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Add legends to figures

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Thomas Dehaeze
2020-06-14 12:31:03 +02:00
parent ad93d4f106
commit 8711591e17
6 changed files with 126 additions and 108 deletions
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figs/dynamics_force_disp_comp_anasys.pdf
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figs/dynamics_force_force_sensor_comp_mass.pdf
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@@ -3,7 +3,7 @@
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
<head>
<!-- 2020-06-14 dim. 12:22 -->
<!-- 2020-06-14 dim. 12:31 -->
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
<title>Finite Element Model with Simscape</title>
<meta name="generator" content="Org mode" />
@@ -34,20 +34,20 @@
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orge9e8230">1. Amplified Piezoelectric Actuator - 3D elements</a>
<li><a href="#org677afcf">1. Amplified Piezoelectric Actuator - 3D elements</a>
<ul>
<li><a href="#org710a905">1.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
<li><a href="#org25c7a89">1.2. Identification of the Dynamics</a></li>
<li><a href="#org11dc96b">1.3. Comparison with Ansys</a></li>
<li><a href="#orgfa4ae15">1.4. Force Sensor</a></li>
<li><a href="#org966ca11">1.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
<li><a href="#org4f69d52">1.2. Identification of the Dynamics</a></li>
<li><a href="#orga73b4fa">1.3. Comparison with Ansys</a></li>
<li><a href="#org7e1d6fb">1.4. Force Sensor</a></li>
</ul>
</li>
</ul>
</div>
</div>
<div id="outline-container-orge9e8230" class="outline-2">
<h2 id="orge9e8230"><span class="section-number-2">1</span> Amplified Piezoelectric Actuator - 3D elements</h2>
<div id="outline-container-org677afcf" class="outline-2">
<h2 id="org677afcf"><span class="section-number-2">1</span> Amplified Piezoelectric Actuator - 3D elements</h2>
<div class="outline-text-2" id="text-1">
<p>
The idea here is to:
@@ -61,8 +61,8 @@ The idea here is to:
</ul>
</div>
<div id="outline-container-org710a905" class="outline-3">
<h3 id="org710a905"><span class="section-number-3">1.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
<div id="outline-container-org966ca11" class="outline-3">
<h3 id="org966ca11"><span class="section-number-3">1.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
<div class="outline-text-3" id="text-1-1">
<p>
We first extract the stiffness and mass matrices.
@@ -113,7 +113,7 @@ Then, we extract the coordinates of the interface nodes.
</table>
<div id="orgce84261" class="figure">
<div id="orgb472295" class="figure">
<p><img src="figs/amplified_piezo_interface_nodes.png" alt="amplified_piezo_interface_nodes.png" />
</p>
<p><span class="figure-number">Figure 1: </span>Interface Nodes for the Amplified Piezo Actuator</p>
@@ -571,20 +571,20 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can use the <c
</div>
<div id="outline-container-org25c7a89" class="outline-3">
<h3 id="org25c7a89"><span class="section-number-3">1.2</span> Identification of the Dynamics</h3>
<div id="outline-container-org4f69d52" class="outline-3">
<h3 id="org4f69d52"><span class="section-number-3">1.2</span> Identification of the Dynamics</h3>
<div class="outline-text-3" id="text-1-2">
<p>
The flexible element is imported using the <code>Reduced Order Flexible Solid</code> simscape block.
</p>
<p>
To model the actuator, an <code>Internal Force</code> block is added between the first and second nodes.
To model the sensors, a <code>Relative Motion Sensor</code> block is added between the second and the third nodes.
To model the actuator, an <code>Internal Force</code> block is added between the nodes 3 and 12.
A <code>Relative Motion Sensor</code> block is added between the nodes 1 and 2 to measure the displacement and the amplified piezo.
</p>
<p>
Two masses are fixed at the ends of the piezo-electric stack actuator.
One mass is fixed at one end of the piezo-electric stack actuator, the other end is fixed to the world frame.
</p>
<p>
@@ -598,7 +598,6 @@ We first set the mass to be zero.
<p>
The dynamics is identified from the applied force to the measured relative displacement.
</p>
<div class="org-src-container">
<pre class="src src-matlab">%% Name of the Simulink File
mdl = 'piezo_amplified_3d';
@@ -625,9 +624,8 @@ And the dynamics is identified.
</p>
<p>
The two identified dynamics are compared in Figure <a href="#orga2eee2b">2</a>.
The two identified dynamics are compared in Figure <a href="#orgfc13fe0">2</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">%% Name of the Simulink File
mdl = 'piezo_amplified_3d';
@@ -642,7 +640,7 @@ Ghm = linearize(mdl, io);
</div>
<div id="orga2eee2b" class="figure">
<div id="orgfc13fe0" class="figure">
<p><img src="figs/dynamics_act_disp_comp_mass.png" alt="dynamics_act_disp_comp_mass.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Dynamics from \(F\) to \(d\) without a payload and with a 10kg payload</p>
@@ -650,8 +648,8 @@ Ghm = linearize(mdl, io);
</div>
</div>
<div id="outline-container-org11dc96b" class="outline-3">
<h3 id="org11dc96b"><span class="section-number-3">1.3</span> Comparison with Ansys</h3>
<div id="outline-container-orga73b4fa" class="outline-3">
<h3 id="orga73b4fa"><span class="section-number-3">1.3</span> Comparison with Ansys</h3>
<div class="outline-text-3" id="text-1-3">
<p>
Let&rsquo;s import the results from an Harmonic response analysis in Ansys.
@@ -662,8 +660,12 @@ Gresp10 = readtable('FEA_HarmResponse_10kg.txt');
</pre>
</div>
<p>
The obtained dynamics from the Simscape model and from the Ansys analysis are compare in Figure <a href="#org587f215">3</a>.
</p>
<div id="orgee19caf" class="figure">
<div id="org587f215" class="figure">
<p><img src="figs/dynamics_force_disp_comp_anasys.png" alt="dynamics_force_disp_comp_anasys.png" />
</p>
<p><span class="figure-number">Figure 3: </span>Comparison of the obtained dynamics using Simscape with the harmonic response analysis using Ansys</p>
@@ -671,9 +673,17 @@ Gresp10 = readtable('FEA_HarmResponse_10kg.txt');
</div>
</div>
<div id="outline-container-orgfa4ae15" class="outline-3">
<h3 id="orgfa4ae15"><span class="section-number-3">1.4</span> Force Sensor</h3>
<div id="outline-container-org7e1d6fb" class="outline-3">
<h3 id="org7e1d6fb"><span class="section-number-3">1.4</span> Force Sensor</h3>
<div class="outline-text-3" id="text-1-4">
<p>
The dynamics is identified from internal forces applied between nodes 3 and 11 to the relative displacement of nodes 11 and 13.
</p>
<p>
The obtained dynamics is shown in Figure <a href="#org2f215c1">4</a>.
</p>
<div class="org-src-container">
<pre class="src src-matlab">m = 0;
</pre>
@@ -711,7 +721,7 @@ Gfm = linearize(mdl, io);
</div>
<div id="orgcfb5aa6" class="figure">
<div id="org2f215c1" class="figure">
<p><img src="figs/dynamics_force_force_sensor_comp_mass.png" alt="dynamics_force_force_sensor_comp_mass.png" />
</p>
<p><span class="figure-number">Figure 4: </span>Dynamics from \(F\) to \(F_m\) for \(m=0\) and \(m = 10kg\)</p>
@@ -722,7 +732,7 @@ Gfm = linearize(mdl, io);
</div>
<div id="postamble" class="status">
<p class="author">Author: Dehaeze Thomas</p>
<p class="date">Created: 2020-06-14 dim. 12:22</p>
<p class="date">Created: 2020-06-14 dim. 12:31</p>
</div>
</body>
</html>

