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@ -117,7 +117,8 @@ Prefix is =detail_design=
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- Encoder support:
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- Possible to fix them to the struts or to the plates
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** TODO [#C] Summary of the specifications
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** DONE [#C] Summary of the specifications
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CLOSED: [2025-04-21 Mon 22:57]
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Flexible joints:
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- Axial Stiffness
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@ -134,7 +135,8 @@ Plates:
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- Maximize flexible modes
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- Correct positioning of bi and si => precisely know the Jacobian matrix
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** TODO [#C] Explain the good wanted flatness for the APA
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** DONE [#C] Explain the good wanted flatness for the APA
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CLOSED: [2025-04-21 Mon 22:57]
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#+begin_quote
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Sur le plan on a une co-planéitée de 0.08mm entre les 2 interfaces (ce
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@ -151,7 +153,8 @@ Le plans que Damien avait fait du corps de l'APA est en pj si tu veux
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illustrer.
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#+end_quote
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** TODO [#C] Understand why hexapod stiffness (maximizing suspension modes) is often the main design goal
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** DONE [#C] Understand why hexapod stiffness (maximizing suspension modes) is often the main design goal
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CLOSED: [2025-04-21 Mon 22:57]
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See for instance cite:afzali-far16_vibrat_dynam_isotr_hexap_analy_studies.
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@ -248,10 +251,10 @@ CLOSED: [2025-04-21 Mon 14:13]
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The detailed mechanical design of the active platform, depicted in Figure ref:fig:detail_design_nano_hexapod_elements, is presented in this section.
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Several primary objectives guided the mechanical design.
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First, in order to have a well known Jacobian matrix (used in the control architecture), accurate positioning of rotation points of the top flexible joint and correct orientation of the struts were wanted.
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First, to ensure a well-defined Jacobian matrix used in the control architecture, accurate positioning of the top flexible joint rotation points and correct orientation of the struts were required.
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Secondly, space constraints necessitated that the entire platform fit within a cylinder with a radius of $120\,\text{mm}$ and a height of $95\,\text{mm}$.
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Thirdly, because good performances were predicted by the multi-body model, the final design was intended to approximate the behavior of the "idealized" Stewart platform as closely as possible.
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This objective implies that the frequencies of flexible modes potentially detrimental to control performance needed to be maximized.
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Thirdly, because performance predicted by the multi-body model was fulfilling the requirements, the final design was intended to approximate the behavior of this "idealized" active platform as closely as possible.
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This objective implies that the frequencies of (un-modelled) flexible modes potentially detrimental to control performance needed to be maximized.
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Finally, considerations for ease of mounting, alignment, and maintenance were incorporated, specifically ensuring that struts could be easily replaced in the event of failure.
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#+name: fig:detail_design_nano_hexapod_elements
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@ -265,9 +268,9 @@ Finally, considerations for ease of mounting, alignment, and maintenance were in
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The strut design, illustrated in Figure ref:fig:detail_design_strut, was driven by several factors.
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Stiff interfaces were required between the amplified piezoelectric actuator and the two flexible joints, as well as between the flexible joints and their respective mounting plates.
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Due to the limited angular stroke of the flexible joints, it was important that the struts could be assembled in such a way that the two cylindrical interfaces were coaxial while the flexible joints were experiencing no stress (i.e. rest position).
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To achieve this, cylindrical washers, shown in Figure ref:fig:detail_design_strut_without_enc, were integrated into the design to allow for poor flatness between the two interface planes of the APA, depicted in Figure ref:fig:detail_design_apa.
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A dedicated mounting bench was also developed, such that each strut could be precisely aligned, even in the presence of machining inaccuracies.
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Due to the limited angular stroke of the flexible joints, it was critical that the struts could be assembled such that the two cylindrical interfaces were coaxial while the flexible joints remained in their unstressed, nominal rest position.
