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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]);