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< title > Flexible Joint - Test Bench< / title >
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< h1 class = "title" > Flexible Joint - Test Bench< / h1 >
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< h2 > Table of Contents< / h2 >
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< li > < a href = "#org7f5c1ab" > 1. Test Bench Description< / a >
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< li > < a href = "#orgb03e5df" > 1.1. Flexible joint Geometry< / a > < / li >
< li > < a href = "#org57bd1c6" > 1.2. Required external applied force< / a > < / li >
< li > < a href = "#org944d593" > 1.3. Required actuator stroke and sensors range< / a > < / li >
< li > < a href = "#org334e651" > 1.4. First try with the APA95ML< / a > < / li >
< li > < a href = "#orgc4f4cc8" > 1.5. Test Bench< / a > < / li >
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< li > < a href = "#orgbe54fa0" > 2. Experimental measurement< / a > < / li >
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< h2 id = "org7f5c1ab" > < span class = "section-number-2" > 1< / span > Test Bench Description< / h2 >
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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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To do so, a test bench is used.
Specifications of the test bench to precisely measure the bending stiffness are described in this section.
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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 > < 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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< h3 id = "orgb03e5df" > < span class = "section-number-3" > 1.1< / span > Flexible joint Geometry< / h3 >
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The flexible joint used for the Nano-Hexapod is shown in Figure < a href = "#orga662ff4" > 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 > < img src = "figs/flexible_joint_geometry.png" alt = "flexible_joint_geometry.png" / >
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< p > < span class = "figure-number" > Figure 2: < / span > Geometry of the flexible joint< / p >
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< p >
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 >
Let’ s define the parameters on Matlab.
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< pre class = "src src-matlab" > kRx = 20; < span class = "org-comment" > % Bending Stiffness [Nm/rad]< / span >
Rxmax = 20e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % Bending Stroke [rad]< / span >
h = 20e< span class = "org-type" > -< / span > 3; < span class = "org-comment" > % Height [m]< / span >
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< h3 id = "org57bd1c6" > < span class = "section-number-3" > 1.2< / span > Required external applied force< / h3 >
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< p >
The bending \(\theta_y\) of the flexible joint due to the force \(F_x\) is:
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\begin{equation}
\theta_y = \frac{M_y}{k_{R_y}} = \frac{F_x h}{k_{R_y}}
\end{equation}
< p >
Therefore, the applied force to test the full range of the flexible joint is:
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\begin{equation}
F_{x,\text{max}} = \frac{k_{R_y} \theta_{y,\text{max}}}{h}
\end{equation}
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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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And we obtain:
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\begin{equation} F_{max} = 20.0\, [N] \end{equation}
< p >
The measurement range of the force sensor should then be higher than \(20\,N\).
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< h3 id = "org944d593" > < span class = "section-number-3" > 1.3< / span > Required actuator stroke and sensors range< / h3 >
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The flexible joint is designed to allow a bending motion of \(\pm 20\,mrad\).
The corresponding actuator stroke to impose such motion is:
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\[ d_{x,\text{max}} = h \tan(R_{x,\text{max}}) \]
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< pre class = "src src-matlab" > dxmax = h< span class = "org-type" > *< / span > tan(Rxmax);
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\begin{equation} d_{max} = 0.4\, [mm] \end{equation}
< p >
In order to test the full range of the flexible joint, the stroke of the actuator should be higher than \(0.4\,mm\).
The measurement range of the displacement sensor should also be higher than \(0.4\,mm\).
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< h3 id = "org334e651" > < span class = "section-number-3" > 1.4< / span > First try with the APA95ML< / h3 >
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< p >
The APA95ML as a stroke of \(100\,\mu m\) and the encoder in parallel can easily measure the required stroke.
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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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< 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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\begin{equation} F_{max} = 5.0\, [N] \end{equation}
< p >
And the tested angular range is:
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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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\begin{equation} \theta_{max} = 5.0\, [mrad] \end{equation}
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< h3 id = "orgc4f4cc8" > < span class = "section-number-3" > 1.5< / span > Test Bench< / h3 >
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< p > < img src = "figs/test-bench-schematic.png" alt = "test-bench-schematic.png" / >
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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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< li > Manual Translation Stage< / li >
< li > Load Cell TE Connectivity < a href = "doc/A700000007147087.pdf" > FC2231-0000-0010-L< / a > < / li >
< 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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< h2 id = "orgbe54fa0" > < span class = "section-number-2" > 2< / span > Experimental measurement< / h2 >
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< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
2021-01-04 10:56:26 +01:00
< p class = "date" > Created: 2020-12-17 jeu. 14:47< / p >
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