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To facilitate this alignment, cylindrical washers (Figure ref:fig:detail_design_strut_without_enc) were integrated into the design to compensate for potential deviations from perfect flatness between the two APA interface planes (Figure ref:fig:detail_design_apa).
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Furthermore, a dedicated mounting bench was developed to enable precise alignment of each strut, even when accounting for typical machining inaccuracies.
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The mounting procedure is described in Section ref:sec:test_struts_mounting.
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Lastly, the design needed to permit the fixation of an encoder parallel to the strut axis, as shown in Figure ref:fig:detail_design_strut_with_enc.
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@ -290,10 +293,9 @@ Lastly, the design needed to permit the fixation of an encoder parallel to the s
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#+end_figure
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The flexible joints, shown in Figure ref:fig:detail_design_flexible_joint, were manufactured using wire-cut electrical discharge machining (EDM).
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This manufacturing process was selected for few reasons.
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First, because of the neck dimension of only $0.25\,\text{mm}$, the part is inherently fragile and is difficult to manufacture with classical machining as cutting forces may damage the part.
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Also wire-cut EDM allows for very tight machining tolerances, which are critical for achieving accurate location of the center of rotation relative to the plate interfaces (indicated by red surfaces in Figure ref:fig:detail_design_flexible_joint) and for maintaining the correct neck dimensions necessary for the desired stiffness and angular stroke properties.
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The material chosen for the flexible joints is a stainless steel designated /X5CrNiCuNb16-4/ (alternatively known as "F16Ph").
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First, the part's inherent fragility, stemming from its $0.25\,\text{mm}$ neck dimension, makes it susceptible to damage from cutting forces typical in classical machining.
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||||
Furthermore, wire-cut EDM allows for the very tight machining tolerances critical for achieving accurate location of the center of rotation relative to the plate interfaces (indicated by red surfaces in Figure ref:fig:detail_design_flexible_joint) and for maintaining the correct neck dimensions necessary for the desired stiffness and angular stroke properties.
|
||||
The material chosen for the flexible joints is a stainless steel designated /X5CrNiCuNb16-4/ (alternatively known as F16Ph).
|
||||
This selection was based on its high specified yield strength (exceeding $1\,\text{GPa}$ after appropriate heat treatment) and its high fatigue resistance.
|
||||
|
||||
As shown in Figure ref:fig:detail_design_flexible_joint, the interface designed to connect with the APA possesses a cylindrical shape, facilitating the use of the aforementioned cylindrical washers for alignment.
|
||||
@ -329,15 +331,15 @@ These parts serve to fix the encoder head and the associated scale (ruler) to th
|
||||
**** Plates
|
||||
|
||||
The design of the top and bottom plates of the active platform was governed by two main requirements: maximizing the frequency of flexible modes and ensuring accurate positioning of the top flexible joints and well-defined orientation of the struts.
|
||||
To maximize the natural frequencies associated with plate flexibility, a simple network of reinforcing ribs was adopted, as shown for the top plate in Figure ref:fig:detail_design_top_plate.
|
||||
While topology optimization methods could have been used, the presented designed was found to give high enough flexible modes.
|
||||
To maximize the natural frequencies associated with plate flexibility, a network of reinforcing ribs was incorporated into the design, as shown for the top plate in Figure ref:fig:detail_design_top_plate.
|
||||
Although topology optimization methods were considered, the implemented ribbed design was found to provide sufficiently high natural frequencies for the flexible modes.
|
||||
|
||||
#+name: fig:detail_design_top_plate
|
||||
#+caption: The mechanical design for the top platform incorporates precisely positioned V-grooves for the joint interfaces (displayed in red). The purpose of the encoder interface (shown in green) is detailed later.
|
||||
#+attr_latex: :scale 1
|
||||
[[file:figs/detail_design_top_plate.png]]
|
||||
|
||||
Joints interfaces on the plate consist of "V-grooves".
|
||||
The interfaces for the joints on the plates incorporate V-grooves (red planes in Figure ref:fig:detail_design_top_plate).
