From 408df4315d6bedd76b83383ecf91d55e03e31ae7 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Wed, 17 Jun 2020 10:55:31 +0200 Subject: [PATCH] Add stuff about piezoelectric actuators --- content/zettels/piezoelectric_actuators.md | 173 ++++++++++++------ .../ling16_topology_piezo_mechanism_types.png | Bin 0 -> 268488 bytes .../piezoelectric_capacitance_voltage_max.png | Bin 0 -> 35637 bytes .../piezoelectric_force_displ_relation.png | Bin 0 -> 80655 bytes static/ox-hugo/piezoelectric_mass_load.png | Bin 0 -> 90582 bytes static/ox-hugo/piezoelectric_spring_load.png | Bin 0 -> 55250 bytes 6 files changed, 120 insertions(+), 53 deletions(-) create mode 100644 static/ox-hugo/ling16_topology_piezo_mechanism_types.png create mode 100644 static/ox-hugo/piezoelectric_capacitance_voltage_max.png create mode 100644 static/ox-hugo/piezoelectric_force_displ_relation.png create mode 100644 static/ox-hugo/piezoelectric_mass_load.png create mode 100644 static/ox-hugo/piezoelectric_spring_load.png diff --git a/content/zettels/piezoelectric_actuators.md b/content/zettels/piezoelectric_actuators.md index 5524416..72e5a7a 100644 --- a/content/zettels/piezoelectric_actuators.md +++ b/content/zettels/piezoelectric_actuators.md @@ -30,59 +30,6 @@ Tags A model of a multi-layer monolithic piezoelectric stack actuator is described in (Fleming, 2010) ([Notes]({{< relref "fleming10_nanop_system_with_force_feedb" >}})). -### Specifications {#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]\\) - - -#### Displacement and Length {#displacement-and-length} - -The maximum displacement specified is the displacement of the actuator when the maximum voltage is applied and when no load is added. - -Typical strain of Piezoelectric Stack Actuators is \\(0.1\%\\), the free displacement \\(d\\) is then related to the length of piezoelectric stack: -\\[ d \approx \frac{L}{1000} \\] - - -#### Blocked Force {#blocked-force} - -The blocked force 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. - - -#### Stiffness {#stiffness} - - -#### Resolution {#resolution} - -The resolution is limited by the noise in the voltage amplified. - -Typical [Signal to Noise Ratio]({{< relref "signal_to_noise_ratio" >}}) of voltage amplified is \\(100dB = 10^{5}\\). -Thus, for a piezoelectric stack with a displacement \\(L\\), the resolution will be - -\begin{equation} - r = \frac{L}{10^5} -\end{equation} - -For a piezoelectric stack with a displacement of \\(100\,[\mu m]\\), the resolution will be \\(\approx 1\,[nm]\\). - - -### Piezoelectric Stack experiencing a mass load {#piezoelectric-stack-experiencing-a-mass-load} - - -### Piezoelectric Stack in contact with a spring load {#piezoelectric-stack-in-contact-with-a-spring-load} - - ## Mechanically Amplified Piezoelectric actuators {#mechanically-amplified-piezoelectric-actuators} The Amplified Piezo Actuators principle is presented in (Frank Claeyssen {\it et al.