Change y to x to match description

Correctly label measured thickness
Analysis of the force sensor stiffness
2021-04-30 14:36:24 +02:00 · 2021-04-30 14:34:01 +02:00 · 2021-03-12 20:08:09 +01:00 · 2021-03-12 15:41:53 +01:00 · 2021-03-10 17:05:19 +01:00 · 2021-03-10 11:43:00 +01:00
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-<head>
-<!-- 2020-12-17 jeu. 14:47 -->
-<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
-<title>Flexible Joint - Test Bench</title>
-<meta name="generator" content="Org mode" />
-<meta name="author" content="Dehaeze Thomas" />
-<link rel="stylesheet" type="text/css" href="https://research.tdehaeze.xyz/css/style.css"/>
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- <a accesskey="h" href="../index.html"> UP </a>
- |
- <a accesskey="H" href="../index.html"> HOME </a>
-</div><div id="content">
-<h1 class="title">Flexible Joint - Test Bench</h1>
-<div id="table-of-contents">
-<h2>Table of Contents</h2>
-<div id="text-table-of-contents">
-<ul>
-<li><a href="#org7f5c1ab">1. Test Bench Description</a>
-<ul>
-<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>
-</ul>
-</li>
-<li><a href="#orgbe54fa0">2. Experimental measurement</a></li>
-</ul>
-</div>
-</div>
-
-<div id="outline-container-org7f5c1ab" class="outline-2">
-<h2 id="org7f5c1ab"><span class="section-number-2">1</span> Test Bench Description</h2>
-<div class="outline-text-2" id="text-1">
-<p>
-The main characteristic of the flexible joint that we want to measure is its bending stiffness \(k_{R_x} \approx k_{R_y}\).
-</p>
-
-<p>
-To do so, a test bench is used.
-Specifications of the test bench to precisely measure the bending stiffness are described in this section.
-</p>
-
-<p>
-The basic idea is to measured the angular deflection of the flexible joint as a function of the applied torque.
-</p>
-
-
-<div id="org9b87bf2" class="figure">
-<p><img src="figs/test-bench-schematic.png" alt="test-bench-schematic.png" />
-</p>
-<p><span class="figure-number">Figure 1: </span>Schematic of the test bench to measure the bending stiffness of the flexible joints</p>
-</div>
-</div>
-
-<div id="outline-container-orgb03e5df" class="outline-3">
-<h3 id="orgb03e5df"><span class="section-number-3">1.1</span> Flexible joint Geometry</h3>
-<div class="outline-text-3" id="text-1-1">
-<p>
-The flexible joint used for the Nano-Hexapod is shown in Figure <a href="#orga662ff4">2</a>.
-Its bending stiffness is foreseen to be \(k_{R_y}\approx 20\,\frac{Nm}{rad}\) and its stroke \(\theta_{y,\text{max}}\approx 20\,mrad\).
-</p>
-
-
-<div id="orga662ff4" class="figure">
-<p><img src="figs/flexible_joint_geometry.png" alt="flexible_joint_geometry.png" />
-</p>
-<p><span class="figure-number">Figure 2: </span>Geometry of the flexible joint</p>
-</div>
-
-<p>
-The height between the flexible point (center of the joint) and the point where external forces are applied is \(h = 20\,mm\).
-</p>
-
-<p>
-Let&rsquo;s define the parameters on Matlab.
-</p>
-<div class="org-src-container">
-<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>
-</pre>
-</div>
-</div>
-</div>
-
-<div id="outline-container-org57bd1c6" class="outline-3">
-<h3 id="org57bd1c6"><span class="section-number-3">1.2</span> Required external applied force</h3>
-<div class="outline-text-3" id="text-1-2">
-<p>
-The bending \(\theta_y\) of the flexible joint due to the force \(F_x\) is:
-</p>
-\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:
-</p>
-\begin{equation}
-  F_{x,\text{max}} = \frac{k_{R_y} \theta_{y,\text{max}}}{h}
-\end{equation}
-
-<div class="org-src-container">
-<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>
-</pre>
-</div>
-
-<p>
-And we obtain:
-</p>
-\begin{equation} F_{max} = 20.0\, [N] \end{equation}
-
-<p>
-The measurement range of the force sensor should then be higher than \(20\,N\).
-</p>
-</div>
-</div>
-
-<div id="outline-container-org944d593" class="outline-3">
-<h3 id="org944d593"><span class="section-number-3">1.3</span> Required actuator stroke and sensors range</h3>
-<div class="outline-text-3" id="text-1-3">
-<p>
-The flexible joint is designed to allow a bending motion of \(\pm 20\,mrad\).