|
||||
The cylindrical portion of each flexible joint is constrained within its corresponding V-groove through two distinct line contacts, illustrated in Figure ref:fig:detail_design_fixation_flexible_joints.
|
||||
These grooves consequently serve to define the nominal orientation of the struts.
|
||||
High machining accuracy for these features is essential to ensure that the flexible joints are in their neutral, unstressed state when the active platform is assembled.
|
||||
@ -380,8 +382,8 @@ The analysis revealed that the first six modes correspond to "suspension" modes,
|
||||
Following these suspension modes, numerous "local" modes associated with the struts themselves were observed in the frequency range between $205\,\text{Hz}$ and $420\,\text{Hz}$.
|
||||
One such mode is represented in Figure ref:fig:detail_design_fem_strut_mode.
|
||||
Although these modes do not appear to induce significant motion of the top platform, they do cause relative displacement between the encoder components (head and scale) mounted on the strut.
|
||||
Consequently, such modes could potentially be problematic if the active platform's position is controlled based on the encoders.
|
||||
The extent to which these modes might pose a problem is difficult to establish at this stage, as it depends on whether they are significantly excited by the APA actuation and their sensitivity to strut alignment.
|
||||
Consequently, such modes could potentially degrade control performance if the active platform's position is regulated using these encoder measurements.
|
||||
The extent to which these modes might be detrimental is difficult to establish at this stage, as it depends on whether they are significantly excited by the APA actuation and their sensitivity to strut alignment.
|
||||
Finally, the FEA indicated that flexible modes of the top plate itself begin to appear at frequencies above $650\,\text{Hz}$, with the first such mode shown in Figure ref:fig:detail_design_fem_plate_mode.
|
||||
|
||||
#+name: fig:detail_design_fem_nano_hexapod
|
||||
@ -410,7 +412,7 @@ Finally, the FEA indicated that flexible modes of the top plate itself begin to
|
||||
|
||||
**** Alternative Encoder Placement
|
||||
|
||||
In anticipation of potential issues arising from the local modes of the struts affecting encoder measurements, an alternative fixation strategy for the encoders was envisaged.
|
||||
In anticipation of potential issues arising from the local modes of the struts affecting encoder measurements, an alternative fixation strategy for the encoders was designed.
|
||||
In this configuration, the encoders are fixed directly to the top and bottom plates instead of the struts, as illustrated in Figure ref:fig:detail_design_enc_plates_design.
|
||||
|
||||
#+name: fig:detail_design_enc_plates_design
|
||||
@ -432,35 +434,11 @@ In this configuration, the encoders are fixed directly to the top and bottom pla
|
||||
#+end_figure
|
||||
|
||||
Dedicated supports, machined from aluminum, were designed for this purpose.
|
||||
It was verified through FEA that the natural modes of these supports occur at sufficiently high frequencies, with the first mode estimated at $1120\,\text{Hz}$.
|
||||
It was verified through FEA that the natural modes of these supports occur at frequencies sufficiently high (first mode estimated at $1120\,\text{Hz}$) to not be problematic for control.
|
||||
Precise positioning of these encoder supports is achieved through machined pockets in both the top and bottom plates, visible in Figure ref:fig:detail_design_top_plate (indicated in green).
|
||||
Although the encoders in this arrangement are aligned parallel to the nominal strut axes, they no longer measure the exact relative displacement along the strut between the flexible joint centers.
|
||||
This geometric discrepancy implies that if the relative motion control of the active platform is based directly on these encoder readings, the kinematic calculations may be slightly inaccurate, potentially affecting the overall positioning accuracy of the platform.
