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<title>Finite Element Model with Simscape</title>
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<title>NASS - Finite Element Models with Simscape</title>
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<meta name="generator" content="Org mode" />
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<meta name="author" content="Dehaeze Thomas" />
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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">Finite Element Model with Simscape</h1>
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<h1 class="title">NASS - Finite Element Models with Simscape</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="#org18d2db8">1. APA300ML</a>
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<li><a href="#orgb231366">1. APA300ML</a>
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<ul>
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<li><a href="#org5c45df4">1.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#orga9811cf">1.2. Piezoelectric parameters</a></li>
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<li><a href="#orgf60bf13">1.3. Simscape Model</a></li>
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<li><a href="#org7589ca6">1.4. Identification of the APA Characteristics</a>
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<li><a href="#orga4e3f9c">1.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#org4f3db59">1.2. Piezoelectric parameters</a></li>
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<li><a href="#org364e184">1.3. Simscape Model</a></li>
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<li><a href="#org8bf66af">1.4. Identification of the APA Characteristics</a>
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<ul>
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<li><a href="#org839ecc0">1.4.1. Stiffness</a></li>
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<li><a href="#org9b9cedd">1.4.2. Resonance Frequency</a></li>
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<li><a href="#org87cbe72">1.4.3. Amplification factor</a></li>
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<li><a href="#org0071048">1.4.4. Stroke</a></li>
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<li><a href="#orgc2b9be5">1.4.1. Stiffness</a></li>
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<li><a href="#orgd55eeff">1.4.2. Resonance Frequency</a></li>
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<li><a href="#org59f7b55">1.4.3. Amplification factor</a></li>
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<li><a href="#orga970d47">1.4.4. Stroke</a></li>
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</ul>
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</li>
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<li><a href="#org4fdb600">1.5. Identification of the Dynamics from actuator to replace displacement</a></li>
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<li><a href="#orga2f4fd6">1.6. Identification of the Dynamics from actuator to force sensor</a></li>
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<li><a href="#org8ece2ce">1.7. Identification for a simpler model</a></li>
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<li><a href="#org43ae9e5">1.8. Integral Force Feedback</a></li>
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<li><a href="#org875f674">1.5. Identification of the Dynamics from actuator to replace displacement</a></li>
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<li><a href="#org926378e">1.6. Identification of the Dynamics from actuator to force sensor</a></li>
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<li><a href="#org0b533cc">1.7. Identification for a simpler model</a></li>
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<li><a href="#orgd7e3154">1.8. Integral Force Feedback</a></li>
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</ul>
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</li>
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<li><a href="#orgc203c93">2. First Flexible Joint Geometry</a>
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<li><a href="#orge12e432">2. First Flexible Joint Geometry</a>
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<ul>
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<li><a href="#orga48c65c">2.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#org5de18c6">2.2. Identification of the parameters using Simscape and looking at the Stiffness Matrix</a></li>
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<li><a href="#orgb2d0259">2.3. Simpler Model</a></li>
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<li><a href="#org91559c3">2.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#org0c0ae39">2.2. Identification of the parameters using Simscape and looking at the Stiffness Matrix</a></li>
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<li><a href="#orgb1eeb49">2.3. Simpler Model</a></li>
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</ul>
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</li>
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<li><a href="#org4dadb53">3. Optimized Flexible Joint</a>
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<li><a href="#org6fa0f81">3. Optimized Flexible Joint</a>
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<ul>
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<li><a href="#orgb1d1e31">3.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#orgc7107db">3.2. Identification of the parameters using Simscape</a></li>
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<li><a href="#org96d2775">3.3. Simpler Model</a></li>
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<li><a href="#org2916e5d">3.4. Comparison with a stiffer Flexible Joint</a></li>
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<li><a href="#orgadfaeb7">3.1. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#org1a74e71">3.2. Identification of the parameters using Simscape</a></li>
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<li><a href="#org3ba1fee">3.3. Simpler Model</a></li>
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<li><a href="#orgec51432">3.4. Comparison with a stiffer Flexible Joint</a></li>
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</ul>
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</li>
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<li><a href="#org79ad15f">4. Complete Strut with Encoder</a>
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<li><a href="#org91975b5">4. Complete Strut with Encoder</a>
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<ul>
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<li><a href="#org26e8494">4.1. Introduction</a></li>
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<li><a href="#orgd702a5f">4.2. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#org42c2461">4.3. Piezoelectric parameters</a></li>
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<li><a href="#orga5ba630">4.4. Identification of the Dynamics</a></li>
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<li><a href="#orgd829824">4.1. Introduction</a></li>
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<li><a href="#orgd7f754c">4.2. Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</a></li>
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<li><a href="#org5019141">4.3. Piezoelectric parameters</a></li>
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<li><a href="#org72bb8f1">4.4. Identification of the Dynamics</a></li>
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</ul>
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</li>
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</ul>
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@ -80,23 +80,26 @@
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In this document, Finite Element Models (FEM) of parts of the Nano-Hexapod are developed and integrated into Simscape for dynamical analysis.