-The corresponding actuator stroke to impose such motion is:
-</p>
-
-<p>
-\[ d_{x,\text{max}} = h \tan(R_{x,\text{max}}) \]
-</p>
-
-<div class="org-src-container">
-<pre class="src src-matlab">dxmax = h<span class="org-type">*</span>tan(Rxmax);
-</pre>
-</div>
-
-\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 \(0.4\,mm\).
-</p>
-</div>
-</div>
-
-<div id="outline-container-org334e651" class="outline-3">
-<h3 id="org334e651"><span class="section-number-3">1.4</span> First try with the APA95ML</h3>
-<div class="outline-text-3" id="text-1-4">
-<p>
-The APA95ML as a stroke of \(100\,\mu m\) and the encoder in parallel can easily measure the required stroke.
-</p>
-
-<p>
-Suppose the full stroke of the APA can be used to bend the flexible joint (ideal case), the measured force will be:
-</p>
-<div class="org-src-container">
-<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>
-</pre>
-</div>
-
-\begin{equation} F_{max} = 5.0\, [N] \end{equation}
-
-<p>
-And the tested angular range is:
-</p>
-<div class="org-src-container">
-<pre class="src src-matlab">Rmax = tan(100e<span class="org-type">-</span>6<span class="org-type">/</span>h);
-</pre>
-</div>
-
-\begin{equation} \theta_{max} = 5.0\, [mrad] \end{equation}
-</div>
-</div>
-
-<div id="outline-container-orgc4f4cc8" class="outline-3">
-<h3 id="orgc4f4cc8"><span class="section-number-3">1.5</span> Test Bench</h3>
-<div class="outline-text-3" id="text-1-5">
-
-<div id="org9367697" class="figure">
-<p><img src="figs/test-bench-schematic.png" alt="test-bench-schematic.png" />
-</p>
-<p><span class="figure-number">Figure 3: </span>Schematic of the test bench to measure the bending stiffness of the flexible joints</p>
-</div>
-
-<div class="note" id="org93975e7">
-<ul class="org-ul">
-<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>
-</ul>
-
-</div>
-</div>
-</div>
-</div>
-
-<div id="outline-container-orgbe54fa0" class="outline-2">
-<h2 id="orgbe54fa0"><span class="section-number-2">2</span> Experimental measurement</h2>
-</div>
-</div>
-<div id="postamble" class="status">
-<p class="author">Author: Dehaeze Thomas</p>
-<p class="date">Created: 2020-12-17 jeu. 14:47</p>
-</div>
-</body>
-</html>
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-
-* Test Bench Description
-** Introduction                                                      :ignore:
-
-The main characteristic of the flexible joint that we want to measure is its bending stiffness $k_{R_x} \approx k_{R_y}$.
-
-To do so, a test bench is used.
-Specifications of the test bench to precisely measure the bending stiffness are described in this section.
-
-The basic idea is to measured the angular deflection of the flexible joint as a function of the applied torque.
-
-#+name: fig:test-bench-schematic
-#+caption: Schematic of the test bench to measure the bending stiffness of the flexible joints
-[[file:figs/test-bench-schematic.png]]
-
-** Matlab Init                                              :noexport:ignore:
-#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
-  <<matlab-dir>>
-#+end_src
-
-#+begin_src matlab :exports none :results silent :noweb yes
-  <<matlab-init>>
-#+end_src
-
-** Flexible joint Geometry
-The flexible joint used for the Nano-Hexapod is shown in Figure [[fig:flexible_joint_geometry]].
-Its bending stiffness is foreseen to be $k_{R_y}\approx 20\,\frac{Nm}{rad}$ and its stroke $\theta_{y,\text{max}}\approx 20\,mrad$.
-
-#+name: fig:flexible_joint_geometry
-#+caption: Geometry of the flexible joint
-[[file:figs/flexible_joint_geometry.png]]
-
-The height between the flexible point (center of the joint) and the point where external forces are applied is $h = 20\,mm$.
-
-Let's define the parameters on Matlab.
