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Thomas Dehaeze 2025-02-25 19:07:35 +01:00
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@ -1203,7 +1203,7 @@ Procedure:
**** Introduction :ignore: **** Introduction :ignore:
Validation with Amplified Piezoelectric Actuator, because: Validation with Amplified Piezoelectric Actuator, because:
- is a good candidate for the nano-hexapod (as will be explained in Section ref:sec:detail_fem_apa) - is a good candidate for the nano-hexapod (as will be explained in Section ref:sec:detail_fem_actuator)
- had one in the lab for experimental testing (APA95ML, Figure ref:fig:detail_fem_apa95ml_picture) - had one in the lab for experimental testing (APA95ML, Figure ref:fig:detail_fem_apa95ml_picture)
It is composed of several piezoelectric stacks (arranged horizontally, in blue), and a shell (in red) that amplifies the motion. The working direction of the APA95ML is vertical. It is composed of several piezoelectric stacks (arranged horizontally, in blue), and a shell (in red) that amplifies the motion. The working direction of the APA95ML is vertical.
- permits to model a mechanical structure (similar to a flexible joint), piezoelectric actuator and piezoelectric sensor - permits to model a mechanical structure (similar to a flexible joint), piezoelectric actuator and piezoelectric sensor
@ -1236,7 +1236,7 @@ Quick explanation of APA:
- explain how the FEM is done: - explain how the FEM is done:
- material properties (Table ref:tab:detail_fem_material_properties) - material properties (Table ref:tab:detail_fem_material_properties)
- mesh (Figure ref:fig:detail_fem_apa95ml_fem) - mesh (Figure ref:fig:detail_fem_apa95ml_mesh)
- explain piezoelectric materials: - explain piezoelectric materials:
- sensors - sensors
- actuators - actuators
@ -1335,7 +1335,7 @@ From [[cite:&fleming14_desig_model_contr_nanop_system p. 123]], the relation bet
\end{subequations} \end{subequations}
Unfortunately, it is difficult to know exactly which material is used in the amplified piezoelectric actuator[fn:1]. Unfortunately, it is difficult to know exactly which material is used in the amplified piezoelectric actuator[fn:1].
However, based on the available properties of the stacks in the data-sheet (summarized in Table ref:tab:stack_parameters), the soft Lead Zirconate Titanate "THP5H" from Thorlabs seemed to match quite well the observed properties. However, based on the available properties of the stacks in the data-sheet (summarized in Table ref:tab:detail_fem_stack_parameters), the soft Lead Zirconate Titanate "THP5H" from Thorlabs seemed to match quite well the observed properties.
The properties of this "THP5H" material used to compute $g_a$ and $g_s$ are listed in Table ref:tab:test_apa_piezo_properties. The properties of this "THP5H" material used to compute $g_a$ and $g_s$ are listed in Table ref:tab:test_apa_piezo_properties.
From these parameters, $g_s = 5.1\,V/\mu m$ and $g_a = 26\,N/V$ were obtained. From these parameters, $g_s = 5.1\,V/\mu m$ and $g_a = 26\,N/V$ were obtained.

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nass-fem.tex
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@ -1,4 +1,4 @@
% Created 2025-02-25 Tue 19:02 % Created 2025-02-25 Tue 19:07
% Intended LaTeX compiler: pdflatex % Intended LaTeX compiler: pdflatex
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt} \documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
@ -95,7 +95,7 @@ typically from hundred thousands to less than 100 DoF
\label{ssec:detail_fem_super_element_validation} \label{ssec:detail_fem_super_element_validation}
Validation with Amplified Piezoelectric Actuator, because: Validation with Amplified Piezoelectric Actuator, because:
\begin{itemize} \begin{itemize}
\item is a good candidate for the nano-hexapod (as will be explained in Section \ref{sec:detail_fem_apa}) \item is a good candidate for the nano-hexapod (as will be explained in Section \ref{sec:detail_fem_actuator})
\item had one in the lab for experimental testing (APA95ML, Figure \ref{fig:detail_fem_apa95ml_picture}) \item had one in the lab for experimental testing (APA95ML, Figure \ref{fig:detail_fem_apa95ml_picture})
It is composed of several piezoelectric stacks (arranged horizontally, in blue), and a shell (in red) that amplifies the motion. The working direction of the APA95ML is vertical. It is composed of several piezoelectric stacks (arranged horizontally, in blue), and a shell (in red) that amplifies the motion. The working direction of the APA95ML is vertical.
\item permits to model a mechanical structure (similar to a flexible joint), piezoelectric actuator and piezoelectric sensor \item permits to model a mechanical structure (similar to a flexible joint), piezoelectric actuator and piezoelectric sensor
@ -132,7 +132,7 @@ Stiffness & \(N/\mu m\) & 16\\
\item explain how the FEM is done: \item explain how the FEM is done:
\begin{itemize} \begin{itemize}
\item material properties (Table \ref{tab:detail_fem_material_properties}) \item material properties (Table \ref{tab:detail_fem_material_properties})
\item mesh (Figure \ref{fig:detail_fem_apa95ml_fem}) \item mesh (Figure \ref{fig:detail_fem_apa95ml_mesh})
\end{itemize} \end{itemize}
\item explain piezoelectric materials: \item explain piezoelectric materials:
\begin{itemize} \begin{itemize}
@ -250,7 +250,7 @@ From \cite[p. 123]{fleming14_desig_model_contr_nanop_system}, the relation betwe
\end{subequations} \end{subequations}
Unfortunately, it is difficult to know exactly which material is used in the amplified piezoelectric actuator\footnote{The manufacturer of the APA95ML was not willing to share the piezoelectric material properties of the stack.}. Unfortunately, it is difficult to know exactly which material is used in the amplified piezoelectric actuator\footnote{The manufacturer of the APA95ML was not willing to share the piezoelectric material properties of the stack.}.
However, based on the available properties of the stacks in the data-sheet (summarized in Table \ref{tab:stack_parameters}), the soft Lead Zirconate Titanate ``THP5H'' from Thorlabs seemed to match quite well the observed properties. However, based on the available properties of the stacks in the data-sheet (summarized in Table \ref{tab:detail_fem_stack_parameters}), the soft Lead Zirconate Titanate ``THP5H'' from Thorlabs seemed to match quite well the observed properties.
The properties of this ``THP5H'' material used to compute \(g_a\) and \(g_s\) are listed in Table \ref{tab:test_apa_piezo_properties}. The properties of this ``THP5H'' material used to compute \(g_a\) and \(g_s\) are listed in Table \ref{tab:test_apa_piezo_properties}.
From these parameters, \(g_s = 5.1\,V/\mu m\) and \(g_a = 26\,N/V\) were obtained. From these parameters, \(g_s = 5.1\,V/\mu m\) and \(g_a = 26\,N/V\) were obtained.