diff --git a/figs/dynamics_force_disp_comp_anasys.pdf b/figs/dynamics_force_disp_comp_anasys.pdf index 8c2a92d..d570cf3 100644 Binary files a/figs/dynamics_force_disp_comp_anasys.pdf and b/figs/dynamics_force_disp_comp_anasys.pdf differ diff --git a/figs/dynamics_force_disp_comp_anasys.png b/figs/dynamics_force_disp_comp_anasys.png index 181880c..fa3ec97 100644 Binary files a/figs/dynamics_force_disp_comp_anasys.png and b/figs/dynamics_force_disp_comp_anasys.png differ diff --git a/figs/dynamics_force_force_sensor_comp_mass.pdf b/figs/dynamics_force_force_sensor_comp_mass.pdf index 4cf04d7..93aa201 100644 --- a/figs/dynamics_force_force_sensor_comp_mass.pdf +++ b/figs/dynamics_force_force_sensor_comp_mass.pdf @@ -3,7 +3,7 @@ 1 0 obj << /Producer (Apache FOP Version 2.4.0-SNAPSHOT: PDFDocumentGraphics2D) -/CreationDate (D:20200614122142+02'00') +/CreationDate (D:20200614123053+02'00') >> endobj 2 0 obj @@ -932,50 +932,52 @@ L !#קk9d$R`Zk(t|TIL (/_2N5hdg\SSE>+`-y3eEE>^K2*AZy9ń*a$cs7dBhj9Y0rgS3xA5d/3b =$2|X{ OOeY79+qlrk,o!=P@G{تL]ጌE`f&.VI(>dxIgSy|B a-E:EUų!F.eC=D -aJ 5<\ovKW2 A!r&CF`mYl;e;{1c"`YIѸc>Dl[oQiľ%ĀXALĉ3d4 6'WL)[Dn>,(BL]" YD:[|fCv 1|w4W 9j`s F?-l%OG'<';bEL ,"C.V]Nhz|RD8">(€88,*s||9r1YS}|.;#tRs"=BWǘ9ll8WZg 1;v vd2kG¶#E>>VY.GڝgD!-ѐxauA{Ƞd2]`YfXz叭fDscC4dxsBFDĀ%%қU-IR;:gyH;$ +d0RsZ2T̎nc'@ ΁IUU8AEClj^ԗ9c=8Fv8ViUm6`mo\d)[dS\U 1^I<4 ,s$gDsg+Q㍗VIO4ZMJsd;V=dEZBR]=m{0= -JNQ @B:OLG/2AL.Rs/<ևb$2UJ+^"?ߢۑth}s"VYk%Ԫǥx~zIЎp_8F+4ejI/ Fjf\QT,ўPun z.3c)/*241WZz kilǵ:+A~t2a_$7Hѳ=DUCcb0IpvFJrK(*Аh,@vk,!=A'A֦ԩ0cs)?eLkD:C'ărhl4\BcgBMP֭a -ᎎko0N"T]kЭ=D#gHQp uDe2[$M[Qmldlj佯{1*di1XQ˿3Ϯ07ܝ(\iuSWO0`O I0o:ʱkhz lx;|a -9"H%b:Qō?Ž#msA;'.bÈF=hw iZHXW/DGAt/#BG*e]LQ08$jk;7/ժ( ]4}):XʥIiUZR __8ċjQ`C2!EgWϥŁ~ kvUKxu̓s_sBiM>$<',_&=ּꏓNB67o4w86BHUu!ZT?:#BI ZT;s)::~^O):W1]W/CHj]E9ho]k\ir_@~cNs=ʂ۩]]co   , ?.[mv!cY͖q1~i(l )9!}/#B`[.N -9,zaH+0׳vl\lmD|[眗5eTDG -+-JՎ2A̢w}n&*CC:c]E>ivYtm < 4ek\CA rekWw.@:shMPg£-M JM|]=ޠnFޠdwiۨxhoTdt{ 7(3XS)LOU -2),bΉ1$l!Y%zkPbs[GC-mRG˖5sY(X98qZ7#c(yx<⽼A\巔y2QL sxA ]YKnHAZ7*`Qx7s9S^7hSDAp(MDq҈XAZ*֜16+m b.` -!Ԛ5SF _)k 2j Vbx AQ۷ a59iG E/;tp-!d*K7(+GMdJ5?fkm^}+ *|t ef<ͻq߻Y^Gg &Qjݥm -w iY=,kХlI$jY BӪ+w i"d[䭢nʖ_gCZc 9Zl by MG d R} As)Yꡜ1HLoƇ.H Vh1vbtHӶf_P.v 451褭UZR15H[/ma9:_ЪS홤Y -U` :~ZM`mA4 &?Wۺ [["ZJlAד1C;d ryk`I|Ah›T_3 R544z/C_|r#}Ats/(v45H%-(S -Q.G bPV;ui N7% ^(<]==m#m72a<|kk 9읧D0؈7{7o_רa_--Yޠ"ǀZs; TZ[ -L9kcaqBU`,Ahisr*e "@gB`YY5J;rDFMQ+WNJ= C%wPH䐱 #sq!Rg)Jr z+ю*XDfvėwqTL3 hDG/! jwazVJJA4eVt aX JC?9Hbe1q/'ʹ $w֙jR:sGg11LY -\o<1"s7 RAڶیo9H/œ)%$jnLކ[jo2zޛN[]֛~xrC7VOl {C1C-đ6Tb~]! *]jatpKKzoWbP7Fxnܣ7u Ͼv 0\aڕ9eRg b΀a&fuAJp &=+tt k3bb49 _Ƅ f`Ⱥ= [OE P(+IAC[ iju35SBs"oQO[g -=wuLA -b(I*uh,wy `ڮ\TD,Cu݇*W1Ғ`B;OF$ݥu Fu[k =\zXf4in./S/*^=M ś֚͛bS7}!rM_ɛZyMYoZp|94ś. śNu/8u4r-r?zqZ 8EAF$4B8ot=|Yl/taBN#M^&N%⴩'qh /t7} \F{ӚBN#V_iV}-/4fK|~lF}1zRɜޔ.fN{ɜ/t~1;@ 3sDn[>iz ?Eė8}?ӭ(N_` 8}N~4fs6 8|Num8_N<tjT^^9Nof5,3p֨8ZqzkȤ4.0M03rk+}"NMΥ=&g|8_O]'r~ e}Ƒ N?7q:yu8ESE N&NoW0r>Q*$NcxE& -ë%oQJ_#ʑ_bNG_*g4QӼuvh{G?aRDN9mɜ~`oڼot~1;97ss^ik`bNs+<111d{NF}A1! :>U/4"^/^Mf0b:-Cċ:kkooN:߈7u!ӏMҗ"O? 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Table of Contents