|
||||
|
||||
# #+name: fig:detail_design_enc_support_modes
|
||||
# #+caption: Finite Element Analysis of the encoder supports. Encoder inertia was taken into account.
|
||||
# #+attr_latex: :options [htbp]
|
||||
# #+begin_figure
|
||||
# #+attr_latex: :caption \subcaption{\label{fig:detail_design_enc_support_mode_1}$1^{\text{st}}$ mode at $1120\,\text{Hz}$}
|
||||
# #+attr_latex: :options {0.33\textwidth}
|
||||
# #+begin_subfigure
|
||||
# #+attr_latex: :scale 0.5
|
||||
# [[file:figs/detail_design_enc_support_mode_1.jpg]]
|
||||
# #+end_subfigure
|
||||
# #+attr_latex: :caption \subcaption{\label{fig:detail_design_enc_support_mode_2}$2^{\text{nd}}$ mode at $2020\,\text{Hz}$}
|
||||
# #+attr_latex: :options {0.33\textwidth}
|
||||
# #+begin_subfigure
|
||||
# #+attr_latex: :scale 0.5
|
||||
# [[file:figs/detail_design_enc_support_mode_2.jpg]]
|
||||
# #+end_subfigure
|
||||
# #+attr_latex: :caption \subcaption{\label{fig:detail_design_enc_support_mode_3}$3^{\text{rd}}$ mode at $2080\,\text{Hz}$}
|
||||
# #+attr_latex: :options {0.33\textwidth}
|
||||
# #+begin_subfigure
|
||||
# #+attr_latex: :scale 0.5
|
||||
# [[file:figs/detail_design_enc_support_mode_3.jpg]]
|
||||
# #+end_subfigure
|
||||
# #+end_figure
|
||||
|
||||
* Multi-Body Model
|
||||
<<sec:detail_design_model>>
|
||||
**** Introduction :ignore:
|
||||
@ -495,7 +473,7 @@ The multi-body representation corresponding to the 4DoF configuration is shown i
|
||||
This model is composed of three distinct solid bodies interconnected by joints, whose stiffness properties were derived from finite element analysis of the joint component.
|
||||
|
||||
#+name: fig:detail_design_simscape_model_flexible_joint
|
||||
#+caption: Multi-Body (using the Simscape software) model of the flexible joints. A 4-DoFs model is shown.
|
||||
#+caption: 4DoF multi-body model of the flexible joints
|
||||
#+attr_latex: :scale 1
|
||||
[[file:figs/detail_design_simscape_model_flexible_joint.png]]
|
||||
|
||||
@ -511,8 +489,8 @@ However, as indicated by the FEA results discussed previously, the flexible mode
|
||||
Therefore, a more sophisticated model of the optical encoder was necessary.
|
||||
|
||||
The optical encoders operate based on the interaction between an encoder head and a graduated scale or ruler.
|
||||
The optical encoder head contains a light source which is illuminating the ruler.
|
||||
The position of the light on the ruler is represented by the reference frame $\{E\}$ in Figure ref:fig:detail_design_simscape_encoder_model.
|
||||
The optical encoder head contains a light source that illuminates the ruler.
|
||||
A reference frame $\{E\}$ fixed to the scale, represents the the light position on the scale, as illustrated in Figure ref:fig:detail_design_simscape_encoder_model.
|
||||
The ruler features a precise grating pattern (in this case, with a $20\,\mu m$ pitch), and its position is associated with the reference frame $\{R\}$.
|
||||
The displacement measured by the encoder corresponds to the relative position of the encoder frame $\{E\}$ (specifically, the point where the light interacts with the scale) with respect to the ruler frame $\{R\}$, projected along the measurement direction defined by the scale.
|
||||
|
||||
@ -536,14 +514,12 @@ An important consequence of this measurement principle is that a relative rotati
|
||||
#+end_subfigure
|
||||
#+end_figure
|
||||
|
||||
**** Simulation
|
||||
**** Validation of the designed active platform
|
||||
|
||||
Utilizing this refined multi-body model, several assessments were conducted.
|
||||
The active platform model was integrated into the larger simulation model with the micro-station.
|
||||
The dynamic behavior was evaluated and considered satisfactory.
|
||||
Furthermore, simulations replicating tomography experiments were performed.