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</p>
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<p>
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It is divided in the following sections:
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</p>
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<ul class="org-ul">
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<li>Section <a href="#org6804357">1</a>:
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<li>Section <a href="#org31bfe65">1</a>:
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A super-element of the Amplified Piezoelectric Actuator APA300ML used for the NASS is exported using Ansys and imported in Simscape.
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The static and dynamical properties of the APA300ML are then estimated using the Simscape model.</li>
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<li>Section <a href="#orgb1abf80">2</a>:
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<li>Section <a href="#orga0ece29">2</a>:
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A first geometry of a Flexible joint is modelled and its characteristics are identified from the Stiffness matrix as well as from the Simscape model.</li>
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<li>Section <a href="#org146537a">3</a>:
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<li>Section <a href="#org513c349">3</a>:
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An optimized flexible joint is developed for the Nano-Hexapod and is then imported in a Simscape model.</li>
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<li>Section <a href="#orgc4b9146">4</a>:
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A super element of a complete strut is exported.</li>
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<li>Section <a href="#orgcff61d6">4</a>:
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A super element of a complete strut is studied.</li>
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</ul>
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<div id="outline-container-org18d2db8" class="outline-2">
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<h2 id="org18d2db8"><span class="section-number-2">1</span> APA300ML</h2>
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<div id="outline-container-orgb231366" class="outline-2">
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<h2 id="orgb231366"><span class="section-number-2">1</span> APA300ML</h2>
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<div class="outline-text-2" id="text-1">
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<p>
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<a id="org6804357"></a>
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<a id="org31bfe65"></a>
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</p>
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<p>
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In this section, the Amplified Piezoelectric Actuator APA300ML (<a href="doc/APA300ML.pdf">doc</a>) is modeled using a Finite Element Software.
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@ -104,19 +107,19 @@ Then a <i>super element</i> is exported and imported in Simscape where its dynam
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</p>
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<p>
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A 3D view of the Amplified Piezoelectric Actuator (APA300ML) is shown in Figure <a href="#org7a29cfe">1</a>.
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A 3D view of the Amplified Piezoelectric Actuator (APA300ML) is shown in Figure <a href="#orgfaefa60">1</a>.
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The remote point used are also shown in this figure.
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</p>
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<div id="org7a29cfe" class="figure">
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<div id="orgfaefa60" class="figure">
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<p><img src="figs/apa300ml_ansys.jpg" alt="apa300ml_ansys.jpg" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Ansys FEM of the APA300ML</p>
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</div>
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</div>
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<div id="outline-container-org5c45df4" class="outline-3">
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<h3 id="org5c45df4"><span class="section-number-3">1.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
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<div id="outline-container-orga4e3f9c" class="outline-3">
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<h3 id="orga4e3f9c"><span class="section-number-3">1.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
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<div class="outline-text-3" id="text-1-1">
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<p>
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We first extract the stiffness and mass matrices.
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@ -570,8 +573,8 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can now use th
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</div>
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</div>
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<div id="outline-container-orga9811cf" class="outline-3">
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<h3 id="orga9811cf"><span class="section-number-3">1.2</span> Piezoelectric parameters</h3>
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<div id="outline-container-org4f3db59" class="outline-3">
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<h3 id="org4f3db59"><span class="section-number-3">1.2</span> Piezoelectric parameters</h3>
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<div class="outline-text-3" id="text-1-2">
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<p>
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In order to make the conversion from applied voltage to generated force or from the strain to the generated voltage, we need to defined some parameters corresponding to the piezoelectric material:
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@ -590,7 +593,7 @@ C = 5e<span class="org-type">-</span>6; <span class="org-comment">% Stack c
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The ratio of the developed force to applied voltage is:
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</p>
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\begin{equation}
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\label{org0bf4f86}
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\label{org26cf049}
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F_a = g_a V_a, \quad g_a = d_{33} n k_a
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\end{equation}
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<p>
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@ -621,7 +624,7 @@ If we take the numerical values, we obtain:
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From (<a href="#citeproc_bib_item_1">Fleming and Leang 2014</a>) (page 123), the relation between relative displacement of the sensor stack and generated voltage is:
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</p>
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\begin{equation}
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\label{org0478126}
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\label{orgd71c6e4}
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V_s = \frac{d_{33}}{\epsilon^T s^D n} \Delta h
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\end{equation}
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<p>
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@ -650,8 +653,8 @@ If we take the numerical values, we obtain:
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</div>
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</div>
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<div id="outline-container-orgf60bf13" class="outline-3">
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<h3 id="orgf60bf13"><span class="section-number-3">1.3</span> Simscape Model</h3>
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<div id="outline-container-org364e184" class="outline-3">
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<h3 id="org364e184"><span class="section-number-3">1.3</span> Simscape Model</h3>
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<div class="outline-text-3" id="text-1-3">
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<p>
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The flexible element is imported using the <code>Reduced Order Flexible Solid</code> simscape block.
