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Add 3D view of simscape

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Thomas Dehaeze 2024-11-06 15:32:15 +01:00
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simscape-micro-station.org
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@ -1375,14 +1375,20 @@ Each solid body can be represented by inertia properties (most of the time compu
Joints are used to impose kinematic constraints between solid bodies, and to specify dynamical properties (i.e. spring stiffness and damping coefficient). Joints are used to impose kinematic constraints between solid bodies, and to specify dynamical properties (i.e. spring stiffness and damping coefficient).
External forces can be used to model disturbances, and "sensors" can be used to measure the relative pose between two defined frames. External forces can be used to model disturbances, and "sensors" can be used to measure the relative pose between two defined frames.
#+name: fig:ustation_simscape_stage_example
#+caption: Example of a stage (here the tilt-stage) represented in the multi-body model (Simscape). It is composed of two solid bodies connected by a 6-DoF joint. One joint DoF (here the tilt angle) can be imposed, the other ones are represented by springs and dampers. Additional disturbances forces for all DoF can be included
[[file:figs/ustation_simscape_stage_example.png]]
The micro-station is therefore modeled by several solid bodies connected by joints. The micro-station is therefore modeled by several solid bodies connected by joints.
A typical stage (here the tilt-stage) is modelled as shown in Figure ref:fig:ustation_simscape_stage_example where two solid bodies (the fixed part and the mobile part) are connected by a 6-DoF joint. A typical stage (here the tilt-stage) is modelled as shown in Figure ref:fig:ustation_simscape_stage_example where two solid bodies (the fixed part and the mobile part) are connected by a 6-DoF joint.
One DoF of the 6-DoF joint is "imposed" by a setpoint (i.e. modeled as infinitely stiff) while the other 5 are each modelled by a spring and a damper. One DoF of the 6-DoF joint is "imposed" by a setpoint (i.e. modeled as infinitely stiff) while the other 5 are each modelled by a spring and a damper.
Additional forces can be used to model disturbances induced by the stage motion. Additional forces can be used to model disturbances induced by the stage motion.
Obtained 3D representation of the multi-body model is shown in Figure ref:fig:ustation_simscape_model.
#+name: fig:ustation_simscape_stage_example #+name: fig:ustation_simscape_model
#+caption: Example of a stage (here the tilt-stage) represented in the multi-body model (Simscape). It is composed of two solid bodies connected by a 6-DoF joint. One joint DoF (here the tilt angle) can be imposed, the other ones are represented by springs and dampers. Additional disturbances forces for all DoF can be included #+caption: 3D view of the micro-station Simscape model
[[file:figs/ustation_simscape_stage_example.png]] #+attr_latex: :width 0.8\linewidth
[[file:figs/ustation_simscape_model.jpg]]
The Ground is modelled by a solid body connected to the "world frame" through a joint only allowing 3 translations. The Ground is modelled by a solid body connected to the "world frame" through a joint only allowing 3 translations.
The granite is then connected to the ground by a 6-DoF joint. The granite is then connected to the ground by a 6-DoF joint.

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simscape-micro-station.tex
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% Created 2024-11-06 Wed 15:24 % Created 2024-11-06 Wed 15:31
% 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}
@ -374,17 +374,24 @@ Each solid body can be represented by inertia properties (most of the time compu
Joints are used to impose kinematic constraints between solid bodies, and to specify dynamical properties (i.e. spring stiffness and damping coefficient). Joints are used to impose kinematic constraints between solid bodies, and to specify dynamical properties (i.e. spring stiffness and damping coefficient).
External forces can be used to model disturbances, and ``sensors'' can be used to measure the relative pose between two defined frames. External forces can be used to model disturbances, and ``sensors'' can be used to measure the relative pose between two defined frames.
The micro-station is therefore modeled by several solid bodies connected by joints.
A typical stage (here the tilt-stage) is modelled as shown in Figure \ref{fig:ustation_simscape_stage_example} where two solid bodies (the fixed part and the mobile part) are connected by a 6-DoF joint.
One DoF of the 6-DoF joint is ``imposed'' by a setpoint (i.e. modeled as infinitely stiff) while the other 5 are each modelled by a spring and a damper.
