From 953eef097846627e061a73d06475c25b7b85f170 Mon Sep 17 00:00:00 2001 From: Thomas Dehaeze Date: Thu, 6 May 2021 16:27:04 +0200 Subject: [PATCH] Add some discussion about the measurements --- test-bench-apa300ml.html | 478 ++++++++++++++++++++------------------- test-bench-apa300ml.org | 18 +- 2 files changed, 259 insertions(+), 237 deletions(-) diff --git a/test-bench-apa300ml.html b/test-bench-apa300ml.html index 37277d5..c0650a8 100644 --- a/test-bench-apa300ml.html +++ b/test-bench-apa300ml.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Amplifier Piezoelectric Actuator APA300ML - Test Bench @@ -39,93 +39,93 @@

Table of Contents

@@ -152,21 +152,21 @@ This include: -
+

apa300ML.png

Figure 1: Picture of the APA300ML

-
-

1 Model of an Amplified Piezoelectric Actuator and Sensor

+
+

1 Model of an Amplified Piezoelectric Actuator and Sensor

-Consider a schematic of the Amplified Piezoelectric Actuator in Figure 2. +Consider a schematic of the Amplified Piezoelectric Actuator in Figure 2.

-
+

apa_model_schematic.png

Figure 2: Amplified Piezoelectric Actuator Schematic

@@ -191,11 +191,11 @@ We wish here to experimental measure \(g_a\) and \(g_s\).

-The block-diagram model of the piezoelectric actuator is then as shown in Figure 3. +The block-diagram model of the piezoelectric actuator is then as shown in Figure 3.

-
+

apa-model-simscape-schematic.png

Figure 3: Model of the APA with Simscape/Simulink

@@ -203,30 +203,30 @@ The block-diagram model of the piezoelectric actuator is then as shown in Figure
-
-

2 Geometrical Measurements

+
+

2 Geometrical Measurements

-The received APA are shown in Figure 4. +The received APA are shown in Figure 4.

-
+

IMG_20210224_143500.jpg

Figure 4: Received APA

-
-

2.1 Measurement Setup

+
+

2.1 Measurement Setup

-The flatness corresponding to the two interface planes are measured as shown in Figure 5. +The flatness corresponding to the two interface planes are measured as shown in Figure 5.

-
+

IMG_20210224_143809.jpg

Figure 5: Measurement Setup

@@ -234,8 +234,8 @@ The flatness corresponding to the two interface planes are measured as shown in
-
-

2.2 Measurement Results

+
+

2.2 Measurement Results

The height (Z) measurements at the 8 locations (4 points by plane) are defined below. @@ -281,10 +281,10 @@ Finally, the flatness is estimated by fitting a plane through the 8 points using

-The obtained flatness are shown in Table 1. +The obtained flatness are shown in Table 1.

- +
@@ -339,10 +339,10 @@ The obtained flatness are shown in Table 1. -
-

3 Electrical Measurements

+
+

3 Electrical Measurements

-
+

The capacitance of the stacks is measure with the LCR-800 Meter (doc)

@@ -350,7 +350,7 @@ The capacitance of the stacks is measure with the +
Table 1: Estimated flatness
@@ -422,7 +422,7 @@ The excitation frequency is set to be 1kHz.
Table 2: Capacitance measured with the LCR meter. The excitation signal is a sinus at 1kHz
-
+

There is clearly a problem with APA300ML number 3

@@ -431,12 +431,12 @@ There is clearly a problem with APA300ML number 3
-
-

4 Stiffness measurement

+
+

4 Stiffness measurement

-
-

4.1 APA test

+
+

4.1 APA test

load('meas_stiff_apa_1_x.mat', 't', 'F', 'd');
@@ -502,22 +502,22 @@ plot(F_l, F_l*fit_l(1) +
-
-

5 Stroke measurement

+
+

5 Stroke measurement

We here wish to estimate the stroke of the APA.

-To do so, one side of the APA is fixed, and a displacement probe is located on the other side as shown in Figure 7. +To do so, one side of the APA is fixed, and a displacement probe is located on the other side as shown in Figure 7.

Then, a voltage is applied on either one or two stacks using a DAC and a voltage amplifier.