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@ -666,7 +669,7 @@ Let’s say we use two stacks as a force sensor and one stack as an actuator
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</ul>
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<p>
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The interface nodes are shown in Figure <a href="#org7a29cfe">1</a>.
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The interface nodes are shown in Figure <a href="#orgfaefa60">1</a>.
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</p>
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<p>
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@ -675,12 +678,12 @@ One mass is fixed at one end of the piezo-electric stack actuator (remove point
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</div>
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</div>
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<div id="outline-container-org7589ca6" class="outline-3">
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<h3 id="org7589ca6"><span class="section-number-3">1.4</span> Identification of the APA Characteristics</h3>
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<div id="outline-container-org8bf66af" class="outline-3">
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<h3 id="org8bf66af"><span class="section-number-3">1.4</span> Identification of the APA Characteristics</h3>
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<div class="outline-text-3" id="text-1-4">
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</div>
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<div id="outline-container-org839ecc0" class="outline-4">
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<h4 id="org839ecc0"><span class="section-number-4">1.4.1</span> Stiffness</h4>
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<div id="outline-container-orgc2b9be5" class="outline-4">
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<h4 id="orgc2b9be5"><span class="section-number-4">1.4.1</span> Stiffness</h4>
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<div class="outline-text-4" id="text-1-4-1">
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<p>
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The transfer function from vertical external force to the relative vertical displacement is identified.
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@ -705,16 +708,16 @@ The specified stiffness in the datasheet is \(k = 1.8\, [N/\mu m]\).
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</div>
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</div>
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<div id="outline-container-org9b9cedd" class="outline-4">
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<h4 id="org9b9cedd"><span class="section-number-4">1.4.2</span> Resonance Frequency</h4>
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<div id="outline-container-orgd55eeff" class="outline-4">
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<h4 id="orgd55eeff"><span class="section-number-4">1.4.2</span> Resonance Frequency</h4>
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<div class="outline-text-4" id="text-1-4-2">
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<p>
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The resonance frequency is specified to be between 650Hz and 840Hz.
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This is also the case for the FEM model (Figure <a href="#org2662235">2</a>).
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This is also the case for the FEM model (Figure <a href="#org5a0e1d6">2</a>).
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</p>
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<div id="org2662235" class="figure">
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<div id="org5a0e1d6" class="figure">
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<p><img src="figs/apa300ml_resonance.png" alt="apa300ml_resonance.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>First resonance is around 800Hz</p>
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@ -722,8 +725,8 @@ This is also the case for the FEM model (Figure <a href="#org2662235">2</a>).
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</div>
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</div>
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<div id="outline-container-org87cbe72" class="outline-4">
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<h4 id="org87cbe72"><span class="section-number-4">1.4.3</span> Amplification factor</h4>
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<div id="outline-container-org59f7b55" class="outline-4">
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<h4 id="org59f7b55"><span class="section-number-4">1.4.3</span> Amplification factor</h4>
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<div class="outline-text-4" id="text-1-4-3">
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<p>
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The amplification factor is the ratio of the vertical displacement to the stack displacement.
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@ -756,8 +759,8 @@ This is actually correct and approximately corresponds to the ratio of the piezo
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</div>
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</div>
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<div id="outline-container-org0071048" class="outline-4">
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<h4 id="org0071048"><span class="section-number-4">1.4.4</span> Stroke</h4>
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<div id="outline-container-orga970d47" class="outline-4">
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<h4 id="orga970d47"><span class="section-number-4">1.4.4</span> Stroke</h4>
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<div class="outline-text-4" id="text-1-4-4">
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<p>
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||||
Estimation of the actuator stroke:
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||||
@ -788,8 +791,8 @@ This is exactly the specified stroke in the data-sheet.
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||||
</div>
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||||
</div>
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||||
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<div id="outline-container-org4fdb600" class="outline-3">
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<h3 id="org4fdb600"><span class="section-number-3">1.5</span> Identification of the Dynamics from actuator to replace displacement</h3>
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||||
<div id="outline-container-org875f674" class="outline-3">
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||||
<h3 id="org875f674"><span class="section-number-3">1.5</span> Identification of the Dynamics from actuator to replace displacement</h3>
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||||
<div class="outline-text-3" id="text-1-5">
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||||
<p>
|
||||
We first set the mass to be approximately zero.
