Add few comments on simscape multibody
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<?xml version='1.0' encoding='UTF-8'?>
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<Info Ref="hac_lac" Type="Relative" />
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<Info />
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<?xml version='1.0' encoding='UTF-8'?>
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<Info Ref="control" Type="Relative" />
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<Info />
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<?xml version='1.0' encoding='UTF-8'?>
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<Info Ref="nass_library" Type="Relative" />
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<?xml version='1.0' encoding='UTF-8'?>
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<Info Ref="active_damping" Type="Relative" />
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<?xml version='1.0' encoding='UTF-8'?>
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<Info Ref="analysis" Type="Relative" />
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<?xml version='1.0' encoding='UTF-8'?>
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<Info Ref="initialize" Type="Relative" />
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<?xml version='1.0' encoding='UTF-8'?>
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<Info Ref="demonstration" Type="Relative" />
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@ -41,6 +41,21 @@
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#+PROPERTY: header-args:latex+ :output-dir figs
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:END:
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* Introduction :ignore:
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The goal here is to make an identification of the micro-station in order to compare the model with the measurements on the real micro-station.
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In order to do so:
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- Decide where to virtually excite the station and where to measure its motion
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- Extract transfer functions from the excitation forces to the measured motion
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- Compare those transfer functions with the modal analysis
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For the excitation, we can choose the same excitation points as the one used for the modal test.
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For the measurement points, we can choose the Center of Mass of each solid body.
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The center of mass of each solid body is not easily defined using Simscape.
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Indeed, we can define the center of mass of any solid body but not of multiple solid bodies. However, one solid body is composed of multiple STEP files.
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One solution could be to use one STEP file for one solid body.
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However, the position of the center of mass can be exported using simulink and then defined on Simscape.
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* ZIP file containing the data and matlab files :ignore:
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#+begin_src bash :exports none :results none
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if [ matlab/identification_micro_station.m -nt data/identification_micro_station.zip ]; then
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@ -56,9 +71,25 @@
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All the files (data and Matlab scripts) are accessible [[file:data/identification_micro_station.zip][here]].
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#+end_note
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* Matlab Init :noexport:ignore:
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#+begin_src matlab :tangle no :exports none :results silent :noweb yes :var current_dir=(file-name-directory buffer-file-name)
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<<matlab-dir>>
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#+end_src
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#+begin_src matlab :exports none :results silent :noweb yes
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<<matlab-init>>
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#+end_src
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* Identification of the micro-station
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#+begin_src matlab
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simulinkproject('../');
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#+end_src
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#+begin_src matlab
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open sim_micro_station_id.slx
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#+end_src
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* Plot the obtained transfer functions
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* Compare with the modal measurements
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* Modal Identification of the micro station
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106
index.org
106
index.org
@ -64,12 +64,10 @@ The project can be opened using the =simulinkproject= function:
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When the project opens, a startup script is ran.
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The startup script is defined below and is exported to the =project_startup.m= script.
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#+begin_src matlab :eval no :tangle src/project_startup.m
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%%
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freqs = logspace(-1, 3, 1000);
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save_fig = false;
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save('./mat/config.mat', 'freqs', 'save_fig');
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%%
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project = simulinkproject;
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projectRoot = project.RootFolder;
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@ -89,11 +87,107 @@ When the project closes, it runs the =project_shutdown.m= script defined below.
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The project also permits to automatically add defined folder to the path when the project is opened.
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* Notes
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Step files are exported from SolidWorks and imported into Simscape.
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Each step file is then considered as a solid body.
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Inertia and mass matrices are computed from the density of the material and the geometry as defined by the step file.
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* Simscape Model
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A [[https://.mathworks.com/products/simscape.html][simscape]] model permits to model multi-physics systems.
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[[https://mathworks.com/products/simmechanics.html][Simscape Multibody]] permits to model multibody systems using blocks representing bodies, joints, constraints, force elements, and sensors.
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** Solid bodies
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Each solid body is represented by a [[https://mathworks.com/help/physmod/sm/ref/solid.html][solid block]].
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The geometry of the solid body can be imported using a =step= file. The properties of the solid body such as its mass, center of mass and moment of inertia can be derived from its density and its geometry as defined by the =step= file. They also can be set by hand.
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** Frames
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Frames are very important in simscape multibody, they defined where the forces are applied, where the joints are located and where the measurements are made.
