From 05bd404570435a1b155b95fa96e20356145c59f9 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Mon, 21 Apr 2025 19:46:46 +0200 Subject: [PATCH] Finish draft --- figs/detail_design_apa.pdf | Bin 656741 -> 657278 bytes figs/detail_design_apa.png | Bin 66160 -> 72672 bytes figs/detail_design_enc_plates.jpg | Bin 662976 -> 509181 bytes figs/detail_design_enc_struts.jpg | Bin 722499 -> 530566 bytes figs/detail_design_enc_support_mode_1.jpg | Bin 0 -> 7698 bytes figs/detail_design_enc_support_mode_2.jpg | Bin 0 -> 7814 bytes figs/detail_design_enc_support_mode_3.jpg | Bin 0 -> 9347 bytes figs/detail_design_encoders_plates.jpg | Bin 1789629 -> 310572 bytes figs/detail_design_fem_encoder_fix.pdf | Bin 45058 -> 45057 bytes ...detail_design_fixation_flexible_joints.pdf | Bin 224990 -> 224990 bytes figs/detail_design_flexible_joint-crop.jpg | Bin 224365 -> 0 bytes figs/detail_design_flexible_joint.pdf | Bin 696325 -> 696975 bytes figs/detail_design_flexible_joint.png | Bin 62687 -> 69750 bytes figs/detail_design_location_bot_flex.pdf | Bin 341822 -> 341821 bytes ...il_design_location_top_flexible_joints.pdf | Bin 387571 -> 387571 bytes figs/detail_design_nano_hexapod_elements.pdf | Bin 2239762 -> 321078 bytes figs/detail_design_nano_hexapod_elements.png | Bin 317411 -> 382616 bytes figs/detail_design_simscape_encoder.pdf | Bin 19000 -> 19000 bytes figs/detail_design_simscape_encoder_disp.pdf | Bin 19412 -> 19412 bytes ...l_design_simscape_model_flexible_joint.pdf | Bin 69998 -> 70000 bytes ...c.jpg => detail_design_strut_with_enc.pdf} | Bin 138149 -> 154101 bytes figs/detail_design_strut_with_enc.png | Bin 0 -> 68558 bytes ...pg => detail_design_strut_without_enc.pdf} | Bin 132718 -> 148808 bytes figs/detail_design_strut_without_enc.png | Bin 0 -> 46964 bytes figs/detail_design_top_plate.pdf | Bin 658192 -> 658192 bytes figs/inkscape/detail_design_apa.svg | 59 +- .../inkscape/detail_design_flexible_joint.svg | 99 ++- .../detail_design_nano_hexapod_elements.svg | 697 ++++++------------ .../inkscape/detail_design_strut_with_enc.svg | 122 +++ .../detail_design_strut_without_enc.svg | 85 +++ nass-design.org | 289 +++++--- nass-design.pdf | Bin 9450068 -> 5181111 bytes nass-design.tex | 278 ++++--- 33 files changed, 934 insertions(+), 695 deletions(-) create mode 100644 figs/detail_design_enc_support_mode_1.jpg create mode 100644 figs/detail_design_enc_support_mode_2.jpg create mode 100644 figs/detail_design_enc_support_mode_3.jpg delete mode 100644 figs/detail_design_flexible_joint-crop.jpg rename figs/{detail_design_strut_with_enc.jpg => detail_design_strut_with_enc.pdf} (89%) create mode 100644 figs/detail_design_strut_with_enc.png rename figs/{detail_design_strut_without_enc.jpg => detail_design_strut_without_enc.pdf} (89%) create mode 100644 figs/detail_design_strut_without_enc.png create mode 100644 figs/inkscape/detail_design_strut_with_enc.svg create mode 100644 figs/inkscape/detail_design_strut_without_enc.svg diff --git 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inkscape:cy="141" inkscape:window-width="2534" inkscape:window-height="1367" inkscape:window-x="11" inkscape:window-y="60" inkscape:window-maximized="1" - inkscape:current-layer="layer1" /> + sodipodi:nodetypes="cc" />EncoderInterfaceSlottedHole diff --git a/figs/inkscape/detail_design_nano_hexapod_elements.svg b/figs/inkscape/detail_design_nano_hexapod_elements.svg index fd93d99..c825501 100644 --- a/figs/inkscape/detail_design_nano_hexapod_elements.svg +++ b/figs/inkscape/detail_design_nano_hexapod_elements.svg @@ -5,8 +5,9 @@ width="1007.2601" height="327.896" viewBox="0 0 1007.2601 327.896" - sodipodi:docname="nano_hexapod_elements.svg" - inkscape:version="1.1 (c4e8f9ed74, 2021-05-24)" + sodipodi:docname="detail_design_nano_hexapod_elements.svg" + inkscape:version="1.4.1 (93de688d07, 2025-03-30)" + xml:space="preserve" xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape" xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd" xmlns:xlink="http://www.w3.org/1999/xlink" @@ -14,50 +15,33 @@ xmlns:svg="http://www.w3.org/2000/svg" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:cc="http://creativecommons.org/ns#" - xmlns:dc="http://purl.org/dc/elements/1.1/"> - - - - image/svg+xml - - - - - - - image/svg+xml - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Top flexible Joint - Top flexible JointActuator - ActuatorEncoder - EncoderRuler support - Ruler supportTop plate - Top plateBottom plate - Bottom plateStrut - Strut - - - - - - Bot Flexible Joint - Bot Flexible Joint - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 95mm - - + y="83.42437">95mm diff --git a/figs/inkscape/detail_design_strut_with_enc.svg b/figs/inkscape/detail_design_strut_with_enc.svg new file mode 100644 index 0000000..a8bd8bf --- /dev/null +++ b/figs/inkscape/detail_design_strut_with_enc.svg @@ -0,0 +1,122 @@ + + + + + + + + + + + + + + + + Encoder + Ruler + + + + diff --git a/figs/inkscape/detail_design_strut_without_enc.svg b/figs/inkscape/detail_design_strut_without_enc.svg new file mode 100644 index 0000000..21c748b --- /dev/null +++ b/figs/inkscape/detail_design_strut_without_enc.svg @@ -0,0 +1,85 @@ + + + +CylindricalWashers diff --git a/nass-design.org b/nass-design.org index 50968c4..e9c304e 100644 --- a/nass-design.org +++ b/nass-design.org @@ -252,29 +252,43 @@ CLOSED: [2025-04-21 Mon 14:13] [[file:figs/detail_design_nano_hexapod_elements.png]] -*Design goals*: -- Position =bi= and =si= -- Maximum height of 95mm -- As close as possible to "perfect" stewart platform: flexible modes at high frequency -- Easy mounting, easy change of strut in case of