-
+

Here are the documentation of the equipment used for this test bench:

@@ -530,92 +530,92 @@ Here are the documentation of the equipment used for this test bench:
-
+

CE0EF55E-07B7-461B-8CDB-98590F68D15B.jpeg

Figure 7: Bench to measured the APA stroke

-
-

5.1 Voltage applied on one stack

+
+

5.1 Voltage applied on one stack

Let’s first look at the relation between the voltage applied to one stack to the displacement of the APA as measured by the displacement probe.

-The applied voltage is shown in Figure 8. +The applied voltage is shown in Figure 8.

-
+

apa_stroke_voltage_time.png

Figure 8: Applied voltage as a function of time

-The obtained displacement is shown in Figure 9. +The obtained displacement is shown in Figure 9. The displacement is set to zero at initial time when the voltage applied is -20V.

-
+

apa_stroke_time_1s.png

Figure 9: Displacement as a function of time for all the APA300ML

-Finally, the displacement is shown as a function of the applied voltage in Figure 10. +Finally, the displacement is shown as a function of the applied voltage in Figure 10. We can clearly see that there is a problem with the APA 3. Also, there is a large hysteresis.

-
+

apa_d_vs_V_1s.png

Figure 10: Displacement as a function of the applied voltage

-
+

-We can clearly see from Figure 10 that there is a problem with the APA number 3. +We can clearly see from Figure 10 that there is a problem with the APA number 3.

-
-

5.2 Voltage applied on two stacks

+
+

5.2 Voltage applied on two stacks

Now look at the relation between the voltage applied to the two other stacks to the displacement of the APA as measured by the displacement probe.

-The obtained displacement is shown in Figure 11. +The obtained displacement is shown in Figure 11. The displacement is set to zero at initial time when the voltage applied is -20V.

-
+

apa_stroke_time_2s.png

Figure 11: Displacement as a function of time for all the APA300ML

-Finally, the displacement is shown as a function of the applied voltage in Figure 12. +Finally, the displacement is shown as a function of the applied voltage in Figure 12. We can clearly see that there is a problem with the APA 3. Also, there is a large hysteresis.

-
+

apa_d_vs_V_2s.png

Figure 12: Displacement as a function of the applied voltage

@@ -623,25 +623,25 @@ Also, there is a large hysteresis.
-
-

5.3 Voltage applied on all three stacks

+
+

5.3 Voltage applied on all three stacks

-Finally, we can combine the two measurements to estimate the relation between the displacement and the voltage applied to the three stacks (Figure 13). +Finally, we can combine the two measurements to estimate the relation between the displacement and the voltage applied to the three stacks (Figure 13).

-
+

apa_d_vs_V_3s.png

Figure 13: Displacement as a function of the applied voltage

-The obtained maximum stroke for all the APA are summarized in Table 3. +The obtained maximum stroke for all the APA are summarized in Table 3.

- +
@@ -696,10 +696,10 @@ The obtained maximum stroke for all the APA are summarized in Table -

6 Test-Bench Description

+
+

6 Test-Bench Description

-
+

Here are the documentation of the equipment used for this test bench:

@@ -714,7 +714,7 @@ Here are the documentation of the equipment used for this test bench:
-
+

test_bench_apa_alone.png

Figure 14: Schematic of the Test Bench

@@ -722,12 +722,12 @@ Here are the documentation of the equipment used for this test bench:
-
-

7 Measurement Procedure

+
+

7 Measurement Procedure

-
-

7.1 Stroke Measurement

+
+

7.1 Stroke Measurement

Using the PD200 amplifier, output a voltage: @@ -755,8 +755,8 @@ Conclude on the obtained stroke.

-
-

7.2 Stiffness Measurement

+
+

7.2 Stiffness Measurement

Add some (known) weight \(\delta m g\) on the suspended mass and measure the deflection \(\delta d\). @@ -776,8 +776,8 @@ Then the obtained stiffness is:

-
-

7.3 Hysteresis measurement

+
+

7.3 Hysteresis measurement

Supply a quasi static sinusoidal excitation \(V_a\) at different voltages. @@ -796,7 +796,7 @@ Then, \(d\) is plotted as a function of \(V_a\) for all the amplitudes.

