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

Update Content - 2020-11-14

Browse Source
This commit is contained in:
Thomas Dehaeze 2020-11-14 16:00:24 +01:00
parent 5114f1749a
commit 53336a71c0
1 changed files with 16 additions and 20 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

36
content/zettels/piezoelectric_actuators.md
View File

@ -4,11 +4,6 @@ author = ["Thomas Dehaeze"]
draft = false draft = false
+++ +++
Backlinks:
- [Actuators]({{< relref "actuators" >}})
- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
Tags Tags
: [Actuators]({{< relref "actuators" >}}), [Voltage Amplifier]({{< relref "voltage_amplifier" >}}) : [Actuators]({{< relref "actuators" >}}), [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
@ -32,11 +27,12 @@ Tags
| Queensgate | [link](https://www.nanopositioning.com/product-category/nanopositioning/nanopositioning-actuators-translators) | UK | | Queensgate | [link](https://www.nanopositioning.com/product-category/nanopositioning/nanopositioning-actuators-translators) | UK |
| Matsusada Precision | [link](https://www.matsusada.com/product/pz/) | Japan | | Matsusada Precision | [link](https://www.matsusada.com/product/pz/) | Japan |
| Sinocera | [link](http://www.china-yec.net/piezoelectric-ceramics/) | China | | Sinocera | [link](http://www.china-yec.net/piezoelectric-ceramics/) | China |
| Fuji Ceramisc | [link](http://www.fujicera.co.jp/en/) | Japan |
### Model {#model} ### Model {#model}
A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgcec2c91)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})). A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgba89e54)) ([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. Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel.
@ -60,14 +56,14 @@ Some manufacturers propose "raw" plate actuators that can be used as actuator /
## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators} ## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org5001506)): The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org2aa3084)):
> 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 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. > The flatter is the actuator, the higher is the amplification.
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org3149aa9)). A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org2b7ba31)).
<a id="org9697be4"></a> <a id="org0387c40"></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 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>" >}} {{< 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>" >}}
@ -159,43 +155,43 @@ For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolut
### Electrical Capacitance {#electrical-capacitance} ### 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](#orgd7dbc72)). The electrical capacitance may limit the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#orgb209f5d)).
This is due to the fact that voltage amplifier has a limitation on the deliverable current. 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. [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="orgd7dbc72"></a> <a id="orgb209f5d"></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" >}} {{< 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} ## 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](#org8d01bc7)). 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](#orgff2ea88)).
<a id="org8d01bc7"></a> <a id="orgff2ea88"></a>
{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}} {{< 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} ## 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](#orgef5702a)): 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](#orgbfa1482)):
\begin{equation} \begin{equation}
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e} \Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
\end{equation} \end{equation}
<a id="orgef5702a"></a> <a id="orgbfa1482"></a>
{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}} {{< 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](#orgb3c806e)). For piezo actuators, force and displacement are inversely related (Figure [5](#orgbee5c88)).
Maximum, or blocked, force (\\(F\_b\\)) occurs when there is no displacement. 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. 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. 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="orgb3c806e"></a> <a id="orgbee5c88"></a>
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}} {{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
@ -207,8 +203,8 @@ Piezoelectric actuators can be driven either using a voltage to charge converter
## Bibliography {#bibliography} ## Bibliography {#bibliography}
<a id="org5001506"></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="org2aa3084"></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="orgcec2c91"></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="orgba89e54"></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="org3149aa9"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.” <a id="org2b7ba31"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”