|
||||
The performance metrics obtained from these simulations were found to be comparable to those achieved during the earlier conceptual design phase simulations.
|
||||
Consequently, as the results closely mirror those presented previously in Section ref:ssec:test_id31_iff_hac_perf, they are not reiterated in detail here.
|
||||
The refined multi-body model of the active platform was integrated into the multi-body micro-station model.
|
||||
Dynamical analysis was performed, confirming that the platform's behavior closely approximates the dynamics of the "idealized" model used during the conceptual design phase.
|
||||
Consequently, closed-loop performance simulations replicating tomography experiments yielded metrics highly comparable to those previously predicted (as presented in Section ref:ssec:nass_hac_tomography).
|
||||
Given this similarity and because analogous simulations are conducted and detailed during the experimental validation phase (Section ref:sec:test_id31_hac), these specific results are not reiterated here.
|
||||
|
||||
* Bibliography :ignore:
|
||||
#+latex: \printbibliography[heading=bibintoc,title={Bibliography}]
|
||||
|
||||
BIN
nass-design.pdf
BIN
nass-design.pdf
Binary file not shown.
@ -1,4 +1,4 @@
|
||||
% Created 2025-04-21 Mon 22:54
|
||||
% Created 2025-04-21 Mon 23:30
|
||||
% Intended LaTeX compiler: pdflatex
|
||||
\documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt}
|
||||
|
||||
@ -25,10 +25,10 @@
|
||||
\clearpage
|
||||
The detailed mechanical design of the active platform, depicted in Figure \ref{fig:detail_design_nano_hexapod_elements}, is presented in this section.
|
||||
Several primary objectives guided the mechanical design.
|
||||
First, in order to have a well known Jacobian matrix (used in the control architecture), accurate positioning of rotation points of the top flexible joint and correct orientation of the struts were wanted.
|
||||
First, to ensure a well-defined Jacobian matrix used in the control architecture, accurate positioning of the top flexible joint rotation points and correct orientation of the struts were required.
|
||||
Secondly, space constraints necessitated that the entire platform fit within a cylinder with a radius of \(120\,\text{mm}\) and a height of \(95\,\text{mm}\).
|
||||
Thirdly, because good performances were predicted by the multi-body model, the final design was intended to approximate the behavior of the ``idealized'' Stewart platform as closely as possible.
|
||||
This objective implies that the frequencies of flexible modes potentially detrimental to control performance needed to be maximized.
|
||||
Thirdly, because performance predicted by the multi-body model was fulfilling the requirements, the final design was intended to approximate the behavior of this ``idealized'' active platform as closely as possible.
|
||||
This objective implies that the frequencies of (un-modelled) flexible modes potentially detrimental to control performance needed to be maximized.
|
||||
Finally, considerations for ease of mounting, alignment, and maintenance were incorporated, specifically ensuring that struts could be easily replaced in the event of failure.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
@ -42,9 +42,9 @@ Finally, considerations for ease of mounting, alignment, and maintenance were in
|
||||
|
||||
The strut design, illustrated in Figure \ref{fig:detail_design_strut}, was driven by several factors.
|
||||
Stiff interfaces were required between the amplified piezoelectric actuator and the two flexible joints, as well as between the flexible joints and their respective mounting plates.
|
||||
Due to the limited angular stroke of the flexible joints, it was important that the struts could be assembled in such a way that the two cylindrical interfaces were coaxial while the flexible joints were experiencing no stress (i.e. rest position).
|
||||
To achieve this, cylindrical washers, shown in Figure \ref{fig:detail_design_strut_without_enc}, were integrated into the design to allow for poor flatness between the two interface planes of the APA, depicted in Figure \ref{fig:detail_design_apa}.
|
||||
A dedicated mounting bench was also developed, such that each strut could be precisely aligned, even in the presence of machining inaccuracies.
|
||||
Due to the limited angular stroke of the flexible joints, it was critical that the struts could be assembled such that the two cylindrical interfaces were coaxial while the flexible joints remained in their unstressed, nominal rest position.