-
+

expected_hysteresis.png

Figure 15: Expected Hysteresis (poel10_explor_activ_hard_mount_vibrat)

@@ -804,8 +804,8 @@ Then, \(d\) is plotted as a function of \(V_a\) for all the amplitudes.
-
-

7.4 Piezoelectric Actuator Constant

+
+

7.4 Piezoelectric Actuator Constant

Using the measurement test-bench, it is rather easy the determine the static gain between the applied voltage \(V_a\) to the induced displacement \(d\). @@ -832,8 +832,8 @@ From the two gains, it is then easy to determine \(g_a\):

-
-

7.5 Piezoelectric Sensor Constant

+
+

7.5 Piezoelectric Sensor Constant

From a quasi static excitation of the piezoelectric stack, measure the gain from \(V_a\) to \(V_s\): @@ -872,8 +872,8 @@ This external force can be some weight added, or a piezo in parallel.

-
-

7.6 Capacitance Measurement

+
+

7.6 Capacitance Measurement

Measure the capacitance of the 3 stacks individually using a precise multi-meter. @@ -881,8 +881,8 @@ Measure the capacitance of the 3 stacks individually using a precise multi-meter

-
-

7.7 Dynamical Behavior

+
+

7.7 Dynamical Behavior

Perform a system identification from \(V_a\) to the measured displacement \(d\) by the interferometer and by the encoder, and to the generated voltage \(V_s\). @@ -898,8 +898,8 @@ This can also be performed with and without the encoder fixed to the APA.

-
-

7.8 Compare the results obtained for all 7 APA300ML

+
+

7.8 Compare the results obtained for all 7 APA300ML

Compare all the obtained parameters for all the test APA. @@ -908,19 +908,19 @@ Compare all the obtained parameters for all the test APA.

-
-

8 Measurement Results

+
+

8 Measurement Results

-
-

9 Test Bench APA300ML - Simscape Model

+
+

9 Test Bench APA300ML - Simscape Model

-
-

9.1 Introduction

+
+

9.1 Introduction

-
-

9.2 Nano Hexapod object

+
+

9.2 Nano Hexapod object

n_hexapod = struct();
@@ -928,8 +928,8 @@ Compare all the obtained parameters for all the test APA.
-
-

9.2.1 APA - 2 DoF

+
+

9.2.1 APA - 2 DoF

n_hexapod.actuator = struct();
@@ -953,8 +953,8 @@ n_hexapod.actuator.Gs = ones(6,1)*1; 
-
9.2.2 APA - Flexible Frame

+

+
9.2.2 APA - Flexible Frame

 

 

 
n_hexapod.actuator.type = 2;
@@ -974,8 +974,8 @@ n_hexapod.actuator.Gs = ones(6,1)*1; 
-
9.2.3 APA - Fully Flexible

+

+
9.2.3 APA - Fully Flexible

 

 

 
n_hexapod.actuator.type = 3;
@@ -993,8 +993,8 @@ n_hexapod.actuator.Gs = ones(6,1)*1; 
-
9.3 Identification

+

+
9.3 Identification

 

 

 
%% Options for Linearized
@@ -1020,12 +1020,12 @@ Ga.OutputName = {'Vs', 
 

 

 
-

-
9.4 Compare 2-DoF with flexible

+

+
9.4 Compare 2-DoF with flexible

 

 

-

-
9.4.1 APA - 2 DoF

+

+
9.4.1 APA - 2 DoF

 

 

 
n_hexapod = struct();
@@ -1058,8 +1058,8 @@ G_2dof.OutputName = {'Vs', 
-
9.4.2 APA - Fully Flexible

+

+
9.4.2 APA - Fully Flexible

 

 

 
n_hexapod = struct();
@@ -1085,21 +1085,21 @@ G_flex.OutputName = {'Vs', 
-
9.4.3 Comparison

+

+
9.4.3 Comparison

 

 

 

 
-

-
10 Test Bench Struts - Simscape Model

+

+
10 Test Bench Struts - Simscape Model

 

 

-

-
10.1 Introduction

+

+
10.1 Introduction

 

-

-
10.2 Nano Hexapod object

+

+
10.2 Nano Hexapod object

 