-#+begin_src matlab
-  kRx = 20; % Bending Stiffness [Nm/rad]
-  Rxmax = 20e-3; % Bending Stroke [rad]
-  h = 20e-3; % Height [m]
-#+end_src
-
-** Required external applied force
-
-The bending $\theta_y$ of the flexible joint due to the force $F_x$ is:
-\begin{equation}
-  \theta_y = \frac{M_y}{k_{R_y}} = \frac{F_x h}{k_{R_y}}
-\end{equation}
-
-Therefore, the applied force to test the full range of the flexible joint is:
-\begin{equation}
-  F_{x,\text{max}} = \frac{k_{R_y} \theta_{y,\text{max}}}{h}
-\end{equation}
-
-#+begin_src matlab
-  Fxmax = kRx*Rxmax/h; % Force to induce maximum stroke [N]
-#+end_src
-
-And we obtain:
-#+begin_src matlab :results value raw replace :exports results
-  sprintf('\\begin{equation} F_{max} = %.1f\\, [N] \\end{equation}', Fxmax)
-#+end_src
-
-#+RESULTS:
-\begin{equation} F_{max} = 20.0\, [N] \end{equation}
-
-The measurement range of the force sensor should then be higher than $20\,N$.
-
-** Required actuator stroke and sensors range
-
-The flexible joint is designed to allow a bending motion of $\pm 20\,mrad$.
-The corresponding actuator stroke to impose such motion is:
-
-\[ d_{x,\text{max}} = h \tan(R_{x,\text{max}}) \]
-
-#+begin_src matlab
-  dxmax = h*tan(Rxmax);
-#+end_src
-
-#+begin_src matlab :results value raw replace :exports results
-  sprintf('\\begin{equation} d_{max} = %.1f\\, [mm] \\end{equation}', 1e3*dxmax)
-#+end_src
-
-#+RESULTS:
-\begin{equation} d_{max} = 0.4\, [mm] \end{equation}
-
-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 $0.4\,mm$.
-
-** First try with the APA95ML
-
-The APA95ML as a stroke of $100\,\mu m$ and the encoder in parallel can easily measure the required stroke.
-
-Suppose the full stroke of the APA can be used to bend the flexible joint (ideal case), the measured force will be:
-#+begin_src matlab
-  Fxmax = kRx*100e-6/h^2; % Force at maximum stroke [N]
-#+end_src
-
-#+begin_src matlab :results value raw replace :exports results
-  sprintf('\\begin{equation} F_{max} = %.1f\\, [N] \\end{equation}', Fxmax)
-#+end_src
-
-#+RESULTS:
-\begin{equation} F_{max} = 5.0\, [N] \end{equation}
-
-And the tested angular range is:
-#+begin_src matlab
-  Rmax = tan(100e-6/h);
-#+end_src
-
-#+begin_src matlab :results value raw replace :exports results
-  sprintf('\\begin{equation} \\theta_{max} = %.1f\\, [mrad] \\end{equation}', 1e3*Rmax)
-#+end_src
-
-#+RESULTS:
-\begin{equation} \theta_{max} = 5.0\, [mrad] \end{equation}
-
-** Test Bench
-
-#+name: fig:test-bench-schematic
-#+caption: Schematic of the test bench to measure the bending stiffness of the flexible joints
-[[file:figs/test-bench-schematic.png]]
-
-#+begin_note
- Manual Translation Stage
- Load Cell TE Connectivity [[file:doc/A700000007147087.pdf][FC2231-0000-0010-L]]
- Encoder: Renishaw [[file:doc/L-9517-9448-05-B_Data_sheet_RESOLUTE_BiSS_en.pdf][Resolute 1nm]]
-#+end_note
-
-* Experimental measurement
--- a/matlab/bench_dimensioning.m
+++ b/matlab/bench_dimensioning.m
@@ -0,0 +1,53 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+% Flexible joint Geometry
+% The flexible joint used for the Nano-Hexapod is shown in Figure [[fig:flexible_joint_geometry]].
+% Its bending stiffness is foreseen to be $k_{R_y}\approx 5\,\frac{Nm}{rad}$ and its stroke $\theta_{y,\text{max}}\approx 25\,mrad$.
+
+% #+name: fig:flexible_joint_geometry
+% #+caption: Geometry of the flexible joint
+% [[file:figs/flexible_joint_geometry.png]]
+
+% The height between the flexible point (center of the joint) and the point where external forces are applied is $h = 20\,mm$.
+
+% Let's define the parameters on Matlab.