failure +Detail design phase: +- key elements were optimized such as: actuator and flexible joints +- relative motion sensor (an encoder) was also selected +- specific kinematics of the Stewart platform (i.e. position of joints and orientation of struts) was not found to be too critical for this application. + Yet, the geometry was fixed in Section [...] +In this section, the mechanical design of the active platform, shown in Figure ref:fig:detail_design_nano_hexapod_elements, is detailed. -Presentation of the obtained design: -- Fixation -- Section on: Complete strut -- Cable management -- Plates design -- FEM results -- Explain again the different specifications in terms of space, payload, etc.. -- CAD view of the nano-hexapod -- Chosen geometry, materials, ease of mounting, cabling, ... -- Validation on Simscape with accurate model? +The main design objectives are: +- Well defined kinematics: Good positioning of the top flexible joint rotation point $\bm{b}_i$ and correct orientation of the struts $\hat{\bm{s}}_i$. + The goal is to have a well defined geometry such that the Jacobian matrix is well defined. +- Space constrains: it should fit within a cylinder with radius of $120\,\text{mm}$ and height of $95\,\text{mm}$ +- As good performances were obtained with the multi-body model. + The final design should behave as close as possible to "perfect" stewart platform. + This means that the frequency of flexible modes that could be problematic for control must be made as high as possible. +- Easy mounting and alignment. +- Easy maintenance: the struts should be easily changed in case for failure. * Mechanical Design <> - -** Struts **** Introduction :ignore: +**** Struts + +The strut design is shown in Figure ref:fig:detail_design_strut. + +The design of the struts was driven by: +- having stiff interface between the amplified piezoelectric actuator and the two flexible joints +- having stiff interface between the flexible joints and the two places (discussed afterwards) +- Because the angular stroke of the flexible joints is fairly limited, it is important to be able to mount the strut such that the two cylindrical interfaces are coaxial. + Do to so: + - A mounting bench was designed + The mounting procedure will be described in Section [...] + # TODO - Add link to section + - Cylindrical washers, shown in Figure ref:fig:detail_design_strut_without_enc, were integrated to allow for adjustments. + The issue was that the flatness between the two interface planes of the APA shown in Figure ref:fig:detail_design_apa could not be guaranteed. + With the added cylindrical washers and the mounting tool, it should be possible to well align the struts even in the presence of machining inaccuracies. +- Possibility to fix the encoder parallel to the strut, as shown in Figure ref:fig:detail_design_strut_with_enc #+name: fig:detail_design_strut #+caption: Design of the Nano-Hexapod struts. Before (\subref{fig:detail_design_strut_without_enc}) and after (\subref{fig:detail_design_strut_with_enc}) encoder integration. @@ -283,65 +297,88 @@ Presentation of the obtained design: #+attr_latex: :caption \subcaption{\label{fig:detail_design_strut_without_enc}Before encoder integration} #+attr_latex: :options {0.49\textwidth} #+begin_subfigure -#+attr_latex: :width 0.95\linewidth -[[file:figs/detail_design_strut_without_enc.jpg]] +#+attr_latex: :scale 0.9 +[[file:figs/detail_design_strut_without_enc.png]] #+end_subfigure #+attr_latex: :caption \subcaption{\label{fig:detail_design_strut_with_enc}With the mounted encoder} #+attr_latex: :options {0.49\textwidth} #+begin_subfigure -#+attr_latex: :width 0.95\linewidth -[[file:figs/detail_design_strut_with_enc.jpg]] +#+attr_latex: :scale 0.9 +[[file:figs/detail_design_strut_with_enc.png]] #+end_subfigure #+end_figure -**** Flexible joints +The flexible joints are manufactured using wire-cut electrical discharge machining, allowing for: +- very tight tolerances: + - allowing good location of the center of rotation with respect to the plate interfaces (red surfaces shown in Figure ref:fig:detail_design_flexible_joint) + - allowing correct neck dimension to have the wanted properties (stiffness and angular stroke) +- Such part is fragile, mainly due to its small "neck" dimension of only $0.25\,\text{mm}$ + Such machining technique has little to no cutting forces. -Flexible joints: X5CrNiCuNb16-4 (F16Ph) -- high yield strength: specified >1GPa using heat treatment -- high fatigue resistance +The flexible joints are made from a stainless steel referenced as "X5CrNiCuNb16-4" (also called "F16Ph"). +This material is chosen for: +- its high yield strength: specified >1GPa using heat treatment. +- its high fatigue resistance + +Figure ref:fig:detail_design_flexible_joint +- Interface with the APA has a cylindrical shape to allow the use of cylindrical washers + A slotted hole has been added to align the flexible joint with the APA using a dowel pin. +- Two threaded holes on the sides can be used to mount the encoders +- The interface with the plate will be latter described. + +The amplified piezoelectric actuators are APA300ML. +Modification of the mechanical interfaces were asked to the manufacturer. +Two planes surfaces and a dowel hole were used, as shown in Figure ref:fig:detail_design_apa. +The amplifying structure, is also made of stainless steel. #+name: fig:detail_design_apa_joints -#+caption: Two main components of the struts: the amplified piezoelectric actuator (\subref{fig:detail_design_apa}) and the flexible joint (\subref{fig:detail_design_flexible_joint}). +#+caption: Two main components of