215 lines
13 KiB
Markdown
215 lines
13 KiB
Markdown
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title = "Piezoelectric Actuators"
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author = ["Thomas Dehaeze"]
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draft = false
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Backlinks:
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- [Actuators]({{< relref "actuators" >}})
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- [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
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Tags
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: [Actuators]({{< relref "actuators" >}}), [Voltage Amplifier]({{< relref "voltage_amplifier" >}})
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## Piezoelectric Stack Actuators {#piezoelectric-stack-actuators}
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### Manufacturers {#manufacturers}
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| Manufacturers | Links | Country |
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|---------------------|----------------------------------------------------------------------------------------------------------------|-----------|
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| Cedrat | [link](http://www.cedrat-technologies.com/) | France |
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| PI | [link](https://www.physikinstrumente.com/en/) | USA |
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| Piezo System | [link](https://www.piezosystem.com/products/piezo%5Factuators/stacktypeactuators/) | Germany |
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| Noliac | [link](http://www.noliac.com/products/actuators/plate-stacks/) | Denmark |
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| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
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| PiezoDrive | [link](https://www.piezodrive.com/actuators/) | Australia |
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| Mechano Transformer | [link](http://www.mechano-transformer.com/en/products/10.html) | Japan |
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| CoreMorrow | [link](http://www.coremorrow.com/en/pro-9-1.html) | China |
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| PiezoData | [link](https://www.piezodata.com/piezo-stack-actuator-2/) | China |
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| Queensgate | [link](https://www.nanopositioning.com/product-category/nanopositioning/nanopositioning-actuators-translators) | UK |
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| Matsusada Precision | [link](https://www.matsusada.com/product/pz/) | Japan |
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| Sinocera | [link](http://www.china-yec.net/piezoelectric-ceramics/) | China |
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### Model {#model}
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A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgcec2c91)) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})).
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Basically, it can be represented by a spring \\(k\_a\\) with the force source \\(F\_a\\) in parallel.
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The relation between the applied voltage \\(V\_a\\) to the generated force \\(F\_a\\) is:
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\\[ F\_a = g\_a V\_a, \quad g\_a = d\_{33} n k\_a \\]
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with:
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- \\(d\_{33}\\) is the piezoelectric strain constant [m/V]
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- \\(n\\) is the number of layers
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- \\(k\_a\\) is the actuator stiffness [N/m]
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## Piezoelectric Plate Actuators {#piezoelectric-plate-actuators}
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Some manufacturers propose "raw" plate actuators that can be used as actuator / sensors.
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| Manufacturers | Links | Country |
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|---------------|-------------------------------------------------------------------|---------|
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| Noliac | [link](http://www.noliac.com/products/actuators/plate-actuators/) | Denmak |
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## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators}
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The Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org5001506)):
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> The displacement amplification effect is related in a first approximation to the ratio of the shell long axis length to the short axis height.
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> The flatter is the actuator, the higher is the amplification.
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A model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org3149aa9)).
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<a id="org9697be4"></a>
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{{< 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>" >}}
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| Manufacturers | Links | Country |
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|---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-----------|
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| Cedrat | [link](https://www.cedrat-technologies.com/en/products/actuators/amplified-piezo-actuators.html) | France |
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| PiezoDrive | [link](https://www.piezodrive.com/actuators/ap-series-amplified-piezoelectric-actuators/) | Australia |
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| Dynamic-Structures | [link](https://www.dynamic-structures.com/category/piezo-actuators-stages) | USA |
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| Thorlabs | [link](https://www.thorlabs.com/newgrouppage9.cfm?objectgroup%5Fid=8700) | USA |
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| Noliac | [link](http://www.noliac.com/products/actuators/amplified-actuators/) | Denmark |
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| 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 |
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| CoreMorrow | [link](http://www.coremorrow.com/en/pro-13-1.html) | China |
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| PiezoData | [link](https://www.piezodata.com/piezoelectric-actuator-amplifier/) | China |
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## Specifications {#specifications}
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### Typical Specifications {#typical-specifications}
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Typical specifications of piezoelectric stack actuators are usually in terms of:
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- Displacement/ Travel range \\([\mu m]\\)
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- Blocked force \\([N]\\)
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- Stiffness \\([N/\mu m]\\)
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- Resolution \\([nm]\\)
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- Length \\([mm]\\)
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- Electrical Capacitance \\([nF]\\)
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### Displacement and Length {#displacement-and-length}
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The maximum displacement specified is the displacement of the actuator when the maximum voltage is applied without any load.
