tdehaeze/digital-brain
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

Update Content - 2020-09-18

Browse Source
This commit is contained in:
Thomas Dehaeze
2020-09-18 11:43:07 +02:00
parent fa57b69657
commit 0ea60cf275
10 changed files with 144 additions and 123 deletions
Download Patch File Download Diff File Expand all files Collapse all files

54
content/zettels/piezoelectric_actuators.md
View File

@@ -4,7 +4,7 @@ author = ["Thomas Dehaeze"]
draft = false
+++
### Backlinks {#backlinks}
Backlinks:
- [Actuators]({{< relref "actuators" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
@@ -35,7 +35,7 @@ Tags
### Model {#model}
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgdda2743)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgf8860c8)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel.
@@ -50,27 +50,27 @@ with:
## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#orga200a60)):
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org98162bd)):
> The displacement amplification effect is related in a first approximation to the ratio of the shell long axis length to the short axis height.
> The flatter is the actuator, the higher is the amplification.
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org46de525)).
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org47bb392)).
<a id="orgeed82ad"></a>
<a id="orgeb77af2"></a>
{{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms <sup id=\"d9e8b33774f1e65d16bd79114db8ac64\"><a class=\"reference-link\" href=\"#ling16_enhan_mathem_model_displ_amplif\" title=\"Mingxiang Ling, Junyi Cao, Minghua Zeng, Jing Lin, \&amp; Daniel J Inman, Enhanced Mathematical Modeling of the Displacement Amplification Ratio for Piezoelectric Compliant Mechanisms, {Smart Materials and Structures}, v(7), 075022 (2016).\">(Mingxiang Ling {\it et al.}, 2016)</a></sup>" >}}
{{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms <sup id=\"d9e8b33774f1e65d16bd79114db8ac64\"><a href=\"#ling16_enhan_mathem_model_displ_amplif\" title=\"Mingxiang Ling, Junyi Cao, Minghua Zeng, Jing Lin, \&amp; Daniel J Inman, Enhanced Mathematical Modeling of the Displacement Amplification Ratio for Piezoelectric Compliant Mechanisms, {Smart Materials and Structures}, v(7), 075022 (2016).\">ling16_enhan_mathem_model_displ_amplif</a></sup>" >}}
| **Manufacturers** | **Links** | **Country** |
|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------|
| Cedrat | [link](https://www.cedrat-technologies.com/en/products/actuators/amplified-piezo-actuators.html) | France |
| PiezoDrive | [link](https://www.piezodrive.com/actuators/ap-series-amplified-piezoelectric-actuators/) | Australia |
| Dynamic-Structures | [link](https://www.dynamic-structures.com/category/piezo-actuators-stages) | USA |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
| Noliac | [link](http://www.noliac.com/products/actuators/amplified-actuators/) | Denmark |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F5.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F3.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5Fmtkk.html) | Japan |
| CoreMorrow | [link](http://www.coremorrow.com/en/pro-13-1.html) | China |
| PiezoData | [link](https://www.piezodata.com/piezoelectric-actuator-amplifier/) | China |
| Manufacturers | Links | Country |
|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------|
| Cedrat | [link](https://www.cedrat-technologies.com/en/products/actuators/amplified-piezo-actuators.html) | France |
| PiezoDrive | [link](https://www.piezodrive.com/actuators/ap-series-amplified-piezoelectric-actuators/) | Australia |
| Dynamic-Structures | [link](https://www.dynamic-structures.com/category/piezo-actuators-stages) | USA |
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
| Noliac | [link](http://www.noliac.com/products/actuators/amplified-actuators/) | Denmark |
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F5.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5F3.html), [link](http://www.mechano-transformer.com/en/products/01a%5Factuator%5Fmtkk.html) | Japan |
| CoreMorrow | [link](http://www.coremorrow.com/en/pro-13-1.html) | China |
| PiezoData | [link](https://www.piezodata.com/piezoelectric-actuator-amplifier/) | China |
## Specifications {#specifications}
@@ -149,51 +149,51 @@ For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolut
### Electrical Capacitance {#electrical-capacitance}
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org9c97b26)).
The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org297ca75)).
This is due to the fact that voltage amplifier has a limitation on the deliverable current.
[Voltage Amplifier]({{< relref "voltage_amplifier" >}}) with high maximum output current should be used if either high bandwidth is wanted or piezoelectric stacks with high capacitance are to be used.
<a id="org9c97b26"></a>
<a id="org297ca75"></a>
{{< figure src="/ox-hugo/piezoelectric_capacitance_voltage_max.png" caption="Figure 2: Maximum sin-wave amplitude as a function of frequency for several piezoelectric capacitance" >}}
## Piezoelectric actuator experiencing a mass load {#piezoelectric-actuator-experiencing-a-mass-load}
When the piezoelectric actuator is supporting a payload, it will experience a static deflection due to its finite stiffness \\(\Delta l\_n = \frac{mg}{k\_p}\\), but its stroke will remain unchanged (Figure [3](#org6172e71)).
When the piezoelectric actuator is supporting a payload, it will experience a static deflection due to its finite stiffness \\(\Delta l\_n = \frac{mg}{k\_p}\\), but its stroke will remain unchanged (Figure [3](#org481d529)).
<a id="org6172e71"></a>
<a id="org481d529"></a>
{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}}
## Piezoelectric actuator in contact with a spring load {#piezoelectric-actuator-in-contact-with-a-spring-load}
Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its maximum stroke \\(\Delta L\\) is less than its free stroke \\(\Delta L\_f\\) (Figure [4](#org802b6e3)):
Then the piezoelectric actuator is in contact with a spring load \\(k\_e\\), its maximum stroke \\(\Delta L\\) is less than its free stroke \\(\Delta L\_f\\) (Figure [4](#orgf063765)):
\begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
\end{equation}
<a id="org802b6e3"></a>
<a id="orgf063765"></a>
{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}}
For piezo actuators, force and displacement are inversely related (Figure [5](#orga68d9e2)).
For piezo actuators, force and displacement are inversely related (Figure [5](#org82b8a4e)).
Maximum, or blocked, force (\\(F\_b\\)) occurs when there is no displacement.
Likewise, at maximum displacement, or free stroke, (\\(\Delta L\_f\\)) no force is generated.
When an external load is applied, the stiffness of the load (\\(k\_e\\)) determines the displacement (\\(\Delta L\_A\\)) and force (\\(\Delta F\_A\\)) that can be produced.
<a id="orga68d9e2"></a>
<a id="org82b8a4e"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
## Bibliography {#bibliography}
<a id="orga200a60"></a>Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. <https://doi.org/10.1080/00150190701351865>.
<a id="org98162bd"></a>Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. <https://doi.org/10.1080/00150190701351865>.
<a id="orgdda2743"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="orgf8860c8"></a>Fleming, A.J. 2010. “Nanopositioning System with Force Feedback for High-Performance Tracking and Vibration Control.” _IEEE/ASME Transactions on Mechatronics_ 15 (3):433–47. <https://doi.org/10.1109/tmech.2009.2028422>.
<a id="org46de525"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
<a id="org47bb392"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”