the struts: the flexible joint (\subref{fig:detail_design_flexible_joint}) and the amplified piezoelectric actuator (\subref{fig:detail_design_apa}). #+attr_latex: :options [htbp] #+begin_figure -#+attr_latex: :caption \subcaption{\label{fig:detail_design_apa}Amplified Piezoelectric Actuator} -#+attr_latex: :options {0.49\textwidth} -#+begin_subfigure -#+attr_latex: :scale 1 -[[file:figs/detail_design_apa.png]] -#+end_subfigure #+attr_latex: :caption \subcaption{\label{fig:detail_design_flexible_joint}Flexible joint} #+attr_latex: :options {0.49\textwidth} #+begin_subfigure #+attr_latex: :scale 1 [[file:figs/detail_design_flexible_joint.png]] #+end_subfigure +#+attr_latex: :caption \subcaption{\label{fig:detail_design_apa}Amplified Piezoelectric Actuator} +#+attr_latex: :options {0.49\textwidth} +#+begin_subfigure +#+attr_latex: :scale 1 +[[file:figs/detail_design_apa.png]] +#+end_subfigure #+end_figure -**** Piezoelectric Amplified Actuators +To correctly measure the relative motion of each strut, the encoders need to measure the relative motion between the two flexible joint's rotational centers. +Two interface parts, made of aluminum, are used to fix the encoder and ruler to the two fleible joints as shown in Figure ref:fig:detail_design_strut_with_enc. -APA: modification for better mounting +**** Plates -**** Encoder support +The two plates of the active platform were designed to: +- Maximize the frequency of flexible modes +- have good positioning of the top flexible joints, and good/known orientation of the struts. -All other parts are made of aluminum. - -** Plates - -Plates: X30Cr13 -- high hardness to not deform - - -- Maximize frequency of flexible modes (show FEM) -- Good tolerances for interfaces with flexible joints - Positioning of =bi= and orientation =si= +To maximize the flexible joints, finite element analysis were used iteratively. +While topology optimization could have been used, a network of reinforcing ribs was used as shown in Figure ref:fig:detail_design_top_plate. #+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]] -The cylindrical component is located (or constrained) within the V-groove via two distinct line contacts. + +The fixation interface for the joints and "V-grooves". +The cylindrical part of the flexible joint is located (or constrained) within the V-groove via two distinct line contacts (Figure ref:fig:detail_design_fixation_flexible_joints). +Therefore, these grooves are defining the initial strut orientation +High machining accuracy is required, such that during the mounting of the active platform, the flexible joints are that "rest" position + +The "flat" interface of each top flexible joint is also in contact with the top platform, as shown in Figure ref:fig:detail_design_location_top_flexible_joints, such that the center of rotation of the top flexible joints $\bm{b}_i$ are well located with respect to the top platform. + +The bottom flexible joints are not Figure ref:fig:detail_design_location_bot_flex + +The two plates are made with a martensitic stainless steel "X30Cr13": +- It has high hardness, such that the reference surfaces to not deform when fixing the flexible joints +- This should allow to assemble and disassemble the struts many times if necessary #+name: fig:detail_design_fixation_flexible_joints #+caption: Fixation of the flexible points to the nano-hexapod plates. Both top and bottom flexible joints are clamped to the plates as shown in (\subref{fig:detail_design_fixation_flexible_joints}). While the top flexible joint is in contact with the top plate for precise positioning of its center of rotation (\subref{fig:detail_design_location_top_flexible_joints}), the bottom joint is just oriented (\subref{fig:detail_design_location_bot_flex}). @@ -366,45 +403,58 @@ The cylindrical component is located (or constrained) within the V-groove via tw #+end_subfigure #+end_figure -** Finite Element Analysis +**** Finite Element Analysis +# TODO - Maybe this picture is not necessary +# #+name: fig:detail_design_enc_struts +# #+caption: Obtained Nano-Hexapod design +# #+attr_latex: :width 0.9\linewidth +# [[file:figs/detail_design_enc_struts.jpg]] -#+name: fig:detail_design_enc_struts -#+caption: Obtained Nano-Hexapod design -#+attr_latex: :width 0.9\linewidth -[[file:figs/detail_design_enc_struts.jpg]] - -- FEM of complete system -- Show modes of the struts +Finite element analysis of the complete active platform was performed to identify problematic modes (Figure ref:fig:detail_design_fem_nano_hexapod): +- First six modes were found to be "suspension" modes were the top plate moves as a rigid body, and the six struts are only moving axially (Figure ref:fig:detail_design_fem_rigid_body_mode) +- Then, between $205\,\text{Hz}$ and $420\,\text{Hz}$ many "local" modes of the struts were observed. + On is represented in Figure ref:fig:detail_design_fem_strut_mode. + While these modes seem not to induce any motion of the top platform, it induces a relative displacement of the encoder with respect to the ruler. + Therefore, when controlling the position of the active platform using the encoders, such modes could be problematic. + Whether these modes are problematic is difficult to estimate at this point as: + - it is not known if the APA will "excite" these modes + - theoretically, if the struts are well aligned, these modes should not be observed + Then, flexible modes of the top plate are appearing above $650\,\text{Hz}$ (Figure ref:fig:detail_design_fem_plate_mode) #+name: fig:detail_design_fem_nano_hexapod #+caption: Measurement of strut flexible modes. First six modes are "suspension" modes in which the top plate behaves as a rigid body (\subref{fig:detail_design_fem_rigid_body_mode}). Then modes of the struts have natural frequencies from $205\,\text{Hz}$ to $420\,\text{Hz}$ (\subref{fig:detail_design_fem_strut_mode}). Finally, the first flexible mode of the top plate is at $650\,\text{Hz}$ (\subref{fig:detail_design_fem_plate_mode}) #+attr_latex: :options [htbp] #+begin_figure -#+attr_latex: :caption \subcaption{\label{fig:detail_design_fem_rigid_body_mode}Suspension modes} -#+attr_latex: :options {0.33\textwidth} +#+attr_latex: :caption \subcaption{\label{fig:detail_design_fem_rigid_body_mode}Suspension mode} +#+attr_latex: :options {0.36\textwidth} #+begin_subfigure -#+attr_latex: :width 0.9\linewidth +#+attr_latex: :width 0.95\linewidth [[file:figs/detail_design_fem_rigid_body_mode.jpg]] #+end_subfigure -#+attr_latex: :caption \subcaption{\label{fig:detail_design_fem_strut_mode}Strut - Local modes} -#+attr_latex: :options {0.33\textwidth} +#+attr_latex: :caption \subcaption{\label{fig:detail_design_fem_strut_mode}Strut - Local mode} +#+attr_latex: :options {0.36\textwidth} #+begin_subfigure -#+attr_latex: :width 0.9\linewidth +#+attr_latex: :width 0.95\linewidth [[file:figs/detail_design_fem_strut_mode.jpg]] #+end_subfigure -#+attr_latex: :caption \subcaption{\label{fig:detail_design_fem_plate_mode}Top plate modes} -#+attr_latex: :options {0.33\textwidth} +#+attr_latex: :caption \subcaption{\label{fig:detail_design_fem_plate_mode}Top plate mode} +#+attr_latex: :options {0.26\textwidth} #+begin_subfigure -#+attr_latex: :width 0.9\linewidth +#+attr_latex: :width 0.95\linewidth [[file:figs/detail_design_fem_plate_mode.jpg]] #+end_subfigure #+end_figure -** Obtained Design +**** Alternative Encoder Placement -- Alternative encoder position: on the plates -- Support made of aluminum +To anticipate potential issue with local modes of the struts, an alternative fixation for the encoder is planned: +- Instead of being fixed to the struts, the encoders are fixed to the plates instead, as shown in Figure ref:fig:detail_design_enc_plates_design. +- The support are made of aluminum, and it is verified that the natural modes are at high enough frequency (Figure ref:fig:detail_design_enc_support_modes). +- The positioning of the encoders are made using pockets in both plates as shown in Figure ref:fig:detail_design_top_plate. +- The encoders are aligned parallel to the struts, but yet they don't exactly measure the relative motion of each strut. +- This means that if relative motion of the active platform is performed based on the encoders, the accuracy of the motion may be affected. + The issue is that the Kinematics may not be correct. #+name: fig:detail_design_enc_plates_design #+caption: Alternative way of using the encoders: they are fixed directly to the plates. @@ -424,30 +474,42 @@ The cylindrical component is located (or constrained) within the V-groove via tw #+end_subfigure #+end_figure - -#+name: fig:detail_design_fem_encoder_fix +#+name: fig:detail_design_enc_support_modes #+caption: Finite Element Analysis of the encoder supports. Encoder inertia was taken into account. -[[file:figs/detail_design_fem_encoder_fix.png]] +#+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 -:PROPERTIES: -:HEADER-ARGS:matlab+: :tangle matlab/detail_design_1_model.m -:END: <> +**** Introduction :ignore: -*Multi body Model*: -- Complete model: two plates, 6 joints, 6 actuators, 6 encoders -- Joint Model -- APA Model -- Encoder model -- Say that obtained dynamics was considered good + possible to perform simulations of tomography experiments with same performance as during the conceptual design +Before all the mechanical parts were ordered, the multi-body model of the active platform was refined using the design parts. -** Introduction :ignore: - -Two configurations: +Two configurations, displayed in Figure ref:fig:detail_design_simscape_encoder, were considered: - Encoders fixed to the struts - Encoders fixed to the plates +Plates were modelled as rigid bodies, with inertia computed from the 3D shape. + #+name: fig:detail_design_simscape_encoder #+caption: 3D representation of the multi-body model. There are two configurations: encoders fixed to the struts (\subref{fig:detail_design_simscape_encoder_struts}) and encoders fixed to the plates (\subref{fig:detail_design_simscape_encoder_plates}). #+attr_latex: :options [htbp] @@ -466,19 +528,45 @@ Two configurations: #+end_subfigure #+end_figure +**** Flexible Joints -** Flexible Joints +Different models of the flexible joints where considered: +- 2DoF: only bending stiffnesses +- 3DoF: added torsional stiffness +- 4DoF: added axial stiffness + +The multi-body model for the 4DoF configuration is shown in Figure ref:fig:detail_design_simscape_model_flexible_joint. +It is composed of three solid bodies connected by joints whose stiffnesses are computed from the finite element model. #+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. #+attr_latex: :scale 1 [[file:figs/detail_design_simscape_model_flexible_joint.png]] -** Amplified Piezoelectric Actuators +**** Amplified Piezoelectric Actuators + +The amplified piezoelectric actuators are modelled as explained in Section [..]