|
||||
To facilitate this alignment, cylindrical washers (Figure \ref{fig:detail_design_strut_without_enc}) were integrated into the design to compensate for potential deviations from perfect flatness between the two APA interface planes (Figure \ref{fig:detail_design_apa}).
|
||||
Furthermore, a dedicated mounting bench was developed to enable precise alignment of each strut, even when accounting for typical machining inaccuracies.
|
||||
The mounting procedure is described in Section \ref{sec:test_struts_mounting}.
|
||||
Lastly, the design needed to permit the fixation of an encoder parallel to the strut axis, as shown in Figure \ref{fig:detail_design_strut_with_enc}.
|
||||
|
||||
@ -65,10 +65,9 @@ Lastly, the design needed to permit the fixation of an encoder parallel to the s
|
||||
\end{figure}
|
||||
|
||||
The flexible joints, shown in Figure \ref{fig:detail_design_flexible_joint}, were manufactured using wire-cut electrical discharge machining (EDM).
|
||||
This manufacturing process was selected for few reasons.
|
||||
First, because of the neck dimension of only \(0.25\,\text{mm}\), the part is inherently fragile and is difficult to manufacture with classical machining as cutting forces may damage the part.
|
||||
Also wire-cut EDM allows for very tight machining tolerances, which are critical for achieving accurate location of the center of rotation relative to the plate interfaces (indicated by red surfaces in Figure \ref{fig:detail_design_flexible_joint}) and for maintaining the correct neck dimensions necessary for the desired stiffness and angular stroke properties.
|
||||
The material chosen for the flexible joints is a stainless steel designated \emph{X5CrNiCuNb16-4} (alternatively known as ``F16Ph'').
|
||||
First, the part's inherent fragility, stemming from its \(0.25\,\text{mm}\) neck dimension, makes it susceptible to damage from cutting forces typical in classical machining.
|
||||
Furthermore, wire-cut EDM allows for the very tight machining tolerances critical for achieving accurate location of the center of rotation relative to the plate interfaces (indicated by red surfaces in Figure \ref{fig:detail_design_flexible_joint}) and for maintaining the correct neck dimensions necessary for the desired stiffness and angular stroke properties.
|
||||
The material chosen for the flexible joints is a stainless steel designated \emph{X5CrNiCuNb16-4} (alternatively known as F16Ph).
|
||||
This selection was based on its high specified yield strength (exceeding \(1\,\text{GPa}\) after appropriate heat treatment) and its high fatigue resistance.
|
||||
|
||||
As shown in Figure \ref{fig:detail_design_flexible_joint}, the interface designed to connect with the APA possesses a cylindrical shape, facilitating the use of the aforementioned cylindrical washers for alignment.
|
||||
@ -101,8 +100,8 @@ These parts serve to fix the encoder head and the associated scale (ruler) to th
|
||||
\subsubsection{Plates}
|
||||
|
||||
The design of the top and bottom plates of the active platform was governed by two main requirements: maximizing the frequency of flexible modes and ensuring accurate positioning of the top flexible joints and well-defined orientation of the struts.
|
||||
To maximize the natural frequencies associated with plate flexibility, a simple network of reinforcing ribs was adopted, as shown for the top plate in Figure \ref{fig:detail_design_top_plate}.
|
||||
While topology optimization methods could have been used, the presented designed was found to give high enough flexible modes.
|
||||
To maximize the natural frequencies associated with plate flexibility, a network of reinforcing ribs was incorporated into the design, as shown for the top plate in Figure \ref{fig:detail_design_top_plate}.
|
||||
Although topology optimization methods were considered, the implemented ribbed design was found to provide sufficiently high natural frequencies for the flexible modes.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
@ -110,7 +109,7 @@ While topology optimization methods could have been used, the presented designed
|
||||
\caption{\label{fig:detail_design_top_plate}The mechanical design for the top platform incorporates precisely positioned V-grooves for the joint interfaces (displayed in red). The purpose of the encoder interface (shown in green) is detailed later.}
|
||||
\end{figure}
|
||||
|
||||
Joints interfaces on the plate consist of ``V-grooves''.
