Add legends to figures
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%%EOF
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<head>
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<!-- 2020-06-14 dim. 12:22 -->
|
<!-- 2020-06-14 dim. 12:31 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<title>Finite Element Model with Simscape</title>
|
<title>Finite Element Model with Simscape</title>
|
||||||
<meta name="generator" content="Org mode" />
|
<meta name="generator" content="Org mode" />
|
||||||
@ -34,20 +34,20 @@
|
|||||||
<h2>Table of Contents</h2>
|
<h2>Table of Contents</h2>
|
||||||
<div id="text-table-of-contents">
|
<div id="text-table-of-contents">
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orge9e8230">1. Amplified Piezoelectric Actuator - 3D elements</a>
|
<li><a href="#org677afcf">1. Amplified Piezoelectric Actuator - 3D elements</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org710a905">1.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
|
<li><a href="#org966ca11">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="#org4f69d52">1.2. Identification of the Dynamics</a></li>
|
||||||
<li><a href="#org11dc96b">1.3. Comparison with Ansys</a></li>
|
<li><a href="#orga73b4fa">1.3. Comparison with Ansys</a></li>
|
||||||
<li><a href="#orgfa4ae15">1.4. Force Sensor</a></li>
|
<li><a href="#org7e1d6fb">1.4. Force Sensor</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
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</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orge9e8230" class="outline-2">
|
<div id="outline-container-org677afcf" class="outline-2">
|
||||||
<h2 id="orge9e8230"><span class="section-number-2">1</span> Amplified Piezoelectric Actuator - 3D elements</h2>
|
<h2 id="org677afcf"><span class="section-number-2">1</span> Amplified Piezoelectric Actuator - 3D elements</h2>
|
||||||
<div class="outline-text-2" id="text-1">
|
<div class="outline-text-2" id="text-1">
|
||||||
<p>
|
<p>
|
||||||
The idea here is to:
|
The idea here is to:
|
||||||
@ -61,8 +61,8 @@ The idea here is to:
|
|||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org710a905" class="outline-3">
|
<div id="outline-container-org966ca11" class="outline-3">
|
||||||
<h3 id="org710a905"><span class="section-number-3">1.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
<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">
|
<div class="outline-text-3" id="text-1-1">
|
||||||
<p>
|
<p>
|
||||||
We first extract the stiffness and mass matrices.
|
We first extract the stiffness and mass matrices.
|
||||||
@ -113,7 +113,7 @@ Then, we extract the coordinates of the interface nodes.
|
|||||||
</table>
|
</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><img src="figs/amplified_piezo_interface_nodes.png" alt="amplified_piezo_interface_nodes.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 1: </span>Interface Nodes for the Amplified Piezo Actuator</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>
|
||||||
|
|
||||||
|
|
||||||
<div id="outline-container-org25c7a89" class="outline-3">
|
<div id="outline-container-org4f69d52" class="outline-3">
|
||||||
<h3 id="org25c7a89"><span class="section-number-3">1.2</span> Identification of the Dynamics</h3>
|
<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">
|
<div class="outline-text-3" id="text-1-2">
|
||||||
<p>
|
<p>
|
||||||
The flexible element is imported using the <code>Reduced Order Flexible Solid</code> simscape block.
|
The flexible element is imported using the <code>Reduced Order Flexible Solid</code> simscape block.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
To model the actuator, an <code>Internal Force</code> block is added between the first and second nodes.
|
To model the actuator, an <code>Internal Force</code> block is added between the nodes 3 and 12.
|
||||||
To model the sensors, a <code>Relative Motion Sensor</code> block is added between the second and the third nodes.
|
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>
|
||||||
|
|
||||||
<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>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
@ -598,7 +598,6 @@ We first set the mass to be zero.
|
|||||||
<p>
|
<p>
|
||||||
The dynamics is identified from the applied force to the measured relative displacement.
|
The dynamics is identified from the applied force to the measured relative displacement.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">%% Name of the Simulink File
|
<pre class="src src-matlab">%% Name of the Simulink File
|
||||||
mdl = 'piezo_amplified_3d';
|
mdl = 'piezo_amplified_3d';
|
||||||
@ -625,9 +624,8 @@ And the dynamics is identified.
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
<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>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">%% Name of the Simulink File
|
<pre class="src src-matlab">%% Name of the Simulink File
|
||||||
mdl = 'piezo_amplified_3d';
|
mdl = 'piezo_amplified_3d';
|
||||||
@ -642,7 +640,7 @@ Ghm = linearize(mdl, io);
|
|||||||
</div>
|
</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><img src="figs/dynamics_act_disp_comp_mass.png" alt="dynamics_act_disp_comp_mass.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 2: </span>Dynamics from \(F\) to \(d\) without a payload and with a 10kg payload</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>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org11dc96b" class="outline-3">
|
<div id="outline-container-orga73b4fa" class="outline-3">
|
||||||
<h3 id="org11dc96b"><span class="section-number-3">1.3</span> Comparison with Ansys</h3>
|
<h3 id="orga73b4fa"><span class="section-number-3">1.3</span> Comparison with Ansys</h3>
|
||||||
<div class="outline-text-3" id="text-1-3">
|
<div class="outline-text-3" id="text-1-3">
|
||||||
<p>
|
<p>
|
||||||
Let’s import the results from an Harmonic response analysis in Ansys.
