in Figure < a href = "#org9fff0ac" > 5< / a > .
< / 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" / >
< / p >
< p > < span class = "figure-number" > Figure 5: < / span > Measurement Setup< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgf6e38fd" class = "outline-3" >
< 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" >
< 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 >
< div class = "org-src-container" >
< pre class = "src src-matlab" > apa1 = 1e< span class = "org-type" > -< / span > 6< span class = "org-type" > *< / span > [0, < span class = "org-type" > -< / span > 0.5 , 3.5 , 3.5 , 42 , 45.5, 52.5 , 46];
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];
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];
apa4 = 1e< span class = "org-type" > -< / span > 6< span class = "org-type" > *< / span > [0, 6.5 , 14.5 , 9 , 16 , 22 , 29.5 , 21];
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];
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];
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];
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];
apa = {apa1, apa2, apa3, apa4, apa5, apa6, apa7b};
< / pre >
< / div >
< p >
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The X/Y Positions of the 8 measurement points are defined below.
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< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > W = 20e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % Width [m]< / span >
L = 61e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % Length [m]< / span >
d = 1e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % Distance from border [m]< / span >
l = 15.5e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % [m]< / span >
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]];
< / pre >
< / div >
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< p >
Finally, the flatness is estimated by fitting a plane through the 8 points using the < code > fminsearch< / code > command.
< / p >
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< div class = "org-src-container" >
< pre class = "src src-matlab" > apa_d = zeros(1, 7);
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > < span class = "org-constant" > i< / span > < / span > = < span class = "org-constant" > 1:7< / span >
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]))));
x0 = [0;0;0];
[x, min_d] = fminsearch(fun,x0);
apa_d(< span class = "org-constant" > i< / span > ) = min_d;
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
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< p >
The obtained flatness are shown in Table < a href = "#org36f0e82" > 1< / a > .
< / p >
< table id = "org36f0e82" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 1:< / span > Estimated flatness< / caption >
< colgroup >
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< col class = "org-left" / >
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< / colgroup >
< thead >
< tr >
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< th scope = "col" class = "org-left" >   < / th >
< th scope = "col" class = "org-right" > < b > Flatness< / b > \([\mu m]\)< / th >
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< / tr >
< / thead >
< tbody >
< tr >
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< td class = "org-left" > APA 1< / td >
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< td class = "org-right" > 8.9< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 2< / td >
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< td class = "org-right" > 3.1< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 3< / td >
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< td class = "org-right" > 9.1< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 4< / td >
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< td class = "org-right" > 3.0< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 5< / td >
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< td class = "org-right" > 1.9< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 6< / td >
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< td class = "org-right" > 7.1< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 7< / td >
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< td class = "org-right" > 18.7< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
< / div >
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< div id = "outline-container-org3da2e64" class = "outline-2" >
< 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 >
The capacitance of the stacks is measure with the < a href = "https://www.gwinstek.com/en-global/products/detail/LCR-800" > LCR-800 Meter< / a > (< a href = "doc/DS_LCR-800_Series_V2_E.pdf" > doc< / a > )
< / p >
< / 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" / >
< / p >
< 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 >
The excitation frequency is set to be 1kHz.
< / 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 >
< colgroup >
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< col class = "org-right" / >
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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 >
< th scope = "col" class = "org-right" > < b > Actuator Stacks< / b > < / th >
< / tr >
< / thead >
< tbody >
< tr >
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< td class = "org-left" > APA 1< / td >
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< td class = "org-right" > 5.10< / td >
< td class = "org-right" > 10.03< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 2< / td >
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< td class = "org-right" > 4.99< / td >
< td class = "org-right" > 9.85< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 3< / td >
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< td class = "org-right" > 1.72< / td >
< td class = "org-right" > 5.18< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 4< / td >
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< td class = "org-right" > 4.94< / td >
< td class = "org-right" > 9.82< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 5< / td >
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< td class = "org-right" > 4.90< / td >
< td class = "org-right" > 9.66< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 6< / td >
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< td class = "org-right" > 4.99< / td >
< td class = "org-right" > 9.91< / td >
< / tr >
< tr >
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< td class = "org-left" > APA 7< / td >
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< td class = "org-right" > 4.85< / td >
< td class = "org-right" > 9.85< / td >
< / tr >
< / tbody >
< / table >
2021-03-01 09:18:16 +01:00
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< div class = "warning" id = "org7282231" >
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< p >
There is clearly a problem with APA300ML number 3
< / p >
< / div >
< / div >
< / div >
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< div id = "outline-container-orgcd8f0b8" class = "outline-2" >
< h2 id = "orgcd8f0b8" > < span class = "section-number-2" > 4< / span > Stiffness measurement< / h2 >
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< div class = "outline-text-2" id = "text-4" >
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< / div >
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< div id = "outline-container-org20509de" class = "outline-3" >
< h3 id = "org20509de" > < span class = "section-number-3" > 4.1< / span > APA test< / h3 >
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< 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 >
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< div id = "outline-container-orgc5606b4" class = "outline-2" >
< h2 id = "orgc5606b4" > < span class = "section-number-2" > 5< / span > Stroke measurement< / h2 >
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< div class = "outline-text-2" id = "text-5" >
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< 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" >
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< 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 >
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< div id = "org0400f6b" class = "figure" >
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< p > < img src = "figs/test_bench_apa_alone.png" alt = "test_bench_apa_alone.png" / >
< / p >
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< p > < span class = "figure-number" > Figure 14: < / span > Schematic of the Test Bench< / p >
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< / div >
< / div >
< / div >
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< 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" >
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< / div >
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< 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" >
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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 -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 >
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< 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" >
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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.
< / 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 >
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< 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" >
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< 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 >
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< div id = "org0fb5c18" class = "figure" >
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< p > < img src = "figs/expected_hysteresis.png" alt = "expected_hysteresis.png" / >
< / p >
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< 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 >
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< / div >
< / div >
< / div >
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< 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" >
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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}
< / div >
< / div >
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< 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" >
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< 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 >
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< 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" >
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< p >
Measure the capacitance of the 3 stacks individually using a precise multi-meter.
< / p >
< / div >
< / div >
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< 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" >
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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 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 >
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< h3 id = "org51816a1" > < span class = "section-number-3" > 7.8< / 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 = "org0b4e69a" > < span class = "section-number-2" > 8< / span > Measurement Results< / h2 >
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< style > . csl-entry { text-indent : -1.5 em ; margin-left : 1.5 em ; } < / style > < h2 class = 'citeproc-org-bib-h2' > Bibliography< / h2 >
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< 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– < / div >
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< p class = "author" > Author: Dehaeze Thomas< / p >
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< p class = "date" > Created: 2021-03-16 mar. 14:30< / p >
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