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@ -802,17 +805,17 @@ The same dynamics is identified for a payload mass of 10Kg.
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</div>
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<div id="orgb9beb05" class="figure">
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||||
<div id="org0bf96a7" class="figure">
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||||
<p><img src="figs/apa300ml_plant_dynamics.png" alt="apa300ml_plant_dynamics.png" />
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||||
</p>
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||||
<p><span class="figure-number">Figure 3: </span>Transfer function from forces applied by the stack to the axial displacement of the APA</p>
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||||
</div>
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<p>
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||||
The root locus corresponding to Direct Velocity Feedback with a mass of 10kg is shown in Figure <a href="#orgcdc7a42">4</a>.
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||||
The root locus corresponding to Direct Velocity Feedback with a mass of 10kg is shown in Figure <a href="#orgf443cba">4</a>.
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</p>
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||||
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||||
<div id="orgcdc7a42" class="figure">
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||||
<div id="orgf443cba" class="figure">
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||||
<p><img src="figs/apa300ml_dvf_root_locus.png" alt="apa300ml_dvf_root_locus.png" />
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</p>
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<p><span class="figure-number">Figure 4: </span>Root Locus for Direct Velocity Feedback</p>
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||||
@ -820,28 +823,28 @@ The root locus corresponding to Direct Velocity Feedback with a mass of 10kg is
|
||||
</div>
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||||
</div>
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||||
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||||
<div id="outline-container-orga2f4fd6" class="outline-3">
|
||||
<h3 id="orga2f4fd6"><span class="section-number-3">1.6</span> Identification of the Dynamics from actuator to force sensor</h3>
|
||||
<div id="outline-container-org926378e" class="outline-3">
|
||||
<h3 id="org926378e"><span class="section-number-3">1.6</span> Identification of the Dynamics from actuator to force sensor</h3>
|
||||
<div class="outline-text-3" id="text-1-6">
|
||||
<p>
|
||||
Let’s use 2 stacks as a force sensor and 1 stack as force actuator.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The transfer function from actuator voltage to sensor voltage is identified and shown in Figure <a href="#org838a459">5</a>.
|
||||
The transfer function from actuator voltage to sensor voltage is identified and shown in Figure <a href="#org0571899">5</a>.
|
||||
</p>
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||||
|
||||
<div id="org838a459" class="figure">
|
||||
<div id="org0571899" class="figure">
|
||||
<p><img src="figs/apa300ml_iff_plant.png" alt="apa300ml_iff_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 5: </span>Transfer function from actuator to force sensor</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
For root locus corresponding to IFF is shown in Figure <a href="#org6a92e46">6</a>.
|
||||
For root locus corresponding to IFF is shown in Figure <a href="#org4c7369c">6</a>.
|
||||
</p>
|
||||
|
||||
<div id="org6a92e46" class="figure">
|
||||
<div id="org4c7369c" class="figure">
|
||||
<p><img src="figs/apa300ml_iff_root_locus.png" alt="apa300ml_iff_root_locus.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 6: </span>Root Locus for IFF</p>
|
||||
@ -849,8 +852,8 @@ For root locus corresponding to IFF is shown in Figure <a href="#org6a92e46">6</
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org8ece2ce" class="outline-3">
|
||||
<h3 id="org8ece2ce"><span class="section-number-3">1.7</span> Identification for a simpler model</h3>
|
||||
<div id="outline-container-org0b533cc" class="outline-3">
|
||||
<h3 id="org0b533cc"><span class="section-number-3">1.7</span> Identification for a simpler model</h3>
|
||||
<div class="outline-text-3" id="text-1-7">
|
||||
<p>
|
||||
The goal in this section is to identify the parameters of a simple APA model from the FEM.
|
||||
@ -862,12 +865,12 @@ The presented model is based on (<a href="#citeproc_bib_item_2">Souleille et al.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The model represents the Amplified Piezo Actuator (APA) from Cedrat-Technologies (Figure <a href="#org6551a86">7</a>).
|
||||
The model represents the Amplified Piezo Actuator (APA) from Cedrat-Technologies (Figure <a href="#orgdda4959">7</a>).
|
||||
The parameters are shown in the table below.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org6551a86" class="figure">
|
||||
<div id="orgdda4959" class="figure">
|
||||
<p><img src="./figs/souleille18_model_piezo.png" alt="souleille18_model_piezo.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 7: </span>Picture of an APA100M from Cedrat Technologies. Simplified model of a one DoF payload mounted on such isolator</p>
|
||||
@ -1016,11 +1019,11 @@ And the DC gain is adjusted for the force sensor:
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The dynamics of the FEM model and the simpler model are compared in Figure <a href="#orgbd0f182">8</a>.
