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kentaro.komori - 2:09 Friday 07 June 2024 (29785) Print this report
Modeling transfer function from the ground to the board on the stack

[Washimi, Komori]

We modeled the transfer function from the ground to the board on the stack.
This time, we adopted a simple triple-stage harmonic oscillator model, treating the stack as a point mass.

Figures 1 (see klog:29667) and 2 (see klog:29764) show the horizontal and vertical transfer functions in [m/m] with measured data points and modeled curves, respectively.
The horizontal spring constant has not been measured, and the inverted pendulum effect is not included in the model, so the horizontal spring constants are modeled differently for each load.
The vertical spring constant was measured in klog:29651.
All Q-values are assumed to be nine.

In the horizontal transfer function, the measured resonant frequencies can be modeled very well, but the magnitude around 30 Hz differs by more than an order of magnitude, and above 30 Hz, the difference is significant.
In the vertical transfer function, the first resonant frequency cannot be explained by the model (somehow the measured data with the load shows a higher resonance than that without load), and the difference between the measured data and the model is significant above 40 Hz.

One possibility for the discrepancy is the modeling approach.
Currently, we are using a point mass model, but we should consider using a rigid body model or performing finite element modeling with bellows.
The next step will be to try these alternative modeling approaches and determine whether the current measured data can be accurately explained.

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