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Typical maximum strain of Piezoelectric Stack Actuators is \\(0.1\%\\).
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The free displacement \\(\Delta L\_{f}\\) is then related to the length \\(L\\) of piezoelectric stack by:
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\begin{equation}
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\Delta L\_f \approx \frac{L}{1000}
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\end{equation}
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> 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.
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Note that this maximum displacement is only attainable at DC.
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For dynamical applications, the electrical capacitance of the piezoelectric actuator is an important factor (see bellow).
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### Blocked Force {#blocked-force}
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The blocked force \\(F\_b\\) is measured by first applying the maximum voltage to the piezoelectric stack without any load.
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Thus, the piezoelectric stack experiences its maximum displacement.
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A force is then applied to return the actuator to its original length.
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This force is measured and recorded as the blocking force.
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The blocking force is also the maximum force that can produce the piezoelectric stack in contact with an infinitely stiff environment.
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> When an actuator is blocked from moving, it will produce its maximum force, which is referred to as the blocked, or blocking, force.
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### Stiffness {#stiffness}
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The stiffness of the actuator is the ratio of the blocking force to the free stroke:
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\begin{equation}
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k\_p = \frac{F\_b}{\Delta L\_f}
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\end{equation}
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with:
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- \\(k\_p\\): stiffness of the piezo actuator
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- \\(F\_b\\): blocking force
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- \\(\Delta L\_f\\): free stroke
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### Resolution {#resolution}
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The resolution is limited by the noise in the [Voltage Amplifier]({{< relref "voltage_amplifier" >}}).
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Typical [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}}) of voltage amplifiers is \\(100dB = 10^{5}\\).
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Thus, for a piezoelectric stack with a displacement \\(L\\), the resolution will be
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\begin{equation}
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r \approx \frac{L}{10^5}
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\end{equation}
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For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolution will be \\(\approx 1\,[nm]\\).
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### Electrical Capacitance {#electrical-capacitance}
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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)).
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This is due to the fact that voltage amplifier has a limitation on the deliverable current.
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[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.
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<a id="orgd7dbc72"></a>
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{{< 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" >}}
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## Piezoelectric actuator experiencing a mass load {#piezoelectric-actuator-experiencing-a-mass-load}
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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)).
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<a id="org8d01bc7"></a>
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{{< figure src="/ox-hugo/piezoelectric_mass_load.png" caption="Figure 3: Motion of a piezoelectric stack actuator under external constant force" >}}
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## Piezoelectric actuator in contact with a spring load {#piezoelectric-actuator-in-contact-with-a-spring-load}
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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)):
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\begin{equation}
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\Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e}
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\end{equation}
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<a id="orgef5702a"></a>
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{{< figure src="/ox-hugo/piezoelectric_spring_load.png" caption="Figure 4: Motion of a piezoelectric stack actuator in contact with a stiff environment" >}}
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For piezo actuators, force and displacement are inversely related (Figure [5](#orgb3c806e)).
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Maximum, or blocked, force (\\(F\_b\\)) occurs when there is no displacement.
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Likewise, at maximum displacement, or free stroke, (\\(\Delta L\_f\\)) no force is generated.
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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.
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<a id="orgb3c806e"></a>
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{{< figure src="/ox-hugo/piezoelectric_force_displ_relation.png" caption="Figure 5: Relation between the maximum force and displacement" >}}
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## Driving Electronics {#driving-electronics}
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Piezoelectric actuators can be driven either using a voltage to charge converter or a [Voltage Amplifier]({{< relref "voltage_amplifier" >}}).
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## Bibliography {#bibliography}
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<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>.
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<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>.
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<a id="org3149aa9"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
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