Update Content - 2020-11-14
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@ -4,11 +4,6 @@ author = ["Thomas Dehaeze"]
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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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@ -32,11 +27,12 @@ Tags
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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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| Fuji Ceramisc | [link](http://www.fujicera.co.jp/en/) | Japan |
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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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A model of a multi-layer monolithic piezoelectric stack actuator is described in ([Fleming 2010](#orgba89e54)) ([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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@ -60,14 +56,14 @@ Some manufacturers propose "raw" plate actuators that can be used as actuator /
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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 Amplified Piezo Actuators principle is presented in ([Claeyssen et al. 2007](#org2aa3084)):
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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 model of an amplified piezoelectric actuator is described in ([Lucinskis and Mangeot 2016](#org2b7ba31)).
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<a id="org9697be4"></a>
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<a id="org0387c40"></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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@ -159,43 +155,43 @@ For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolut
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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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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)).
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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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<a id="orgb209f5d"></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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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)).
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<a id="org8d01bc7"></a>
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<a id="orgff2ea88"></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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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)):
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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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<a id="orgbfa1482"></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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For piezo actuators, force and displacement are inversely related (Figure [5](#orgbee5c88)).
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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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<a id="orgbee5c88"></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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@ -207,8 +203,8 @@ Piezoelectric actuators can be driven either using a voltage to charge converter
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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="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>.
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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="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>.
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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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<a id="org2b7ba31"></a>Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”
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