|
||||
The interfaces for the joints on the plates incorporate V-grooves (red planes in Figure \ref{fig:detail_design_top_plate}).
|
||||
The cylindrical portion of each flexible joint is constrained within its corresponding V-groove through two distinct line contacts, illustrated in Figure \ref{fig:detail_design_fixation_flexible_joints}.
|
||||
These grooves consequently serve to define the nominal orientation of the struts.
|
||||
High machining accuracy for these features is essential to ensure that the flexible joints are in their neutral, unstressed state when the active platform is assembled.
|
||||
@ -151,8 +150,8 @@ The analysis revealed that the first six modes correspond to ``suspension'' mode
|
||||
Following these suspension modes, numerous ``local'' modes associated with the struts themselves were observed in the frequency range between \(205\,\text{Hz}\) and \(420\,\text{Hz}\).
|
||||
One such mode is represented in Figure \ref{fig:detail_design_fem_strut_mode}.
|
||||
Although these modes do not appear to induce significant motion of the top platform, they do cause relative displacement between the encoder components (head and scale) mounted on the strut.
|
||||
Consequently, such modes could potentially be problematic if the active platform's position is controlled based on the encoders.
|
||||
The extent to which these modes might pose a problem is difficult to establish at this stage, as it depends on whether they are significantly excited by the APA actuation and their sensitivity to strut alignment.
|
||||
Consequently, such modes could potentially degrade control performance if the active platform's position is regulated using these encoder measurements.
|
||||
The extent to which these modes might be detrimental is difficult to establish at this stage, as it depends on whether they are significantly excited by the APA actuation and their sensitivity to strut alignment.
|
||||
Finally, the FEA indicated that flexible modes of the top plate itself begin to appear at frequencies above \(650\,\text{Hz}\), with the first such mode shown in Figure \ref{fig:detail_design_fem_plate_mode}.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
@ -178,7 +177,7 @@ Finally, the FEA indicated that flexible modes of the top plate itself begin to
|
||||
\end{figure}
|
||||
\subsubsection{Alternative Encoder Placement}
|
||||
|
||||
In anticipation of potential issues arising from the local modes of the struts affecting encoder measurements, an alternative fixation strategy for the encoders was envisaged.
|
||||
In anticipation of potential issues arising from the local modes of the struts affecting encoder measurements, an alternative fixation strategy for the encoders was designed.
|
||||
In this configuration, the encoders are fixed directly to the top and bottom plates instead of the struts, as illustrated in Figure \ref{fig:detail_design_enc_plates_design}.
|
||||
|
||||
\begin{figure}[htbp]
|
||||
@ -198,7 +197,7 @@ In this configuration, the encoders are fixed directly to the top and bottom pla
|
||||
\end{figure}
|
||||
|
||||
Dedicated supports, machined from aluminum, were designed for this purpose.
|
||||
It was verified through FEA that the natural modes of these supports occur at sufficiently high frequencies, with the first mode estimated at \(1120\,\text{Hz}\).
|
||||
It was verified through FEA that the natural modes of these supports occur at frequencies sufficiently high (first mode estimated at \(1120\,\text{Hz}\)) to not be problematic for control.
|
||||
Precise positioning of these encoder supports is achieved through machined pockets in both the top and bottom plates, visible in Figure \ref{fig:detail_design_top_plate} (indicated in green).
|
||||
Although the encoders in this arrangement are aligned parallel to the nominal strut axes, they no longer measure the exact relative displacement along the strut between the flexible joint centers.
|
||||
This geometric discrepancy implies that if the relative motion control of the active platform is based directly on these encoder readings, the kinematic calculations may be slightly inaccurate, potentially affecting the overall positioning accuracy of the platform.