. +# Add link to section +Two different models can be used in the multi-body model: +- a 2DoF "axial" model +- a "super-element" extracted from the finite element model + +**** Encoders + +Up to now, relative displacement sensors were implemented as a relative distance measurement between $\bm{a}_i$ and $\bm{b}_i$. + +As shown in the previous section, flexible modes of the struts may negatively impact the encoder signal. +It was therefore necessary to better model the encoder. + +The optical encoder works: +- Encoder heads contains a light source shine on the ruler, and a photo-diode. + This is represented by frame $\{E\}$ in Figure ref:fig:detail_design_simscape_encoder. +- ruler or scale with a grating (here with a $20\,\mu m$ pitch). A reference frame is indicated by $\{R\}$ + +Therefore, the measured displacement is the relative position of $\{E\}$ (i.e. there the light "hits" the scale) with respect to frame $\{R\}$, in the direction of the scale. - -** Encoders +In that case, a rotation of the encoder, as shown in figure ref:fig:detail_design_simscape_encoder_disp induces a measured displacement. #+name: fig:detail_design_simscape_encoder_model #+caption: 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}). @@ -498,6 +586,14 @@ Two configurations: #+end_subfigure #+end_figure +**** Simulation + +Based on this refined model: +- the active platform could be integrated on top of the micro-station's model. +- the obtained dynamics was considered good +- simulations of tomography experiments were performed, and similar performance were obtained as during the conceptual design +- this is not presented here as results are very similar to the simulations performed in Section [...] + # Add link to section * Conclusion <> @@ -505,24 +601,3 @@ Two configurations: * Bibliography :ignore: #+latex: \printbibliography[heading=bibintoc,title={Bibliography}] -* Helping Functions :noexport: -** Initialize Path -#+NAME: m-init-path -#+BEGIN_SRC matlab -%% Path for functions, data and scripts -addpath('./matlab/mat/'); % Path for data -addpath('./matlab/'); % Path for scripts -#+END_SRC - 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diff --git a/nass-design.tex b/nass-design.tex index e7422d6..769f4e1 100644 --- a/nass-design.tex +++ b/nass-design.tex @@ -1,4 +1,4 @@ -% Created 2025-04-21 Mon 16:49 +% Created 2025-04-21 Mon 19:46 % Intended LaTeX compiler: pdflatex \documentclass[a4paper, 10pt, DIV=12, parskip=full, bibliography=totoc]{scrreprt} @@ -30,87 +30,124 @@ \end{figure} -\textbf{Design goals}: +Detail design phase: \begin{itemize} -\item Position \texttt{bi} and \texttt{si} -\item Maximum height of 95mm -\item As close as possible to ``perfect'' stewart platform: flexible modes at high frequency -\item Easy mounting, easy change of strut in case of failure +\item key elements were optimized such as: actuator and flexible joints +\item relative motion sensor (an encoder) was also selected +\item specific kinematics of the Stewart platform (i.e. position of joints and orientation of struts) was not found to be too critical for this application. +Yet, the geometry was fixed in Section [\ldots{}] \end{itemize} +In this section, the mechanical design of the active platform, shown in Figure \ref{fig:detail_design_nano_hexapod_elements}, is detailed. -Presentation of the obtained design: +The main design objectives are: \begin{itemize} -\item Fixation -\item Section on: Complete strut -\item Cable management -\item Plates design -\item FEM results -\item Explain again the different specifications in terms of space, payload, etc.. -\item CAD view of the nano-hexapod -\item Chosen geometry, materials, ease of mounting, cabling, \ldots{} -\item Validation on Simscape with accurate model? +\item Well defined kinematics: Good positioning of the top flexible joint rotation point \(\bm{b}_i\) and correct orientation of the struts \(\hat{\bm{s}}_i\). +The goal is to have a well defined geometry such that the Jacobian matrix is well defined. +\item Space constrains: it should fit within a cylinder with radius of \(120\,\text{mm}\) and height of \(95\,\text{mm}\) +\item As good performances were obtained with the multi-body model. +The final design should behave as close as possible to ``perfect'' stewart platform. +This means that the frequency of flexible modes that could be problematic for control must be made as high as possible. +\item Easy mounting and alignment. +\item Easy maintenance: the struts should be easily changed in case for failure. \end{itemize} \chapter{Mechanical Design} \label{sec:detail_design_mechanics} -\section{Struts} +\subsubsection{Struts} + +The strut design is shown in Figure \ref{fig:detail_design_strut}. + +The design of the struts was driven by: +\begin{itemize} +\item having stiff interface between the amplified piezoelectric actuator and the two flexible joints +\item having stiff interface between the flexible joints and the two places (discussed afterwards) +\item Because the angular stroke of the flexible joints is fairly limited, it is important to be able to mount the strut such that the two cylindrical interfaces are coaxial. +Do to so: +\begin{itemize} +\item A mounting bench was designed +The mounting procedure will be described in Section [\ldots{}] +\item Cylindrical washers, shown in Figure \ref{fig:detail_design_strut_without_enc}, were integrated to allow for adjustments. +The issue was that the flatness between the two interface planes of the APA shown in Figure \ref{fig:detail_design_apa} could not be guaranteed. +With the added cylindrical washers and the mounting tool, it should be possible to well align the struts even in the presence of machining inaccuracies. +\end{itemize} +\item Possibility to fix the encoder parallel to the strut, as shown in Figure \ref{fig:detail_design_strut_with_enc} +\end{itemize} + \begin{figure}[htbp] \begin{subfigure}{0.49\textwidth} \begin{center} -\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_design_strut_without_enc.jpg} +\includegraphics[scale=1,scale=0.9]{figs/detail_design_strut_without_enc.png} \end{center} \subcaption{\label{fig:detail_design_strut_without_enc}Before encoder integration} \end{subfigure} \begin{subfigure}{0.49\textwidth} \begin{center} -\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_design_strut_with_enc.jpg} +\includegraphics[scale=1,scale=0.9]{figs/detail_design_strut_with_enc.png} \end{center} \subcaption{\label{fig:detail_design_strut_with_enc}With the mounted encoder} \end{subfigure} \caption{\label{fig:detail_design_strut}Design of the Nano-Hexapod struts. Before (\subref{fig:detail_design_strut_without_enc}) and after (\subref{fig:detail_design_strut_with_enc}) encoder integration.