 

 
n_hexapod = struct();
@@ -1107,8 +1107,8 @@ G_flex.OutputName = {'Vs', 
-
10.2.1 Flexible Joint - Bot

+

+
10.2.1 Flexible Joint - Bot

 

 

 
n_hexapod.flex_bot = struct();
@@ -1129,8 +1129,8 @@ n_hexapod.flex_bot.cz  = ones(6,1)*1e2; 
 

 
-

-
10.2.2 Flexible Joint - Top

+

+
10.2.2 Flexible Joint - Top

 

 

 
n_hexapod.flex_top = struct();
@@ -1151,8 +1151,8 @@ n_hexapod.flex_top.cz  = ones(6,1)*1e2; 
 

 
-

-
10.2.3 APA - 2 DoF

+

+
10.2.3 APA - 2 DoF

 

 

 
n_hexapod.actuator = struct();
@@ -1176,8 +1176,8 @@ n_hexapod.actuator.Gs = ones(6,1)*1; 
-
10.2.4 APA - Flexible Frame

+

+
10.2.4 APA - Flexible Frame

 

 

 
n_hexapod.actuator.type = 2;
@@ -1197,8 +1197,8 @@ n_hexapod.actuator.Gs = ones(6,1)*1; 
-
10.2.5 APA - Fully Flexible

+

+
10.2.5 APA - Fully Flexible

 

 

 
n_hexapod.actuator.type = 3;
@@ -1217,8 +1217,8 @@ n_hexapod.actuator.Gs = ones(6,1)*1; 
-
10.3 Identification

+

+
10.3 Identification

 

 

 
%% Options for Linearized
@@ -1244,12 +1244,12 @@ Gs.OutputName = {'Vs', 
 

 

 
-

-
10.4 Compare flexible joints

+

+
10.4 Compare flexible joints

 

 

-

-
10.4.1 Perfect

+

+
10.4.1 Perfect

 

 

 
n_hexapod.flex_bot.type = 1; % 1: 2dof / 2: 3dof / 3: 4dof
@@ -1266,8 +1266,8 @@ Gp.OutputName = {'Vs', 
 

 

 
-

-
10.4.2 Top Flexible

+

+
10.4.2 Top Flexible

 

 

 
n_hexapod.flex_bot.type = 1; % 1: 2dof / 2: 3dof / 3: 4dof
@@ -1284,8 +1284,8 @@ Gt.OutputName = {'Vs', 
 

 

 
-

-
10.4.3 Bottom Flexible

+

+
10.4.3 Bottom Flexible

 

 

 
n_hexapod.flex_bot.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof
@@ -1302,8 +1302,8 @@ Gb.OutputName = {'Vs', 
 

 

 
-

-
10.4.4 Both Flexible

+

+
10.4.4 Both Flexible

 

 

 
n_hexapod.flex_bot.type = 3; % 1: 2dof / 2: 3dof / 3: 4dof
@@ -1320,43 +1320,43 @@ Gf.OutputName = {'Vs', 
 

 

 
-

-
10.4.5 Comparison

+

+
10.4.5 Comparison

 

 

 

-

-
11 Resonance frequencies - APA300ML

+

+
11 Resonance frequencies - APA300ML

 

 

-

-
11.1 Introduction

+

+
11.1 Introduction

 

 

 Three main resonances are foreseen to be problematic for the control of the APA300ML:
 

 
    
-
  • Mode in X-bending at 189Hz (Figure 16)
    • 
-
  • Mode in Y-bending at 285Hz (Figure 17)
    • 
-
  • Mode in Z-torsion at 400Hz (Figure 18)
    • 
+
  • Mode in X-bending at 189Hz (Figure 16)
    • 
+
  • Mode in Y-bending at 285Hz (Figure 17)
    • 
+
  • Mode in Z-torsion at 400Hz (Figure 18)
    • 
 

 
 
-

+

 
mode_bending_x.gif
 

 
Figure 16: X-bending mode (189Hz)

 

 
 
-

+

 
mode_bending_y.gif
 

 
Figure 17: Y-bending mode (285Hz)

 

 
 
-

+

 
mode_torsion_z.gif
 

 
Figure 18: Z-torsion mode (400Hz)

@@ -1372,16 +1372,16 @@ In this section, we try to find the resonance frequency of these modes when one
 

 

 
-

-
11.2 Setup

+

+
11.2 Setup

 

 

-The measurement setup is shown in Figure 19.
+The measurement setup is shown in Figure 19.
 A Laser vibrometer is measuring the difference of motion of two points.
 The APA is excited with an instrumented hammer and the transfer function from the hammer to the measured rotation is computed.
 