|
||||
@ -233,7 +232,7 @@ This model is composed of three distinct solid bodies interconnected by joints,
|
||||
\begin{figure}[htbp]
|
||||
\centering
|
||||
\includegraphics[scale=1,scale=1]{figs/detail_design_simscape_model_flexible_joint.png}
|
||||
\caption{\label{fig:detail_design_simscape_model_flexible_joint}Multi-Body (using the Simscape software) model of the flexible joints. A 4-DoFs model is shown.}
|
||||
\caption{\label{fig:detail_design_simscape_model_flexible_joint}4DoF multi-body model of the flexible joints}
|
||||
\end{figure}
|
||||
\subsubsection{Amplified Piezoelectric Actuators}
|
||||
|
||||
@ -246,8 +245,8 @@ However, as indicated by the FEA results discussed previously, the flexible mode
|
||||
Therefore, a more sophisticated model of the optical encoder was necessary.
|
||||
|
||||
The optical encoders operate based on the interaction between an encoder head and a graduated scale or ruler.
|
||||
The optical encoder head contains a light source which is illuminating the ruler.
|
||||
The position of the light on the ruler is represented by the reference frame \(\{E\}\) in Figure \ref{fig:detail_design_simscape_encoder_model}.
|
||||
The optical encoder head contains a light source that illuminates the ruler.
|
||||
A reference frame \(\{E\}\) fixed to the scale, represents the the light position on the scale, as illustrated in Figure \ref{fig:detail_design_simscape_encoder_model}.
|
||||
The ruler features a precise grating pattern (in this case, with a \(20\,\mu m\) pitch), and its position is associated with the reference frame \(\{R\}\).
|
||||
The displacement measured by the encoder corresponds to the relative position of the encoder frame \(\{E\}\) (specifically, the point where the light interacts with the scale) with respect to the ruler frame \(\{R\}\), projected along the measurement direction defined by the scale.
|
||||
|
||||
@ -268,13 +267,11 @@ An important consequence of this measurement principle is that a relative rotati
|
||||
\end{subfigure}
|
||||
\caption{\label{fig:detail_design_simscape_encoder_model}Representation of the encoder model in the multi-body model. Measurement \(d_i\) corresponds to the \(x\) position of the encoder frame \(\{E\}\) expresssed in the ruller frame \(\{R\}\) (\subref{fig:detail_design_simscape_encoder}). A rotation of the encoder therefore induces a measured displacement (\subref{fig:detail_design_simscape_encoder_disp}).}
|
||||
\end{figure}
|
||||
\subsubsection{Simulation}
|
||||
\subsubsection{Validation of the designed active platform}
|
||||
|
||||
Utilizing this refined multi-body model, several assessments were conducted.
|
||||
The active platform model was integrated into the larger simulation model with the micro-station.
|
||||
The dynamic behavior was evaluated and considered satisfactory.
|
||||
Furthermore, simulations replicating tomography experiments were performed.
|
||||
The performance metrics obtained from these simulations were found to be comparable to those achieved during the earlier conceptual design phase simulations.
|
||||
Consequently, as the results closely mirror those presented previously in Section \ref{ssec:test_id31_iff_hac_perf}, they are not reiterated in detail here.
|
||||
The refined multi-body model of the active platform was integrated into the multi-body micro-station model.
|
||||
Dynamical analysis was performed, confirming that the platform's behavior closely approximates the dynamics of the ``idealized'' model used during the conceptual design phase.
|
||||
Consequently, closed-loop performance simulations replicating tomography experiments yielded metrics highly comparable to those previously predicted (as presented in Section \ref{ssec:nass_hac_tomography}).
|
||||
Given this similarity and because analogous simulations are conducted and detailed during the experimental validation phase (Section \ref{sec:test_id31_hac}), these specific results are not reiterated here.
|
||||
\printbibliography[heading=bibintoc,title={Bibliography}]
|
||||
\end{document}
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user