}, 2007): @@ -97,6 +44,10 @@ A model of an amplified piezoelectric actuator is described in (Lucinskis \& Mangeot, 2016). + + +{{< figure src="/ox-hugo/ling16_topology_piezo_mechanism_types.png" caption="Figure 1: Topology of several types of compliant mechanisms (Mingxiang Ling {\it et al.}, 2016)" >}} + | Manufacturers | Links | |---------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | Cedrat | [link](https://www.cedrat-technologies.com/en/products/actuators/amplified-piezo-actuators.html) | @@ -107,6 +58,120 @@ A model of an amplified piezoelectric actuator is described in }}) 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 gives the maximum voltage that can be used to drive the piezoelectric actuator as a function of frequency (Figure [2](#org3da123f)). + + + +{{< 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](#orgab6e282)). + + + +{{< 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](#orgcf60838)): + +\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](#orga8ee6e8)). +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" >}} + # Bibliography Fleming, A., *Nanopositioning system with force feedback for high-performance tracking and vibration control*, IEEE/ASME Transactions on Mechatronics, *15(3)*, 433–447 (2010). http://dx.doi.org/10.1109/tmech.2009.2028422 [↩](#c823f68dd2a72b9667a61b3c046b4731) @@ -114,6 +179,8 @@ A model of an amplified piezoelectric actuator is described in Lucinskis, R., & Mangeot, C. (2016). *Dynamic characterization of an amplified piezoelectric actuator*. Retrieved from [](). . [↩](#849750850d9986ed326e74bd3c448d03) +Ling, M., Cao, J., Zeng, M., Lin, J., & Inman, D. J., *Enhanced mathematical modeling of the displacement amplification ratio for piezoelectric compliant mechanisms*, Smart Materials and Structures, *25(7)*, 075022 (2016). http://dx.doi.org/10.1088/0964-1726/25/7/075022 [↩](#d9e8b33774f1e65d16bd79114db8ac64) + ## Backlinks {#backlinks} diff --git a/static/ox-hugo/ling16_topology_piezo_mechanism_types.png b/static/ox-hugo/ling16_topology_piezo_mechanism_types.png new file mode 100644 index 0000000000000000000000000000000000000000..04ef92cfbabbe6745c15009ae64a4bd6d2154276 GIT binary patch literal 268488 zcmYg%1z1#J*X;~B^hl`mfJg`u0+J3hbT!4jevB6 zL)^pn{r|o9d3YQ=oEgshzI(5|_F9`rbyYbMLK;F42t=YFFRcjz;ZT4;Si}%K;7VcQ z8V3jj11U%&wY}1JGCcjLI%m2AD}4tQ)KtmIeKtps_b73smzW`hPn=|aF0>k#x*!*Q z%jk(BA`HcHP1`tOFv53kRJdO>rNY%mF(OtQ-nU+Zmgnh|SU8gHeiB(KXZ?eFgLhxz z$COBEoKVReb#_X^|GvC)$<^@y|L_0)b5Z+g0x$CayM?fmBL_|JKllIlMU~*O^8fn` z;F`0d@RLRm@QudSoaf?