|
||||
The dynamics of the FEM model and the simpler model are compared in Figure <a href="#org25d35cd">8</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgbd0f182" class="figure">
|
||||
<div id="org25d35cd" class="figure">
|
||||
<p><img src="figs/apa300ml_comp_simpler_model.png" alt="apa300ml_comp_simpler_model.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 8: </span>Comparison of the Dynamics between the FEM model and the simplified one</p>
|
||||
@ -1031,10 +1034,10 @@ The simplified model has also been implemented in Simscape.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The dynamics of the Simscape simplified model is identified and compared with the FEM one in Figure <a href="#orgc032d03">9</a>.
|
||||
The dynamics of the Simscape simplified model is identified and compared with the FEM one in Figure <a href="#org3ca18e2">9</a>.
|
||||
</p>
|
||||
|
||||
<div id="orgc032d03" class="figure">
|
||||
<div id="org3ca18e2" class="figure">
|
||||
<p><img src="figs/apa300ml_comp_simpler_simscape.png" alt="apa300ml_comp_simpler_simscape.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 9: </span>Comparison of the Dynamics between the FEM model and the simplified simscape model</p>
|
||||
@ -1042,8 +1045,8 @@ The dynamics of the Simscape simplified model is identified and compared with th
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org43ae9e5" class="outline-3">
|
||||
<h3 id="org43ae9e5"><span class="section-number-3">1.8</span> Integral Force Feedback</h3>
|
||||
<div id="outline-container-orgd7e3154" class="outline-3">
|
||||
<h3 id="orgd7e3154"><span class="section-number-3">1.8</span> Integral Force Feedback</h3>
|
||||
<div class="outline-text-3" id="text-1-8">
|
||||
<p>
|
||||
In this section, Integral Force Feedback control architecture is applied on the APA300ML.
|
||||
@ -1059,18 +1062,18 @@ The payload mass is set to 10kg.
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The obtained dynamics is shown in Figure <a href="#orga6e0dfc">10</a>.
|
||||
The obtained dynamics is shown in Figure <a href="#org41e4933">10</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orga6e0dfc" class="figure">
|
||||
<div id="org41e4933" class="figure">
|
||||
<p><img src="figs/piezo_amplified_iff_plant.png" alt="piezo_amplified_iff_plant.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 10: </span>IFF Plant</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
The controller is defined below and the loop gain is shown in Figure <a href="#orgeb0376d">11</a>.
|
||||
The controller is defined below and the loop gain is shown in Figure <a href="#org8791595">11</a>.
|
||||
</p>
|
||||
<div class="org-src-container">
|
||||
<pre class="src src-matlab">Kiff = <span class="org-type">-</span>1e3<span class="org-type">/</span>s;
|
||||
@ -1078,29 +1081,29 @@ The controller is defined below and the loop gain is shown in Figure <a href="#o
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orgeb0376d" class="figure">
|
||||
<div id="org8791595" class="figure">
|
||||
<p><img src="figs/piezo_amplified_iff_loop_gain.png" alt="piezo_amplified_iff_loop_gain.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 11: </span>IFF Loop Gain</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
Now the closed-loop system is identified again and compare with the open loop system in Figure <a href="#org51f452b">12</a>.
|
||||
Now the closed-loop system is identified again and compare with the open loop system in Figure <a href="#org9002d80">12</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
It is the expected behavior as shown in the Figure <a href="#orged35295">13</a> (from (<a href="#citeproc_bib_item_2">Souleille et al. 2018</a>)).
|
||||
It is the expected behavior as shown in the Figure <a href="#orgf085b71">13</a> (from (<a href="#citeproc_bib_item_2">Souleille et al. 2018</a>)).
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org51f452b" class="figure">
|
||||
<div id="org9002d80" class="figure">
|
||||
<p><img src="figs/piezo_amplified_iff_comp.png" alt="piezo_amplified_iff_comp.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 12: </span>OL and CL transfer functions</p>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="orged35295" class="figure">
|
||||
<div id="orgf085b71" class="figure">
|
||||
<p><img src="figs/souleille18_results.png" alt="souleille18_results.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 13: </span>Results obtained in <a class='org-ref-reference' href="#souleille18_concep_activ_mount_space_applic">souleille18_concep_activ_mount_space_applic</a></p>
|
||||
@ -1110,14 +1113,14 @@ It is the expected behavior as shown in the Figure <a href="#orged35295">13</a>
|
||||
</div>
|
||||
|
||||
|
||||
<div id="outline-container-orgc203c93" class="outline-2">
|
||||
<h2 id="orgc203c93"><span class="section-number-2">2</span> First Flexible Joint Geometry</h2>
|
||||
<div id="outline-container-orge12e432" class="outline-2">
|
||||
<h2 id="orge12e432"><span class="section-number-2">2</span> First Flexible Joint Geometry</h2>
|
||||
<div class="outline-text-2" id="text-2">
|
||||
<p>
|
||||
<a id="orgb1abf80"></a>
|
||||
<a id="orga0ece29"></a>
|
||||
</p>
|
||||
<p>
|
||||
The studied flexor is shown in Figure <a href="#orgd3ad3b1">14</a>.