20
index.org
View File

@@ -154,10 +154,10 @@ Using =K=, =M= and =int_xyz=, we can use the =Reduced Order Flexible Solid= sims
** Identification of the Dynamics
The flexible element is imported using the =Reduced Order Flexible Solid= simscape block.
To model the actuator, an =Internal Force= block is added between the first and second nodes.
To model the sensors, a =Relative Motion Sensor= block is added between the second and the third nodes.
To model the actuator, an =Internal Force= block is added between the nodes 3 and 12.
A =Relative Motion Sensor= block is added between the nodes 1 and 2 to measure the displacement and the amplified piezo.
Two masses are fixed at the ends of the piezo-electric stack actuator.
One mass is fixed at one end of the piezo-electric stack actuator, the other end is fixed to the world frame.
We first set the mass to be zero.
#+begin_src matlab
@@ -165,7 +165,6 @@ We first set the mass to be zero.
#+end_src
The dynamics is identified from the applied force to the measured relative displacement.
#+begin_src matlab
%% Name of the Simulink File
mdl = 'piezo_amplified_3d';
@@ -186,7 +185,6 @@ Then, we add 10Kg of mass:
And the dynamics is identified.
The two identified dynamics are compared in Figure [[fig:dynamics_act_disp_comp_mass]].
#+begin_src matlab
%% Name of the Simulink File
mdl = 'piezo_amplified_3d';
@@ -245,6 +243,8 @@ Let's import the results from an Harmonic response analysis in Ansys.
Gresp10 = readtable('FEA_HarmResponse_10kg.txt');
#+end_src
The obtained dynamics from the Simscape model and from the Ansys analysis are compare in Figure [[fig:dynamics_force_disp_comp_anasys]].
#+begin_src matlab :exports none
freqs = logspace(1, 5, 1000);
@@ -285,6 +285,8 @@ Let's import the results from an Harmonic response analysis in Ansys.
ylim([-390 30]);
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
hold off;
legend('location', 'southwest');
linkaxes([ax1,ax2],'x');
xlim([freqs(1), freqs(end)]);
#+end_src
@@ -299,6 +301,10 @@ Let's import the results from an Harmonic response analysis in Ansys.
[[file:figs/dynamics_force_disp_comp_anasys.png]]
** Force Sensor
The dynamics is identified from internal forces applied between nodes 3 and 11 to the relative displacement of nodes 11 and 13.
The obtained dynamics is shown in Figure [[fig:dynamics_force_force_sensor_comp_mass]].
#+begin_src matlab
m = 0;
#+end_src
@@ -348,9 +354,9 @@ Let's import the results from an Harmonic response analysis in Ansys.
ax2 = subplot(2,1,2);
hold on;
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gf, freqs, 'Hz')))), '-', ...
'DisplayName', '$m = 1kg$');
'DisplayName', '$m = 0kg$');
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gfm, freqs, 'Hz')))), '-', ...
'DisplayName', '$m = 1kg$');
'DisplayName', '$m = 10kg$');
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
yticks(-360:90:360);
ylim([-390 30]);