211 lines
13 KiB
Markdown
211 lines
13 KiB
Markdown
+++
|
||
title = "Piezoelectric Actuators"
|
||
author = ["Thomas Dehaeze"]
|
||
draft = false
|
||
+++
|
||
|
||
Tags
|
||
: [Actuators]({{< relref "actuators" >}}), [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
|
||
|
||
|
||
## Piezoelectric Stack Actuators {#piezoelectric-stack-actuators}
|
||
|
||
|
||
### Manufacturers {#manufacturers}
|
||
|
||
| Manufacturers | Links | Country |
|
||
|---------------------|----------------------------------------------------------------------------------------------------------------|-----------|
|
||
| Cedrat | [link](http://www.cedrat-technologies.com/) | France |
|
||
| PI | [link](https://www.physikinstrumente.com/en/) | USA |
|
||
| Piezo System | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) | Germany |
|
||
| Noliac | [link](http://www.noliac.com/products/actuators/plate-stacks/) | Denmark |
|
||
| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
|
||
| PiezoDrive | [link](https://www.piezodrive.com/actuators/) | Australia |
|
||
| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/10.html) | Japan |
|
||
| CoreMorrow | [link](http://www.coremorrow.com/en/pro-9-1.html) | China |
|
||
| PiezoData | [link](https://www.piezodata.com/piezo-stack-actuator-2/) | China |
|
||
| Queensgate | [link](https://www.nanopositioning.com/product-category/nanopositioning/nanopositioning-actuators-translators) | UK |
|
||
| Matsusada Precision | [link](https://www.matsusada.com/product/pz/) | Japan |
|
||
| Sinocera | [link](http://www.china-yec.net/piezoelectric-ceramics/) | China |
|
||
| Fuji Ceramisc | [link](http://www.fujicera.co.jp/en/) | Japan |
|
||
|
||
|
||
### Model {#model}
|
||
|
||
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.
|
||
|
||
The relation between the applied voltage \\(V\_a\\) to the generated force \\(F\_a\\) is:
|
||
\\[ F\_a = g\_a V\_a, \quad g\_a = d\_{33} n k\_a \\]
|
||
with:
|
||
|
||
- \\(d\_{33}\\) is the piezoelectric strain constant [m/V]
|
||
- \\(n\\) is the number of layers
|
||
- \\(k\_a\\) is the actuator stiffness [N/m]
|
||
|
||
|
||
## Piezoelectric Plate Actuators {#piezoelectric-plate-actuators}
|
||
|
||
Some manufacturers propose "raw" plate actuators that can be used as actuator / sensors.
|
||
|
||
| Manufacturers | Links | Country |
|
||
|---------------|-------------------------------------------------------------------|---------|
|
||
| Noliac | [link](http://www.noliac.com/products/actuators/plate-actuators/) | Denmak |
|
||
|
||
|
||
## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
|
||
|
||
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 flatter is the actuator, the higher is the amplification.
|
||
|
||
A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org2b7ba31)).
|
||
|
||
<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, \& 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 |
|
||
|
||
|
||
## Specifications {#specifications}
|
||
|
||
|
||
### Typical Specifications {#typical-specifications}
|
||
|
||
Typical specifications of piezoelectric stack actuators are usually in terms of:
|
||
|
||
- Displacement/ Travel range \\([\mu m]\\)
|
||
- Blocked force \\([N]\\)
|
||
- Stiffness \\([N/\mu m]\\)
|
||
- Resolution \\([nm]\\)
|
||
- Length \\([mm]\\)
|
||
- Electrical Capacitance \\([nF]\\)
|
||
|
||
|
||
### Displacement and Length {#displacement-and-length}
|
||
|
||
The maximum displacement specified is the displacement of the actuator when the maximum voltage is applied without any load.
|
||
|
||
Typical maximum strain of Piezoelectric Stack Actuators is \\(0.1\%\\).
|
||
The free displacement \\(\Delta L\_{f}\\) is then related to the length \\(L\\) of piezoelectric stack by:
|
||
|
||
\begin{equation}
|
||
\Delta L\_f \approx \frac{L}{1000}
|
||
\end{equation}
|
||
|
||
> A “free” actuator — one that experiences no resistance to movement — will produce its maximum displacement, often referred to as “free stroke,” and generate zero force.
|
||
|
||
Note that this maximum displacement is only attainable at DC.
|
||
For dynamical applications, the electrical capacitance of the piezoelectric actuator is an important factor (see bellow).
|
||
|
||
|
||
### Blocked Force {#blocked-force}
|
||
|
||
The blocked force \\(F\_b\\) is measured by first applying the maximum voltage to the piezoelectric stack without any load.
|
||
Thus, the piezoelectric stack experiences its maximum displacement.
|
||
|
||
A force is then applied to return the actuator to its original length.
|
||
This force is measured and recorded as the blocking force.
|
||
|
||
The blocking force is also the maximum force that can produce the piezoelectric stack in contact with an infinitely stiff environment.
|
||
|
||
> When an actuator is blocked from moving, it will produce its maximum force, which is referred to as the blocked, or blocking, force.
|
||
|
||
|
||
### Stiffness {#stiffness}
|
||
|
||
The stiffness of the actuator is the ratio of the blocking force to the free stroke:
|
||
|
||
\begin{equation}
|
||
k\_p = \frac{F\_b}{\Delta L\_f}
|
||
\end{equation}
|
||
|
||
with:
|
||
|
||
- \\(k\_p\\): stiffness of the piezo actuator
|
||
- \\(F\_b\\): blocking force
|
||
- \\(\Delta L\_f\\): free stroke
|
||
|
||
|
||
### Resolution {#resolution}
|
||
|
||
The resolution is limited by the noise in the [Voltage Amplifier]({{< relref "voltage_amplifier" >}}).
|
||
|
||
Typical [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}}) of voltage amplifiers is \\(100dB = 10^{5}\\).
|
||
Thus, for a piezoelectric stack with a displacement \\(L\\), the resolution will be
|
||
|
||
\begin{equation}
|
||
r \approx \frac{L}{10^5}
|
||
\end{equation}
|
||
|
||
For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolution will be \\(\approx 1\,[nm]\\).
|
||
|
||
|
||
### 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](#orgb209f5d)).
|
||
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="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" >}}
|
||
|
||
|
||
## 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](#orgff2ea88)).
|
||
|
||
<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" >}}
|
||
|
||
|
||
## 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](#orgbfa1482)):
|
||
|
||
\begin{equation}
|
||
\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
|
||
\end{equation}
|
||
|
||
<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" >}}
|
||
|
||
For piezo actuators, force and displacement are inversely related (Figure [5](#orgbee5c88)).
|
||
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="orgbee5c88"></a>
|
||
|
||
{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
|
||
|
||
|
||
## Driving Electronics {#driving-electronics}
|
||
|
||
Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier]({{< relref "voltage_amplifier" >}}).
|
||
|
||
|
||
## Bibliography {#bibliography}
|
||
|
||
<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="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="org2b7ba31"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
|