-
-

1 Amplified Piezoelectric Actuator - 3D elements

+
+

1 Amplified Piezoelectric Actuator - 3D elements

The idea here is to: @@ -61,8 +61,8 @@ The idea here is to:

-
-

1.1 Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates

+
+

1.1 Import Mass Matrix, Stiffness Matrix, and Interface Nodes Coordinates

We first extract the stiffness and mass matrices. @@ -113,7 +113,7 @@ Then, we extract the coordinates of the interface nodes. -

+

amplified_piezo_interface_nodes.png

Figure 1: Interface Nodes for the Amplified Piezo Actuator

@@ -571,20 +571,20 @@ Using K, M and int_xyz, we can use the -
-

1.2 Identification of the Dynamics

+
+

1.2 Identification of the Dynamics

The flexible element is imported using the Reduced Order Flexible Solid simscape block.

-To model the actuator, an Internal Force block is added between the first and second nodes. -To model the sensors, a Relative Motion Sensor block is added between the second and the third nodes. +To model the actuator, an Internal Force block is added between the nodes 3 and 12. +A Relative Motion Sensor block is added between the nodes 1 and 2 to measure the displacement and the amplified piezo.

-Two masses are fixed at the ends of the piezo-electric stack actuator. +One mass is fixed at one end of the piezo-electric stack actuator, the other end is fixed to the world frame.

@@ -598,7 +598,6 @@ We first set the mass to be zero.

The dynamics is identified from the applied force to the measured relative displacement.

- 
%% Name of the Simulink File
 mdl = 'piezo_amplified_3d';
@@ -625,9 +624,8 @@ And the dynamics is identified.
 

 
 

-The two identified dynamics are compared in Figure 2.
+The two identified dynamics are compared in Figure 2.
 