|
||||
The studied flexor is shown in Figure <a href="#orgcd75ab8">14</a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
@ -1130,14 +1133,14 @@ A simplified model of the flexor is then developped.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orgd3ad3b1" class="figure">
|
||||
<div id="orgcd75ab8" class="figure">
|
||||
<p><img src="figs/flexor_id16_screenshot.png" alt="flexor_id16_screenshot.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 14: </span>Flexor studied</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orga48c65c" class="outline-3">
|
||||
<h3 id="orga48c65c"><span class="section-number-3">2.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div id="outline-container-org91559c3" class="outline-3">
|
||||
<h3 id="org91559c3"><span class="section-number-3">2.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div class="outline-text-3" id="text-2-1">
|
||||
<p>
|
||||
We first extract the stiffness and mass matrices.
|
||||
@ -1549,8 +1552,8 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can use the <c
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org5de18c6" class="outline-3">
|
||||
<h3 id="org5de18c6"><span class="section-number-3">2.2</span> Identification of the parameters using Simscape and looking at the Stiffness Matrix</h3>
|
||||
<div id="outline-container-org0c0ae39" class="outline-3">
|
||||
<h3 id="org0c0ae39"><span class="section-number-3">2.2</span> Identification of the parameters using Simscape and looking at the Stiffness Matrix</h3>
|
||||
<div class="outline-text-3" id="text-2-2">
|
||||
<p>
|
||||
The flexor is now imported into Simscape and its parameters are estimated using an identification.
|
||||
@ -1607,15 +1610,15 @@ And we find the same parameters as the one estimated from the Stiffness matrix.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgb2d0259" class="outline-3">
|
||||
<h3 id="orgb2d0259"><span class="section-number-3">2.3</span> Simpler Model</h3>
|
||||
<div id="outline-container-orgb1eeb49" class="outline-3">
|
||||
<h3 id="orgb1eeb49"><span class="section-number-3">2.3</span> Simpler Model</h3>
|
||||
<div class="outline-text-3" id="text-2-3">
|
||||
<p>
|
||||
Let’s now model the flexible joint with a “perfect” Bushing joint as shown in Figure <a href="#org8f309d8">15</a>.
|
||||
Let’s now model the flexible joint with a “perfect” Bushing joint as shown in Figure <a href="#orgc8a4dd1">15</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org8f309d8" class="figure">
|
||||
<div id="orgc8a4dd1" class="figure">
|
||||
<p><img src="figs/flexible_joint_simscape.png" alt="flexible_joint_simscape.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 15: </span>Bushing Joint used to model the flexible joint</p>
|
||||
@ -1640,7 +1643,7 @@ The two obtained dynamics are compared in Figure
|
||||
</p>
|
||||
|
||||
|
||||
<div id="orge65cd1b" class="figure">
|
||||
<div id="org168dbda" class="figure">
|
||||
<p><img src="figs/flexor_ID16_compare_bushing_joint.png" alt="flexor_ID16_compare_bushing_joint.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 16: </span>Comparison of the Joint compliance between the FEM model and the simpler model</p>
|
||||
@ -1649,29 +1652,29 @@ The two obtained dynamics are compared in Figure
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org4dadb53" class="outline-2">
|
||||
<h2 id="org4dadb53"><span class="section-number-2">3</span> Optimized Flexible Joint</h2>
|
||||
<div id="outline-container-org6fa0f81" class="outline-2">
|
||||
<h2 id="org6fa0f81"><span class="section-number-2">3</span> Optimized Flexible Joint</h2>
|
||||
<div class="outline-text-2" id="text-3">
|
||||
<p>
|
||||
<a id="org146537a"></a>
|
||||
<a id="org513c349"></a>
|
||||
</p>
|
||||
<p>
|
||||
The joint geometry has been optimized using Ansys to have lower bending stiffness while keeping a large axial stiffness.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The obtained geometry is shown in Figure <a href="#org89612a5">17</a>.
|
||||
The obtained geometry is shown in Figure <a href="#orge1d8231">17</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org89612a5" class="figure">
|
||||
<div id="orge1d8231" class="figure">
|
||||
<p><img src="figs/flexor_025_MDoF.jpg" alt="flexor_025_MDoF.jpg" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 17: </span>Flexor studied</p>
|
||||
</div>
|
||||
</div>
|
||||
<div id="outline-container-orgb1d1e31" class="outline-3">
|
||||
<h3 id="orgb1d1e31"><span class="section-number-3">3.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div id="outline-container-orgadfaeb7" class="outline-3">
|
||||
<h3 id="orgadfaeb7"><span class="section-number-3">3.1</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div class="outline-text-3" id="text-3-1">
|
||||
<p>
|
||||
We first extract the stiffness and mass matrices.