+
+kRx = 5; % Bending Stiffness [Nm/rad]
+Rxmax = 25e-3; % Bending Stroke [rad]
+h = 20e-3; % Height [m]
+
+% Required external applied force
+
+% The bending $\theta_y$ of the flexible joint due to the force $F_x$ is:
+% \begin{equation}
+%   \theta_y = \frac{M_y}{k_{R_y}} = \frac{F_x h}{k_{R_y}}
+% \end{equation}
+
+% Therefore, the applied force to test the full range of the flexible joint is:
+% \begin{equation}
+%   F_{x,\text{max}} = \frac{k_{R_y} \theta_{y,\text{max}}}{h}
+% \end{equation}
+
+
+Fxmax = kRx*Rxmax/h; % Force to induce maximum stroke [N]
+
+
+
+% And we obtain:
+
+sprintf('\\begin{equation} F_{x,max} = %.1f\\, [N] \\end{equation}', Fxmax)
+
+% Required actuator stroke and sensors range
+
+% The flexible joint is designed to allow a bending motion of $\pm 25\,mrad$.
+% The corresponding stroke at the location of the force sensor is:
+% \[ d_{x,\text{max}} = h \tan(R_{x,\text{max}}) \]
+
+
+dxmax = h*tan(Rxmax);
+
+sprintf('\\begin{equation} d_{max} = %.1f\\, [mm] \\end{equation}', 1e3*dxmax)
--- a/matlab/error_budget.m
+++ b/matlab/error_budget.m
@@ -0,0 +1,67 @@
+%% Clear Workspace and Close figures
+clear; close all; clc;
+
+%% Intialize Laplace variable
+s = zpk('s');
+
+% Finite Element Model
+% From the Finite Element Model, the stiffness and stroke of the flexible joint have been computed and summarized in Tables [[tab:axial_shear_characteristics]] and [[tab:bending_torsion_characteristics]].
+
+
+%% Stiffness
+ka = 94e6; % Axial Stiffness [N/m]
+ks = 13e6; % Shear Stiffness [N/m]
+kb = 5;    % Bending Stiffness [Nm/rad]
+kt = 260;  % Torsional Stiffness [Nm/rad]
+
+%% Maximum force
+Fa = 469;    % Axial Force before yield [N]
+Fs = 242;    % Shear Force before yield [N]
+Fb = 0.118;  % Bending Force before yield [Nm]
+Ft = 1.508; % Torsional Force before yield [Nm]
+
+%% Compute the corresponding stroke
+Xa = Fa/ka; % Axial Stroke before yield [m]
+Xs = Fs/ks; % Shear Stroke before yield [m]
+Xb = Fb/kb; % Bending Stroke before yield [rad]
+Xt = Ft/kt; % Torsional Stroke before yield [rad]
+
+% Setup
+
+% The setup is schematically represented in Figure [[fig:test_bench_flex_side_bis]].
+
+% The force is applied on top of the flexible joint with a distance $h$ with the joint's center.
+% The displacement of the flexible joint is also measured at the same height.
+
+% The height between the joint's center and the force application point is:
+
+h = 25e-3; % Height [m]
+
+% Estimation error due to force sensor compression
+% The measured displacement is not done directly at the joint's location.
+% The force sensor compression will then induce an error on the joint's stiffness.
+
+% The force sensor stiffness $k_F$ is estimated to be around:
+
+kF = 50/0.05e-3; % [N/m]
+
+sprintf('k_F = %.1e [N/m]', kF)
+
+% Estimation error due to height estimation error
+% Let's consider an error in the estimation of the height from the application of the force to the joint's center:
+% \begin{equation}
+% h_{\text{est}} = h (1 + \epsilon)
+% \end{equation}
+
+% The computed bending stiffness will be:
+% \begin{equation}
+%   k_\text{est} \approx h_{\text{est}}^2 \frac{F_x}{d_x}
+% \end{equation}
+
+% And the stiffness estimation error is:
+% \begin{equation}
+% \frac{k_{\text{est}}}{k_{R_y}} = (1 + \epsilon)^2
