From 2deb41939d3936b3cc656e00d848d3d5ca430875 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Tue, 5 May 2020 11:38:27 +0200 Subject: [PATCH] Add link to centrifugal forces study --- docs/centrifugal_forces.html | 194 +++++++++++++++++++++++++++++++++++ docs/index.html | 9 +- org/index.org | 3 + 3 files changed, 204 insertions(+), 2 deletions(-) create mode 100644 docs/centrifugal_forces.html diff --git a/docs/centrifugal_forces.html b/docs/centrifugal_forces.html new file mode 100644 index 0000000..f1ad876 --- /dev/null +++ b/docs/centrifugal_forces.html @@ -0,0 +1,194 @@ + + + + + + + + +Centrifugal Forces + + + + + + + + + + + + +
+ UP + | + HOME +
+

Centrifugal Forces

+ + +

+In this document, we wish to estimate the centrifugal forces due to the spindle’s rotation when the sample’s center of mass is off-centered with respect to the rotation axis. +

+ +

+This is the case then the sample is moved by the micro-hexapod. +

+ +

+The centrifugal forces are defined as represented Figure 1 where: +

+ + + +
+

centrifugal.png +

+

Figure 1: Centrifugal forces

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+ +
+

1 Parameters

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+

+We define some parameters for the computation. +

+ +

+The mass of the sample can vary from \(1\,kg\) to \(50\,kg\) to which is added to mass of the metrology reflector and the nano-hexapod’s top platform (here set to \(15\,kg\)). +

+ +
+
M_light = 16; % mass of excentred parts mooving [kg]
+M_heavy = 65; % [kg]
+
+
+ +

+For the light mass, the rotation speed is 60rpm whereas for the heavy mass, it is equal to 1rpm. +

+
+
w_light = 2*pi; % rotational speed [rad/s]
+w_heavy = 2*pi/60; % rotational speed [rad/s]
+
+
+ +

+Finally, we consider a mass eccentricity of \(10\,mm\). +

+
+
R = 0.1; % Excentricity [m]
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+
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+
+ +
+

2 Centrifugal forces for light and heavy sample

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+

+From the formula \(F_c = m \omega^2 r\), we obtain the values shown below. +

+ + + + +++ ++ + + + + + + + + + + + + + + + + + +
 Force [N]
light63.2
heavy0.1
+
+
+ +
+

3 Centrifugal forces as a function of the rotation speed

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+The centrifugal forces as a function of the rotation speed for light and heavy sample is shown on Figure 2. +

+ + +
+

centrifugal_forces_rpm.png +

+

Figure 2: Centrifugal forces function of the rotation speed

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4 Maximum rotation speed as a function of the mass

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+We plot the maximum rotation speed as a function of the mass for different maximum force that we can use to counteract the centrifugal forces (Figure 3). +

+ +

+From a specified maximum allowed centrifugal force (here set to \(100\,[N]\)), the maximum rotation speed as a function of the sample’s mass is shown in Figure 3. +

+ +
+
F_max = 100; % Maximum accepted centrifugal forces [N]
+
+R = 0.1;
+
+M_sample = 0:1:100;
+M_reflector = 15;
+
+
+ + +
+

max_force_rpm.png +

+

Figure 3: Maximum rotation speed as a function of the sample mass for an allowed centrifugal force of \(100\,[N]\)

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+

Author: Dehaeze Thomas

+

Created: 2020-05-05 mar. 10:34

+
+ + diff --git a/docs/index.html b/docs/index.html index f258337..ad27033 100644 --- a/docs/index.html +++ b/docs/index.html @@ -4,7 +4,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Simscape Model of the Nano-Active-Stabilization-System @@ -152,6 +152,11 @@ This is discussed here.

We also discuss how the disturbances are implemented in the model.

+ +

+Centrifugal forces can be viewed as a constant force disturbance in the frame of the nano-hexapod. +Some numerical analysis of such forces are done here. +

@@ -244,7 +249,7 @@ These functions are all defined here.

Author: Dehaeze Thomas

-

Created: 2020-05-05 mar. 10:44

+

Created: 2020-05-05 mar. 11:38

diff --git a/org/index.org b/org/index.org index 679b9a5..789696a 100644 --- a/org/index.org +++ b/org/index.org @@ -47,6 +47,9 @@ This is discussed [[./disturbances.org][here]]. We also discuss how the disturbances are implemented in the model. +Centrifugal forces can be viewed as a constant force disturbance in the frame of the nano-hexapod. +Some numerical analysis of such forces are done [[file:centrifugal_forces.org][here]]. + * Simulation of Experiment ([[./experiments.org][link]]) Now that the dynamics of the Model have been tuned and the Disturbances have included, we can simulate experiments.