|
||||
@ -2085,8 +2088,8 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can use the <c
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgc7107db" class="outline-3">
|
||||
<h3 id="orgc7107db"><span class="section-number-3">3.2</span> Identification of the parameters using Simscape</h3>
|
||||
<div id="outline-container-org1a74e71" class="outline-3">
|
||||
<h3 id="org1a74e71"><span class="section-number-3">3.2</span> Identification of the parameters using Simscape</h3>
|
||||
<div class="outline-text-3" id="text-3-2">
|
||||
<p>
|
||||
The flexor is now imported into Simscape and its parameters are estimated using an identification.
|
||||
@ -2143,15 +2146,15 @@ And we find the same parameters as the one estimated from the Stiffness matrix.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org96d2775" class="outline-3">
|
||||
<h3 id="org96d2775"><span class="section-number-3">3.3</span> Simpler Model</h3>
|
||||
<div id="outline-container-org3ba1fee" class="outline-3">
|
||||
<h3 id="org3ba1fee"><span class="section-number-3">3.3</span> Simpler Model</h3>
|
||||
<div class="outline-text-3" id="text-3-3">
|
||||
<p>
|
||||
Let’s now model the flexible joint with a “perfect” Bushing joint as shown in Figure <a href="#org8f309d8">15</a>.
|
||||
Let’s now model the flexible joint with a “perfect” Bushing joint as shown in Figure <a href="#orgc8a4dd1">15</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org9fc5457" class="figure">
|
||||
<div id="org1f2487e" class="figure">
|
||||
<p><img src="figs/flexible_joint_simscape.png" alt="flexible_joint_simscape.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 18: </span>Bushing Joint used to model the flexible joint</p>
|
||||
@ -2176,7 +2179,7 @@ The two obtained dynamics are compared in Figure
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org3f0ca2d" class="figure">
|
||||
<div id="org520525f" class="figure">
|
||||
<p><img src="figs/flexor_ID16_compare_bushing_joint.png" alt="flexor_ID16_compare_bushing_joint.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 19: </span>Comparison of the Joint compliance between the FEM model and the simpler model</p>
|
||||
@ -2184,8 +2187,8 @@ The two obtained dynamics are compared in Figure
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org2916e5d" class="outline-3">
|
||||
<h3 id="org2916e5d"><span class="section-number-3">3.4</span> Comparison with a stiffer Flexible Joint</h3>
|
||||
<div id="outline-container-orgec51432" class="outline-3">
|
||||
<h3 id="orgec51432"><span class="section-number-3">3.4</span> Comparison with a stiffer Flexible Joint</h3>
|
||||
<div class="outline-text-3" id="text-3-4">
|
||||
<p>
|
||||
The stiffness matrix with the flexible joint with a “hinge” size of 0.50mm is loaded.
|
||||
@ -2252,37 +2255,37 @@ Its parameters are compared with the Flexible Joint with a size of 0.25mm in the
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org79ad15f" class="outline-2">
|
||||
<h2 id="org79ad15f"><span class="section-number-2">4</span> Complete Strut with Encoder</h2>
|
||||
<div id="outline-container-org91975b5" class="outline-2">
|
||||
<h2 id="org91975b5"><span class="section-number-2">4</span> Complete Strut with Encoder</h2>
|
||||
<div class="outline-text-2" id="text-4">
|
||||
<p>
|
||||
<a id="orgc4b9146"></a>
|
||||
<a id="orgcff61d6"></a>
|
||||
</p>
|
||||
</div>
|
||||
<div id="outline-container-org26e8494" class="outline-3">
|
||||
<h3 id="org26e8494"><span class="section-number-3">4.1</span> Introduction</h3>
|
||||
<div id="outline-container-orgd829824" class="outline-3">
|
||||
<h3 id="orgd829824"><span class="section-number-3">4.1</span> Introduction</h3>
|
||||
<div class="outline-text-3" id="text-4-1">
|
||||
<p>
|
||||
Now, the full nano-hexapod strut is modelled using Ansys.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
The 3D as well as the interface nodes are shown in Figure <a href="#org8a816bb">20</a>.
|
||||
The 3D as well as the interface nodes are shown in Figure <a href="#org9f2a66d">20</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org8a816bb" class="figure">
|
||||
<div id="org9f2a66d" class="figure">
|
||||
<p><img src="figs/strut_encoder_nodes.jpg" alt="strut_encoder_nodes.jpg" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 20: </span>Interface points</p>
|
||||
</div>
|
||||
|
||||
<p>
|
||||
A side view is shown in Figure <a href="#org4c74f6e">21</a>.
|
||||
A side view is shown in Figure <a href="#org3437ed1">21</a>.
|
||||
</p>
|
||||
|
||||
|
||||
<div id="org4c74f6e" class="figure">
|
||||
<div id="org3437ed1" class="figure">
|
||||
<p><img src="figs/strut_encoder_nodes_side.jpg" alt="strut_encoder_nodes_side.jpg" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 21: </span>Interface points - Side view</p>
|
||||
@ -2294,8 +2297,8 @@ The flexible joints used have a 0.25mm width size.