} \end{figure} -\subsubsection{Flexible joints} -Flexible joints: X5CrNiCuNb16-4 (F16Ph) +The flexible joints are manufactured using wire-cut electrical discharge machining, allowing for: \begin{itemize} -\item high yield strength: specified >1GPa using heat treatment -\item high fatigue resistance +\item very tight tolerances: +\begin{itemize} +\item allowing good location of the center of rotation with respect to the plate interfaces (red surfaces shown in Figure \ref{fig:detail_design_flexible_joint}) +\item allowing correct neck dimension to have the wanted properties (stiffness and angular stroke) +\end{itemize} +\item Such part is fragile, mainly due to its small ``neck'' dimension of only \(0.25\,\text{mm}\) +Such machining technique has little to no cutting forces. \end{itemize} +The flexible joints are made from a stainless steel referenced as ``X5CrNiCuNb16-4'' (also called ``F16Ph''). +This material is chosen for: +\begin{itemize} +\item its high yield strength: specified >1GPa using heat treatment. +\item its high fatigue resistance +\end{itemize} + +Figure \ref{fig:detail_design_flexible_joint} +\begin{itemize} +\item Interface with the APA has a cylindrical shape to allow the use of cylindrical washers +A slotted hole has been added to align the flexible joint with the APA using a dowel pin. +\item Two threaded holes on the sides can be used to mount the encoders +\item The interface with the plate will be latter described. +\end{itemize} + +The amplified piezoelectric actuators are APA300ML. +Modification of the mechanical interfaces were asked to the manufacturer. +Two planes surfaces and a dowel hole were used, as shown in Figure \ref{fig:detail_design_apa}. +The amplifying structure, is also made of stainless steel. + \begin{figure}[htbp] \begin{subfigure}{0.49\textwidth} \begin{center} -\includegraphics[scale=1,scale=1]{figs/detail_design_apa.png} -\end{center} -\subcaption{\label{fig:detail_design_apa}Amplified Piezoelectric Actuator} -\end{subfigure} -\begin{subfigure}{0.49\textwidth} -\begin{center} \includegraphics[scale=1,scale=1]{figs/detail_design_flexible_joint.png} \end{center} \subcaption{\label{fig:detail_design_flexible_joint}Flexible joint} \end{subfigure} -\caption{\label{fig:detail_design_apa_joints}Two main components of the struts: the amplified piezoelectric actuator (\subref{fig:detail_design_apa}) and the flexible joint (\subref{fig:detail_design_flexible_joint}).} +\begin{subfigure}{0.49\textwidth} +\begin{center} +\includegraphics[scale=1,scale=1]{figs/detail_design_apa.png} +\end{center} +\subcaption{\label{fig:detail_design_apa}Amplified Piezoelectric Actuator} +\end{subfigure} +\caption{\label{fig:detail_design_apa_joints}Two main components of the struts: the flexible joint (\subref{fig:detail_design_flexible_joint}) and the amplified piezoelectric actuator (\subref{fig:detail_design_apa}).} \end{figure} -\subsubsection{Piezoelectric Amplified Actuators} -APA: modification for better mounting -\subsubsection{Encoder support} +To correctly measure the relative motion of each strut, the encoders need to measure the relative motion between the two flexible joint's rotational centers. +Two interface parts, made of aluminum, are used to fix the encoder and ruler to the two fleible joints as shown in Figure \ref{fig:detail_design_strut_with_enc}. +\subsubsection{Plates} -All other parts are made of aluminum. -\section{Plates} - -Plates: X30Cr13 +The two plates of the active platform were designed to: \begin{itemize} -\item high hardness to not deform +\item Maximize the frequency of flexible modes +\item have good positioning of the top flexible joints, and good/known orientation of the struts. \end{itemize} - -\begin{itemize} -\item Maximize frequency of flexible modes (show FEM) -\item Good tolerances for interfaces with flexible joints -Positioning of \texttt{bi} and orientation \texttt{si} -\end{itemize} +To maximize the flexible joints, finite element analysis were used iteratively. +While topology optimization could have been used, a network of reinforcing ribs was used as shown in Figure \ref{fig:detail_design_top_plate}. \begin{figure}[htbp] \centering @@ -118,7 +155,21 @@ Positioning of \texttt{bi} and orientation \texttt{si} \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} -The cylindrical component is located (or constrained) within the V-groove via two distinct line contacts. + +The fixation interface for the joints and ``V-grooves''. +The cylindrical part of the flexible joint is located (or constrained) within the V-groove via two distinct line contacts (Figure \ref{fig:detail_design_fixation_flexible_joints}). +Therefore, these grooves are defining the initial strut orientation +High machining accuracy is required, such that during the mounting of the active platform, the flexible joints are that ``rest'' position + +The ``flat'' interface of each top