287 lines
9.0 KiB
HTML
287 lines
9.0 KiB
HTML
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<!-- 2021-02-02 mar. 19:12 -->
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<title>Flexible Joint - Test Bench</title>
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<meta name="author" content="Dehaeze Thomas" />
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<a accesskey="h" href="../index.html"> UP </a>
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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">Flexible Joint - Test Bench</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="#org0ce044b">1. Flexible Joints - Requirements</a></li>
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<li><a href="#orgdb39e09">2. Test Bench Description</a>
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<ul>
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<li><a href="#org5eb807b">2.1. Flexible joint Geometry</a></li>
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<li><a href="#org48c52dd">2.2. Required external applied force</a></li>
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<li><a href="#org1d2ec69">2.3. Required actuator stroke and sensors range</a></li>
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<li><a href="#orge2c3db5">2.4. First try with the APA95ML</a></li>
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<li><a href="#orge4c6045">2.5. Test Bench</a></li>
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</ul>
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</li>
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<li><a href="#orgfa48374">3. Experimental measurement</a></li>
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</ul>
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</div>
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</div>
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<hr>
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<p>This report is also available as a <a href="./test-bench-flexible-joints.pdf">pdf</a>.</p>
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<hr>
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<div id="outline-container-org0ce044b" class="outline-2">
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<h2 id="org0ce044b"><span class="section-number-2">1</span> Flexible Joints - Requirements</h2>
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<div class="outline-text-2" id="text-1">
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<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
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<colgroup>
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<col class="org-left" />
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<col class="org-left" />
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</colgroup>
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<thead>
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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-left"><b>Specification</b></th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td class="org-left">Axial Stiffness</td>
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<td class="org-left">> 200 [N/um]</td>
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</tr>
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<tr>
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<td class="org-left">Shear Stiffness</td>
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<td class="org-left">> 1 [N/um]</td>
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</tr>
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<tr>
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<td class="org-left">Bending Stiffness</td>
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<td class="org-left">< 100 [Nm/rad]</td>
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</tr>
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<tr>
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<td class="org-left">Torsion Stiffness</td>
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<td class="org-left">< 500 [Nm/rad]</td>
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</tr>
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<tr>
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<td class="org-left">Bending Stroke</td>
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<td class="org-left">> 1 [mrad]</td>
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</tr>
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<tr>
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<td class="org-left">Torsion Stroke</td>
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<td class="org-left">> 5 [urad]</td>
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</tr>
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</tbody>
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</table>
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</div>
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</div>
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<div id="outline-container-orgdb39e09" class="outline-2">
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<h2 id="orgdb39e09"><span class="section-number-2">2</span> Test Bench Description</h2>
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<div class="outline-text-2" id="text-2">
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<p>
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The main characteristic of the flexible joint that we want to measure is its bending stiffness \(k_{R_x} \approx k_{R_y}\).
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</p>
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<p>
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To do so, a test bench is used.
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Specifications of the test bench to precisely measure the bending stiffness are described in this section.
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</p>
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<p>
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The basic idea is to measured the angular deflection of the flexible joint as a function of the applied torque.
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</p>
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<div id="org73fb3d5" class="figure">
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<p><img src="figs/test-bench-schematic.png" alt="test-bench-schematic.png" />
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</p>
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<p><span class="figure-number">Figure 1: </span>Schematic of the test bench to measure the bending stiffness of the flexible joints</p>
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</div>
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</div>
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<div id="outline-container-org5eb807b" class="outline-3">
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<h3 id="org5eb807b"><span class="section-number-3">2.1</span> Flexible joint Geometry</h3>
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<div class="outline-text-3" id="text-2-1">
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<p>
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The flexible joint used for the Nano-Hexapod is shown in Figure <a href="#orge14f21a">2</a>.
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Its bending stiffness is foreseen to be \(k_{R_y}\approx 20\,\frac{Nm}{rad}\) and its stroke \(\theta_{y,\text{max}}\approx 20\,mrad\).
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</p>
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<div id="orge14f21a" class="figure">
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<p><img src="figs/flexible_joint_geometry.png" alt="flexible_joint_geometry.png" />
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</p>
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<p><span class="figure-number">Figure 2: </span>Geometry of the flexible joint</p>
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</div>
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<p>
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The height between the flexible point (center of the joint) and the point where external forces are applied is \(h = 20\,mm\).
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</p>
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<p>
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Let’s define the parameters on Matlab.