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orgd702a5f" class="outline-3">
|
||||
<h3 id="orgd702a5f"><span class="section-number-3">4.2</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div id="outline-container-orgd7f754c" class="outline-3">
|
||||
<h3 id="orgd7f754c"><span class="section-number-3">4.2</span> Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates</h3>
|
||||
<div class="outline-text-3" id="text-4-2">
|
||||
<p>
|
||||
We first extract the stiffness and mass matrices.
|
||||
@ -2757,8 +2760,8 @@ Using <code>K</code>, <code>M</code> and <code>int_xyz</code>, we can use the <c
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-org42c2461" class="outline-3">
|
||||
<h3 id="org42c2461"><span class="section-number-3">4.3</span> Piezoelectric parameters</h3>
|
||||
<div id="outline-container-org5019141" class="outline-3">
|
||||
<h3 id="org5019141"><span class="section-number-3">4.3</span> Piezoelectric parameters</h3>
|
||||
<div class="outline-text-3" id="text-4-3">
|
||||
<p>
|
||||
Parameters for the APA300ML:
|
||||
@ -2782,8 +2785,8 @@ ns = 1; <span class="org-comment">% Number of stacks used as force sensor</span>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div id="outline-container-orga5ba630" class="outline-3">
|
||||
<h3 id="orga5ba630"><span class="section-number-3">4.4</span> Identification of the Dynamics</h3>
|
||||
<div id="outline-container-org72bb8f1" class="outline-3">
|
||||
<h3 id="org72bb8f1"><span class="section-number-3">4.4</span> Identification of the Dynamics</h3>
|
||||
<div class="outline-text-3" id="text-4-4">
|
||||
<p>
|
||||
The dynamics is identified from the applied force to the measured relative displacement.
|
||||
@ -2795,7 +2798,7 @@ The same dynamics is identified for a payload mass of 10Kg.
|
||||
</div>
|
||||
|
||||
|
||||
<div id="org4ba34f1" class="figure">
|
||||
<div id="orgda90142" class="figure">
|
||||
<p><img src="figs/dynamics_encoder_full_strut.png" alt="dynamics_encoder_full_strut.png" />
|
||||
</p>
|
||||
<p><span class="figure-number">Figure 22: </span>Dynamics from the force actuator to the measured motion by the encoder</p>
|
||||
@ -2816,7 +2819,7 @@ The same dynamics is identified for a payload mass of 10Kg.
|
||||
</div>
|
||||
<div id="postamble" class="status">
|
||||
<p class="author">Author: Dehaeze Thomas</p>
|
||||
<p class="date">Created: 2020-11-12 jeu. 18:48</p>
|
||||
<p class="date">Created: 2020-11-13 ven. 08:56</p>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
@ -1,4 +1,4 @@
|
||||
#+TITLE: Finite Element Model with Simscape
|
||||
#+TITLE: NASS - Finite Element Models with Simscape
|
||||
:DRAWER:
|
||||
#+STARTUP: overview
|
||||
|
||||
@ -38,6 +38,7 @@
|
||||
|
||||
In this document, Finite Element Models (FEM) of parts of the Nano-Hexapod are developed and integrated into Simscape for dynamical analysis.
|
||||
|
||||
It is divided in the following sections:
|
||||
- Section [[sec:APA300ML]]:
|
||||
A super-element of the Amplified Piezoelectric Actuator APA300ML used for the NASS is exported using Ansys and imported in Simscape.
|
||||
The static and dynamical properties of the APA300ML are then estimated using the Simscape model.
|
||||
@ -46,7 +47,7 @@ In this document, Finite Element Models (FEM) of parts of the Nano-Hexapod are d
|
||||
- Section [[sec:flexor_025]]:
|
||||
An optimized flexible joint is developed for the Nano-Hexapod and is then imported in a Simscape model.
|
||||
- Section [[sec:strut_encoder]]:
|
||||
A super element of a complete strut is exported.
|
||||
A super element of a complete strut is studied.
|
||||
|
||||
* APA300ML
|
||||
:PROPERTIES:
|
||||
|
||||
Loading…
Reference in New Issue
Block a user