diff --git a/index.org b/index.org index 55f9447..8281216 100644 --- a/index.org +++ b/index.org @@ -386,15 +386,16 @@ To estimate the PSD of the position error $\epsilon$ and thus the RMS residual m <> ** 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. The general procedure to identify the dynamics of the micro-station is shown in Figure [[fig:vibration_analysis_procedure]]. - The steps are: 1. extract a Response Model (Frequency Response Functions) from measurements 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]] 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 <> 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*. -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: -- An *acquisition system* (OROS) with 24bits ADCs -- 3 tri-axis *Accelerometers* -- An *Instrumented Hammer* +In order to perform the modal analysis, the following devices were used: +- An acquisition system (OROS) with 24bits ADCs +- 3 tri-axis Accelerometers +- An Instrumented Hammer -The measurement thus consists of: -- Exciting the structure at the same location with the Hammer (Figure [[fig:hammer_z]]) -- Move the accelerometers to measure all the DOF of the structure. +The measurement consists of: +- Exciting the structure at the same location with the instrumented hammer (Figure [[fig:hammer_z]]) +- Fix the accelerometers on each of the stages to measure all the DOF of the structure. The position of the accelerometers are: - 4 on the first 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. -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 #+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 <> -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 #+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 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. 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 #+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. #+end_important