80 lines
3.4 KiB
Markdown
80 lines
3.4 KiB
Markdown
|
+++
|
|||
|
|
title = "Review of active vibration isolation strategies"
|
|||
|
|
author = ["Thomas Dehaeze"]
|
|||
|
|
draft = false
|
|||
|
|
+++
|
|||
|
|
|
|||
|
|
Tags
|
|||
|
|
: [Vibration Isolation]({{< relref "vibration_isolation" >}})
|
|||
|
|
|
|||
|
|
Reference
|
|||
|
|
: <sup id="2d69d483f210ca387ca8061596ec27ea"><a href="#collette11_review_activ_vibrat_isolat_strat" title="Christophe Collette, Stef Janssens \& Kurt Artoos, Review of Active Vibration Isolation Strategies, {Recent Patents on Mechanical Engineeringe}, v(3), 212-219 (2011).">(Christophe Collette {\it et al.}, 2011)</a></sup>
|
|||
|
|
|
|||
|
|
Author(s)
|
|||
|
|
: Collette, C., Janssens, S., & Artoos, K.
|
|||
|
|
|
|||
|
|
Year
|
|||
|
|
: 2011
|
|||
|
|
|
|||
|
|
|
|||
|
|
## Background and Motivations {#background-and-motivations}
|
|||
|
|
|
|||
|
|
|
|||
|
|
### Passive Isolation Tradeoffs {#passive-isolation-tradeoffs}
|
|||
|
|
|
|||
|
|
<div class="cbox">
|
|||
|
|
<div></div>
|
|||
|
|
|
|||
|
|
\\[ X(s) = \underbrace{\frac{cs + k}{ms^2 + cs + k}}\_{T\_{wx}(s)} W(s) + \underbrace{\frac{1}{ms^2 + cs + k}}\_{T\_{Fx}(s)} F(s) \\]
|
|||
|
|
|
|||
|
|
</div>
|
|||
|
|
|
|||
|
|
- \\(T\_{wx}(s)\\) is called the **transmissibility** of the isolator. It characterize the way seismic vibrations \\(w\\) are transmitted to the equipment.
|
|||
|
|
- \\(T\_{Fx}(s)\\) is called the **compliance**. It characterize the capacity of disturbing forces \\(F\\) to create motion \\(x\\) of the equipment.
|
|||
|
|
|
|||
|
|
In order to minimize the vibrations of a sensitive equipment, a general objective to design a good isolator is to minimize both \\(\abs{T\_{wx}}\\) and \\(\abs{T\_{Fx}}\\) in the frequency range of interest.
|
|||
|
|
|
|||
|
|
To decrease the amplitude of the overshoot at the resonance frequency, **damping** can be increased.
|
|||
|
|
The price to pay is degradation of the isolation at high frequency (the roll off becomes \\(-1\\) instead of \\(-2\\)).
|
|||
|
|
|
|||
|
|
**First Trade-off**: Trade-off between damping and isolation.
|
|||
|
|
|
|||
|
|
To improve the transmissibility, the resonance frequency can be decreased.
|
|||
|
|
However, the systems becomes more sensitive to external force \\(F\\) applied on the equipment.
|
|||
|
|
|
|||
|
|
**Second trade-off**: Trade-off between isolation and robustness to external force
|
|||
|
|
|
|||
|
|
|
|||
|
|
### Active Isolation {#active-isolation}
|
|||
|
|
|
|||
|
|
We apply a feedback control.
|
|||
|
|
The general expression of the force delivered by the actuator is \\(f = g\_a \ddot{x} + g\_v \dot{x} + g\_p x\\). \\(g\_a\\), \\(g\_v\\) and \\(g\_p\\) are constant gains.
|
|||
|
|
|
|||
|
|
<a id="table--table:active-isolation"></a>
|
|||
|
|
<div class="table-caption">
|
|||
|
|
<span class="table-number"><a href="#table--table:active-isolation">Table 1</a></span>:
|
|||
|
|
Active isolation techniques
|
|||
|
|
</div>
|
|||
|
|
|
|||
|
|
| **Feedback Signal** | **Effect** | **Applications** |
|
|||
|
|
|---------------------|------------------------------------------|------------------|
|
|||
|
|
| Acceleration | Add virtual mass | Few |
|
|||
|
|
| Velocity | Add virtual dashpot connected to the sky | Sky-Hook Damping |
|
|||
|
|
| Position | Add virtual spring connected to the sky | Sky-Hook Spring |
|
|||
|
|
|
|||
|
|
|
|||
|
|
## Practical Realizations {#practical-realizations}
|
|||
|
|
|
|||
|
|
|
|||
|
|
## Sensor Limitations {#sensor-limitations}
|
|||
|
|
|
|||
|
|
|
|||
|
|
## Conclusions {#conclusions}
|
|||
|
|
|
|||
|
|
<a id="orgef29aaf"></a>
|
|||
|
|
|
|||
|
|
{{< figure src="/ox-hugo/collette11_comp_isolation_strategies.png" caption="Figure 1: Comparison of Active Vibration Isolation Strategies" >}}
|
|||
|
|
|
|||
|
|
# Bibliography
|
|||
|
|
<a id="collette11_review_activ_vibrat_isolat_strat"></a>Collette, C., Janssens, S., & Artoos, K., *Review of active vibration isolation strategies*, Recent Patents on Mechanical Engineeringe, *4(3)*, 212–219 (2011). http://dx.doi.org/10.2174/2212797611104030212 [↩](#2d69d483f210ca387ca8061596ec27ea)
|