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"> kRx = 20; <span class="org-comment">% Bending Stiffness [Nm/rad]</span>
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Rxmax = 20e<span class="org-type">-</span>3; <span class="org-comment">% Bending Stroke [rad]</span>
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h = 20e<span class="org-type">-</span>3; <span class="org-comment">% Height [m]</span>
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</pre>
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</div>
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</div>
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</div>
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<div id="outline-container-org48c52dd" class="outline-3">
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<h3 id="org48c52dd"><span class="section-number-3">2.2</span> Required external applied force</h3>
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<div class="outline-text-3" id="text-2-2">
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<p>
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The bending \(\theta_y\) of the flexible joint due to the force \(F_x\) is:
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</p>
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\begin{equation}
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\theta_y = \frac{M_y}{k_{R_y}} = \frac{F_x h}{k_{R_y}}
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\end{equation}
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<p>
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Therefore, the applied force to test the full range of the flexible joint is:
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</p>
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\begin{equation}
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F_{x,\text{max}} = \frac{k_{R_y} \theta_{y,\text{max}}}{h}
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\end{equation}
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<div class="org-src-container">
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<pre class="src src-matlab"> Fxmax = kRx<span class="org-type">*</span>Rxmax<span class="org-type">/</span>h; <span class="org-comment">% Force to induce maximum stroke [N]</span>
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</pre>
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</div>
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<p>
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And we obtain:
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</p>
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\begin{equation} F_{max} = 20.0\, [N] \end{equation}
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<p>
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The measurement range of the force sensor should then be higher than \(20\,N\).
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</p>
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</div>
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</div>
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<div id="outline-container-org1d2ec69" class="outline-3">
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<h3 id="org1d2ec69"><span class="section-number-3">2.3</span> Required actuator stroke and sensors range</h3>
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<div class="outline-text-3" id="text-2-3">
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<p>
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The flexible joint is designed to allow a bending motion of \(\pm 20\,mrad\).
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The corresponding actuator stroke to impose such motion is:
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</p>
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<p>
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\[ d_{x,\text{max}} = h \tan(R_{x,\text{max}}) \]
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"> dxmax = h<span class="org-type">*</span>tan(Rxmax);
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</pre>
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</div>
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\begin{equation} d_{max} = 0.4\, [mm] \end{equation}
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<p>
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In order to test the full range of the flexible joint, the stroke of the actuator should be higher than \(0.4\,mm\).
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The measurement range of the displacement sensor should also be higher than \(0.4\,mm\).
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</p>
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</div>
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</div>
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<div id="outline-container-orge2c3db5" class="outline-3">
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<h3 id="orge2c3db5"><span class="section-number-3">2.4</span> First try with the APA95ML</h3>
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<div class="outline-text-3" id="text-2-4">
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<p>
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The APA95ML as a stroke of \(100\,\mu m\) and the encoder in parallel can easily measure the required stroke.
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</p>
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<p>
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Suppose the full stroke of the APA can be used to bend the flexible joint (ideal case), the measured force will be:
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"> Fxmax = kRx<span class="org-type">*</span>100e<span class="org-type">-</span>6<span class="org-type">/</span>h<span class="org-type">^</span>2; <span class="org-comment">% Force at maximum stroke [N]</span>
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</pre>
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</div>
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\begin{equation} F_{max} = 5.0\, [N] \end{equation}
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<p>
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And the tested angular range is:
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</p>
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<div class="org-src-container">
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<pre class="src src-matlab"> Rmax = tan(100e<span class="org-type">-</span>6<span class="org-type">/</span>h);
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</pre>
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</div>
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\begin{equation} \theta_{max} = 5.0\, [mrad] \end{equation}
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</div>
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</div>
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<div id="outline-container-orge4c6045" class="outline-3">
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<h3 id="orge4c6045"><span class="section-number-3">2.5</span> Test Bench</h3>
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<div class="outline-text-3" id="text-2-5">
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<div id="org8101cfa" class="figure">
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<p><img src="figs/test-bench-schematic.png" alt="test-bench-schematic.png" />
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</p>
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<p><span class="figure-number">Figure 3: </span>Schematic of the test bench to measure the bending stiffness of the flexible joints</p>
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</div>
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<div class="note" id="orgfde2443">
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<ul class="org-ul">
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<li>Manual Translation Stage</li>
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<li>Load Cell TE Connectivity <a href="doc/A700000007147087.pdf">FC2231-0000-0010-L</a></li>
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<li>Encoder: Renishaw <a href="doc/L-9517-9448-05-B_Data_sheet_RESOLUTE_BiSS_en.pdf">Resolute 1nm</a></li>
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</ul>
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</div>
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</div>
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</div>
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</div>
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<div id="outline-container-orgfa48374" class="outline-2">
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<h2 id="orgfa48374"><span class="section-number-2">3</span> Experimental measurement</h2>
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</div>
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</div>
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<div id="postamble" class="status">
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<p class="author">Author: Dehaeze Thomas</p>
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<p class="date">Created: 2021-02-02 mar. 19:12</p>
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</div>
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