Additional forces can be used to model disturbances induced by the stage motion.
\begin{figure}[htbp] \begin{figure}[htbp]
\centering \centering
\includegraphics[scale=1]{figs/ustation_simscape_stage_example.png} \includegraphics[scale=1]{figs/ustation_simscape_stage_example.png}
\caption{\label{fig:ustation_simscape_stage_example}Example of a stage (here the tilt-stage) represented in the multi-body model (Simscape). It is composed of two solid bodies connected by a 6-DoF joint. One joint DoF (here the tilt angle) can be imposed, the other ones are represented by springs and dampers. Additional disturbances forces for all DoF can be included} \caption{\label{fig:ustation_simscape_stage_example}Example of a stage (here the tilt-stage) represented in the multi-body model (Simscape). It is composed of two solid bodies connected by a 6-DoF joint. One joint DoF (here the tilt angle) can be imposed, the other ones are represented by springs and dampers. Additional disturbances forces for all DoF can be included}
\end{figure} \end{figure}
The micro-station is therefore modeled by several solid bodies connected by joints.
A typical stage (here the tilt-stage) is modelled as shown in Figure \ref{fig:ustation_simscape_stage_example} where two solid bodies (the fixed part and the mobile part) are connected by a 6-DoF joint.
One DoF of the 6-DoF joint is ``imposed'' by a setpoint (i.e. modeled as infinitely stiff) while the other 5 are each modelled by a spring and a damper.
Additional forces can be used to model disturbances induced by the stage motion.
Obtained 3D representation of the multi-body model is shown in Figure \ref{fig:ustation_simscape_model}.
\begin{figure}[htbp]
\centering
\includegraphics[scale=1,width=0.8\linewidth]{figs/ustation_simscape_model.jpg}
\caption{\label{fig:ustation_simscape_model}3D view of the micro-station Simscape model}
\end{figure}
The Ground is modelled by a solid body connected to the ``world frame'' through a joint only allowing 3 translations. The Ground is modelled by a solid body connected to the ``world frame'' through a joint only allowing 3 translations.
The granite is then connected to the ground by a 6-DoF joint. The granite is then connected to the ground by a 6-DoF joint.
The translation stage is connected to the granite by a 6-DoF joint, but the \(D_y\) motion is imposed. The translation stage is connected to the granite by a 6-DoF joint, but the \(D_y\) motion is imposed.
@ -535,7 +542,7 @@ Considering how complex the micro-station compliance dynamics is, the model comp
\caption{\label{fig:ustation_frf_compliance_model}Compliance of the micro-station expressed in frame \(\{\mathcal{X}\}\). Measured FRF are display by solid lines, while FRF extracted from the multi-body models are shown by dashed lines. Both translation terms (\subref{fig:ustation_frf_compliance_xyz_model}) and rotational terms (\subref{fig:ustation_frf_compliance_Rxyz_model}) are displayed.} \caption{\label{fig:ustation_frf_compliance_model}Compliance of the micro-station expressed in frame \(\{\mathcal{X}\}\). Measured FRF are display by solid lines, while FRF extracted from the multi-body models are shown by dashed lines. Both translation terms (\subref{fig:ustation_frf_compliance_xyz_model}) and rotational terms (\subref{fig:ustation_frf_compliance_Rxyz_model}) are displayed.}
\end{figure} \end{figure}
\chapter{Estimation of disturbances} \chapter{Estimation of Disturbances}
\label{sec:ustation_disturbances} \label{sec:ustation_disturbances}
The goal in this section is to obtain realistic representation of disturbances affecting the micro-station. The goal in this section is to obtain realistic representation of disturbances affecting the micro-station.
These disturbance sources will then be used during time domain simulations to accurately model the micro-station behavior. These disturbance sources will then be used during time domain simulations to accurately model the micro-station behavior.
@ -547,7 +554,7 @@ In practice, the disturbance forces cannot be directly measured, and the effect
To estimate the equivalent disturbance force that induces such vibration, the transfer function from disturbances sources (i.e. forces applied in the stages' joint) to the displacement of the micro-station's top platform with respect to the granite are extracted from the Simscape model (Section \ref{ssec:ustation_disturbances_sensitivity}). To estimate the equivalent disturbance force that induces such vibration, the transfer function from disturbances sources (i.e. forces applied in the stages' joint) to the displacement of the micro-station's top platform with respect to the granite are extracted from the Simscape model (Section \ref{ssec:ustation_disturbances_sensitivity}).
Finally, the obtained disturbance sources are compared in Section \ref{ssec:ustation_disturbances_results}. Finally, the obtained disturbance sources are compared in Section \ref{ssec:ustation_disturbances_results}.
\section{Measurements of disturbances} \section{Disturbance measurements}
\label{ssec:ustation_disturbances_meas} \label{ssec:ustation_disturbances_meas}
In this section, the ground motion disturbances is directly measured using geophones. In this section, the ground motion disturbances is directly measured using geophones.
Vibrations induced by the scanning of the translation stage and of the spindle are also measured using dedicated setups. Vibrations induced by the scanning of the translation stage and of the spindle are also measured using dedicated setups.