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They can be defined from the solid body geometry, or using the [[https://mathworks.com/help/physmod/sm/ref/rigidtransform.html][rigid transform block]].
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** Joints
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Solid Bodies are connected with joints (between frames of the two solid bodies).
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There are various types of joints that are all described [[https://mathworks.com/help/physmod/sm/ug/joints.html][here]].
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#+name: tab:joint_dof
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#+caption: Degrees of freedom associated with each joint
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| Joint Block | Translational DOFs | Rotational DOFs |
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|-------------------+--------------------+-----------------|
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| 6-DOF | 3 | 3 |
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| Bearing | 1 | 3 |
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| Bushing | 3 | 3 |
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| Cartesian | 3 | 0 |
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| Constant Velocity | 0 | 2 |
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| Cylindrical | 1 | 1 |
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| Gimbal | 0 | 3 |
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| Leadscrew | 1 (coupled) | 1 (coupled) |
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| Pin Slot | 1 | 1 |
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| Planar | 2 | 1 |
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| Prismatic | 1 | 0 |
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| Rectangular | 2 | 0 |
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| Revolute | 0 | 1 |
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| Spherical | 1 | 3 |
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| Telescoping | 1 | 3 |
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| Universal | 0 | 2 |
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| Weld | 0 | 0 |
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Joint blocks are assortments of joint primitives:
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- *Prismatic*: allows translation along a single standard axis: =Px=, =Py=, =Pz=
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- *Revolute*: allows rotation about a single standard axis: =Rx=, =Ry=, =Rz=
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- *Spherical*: allow rotation about any 3D axis: =S=
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- *Lead Screw*: allows coupled rotation and translation on a standard axis: =LSz=
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- *Constant Velocity*: Allows rotation at constant velocity between intersection through arbitrarily aligned shafts: =CV=
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#+name: tab:joint_primitive
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#+caption: Joint primitives for each joint type
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| Joint Block | Px | Py | Pz | Rx | Ry | Rz | S | CV | LSz |
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|-------------------+----+----+----+----+----+----+---+----+-----|
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| 6-DOF | x | x | x | | | | x | | |
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| Bearing | | | x | x | x | x | | | |
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| Bushing | x | x | x | x | x | x | | | |
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| Cartesian | x | x | x | | | | | | |
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| Constant Velocity | | | | | | | | x | |
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| Cylindrical | | | x | | | x | | | |
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| Gimbal | | | | x | x | x | | | |
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| Leadscrew | | | | | | | | | x |
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| Pin Slot | x | | | | | x | | | |
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| Planar | x | x | | | | x | | | |
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| Prismatic | | | x | | | | | | |
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| Rectangular | x | x | | | | | | | |
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| Revolute | | | | | | x | | | |
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| Spherical | | | | | | | x | | |
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| Telescoping | | | x | | | | x | | |
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| Universal | | | | x | x | | | | |
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| Weld | | | | | | | | | |
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For each of the joint primitive, we can specify the dynamical properties:
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- The *spring stiffness*: either linear or rotational one
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- The *damping coefficient*
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For the actuation, we can either specify the motion or the force:
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- the force applied in the corresponding DOF is provided by the input
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- the motion is provided by the input
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A sensor can be added to measure either the position, velocity or acceleration of the joint DOF.
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Composite Force/Torque sensing:
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- Constraint force
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- Total force: gives the sum across all joint primitives over all sources: actuation inputs, internal springs and dampers.
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** Measurements
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A transform sensor block measures the spatial relationship between two frames: the base =B= and the follower =F=.
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It can give the rotational and translational position, velocity and acceleration.
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The measurement frame should be specified: it corresponds to the frame in which to resolve the selected spatial measurements. The default is =world=.
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If we want to simulate an *inertial sensor*, we just have to choose =B= to be the =world= frame.
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*Force sensors* are included in the joints blocks.
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** Excitation
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We can apply *external forces* to the model by using an [[https://mathworks.com/help/physmod/sm/ref/externalforceandtorque.html][external force and torque block]].
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Internal force, acting reciprocally between base and following origins is implemented using the [[https://mathworks.com/help/physmod/sm/ref/internalforce.html][internal force block]] even though it is usually included in one joint block.
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* Notes
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** Simscape files for identification
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|------------------------+----+----+----+------+------|
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| Simscape Name | Ty | Ry | Rz | Hexa | NASS |
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