-
 

 
%% Name of the Simulink File
 mdl = 'piezo_amplified_3d';
@@ -642,7 +640,7 @@ Ghm = linearize(mdl, io);
 

 
 
-

+

 
dynamics_act_disp_comp_mass.png
 

 
Figure 2: Dynamics from \(F\) to \(d\) without a payload and with a 10kg payload

@@ -650,8 +648,8 @@ Ghm = linearize(mdl, io);
 

 

 
-

-
1.3 Comparison with Ansys

+

+
1.3 Comparison with Ansys

 

 

 Let’s import the results from an Harmonic response analysis in Ansys.
@@ -662,8 +660,12 @@ Gresp10 = readtable('FEA_HarmResponse_10kg.txt');
+

+The obtained dynamics from the Simscape model and from the Ansys analysis are compare in Figure 3. +

-
+ +

dynamics_force_disp_comp_anasys.png

Figure 3: Comparison of the obtained dynamics using Simscape with the harmonic response analysis using Ansys

@@ -671,9 +673,17 @@ Gresp10 = readtable('FEA_HarmResponse_10kg.txt');
-
-

1.4 Force Sensor

+
+

1.4 Force Sensor

+

+The dynamics is identified from internal forces applied between nodes 3 and 11 to the relative displacement of nodes 11 and 13. +

+ +

+The obtained dynamics is shown in Figure 4. +

+ 
m = 0;
@@ -711,7 +721,7 @@ Gfm = linearize(mdl, io);
-
+

dynamics_force_force_sensor_comp_mass.png

Figure 4: Dynamics from \(F\) to \(F_m\) for \(m=0\) and \(m = 10kg\)

@@ -722,7 +732,7 @@ Gfm = linearize(mdl, io);

Author: Dehaeze Thomas

-

Created: 2020-06-14 dim. 12:22

+

Created: 2020-06-14 dim. 12:31

diff --git a/index.org b/index.org index 8137af7..ffe69be 100644 --- a/index.org +++ b/index.org @@ -154,10 +154,10 @@ Using =K=, =M= and =int_xyz=, we can use the =Reduced Order Flexible Solid= sims ** Identification of the Dynamics The flexible element is imported using the =Reduced Order Flexible Solid= simscape block. -To model the actuator, an =Internal Force= block is added between the first and second nodes. -To model the sensors, a =Relative Motion Sensor= block is added between the second and the third nodes. +To model the actuator, an =Internal Force= block is added between the nodes 3 and 12. +A =Relative Motion Sensor= block is added between the nodes 1 and 2 to measure the displacement and the amplified piezo. -Two masses are fixed at the ends of the piezo-electric stack actuator. +One mass is fixed at one end of the piezo-electric stack actuator, the other end is fixed to the world frame. We first set the mass to be zero. #+begin_src matlab @@ -165,7 +165,6 @@ We first set the mass to be zero. #+end_src The dynamics is identified from the applied force to the measured relative displacement. - #+begin_src matlab %% Name of the Simulink File mdl = 'piezo_amplified_3d'; @@ -186,7 +185,6 @@ Then, we add 10Kg of mass: And the dynamics is identified. The two identified dynamics are compared in Figure [[fig:dynamics_act_disp_comp_mass]]. - #+begin_src matlab %% Name of the Simulink File mdl = 'piezo_amplified_3d'; @@ -245,6 +243,8 @@ Let's import the results from an Harmonic response analysis in Ansys. Gresp10 = readtable('FEA_HarmResponse_10kg.txt'); #+end_src +The obtained dynamics from the Simscape model and from the Ansys analysis are compare in Figure [[fig:dynamics_force_disp_comp_anasys]]. + #+begin_src matlab :exports none freqs = logspace(1, 5, 1000); @@ -285,6 +285,8 @@ Let's import the results from an Harmonic response analysis in Ansys. ylim([-390 30]); xlabel('Frequency [Hz]'); ylabel('Phase [deg]'); hold off; + legend('location', 'southwest'); + linkaxes([ax1,ax2],'x'); xlim([freqs(1), freqs(end)]); #+end_src @@ -299,6 +301,10 @@ Let's import the results from an Harmonic response analysis in Ansys. [[file:figs/dynamics_force_disp_comp_anasys.png]] ** Force Sensor +The dynamics is identified from internal forces applied between nodes 3 and 11 to the relative displacement of nodes 11 and 13. + +The obtained dynamics is shown in Figure [[fig:dynamics_force_force_sensor_comp_mass]]. + #+begin_src matlab m = 0; #+end_src @@ -348,9 +354,9 @@ Let's import the results from an Harmonic response analysis in Ansys. ax2 = subplot(2,1,2); hold on; plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gf, freqs, 'Hz')))), '-', ... - 'DisplayName', '$m = 1kg$'); + 'DisplayName', '$m = 0kg$'); plot(freqs, 180/pi*unwrap(angle(squeeze(freqresp(Gfm, freqs, 'Hz')))), '-', ... - 'DisplayName', '$m = 1kg$'); + 'DisplayName', '$m = 10kg$'); set(gca, 'XScale', 'log'); set(gca, 'YScale', 'lin'); yticks(-360:90:360); ylim([-390 30]);