~^|F^_7n3chvKG96tKW((8w^VoeNSra9v^m)wTkV7G_ico zv9R$#k7PmT3q;bgSfhp5)wWsJF6^oq6l^F12k^)U>U;rP)U9ZTT!*ou5}dU^cIMm& zj=}Hgs~j=phB4=w_j%;Re!_hib}Gh#10gH>aismmV;^s#6!+iB@`kqa-sR>a)6>6N zvm0B5^&~06_j-OUS6L3A3Nyc69DR~CV>%d7YW?^~ccz03+kRH}s@@N7I>l=`FS;ag z3wCI#UK!FbR!s*v)Pd#I@Zs0m{w70I`M{zdh=Me(|4BPG$(*dlNZ($u6{hsPr%s2P zVQCoBX{0@$Xr45rNZz+Q{z|d+3m9a`TjV2%6SF(7&3sj^t#0+eN z77eFgYPw&p5alL5Eoq<=si;uW78G`4Kk&3<)%ZYT7@lOLEAmFu$zaKi{Ce^BUdbz& zDoYX#Y4oX|#09L-|GIkordY2H6M!lCRAxKrYU05WS^8t-iPS-DQLbK9kEopa%Cv}_ z0-dNUn^^}|Lf*8}0+{=2Zq%?tX(86?L5zB#L18NoQr3tu002RXLjqRVRp zt)2FIQ{u73FV$MjE_eb$Bj@5KKcBU&`dUcHmh_G4J;PsKg&{hgHkW!+a%^5g&r5{4@Wrtjw zo;YN@JwyeWDumzl9&9;)mFZpJ(p#{!zjb|{#8cMSNkPtfrV##DdA@<`V5T|>BexOk zyo#Exj7t0Du}^9@)%r(wL$lmDDDOX+%I9I%xh_PUnIr54-JEZ9W9q!QZarET4|(AP zgHmXniNw$mB(!g=m8;lmk~{4@R9836;A9IIL+a~K?A&j)iHtH>M5uv}RW?RGnT|RlyDT7uh#b&g691iR!rBauzP8 zCaK&DxWt{RA+a7o3vw$zdp0$Mikv0++4=p&_MZVi`p=i&`WXe@{OYC`7j|+=O(neg$GJ#Wn}(|t85y+UyNrAG1?+U4=DzOYOl@xNrJ%N9 zTOR)r%w^PjUghn&mp+Z(V5Lbmp3xQ(lq%Slb-UpE35wM4euzh=oy7fyq|($lAmxF~ zI-ds@5l3I&QdHE~rC;eaCTO+0WKlr@A&C_@l*qlFa*M_>9b#D6^Qa^%{4)@>Pjuk+l)Ru*P-snj ziUJw!1U1kOl3R|f4ItKiO&Cv@nF*w70jN z&_c~q4Ndajw2sizT_s9-6#*M^#*NQO5$5K_t3SJr>cdH&Humo~b-NE&as2+_EiE($ z)hqK58=)8D5<9mUt$Tlsp;-TObT*I{+2Hp5%zy3PnTV;x0<9w@PX|7ulhFryrIV9U z!%Ume;@wKC$`4K6@2NPaHqe*8V@0hPkKZzWnFbEu|2nl{ZF{x3Q!zS@kIz)w-P$?O zz7Q=hUi9n0cUiZck&Ef?X!y`{G4=0x&j*f^3<1g3Jy2T? z_N8sx5%l763V#&iOT_@)wCC$qr)~I`8DctF1fvDt{m&mK9aPVGv$d4{iOX_aH>!=^ z{I^|iEb6wjVWjxYVZXk+A&e~(Ch8o#c{V%EqZ&>cv>zWiBzH0>=EpN2dV8#9iy4wQ ze(@|u%=dZH)|bLMRYw1@-n4kBlfT~#7f-h-#*2RqB{Vgwr9B_rJ~*QKAnI(X(IpyAW-X~S(B>Fko5SAsd~<@~%cTlc%yvy)0XMuK6AVcuEp z(EmR7nqyayhIE!+`wh+Bk5QlIzLoW)Nc7VFe7V_`q1&c?_-rc{?ITN121sye*p1b{}v&|-!Zcs)I8JgPcQNQ1g;R+Lgjzb zBbcVX=QZ)`k#p)M?6K@MV-y(#1~TnGn|RU(3abRk$wP=J`rD32)eJE6e*9$bRb*qh zP4IhP|03tS4QF(jS!lX4faHGBdRl0~rV1S|>6@)_+^BM1<-&i-8qbDLsAV}|&Lpk( zuuw*poI31N-~^ZI{&akxlEPRv*pqmNJ{;~}yb8Y&_H6AZ?YlmA&HQe0d48}w5#avU z>6K*gIGCvP8;2Iwc4q*IhgtjIacNTgLdUrtn*!{z&CS*}JB8D7?@ApqKE9w+ryQ4t zcJxF^q^Ji=!|rp=5~=XktNQvYZW&pZjf*M1(sRp!h>A)jiI{}BWe?HFv;7UvfS-_n z+uh`7U6a6!z(s$d7NJT@+{7GzU+#{!5OF=;KFoSjXIY63XTTyE-O>iD=#0-qL_|eJ zu@w|X!;9L?3FlhQE4X)k<7+A+_kPJ$blWxM_{eJ**NN7u=J4A~itAOzi5vTw z@`KZ+^9Vws`pn(gon+GBvX;!nOWpB8$K9zMSpvV)k8Ug0K@QhD^;Q^*2(5fA?D5CeFK()rQ#59_poTWJ)f`W(@ErQGbY7k|AMy;3)~!F{G_u2-r7hd^S{o?nScQWC)0>u zM8_<6nh#vJYDZ4qZZqGYZ!-k9b*EA8_l4fK98gTf#z$FcsL%-2jA&^Jt0;2%_dnz; z;}EXf=H@I3479ys+g(kG7}FlKh#@xhXf>#<8R_=}pqERz+$6*(*)&Vz&`a2U z5zaY4`8NIS3&WoDQr;YAi?af?pV(6T^Lx&>%i&R;0hqJ(stVDBv*>d&38z;`FcGfu zM444k(zQN6u98ZsUT|(?QNs2k zESv*y>)XqXxLNe1F=q>}+4M8cvM;#OubT>YXY_4sY!b6qx*0`wH#Kfbwspnq109)} zBRuxjPJH*ikL

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