|
Let’s import the results from an Harmonic response analysis in Ansys.
|
||||||
@ -662,8 +660,12 @@ Gresp10 = readtable('FEA_HarmResponse_10kg.txt');
|
|||||||
</pre>
|
</pre>
|
||||||
</div>
|
</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><img src="figs/dynamics_force_disp_comp_anasys.png" alt="dynamics_force_disp_comp_anasys.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 3: </span>Comparison of the obtained dynamics using Simscape with the harmonic response analysis using Ansys</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>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgfa4ae15" class="outline-3">
|
<div id="outline-container-org7e1d6fb" class="outline-3">
|
||||||
<h3 id="orgfa4ae15"><span class="section-number-3">1.4</span> Force Sensor</h3>
|
<h3 id="org7e1d6fb"><span class="section-number-3">1.4</span> Force Sensor</h3>
|
||||||
<div class="outline-text-3" id="text-1-4">
|
<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">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">m = 0;
|
<pre class="src src-matlab">m = 0;
|
||||||
</pre>
|
</pre>
|
||||||
@ -711,7 +721,7 @@ Gfm = linearize(mdl, io);
|
|||||||
</div>
|
</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><img src="figs/dynamics_force_force_sensor_comp_mass.png" alt="dynamics_force_force_sensor_comp_mass.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 4: </span>Dynamics from \(F\) to \(F_m\) for \(m=0\) and \(m = 10kg\)</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>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Dehaeze Thomas</p>
|
<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>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
</html>
|
</html>
|
||||||
|
|||||||
20
index.org
20
index.org
@ -154,10 +154,10 @@ Using =K=, =M= and =int_xyz=, we can use the =Reduced Order Flexible Solid= sims
|
|||||||
** Identification of the Dynamics
|
** Identification of the Dynamics
|
||||||
The flexible element is imported using the =Reduced Order Flexible Solid= simscape block.
|
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 actuator, an =Internal Force= block is added between the nodes 3 and 12.
|
||||||
To model the sensors, a =Relative Motion Sensor= block is added between the second and the third nodes.
|
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.
|
We first set the mass to be zero.
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
@ -165,7 +165,6 @@ We first set the mass to be zero.
|
|||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
The dynamics is identified from the applied force to the measured relative displacement.
|
The dynamics is identified from the applied force to the measured relative displacement.
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'piezo_amplified_3d';
|
mdl = 'piezo_amplified_3d';
|
||||||
@ -186,7 +185,6 @@ Then, we add 10Kg of mass:
|
|||||||
And the dynamics is identified.
|
And the dynamics is identified.
|
||||||
|
|
||||||
The two identified dynamics are compared in Figure [[fig:dynamics_act_disp_comp_mass]].
|
The two identified dynamics are compared in Figure [[fig:dynamics_act_disp_comp_mass]].
|
||||||
|
|
||||||
#+begin_src matlab
|
#+begin_src matlab
|
||||||
%% Name of the Simulink File
|
%% Name of the Simulink File
|
||||||
mdl = 'piezo_amplified_3d';
|
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');
|
Gresp10 = readtable('FEA_HarmResponse_10kg.txt');
|
||||||
#+end_src
|
#+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
|
#+begin_src matlab :exports none
|
||||||
freqs = logspace(1, 5, 1000);
|
freqs = logspace(1, 5, 1000);
|
||||||
|
|
||||||
@ -285,6 +285,8 @@ Let's import the results from an Harmonic response analysis in Ansys.
|
|||||||
ylim([-390 30]);
|
ylim([-390 30]);
|
||||||
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
xlabel('Frequency [Hz]'); ylabel('Phase [deg]');
|
||||||
hold off;
|
hold off;
|
||||||
|
legend('location', 'southwest');
|
||||||
|
|
||||||
linkaxes([ax1,ax2],'x');
|
linkaxes([ax1,ax2],'x');
|
||||||
xlim([freqs(1), freqs(end)]);
|
xlim([freqs(1), freqs(end)]);
|
||||||
#+end_src
|
#+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]]
|
[[file:figs/dynamics_force_disp_comp_anasys.png]]
|
||||||
|
|
||||||
** Force Sensor
|
** 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
|
#+begin_src matlab
|
||||||
m = 0;
|
m = 0;
|
||||||
#+end_src
|
#+end_src
|
||||||
@ -348,9 +354,9 @@ Let's import the results from an Harmonic response analysis in Ansys.
|
|||||||
ax2 = subplot(2,1,2);
|
ax2 = subplot(2,1,2);
|
||||||
hold on;
|
hold on;
|
||||||
plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gf, freqs, 'Hz')))), '-', ...
|
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')))), '-', ...
|
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');
|
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin');
|
||||||
yticks(-360:90:360);
|
yticks(-360:90:360);
|
||||||
ylim([-390 30]);
|
ylim([-390 30]);
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user