flexible joint is also in contact with the top platform, as shown in Figure \ref{fig:detail_design_location_top_flexible_joints}, such that the center of rotation of the top flexible joints \(\bm{b}_i\) are well located with respect to the top platform. + +The bottom flexible joints are not Figure \ref{fig:detail_design_location_bot_flex} + +The two plates are made with a martensitic stainless steel ``X30Cr13'': +\begin{itemize} +\item It has high hardness, such that the reference surfaces to not deform when fixing the flexible joints +\item This should allow to assemble and disassemble the struts many times if necessary +\end{itemize} \begin{figure} \begin{subfigure}{0.33\textwidth} @@ -141,46 +192,54 @@ The cylindrical component is located (or constrained) within the V-groove via tw \end{subfigure} \caption{\label{fig:detail_design_fixation_flexible_joints}Fixation of the flexible points to the nano-hexapod plates. Both top and bottom flexible joints are clamped to the plates as shown in (\subref{fig:detail_design_fixation_flexible_joints}). While the top flexible joint is in contact with the top plate for precise positioning of its center of rotation (\subref{fig:detail_design_location_top_flexible_joints}), the bottom joint is just oriented (\subref{fig:detail_design_location_bot_flex}).} \end{figure} -\section{Finite Element Analysis} - - -\begin{figure}[htbp] -\centering -\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_design_enc_struts.jpg} -\caption{\label{fig:detail_design_enc_struts}Obtained Nano-Hexapod design} -\end{figure} +\subsubsection{Finite Element Analysis} +Finite element analysis of the complete active platform was performed to identify problematic modes (Figure \ref{fig:detail_design_fem_nano_hexapod}): \begin{itemize} -\item FEM of complete system -\item Show modes of the struts +\item First six modes were found to be ``suspension'' modes were the top plate moves as a rigid body, and the six struts are only moving axially (Figure \ref{fig:detail_design_fem_rigid_body_mode}) +\item Then, between \(205\,\text{Hz}\) and \(420\,\text{Hz}\) many ``local'' modes of the struts were observed. +On is represented in Figure \ref{fig:detail_design_fem_strut_mode}. +While these modes seem not to induce any motion of the top platform, it induces a relative displacement of the encoder with respect to the ruler. +Therefore, when controlling the position of the active platform using the encoders, such modes could be problematic. +Whether these modes are problematic is difficult to estimate at this point as: +\begin{itemize} +\item it is not known if the APA will ``excite'' these modes +\item theoretically, if the struts are well aligned, these modes should not be observed +\end{itemize} +Then, flexible modes of the top plate are appearing above \(650\,\text{Hz}\) (Figure \ref{fig:detail_design_fem_plate_mode}) \end{itemize} \begin{figure}[htbp] -\begin{subfigure}{0.33\textwidth} +\begin{subfigure}{0.36\textwidth} \begin{center} -\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_design_fem_rigid_body_mode.jpg} +\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_design_fem_rigid_body_mode.jpg} \end{center} -\subcaption{\label{fig:detail_design_fem_rigid_body_mode}Suspension modes} +\subcaption{\label{fig:detail_design_fem_rigid_body_mode}Suspension mode} \end{subfigure} -\begin{subfigure}{0.33\textwidth} +\begin{subfigure}{0.36\textwidth} \begin{center} -\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_design_fem_strut_mode.jpg} +\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_design_fem_strut_mode.jpg} \end{center} -\subcaption{\label{fig:detail_design_fem_strut_mode}Strut - Local modes} +\subcaption{\label{fig:detail_design_fem_strut_mode}Strut - Local mode} \end{subfigure} -\begin{subfigure}{0.33\textwidth} +\begin{subfigure}{0.26\textwidth} \begin{center} -\includegraphics[scale=1,width=0.9\linewidth]{figs/detail_design_fem_plate_mode.jpg} +\includegraphics[scale=1,width=0.95\linewidth]{figs/detail_design_fem_plate_mode.jpg} \end{center} -\subcaption{\label{fig:detail_design_fem_plate_mode}Top plate modes} +\subcaption{\label{fig:detail_design_fem_plate_mode}Top plate mode} \end{subfigure} \caption{\label{fig:detail_design_fem_nano_hexapod}Measurement of strut flexible modes. First six modes are ``suspension'' modes in which the top plate behaves as a rigid body (\subref{fig:detail_design_fem_rigid_body_mode}). Then modes of the struts have natural frequencies from \(205\,\text{Hz}\) to \(420\,\text{Hz}\) (\subref{fig:detail_design_fem_strut_mode}). Finally, the first flexible mode of the top plate is at \(650\,\text{Hz}\) (\subref{fig:detail_design_fem_plate_mode})} \end{figure} -\section{Obtained Design} +\subsubsection{Alternative Encoder Placement} +To anticipate potential issue with local modes of the struts, an alternative fixation for the encoder is planned: \begin{itemize} -\item Alternative encoder position: on the plates -\item Support made of aluminum +\item Instead of being fixed to the struts, the encoders are fixed to the plates instead, as shown in Figure \ref{fig:detail_design_enc_plates_design}. +\item The support are made of aluminum, and it is verified that the natural modes are at high enough frequency (Figure \ref{fig:detail_design_enc_support_modes}). +\item The positioning of the encoders are made using pockets in both plates as shown in Figure \ref{fig:detail_design_top_plate}. +\item The encoders are aligned parallel to the struts, but yet they don't exactly measure the relative motion of each strut. +\item This means that if relative motion of the active platform is performed based on the encoders, the accuracy of the motion may be affected. +The issue is that the Kinematics may not be correct. \end{itemize} \begin{figure}[htbp] @@ -199,30 +258,39 @@ The cylindrical component is located (or constrained) within the V-groove via tw \caption{\label{fig:detail_design_enc_plates_design}Alternative way of using the encoders: they are fixed directly to the plates.