diff --git a/content/zettels/piezoelectric_actuators.md b/content/zettels/piezoelectric_actuators.md index 507b074..c63dd68 100644 --- a/content/zettels/piezoelectric_actuators.md +++ b/content/zettels/piezoelectric_actuators.md @@ -4,11 +4,6 @@ author = ["Thomas Dehaeze"] draft = false +++ -Backlinks: - -- [Actuators]({{< relref "actuators" >}}) -- [Voltage Amplifier]({{< relref "voltage_amplifier" >}}) - Tags : [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 | | 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](#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. @@ -60,14 +56,14 @@ Some manufacturers propose "raw" plate actuators that can be used as actuator / ## 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 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)). - + {{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms ling16_enhan_mathem_model_displ_amplif" >}} @@ -159,43 +155,43 @@ 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](#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. [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. - + {{< 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](#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)). - + {{< 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](#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} \Delta L = \Delta L\_f \frac{k\_p}{k\_p + k\_e} \end{equation} - + {{< 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. 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. - + {{< 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} -Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. . +Claeyssen, Frank, R. Le Letty, F. Barillot, and O. Sosnicki. 2007. “Amplified Piezoelectric Actuators: Static & Dynamic Applications.” _Ferroelectrics_ 351 (1):3–14. . -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. . +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. . -Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.” +Lucinskis, R., and C. Mangeot. 2016. “Dynamic Characterization of an Amplified Piezoelectric Actuator.”