+% \end{equation}
+
+
+h_err = 0.2e-3; % Height estimation error [m]
--- a/matlab/mat/calibration_force_sensor.mat
+++ b/matlab/mat/calibration_force_sensor.mat
--- a/matlab/mat/flex_meas_dim.mat
+++ b/matlab/mat/flex_meas_dim.mat
--- a/matlab/mat/force_sensor_noise_meas.mat
+++ b/matlab/mat/force_sensor_noise_meas.mat
--- a/matlab/mat/force_sensor_stiffness_meas.mat
+++ b/matlab/mat/force_sensor_stiffness_meas.mat
--- a/matlab/mat/meas_probe_against_encoder.mat
+++ b/matlab/mat/meas_probe_against_encoder.mat
--- a/matlab/mat/meas_stiff_flex_10_x.mat
+++ b/matlab/mat/meas_stiff_flex_10_x.mat
--- a/matlab/mat/meas_stiff_flex_10_y.mat
+++ b/matlab/mat/meas_stiff_flex_10_y.mat
--- a/matlab/mat/meas_stiff_flex_11_x.mat
+++ b/matlab/mat/meas_stiff_flex_11_x.mat
--- a/matlab/mat/meas_stiff_flex_11_y.mat
+++ b/matlab/mat/meas_stiff_flex_11_y.mat
--- a/matlab/mat/meas_stiff_flex_12_x.mat
+++ b/matlab/mat/meas_stiff_flex_12_x.mat
--- a/matlab/mat/meas_stiff_flex_12_xy.mat
+++ b/matlab/mat/meas_stiff_flex_12_xy.mat
--- a/matlab/mat/meas_stiff_flex_12_y.mat
+++ b/matlab/mat/meas_stiff_flex_12_y.mat
--- a/matlab/mat/meas_stiff_flex_13_x.mat
+++ b/matlab/mat/meas_stiff_flex_13_x.mat
--- a/matlab/mat/meas_stiff_flex_13_y.mat
+++ b/matlab/mat/meas_stiff_flex_13_y.mat
--- a/matlab/mat/meas_stiff_flex_14_x.mat
+++ b/matlab/mat/meas_stiff_flex_14_x.mat
--- a/matlab/mat/meas_stiff_flex_14_y.mat
+++ b/matlab/mat/meas_stiff_flex_14_y.mat
--- a/matlab/mat/meas_stiff_flex_15_x.mat
+++ b/matlab/mat/meas_stiff_flex_15_x.mat
--- a/Show More
+++ b/Show More
Author	SHA1	Message	Date
Thomas Dehaeze	1e3b14eb57	Change y to x to match description	2021-04-30 14:36:24 +02:00
Thomas Dehaeze	e18d8db4bb	Correctly label measured thickness	2021-04-30 14:34:01 +02:00
Thomas Dehaeze	8f729963ee	Analysis of the force sensor stiffness	2021-03-12 20:08:09 +01:00
Thomas Dehaeze	b4c03be3ef	force sensor stiffness	2021-03-12 15:41:53 +01:00
Thomas Dehaeze	d432e1de25	measure force sensor stiffness	2021-03-10 17:05:19 +01:00
Thomas Dehaeze	0fd8fddc34	"Huddle test" + calibration analysis	2021-03-10 11:43:00 +01:00
Thomas Dehaeze	02b86e883e	calib force sensor + huddle test	2021-03-09 15:15:25 +01:00
Thomas Dehaeze	4006603d23	Analyze measurement of flexible joints	2021-03-04 17:29:33 +01:00
Thomas Dehaeze	d7a8a125c3	measure APA	2021-03-04 11:35:07 +01:00
Thomas Dehaeze	e7fa0d0b80	measure all flexible joints	2021-03-03 16:48:38 +01:00
Thomas Dehaeze	a71218a739	Add notes	2021-03-02 22:59:58 +01:00
Thomas Dehaeze	af4fd4fe55	Add measured flex dimensions	2021-03-02 22:58:54 +01:00
Thomas Dehaeze	ac4536c426	First analysis of stiffness	2021-03-02 22:27:50 +01:00
Thomas Dehaeze	19f003e172	first stiff meas of flexible joint	2021-03-02 17:54:49 +01:00
Thomas Dehaeze	29ebdc27e0	Rework the presentation of results + analysis	2021-02-18 11:38:56 +01:00
Thomas Dehaeze	77f2339a9d	Add CAD view of the bench	2021-02-16 21:24:22 +01:00
Thomas Dehaeze	a45916ca7e	Analyze data	2021-02-16 19:32:48 +01:00
Thomas Dehaeze	dee3acdce7	first measurements	2021-02-16 16:54:26 +01:00
Thomas Dehaeze	d7116e94ee	add Simulink file	2021-02-16 11:32:23 +01:00
Thomas Dehaeze	1435f92167	Add doc and matlab folder	2021-02-16 10:45:47 +01:00
Thomas Dehaeze	0edcc871dd	Export to pdf	2021-02-02 19:13:38 +01:00