} \end{figure} - \begin{figure}[htbp] -\centering -\includegraphics[scale=1]{figs/detail_design_fem_encoder_fix.png} -\caption{\label{fig:detail_design_fem_encoder_fix}Finite Element Analysis of the encoder supports. Encoder inertia was taken into account.} +\begin{subfigure}{0.33\textwidth} +\begin{center} +\includegraphics[scale=1,scale=0.5]{figs/detail_design_enc_support_mode_1.jpg} +\end{center} +\subcaption{\label{fig:detail_design_enc_support_mode_1}$1^{\text{st}}$ mode at $1120\,\text{Hz}$} +\end{subfigure} +\begin{subfigure}{0.33\textwidth} +\begin{center} +\includegraphics[scale=1,scale=0.5]{figs/detail_design_enc_support_mode_2.jpg} +\end{center} +\subcaption{\label{fig:detail_design_enc_support_mode_2}$2^{\text{nd}}$ mode at $2020\,\text{Hz}$} +\end{subfigure} +\begin{subfigure}{0.33\textwidth} +\begin{center} +\includegraphics[scale=1,scale=0.5]{figs/detail_design_enc_support_mode_3.jpg} +\end{center} +\subcaption{\label{fig:detail_design_enc_support_mode_3}$3^{\text{rd}}$ mode at $2080\,\text{Hz}$} +\end{subfigure} +\caption{\label{fig:detail_design_enc_support_modes}Finite Element Analysis of the encoder supports. Encoder inertia was taken into account.} \end{figure} \chapter{Multi-Body Model} \label{sec:detail_design_model} +Before all the mechanical parts were ordered, the multi-body model of the active platform was refined using the design parts. -\textbf{Multi body Model}: -\begin{itemize} -\item Complete model: two plates, 6 joints, 6 actuators, 6 encoders -\item Joint Model -\item APA Model -\item Encoder model -\item Say that obtained dynamics was considered good + possible to perform simulations of tomography experiments with same performance as during the conceptual design -\end{itemize} - -Two configurations: +Two configurations, displayed in Figure \ref{fig:detail_design_simscape_encoder}, were considered: \begin{itemize} \item Encoders fixed to the struts \item Encoders fixed to the plates \end{itemize} +Plates were modelled as rigid bodies, with inertia computed from the 3D shape. + \begin{figure}[htbp] \begin{subfigure}{0.49\textwidth} \begin{center} @@ -238,18 +306,49 @@ Two configurations: \end{subfigure} \caption{\label{fig:detail_design_simscape_encoder}3D representation of the multi-body model. There are two configurations: encoders fixed to the struts (\subref{fig:detail_design_simscape_encoder_struts}) and encoders fixed to the plates (\subref{fig:detail_design_simscape_encoder_plates}).} \end{figure} -\section{Flexible Joints} +\subsubsection{Flexible Joints} + +Different models of the flexible joints where considered: +\begin{itemize} +\item 2DoF: only bending stiffnesses +\item 3DoF: added torsional stiffness +\item 4DoF: added axial stiffness +\end{itemize} + +The multi-body model for the 4DoF configuration is shown in Figure \ref{fig:detail_design_simscape_model_flexible_joint}. +It is composed of three solid bodies connected by joints whose stiffnesses are computed from the finite element model. \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.} \end{figure} -\section{Amplified Piezoelectric Actuators} +\subsubsection{Amplified Piezoelectric Actuators} + +The amplified piezoelectric actuators are modelled as explained in Section [..]. +Two different models can be used in the multi-body model: +\begin{itemize} +\item a 2DoF ``axial'' model +\item a ``super-element'' extracted from the finite element model +\end{itemize} +\subsubsection{Encoders} + +Up to now, relative displacement sensors were implemented as a relative distance measurement between \(\bm{a}_i\) and \(\bm{b}_i\). + +As shown in the previous section, flexible modes of the struts may negatively impact the encoder signal. +It was therefore necessary to better model the encoder. + +The optical encoder works: +\begin{itemize} +\item Encoder heads contains a light source shine on the ruler, and a photo-diode. +This is represented by frame \(\{E\}\) in Figure \ref{fig:detail_design_simscape_encoder}. +\item ruler or scale with a grating (here with a \(20\,\mu m\) pitch). A reference frame is indicated by \(\{R\}\) +\end{itemize} + +Therefore, the measured displacement is the relative position of \(\{E\}\) (i.e. there the light ``hits'' the scale) with respect to frame \(\{R\}\), in the direction of the scale. - -\section{Encoders} +In that case, a rotation of the encoder, as shown in figure \ref{fig:detail_design_simscape_encoder_disp} induces a measured displacement. \begin{figure}[htbp] \begin{subfigure}{0.49\textwidth} @@ -266,6 +365,15 @@ Two configurations: \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} + +Based on this refined model: +\begin{itemize} +\item the active platform could be integrated on top of the micro-station's model. +\item the obtained dynamics was considered good +\item simulations of tomography experiments were performed, and similar performance were obtained as during the conceptual design +\item this is not presented here as results are very similar to the simulations performed in Section [\ldots{}] +\end{itemize} \chapter{Conclusion} \label{sec:detail_design_conclusion} \printbibliography[heading=bibintoc,title={Bibliography}]

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