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Re-read section about the dynamical measurements

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Thomas Dehaeze 2020-04-29 17:23:31 +02:00
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@ -386,15 +386,16 @@ To estimate the PSD of the position error $\epsilon$ and thus the RMS residual m
<<sec:micro_station_dynamics>> <<sec:micro_station_dynamics>>
** Introduction :ignore: ** Introduction :ignore:
As explained before, it is very important to have a good estimation of the micro-station dynamics as it will be coupled with the dynamics of the nano-hexapod and thus is very important for both the design of the nano-hexapod and controller. As explained before, it is very important to have a good estimation of the micro-station dynamics as it will be used:
- to tune the developed multi-body model of the micro-station with which the simulations will be performed
- for the design of the nano-hexapod as it will be coupled with the micro-station
- for the design of the controller
The estimated dynamics will also be used to tune the developed multi-body model of the micro-station with which the simulations will be performed.
All the measurements performed on the micro-station are detailed in [[https://tdehaeze.github.io/meas-analysis/][this]] document and summarized in the following sections. All the measurements performed on the micro-station are detailed in [[https://tdehaeze.github.io/meas-analysis/][this]] document and summarized in the following sections.
The general procedure to identify the dynamics of the micro-station is shown in Figure [[fig:vibration_analysis_procedure]]. The general procedure to identify the dynamics of the micro-station is shown in Figure [[fig:vibration_analysis_procedure]].
The steps are: The steps are:
1. extract a Response Model (Frequency Response Functions) from measurements 1. extract a Response Model (Frequency Response Functions) from measurements
2. convert the Response Model into a Modal Model (Natural Frequencies and Mode Shapes) 2. convert the Response Model into a Modal Model (Natural Frequencies and Mode Shapes)
@ -405,24 +406,25 @@ The steps are:
[[file:figs/vibration_analysis_procedure.png]] [[file:figs/vibration_analysis_procedure.png]]
The extraction of the Spatial Model (3rd step) was not performed as it requires a lot of time and was not judge necessary. The extraction of the Spatial Model (3rd step) was not performed as it requires a lot of time and was not judge necessary.
Instead, the model will be tuned using both the modal model and the response model.
** Setup ** Experimental Setup
<<sec:id_setup>> <<sec:id_setup>>
To measure the dynamics of such complicated system, it as been chosen to perform a modal analysis. To measure the dynamics of such complicated system, it as been chosen to perform a modal analysis.
To limit the number of degrees of freedom to be measured, we suppose that in the frequency range of interest (DC-300Hz), each of the positioning stage is behaving as a *solid body*. To limit the number of degrees of freedom to be measured, we suppose that in the frequency range of interest (DC-300Hz), each of the positioning stage is behaving as a *solid body*.
Thus, to fully describe the dynamics of the station, we (only) need to measure 6 degrees of freedom on each of the positioning stage (that is 36 degrees of freedom for the 6 solid bodies). Thus, to fully describe the dynamics of the station, we (only) need to measure 6 degrees of freedom for each positioning stage (that is 36 degrees of freedom for the 6 considered solid bodies).
In order to perform the *Modal Analysis*, the following devices were used: In order to perform the modal analysis, the following devices were used:
- An *acquisition system* (OROS) with 24bits ADCs - An acquisition system (OROS) with 24bits ADCs
- 3 tri-axis *Accelerometers* - 3 tri-axis Accelerometers
- An *Instrumented Hammer* - An Instrumented Hammer
The measurement thus consists of: The measurement consists of:
- Exciting the structure at the same location with the Hammer (Figure [[fig:hammer_z]]) - Exciting the structure at the same location with the instrumented hammer (Figure [[fig:hammer_z]])
- Move the accelerometers to measure all the DOF of the structure. - Fix the accelerometers on each of the stages to measure all the DOF of the structure.
The position of the accelerometers are: The position of the accelerometers are:
- 4 on the first granite - 4 on the first granite
- 4 on the second granite - 4 on the second granite
@ -433,7 +435,7 @@ The measurement thus consists of:
In total, 69 degrees of freedom are measured (23 tri axis accelerometers) which is more that what was required. In total, 69 degrees of freedom are measured (23 tri axis accelerometers) which is more that what was required.
We chose to have some redundancy in the measurement to be able to verify that the solid-body assumption is correct for each of the stage. It was chosen to have some redundancy in the measurement to be able to verify the correctness of the solid-body assumption.
#+name: fig:hammer_z #+name: fig:hammer_z
#+caption: Example of one hammer impact #+caption: Example of one hammer impact
@ -446,9 +448,10 @@ We chose to have some redundancy in the measurement to be able to verify that th
** Results ** Results
<<sec:id_results>> <<sec:id_results>>
From the measurements, we obtain all the transfer functions from forces applied at the location of the hammer impacts to the x-y-z acceleration of each solid body at the location of each accelerometer. From the measurements are extracted all the transfer functions from forces applied at the location of the hammer impacts to the x-y-z acceleration of each solid body at the location of each accelerometer.
Modal shapes and natural frequencies are then computed. Example of mode shapes are shown in Figures [[fig:mode1]] [[fig:mode6]]. Modal shapes and natural frequencies are then computed.
Example of the obtained micro-station's mode shapes are shown in Figures [[fig:mode1]] and [[fig:mode6]].
#+name: fig:mode1 #+name: fig:mode1
#+caption: First mode that shows a suspension mode, probably due to bad leveling of one Airloc #+caption: First mode that shows a suspension mode, probably due to bad leveling of one Airloc
@ -465,9 +468,9 @@ From the reduced transfer function matrix, we can re-synthesize the response at
#+begin_important #+begin_important
This confirms the fact that the stages are indeed behaving as a solid body in the frequency band of interest. This confirms the fact that the stages are indeed behaving as a solid body in the frequency band of interest.
This thus means that a multi-body model can be used to represent the dynamics of the micro-station.
#+end_important
This thus means that *a multi-body model can be used to correctly represent the dynamics of the micro-station*.
#+end_important
Many Frequency Response Functions (FRF) are obtained from the measurements. Many Frequency Response Functions (FRF) are obtained from the measurements.
Examples of FRF are shown in Figure [[fig:frf_all_bodies_one_direction]]. Examples of FRF are shown in Figure [[fig:frf_all_bodies_one_direction]].
@ -479,7 +482,8 @@ These FRF will be used to compare the dynamics of the multi-body model with the
** Conclusion ** Conclusion
#+begin_important #+begin_important
The modal analysis of the micro-station confirmed the fact that a multi-body model should be able to correctly represents the micro-station dynamics. The dynamical measurements made on the micro-station confirmed the fact that a multi-body model is a good option to correctly represents the micro-station dynamics.
In Section [[sec:multi_body_model]], the obtained Frequency Response Functions will be used to compare the model dynamics with the micro-station dynamics. In Section [[sec:multi_body_model]], the obtained Frequency Response Functions will be used to compare the model dynamics with the micro-station dynamics.
#+end_important #+end_important