 
-

+

 
    
 
  • Laser Doppler Vibrometer Polytec OFV512
    • 
 
  • Instrumented hammer
    • 
@@ -1390,7 +1390,7 @@ The APA is excited with an instrumented hammer and the transfer function from th
 

 
 
-

+

 
measurement_setup_torsion.png
 

 
Figure 19: Measurement setup with a Laser Doppler Vibrometer and one instrumental hammer

@@ -1398,17 +1398,17 @@ The APA is excited with an instrumented hammer and the transfer function from th
 

 

 
-

-
11.3 Bending - X

+

+
11.3 Bending - X

 

 

-The setup to measure the X-bending motion is shown in Figure 20.
+The setup to measure the X-bending motion is shown in Figure 20.
 The APA is excited with an instrumented hammer having a solid metallic tip.
 The impact point is on the back-side of the APA aligned with the top measurement point.
 

 
 
-

+

 
measurement_setup_X_bending.png
 

 
Figure 20: X-Bending measurement setup

@@ -1437,14 +1437,14 @@ The transfer function from the input force to the output “rotation”
 

 
 

-The result is shown in Figure 21.
+The result is shown in Figure 21.
 

 
 

 The can clearly observe a nice peak at 280Hz, and then peaks at the odd “harmonics” (third “harmonic” at 840Hz, and fifth “harmonic” at 1400Hz).
 

 
-

+

 
apa300ml_meas_freq_bending_x.png
 

 
Figure 21: Obtained FRF for the X-bending

@@ -1452,11 +1452,11 @@ The can clearly observe a nice peak at 280Hz, and then peaks at the odd “h
 

 

 
-

-
11.4 Bending - Y

+

+
11.4 Bending - Y

 

 

-The setup to measure the Y-bending is shown in Figure 22.
+The setup to measure the Y-bending is shown in Figure 22.
 

 
 

@@ -1464,7 +1464,7 @@ The impact point of the instrumented hammer is located on the back surface of th
 

 
 
-

+

 
measurement_setup_Y_bending.png
 

 
Figure 22: Y-Bending measurement setup

@@ -1480,12 +1480,12 @@ The data is loaded, and the transfer function from the force to the measured rot
 

 
 

-The results are shown in Figure 23.
+The results are shown in Figure 23.
 The main resonance is at 412Hz, and we also see the third “harmonic” at 1220Hz.
 

 
 
-

+

 
apa300ml_meas_freq_bending_y.png
 

 
Figure 23: Obtained FRF for the Y-bending

@@ -1493,11 +1493,11 @@ The main resonance is at 412Hz, and we also see the third “harmonic”
 

 

 
-

-
11.5 Torsion - Z

+

+
11.5 Torsion - Z

 

 

-Finally, we measure the Z-torsion resonance as shown in Figure 24.
+Finally, we measure the Z-torsion resonance as shown in Figure 24.
 

 
 

@@ -1505,7 +1505,7 @@ The excitation is shown on the other side of the APA, on the side to excite the
 

 
 
-

+

 
measurement_setup_torsion_bis.png
 

 
Figure 24: Z-Torsion measurement setup

@@ -1521,13 +1521,13 @@ The data is loaded, and the transfer function computed.
 

 
 

-The results are shown in Figure 25.
+The results are shown in Figure 25.
 We observe a first peak at 267Hz, which corresponds to the X-bending mode that was measured at 280Hz.
 And then a second peak at 415Hz, which corresponds to the X-bending mode that was measured at 412Hz.
 The mode in pure torsion is probably at higher frequency (peak around 1kHz?).
 

 
-

+

 
apa300ml_meas_freq_torsion_z.png
 

 
Figure 25: Obtained FRF for the Z-torsion

@@ -1535,14 +1535,14 @@ The mode in pure torsion is probably at higher frequency (peak around 1kHz?).
 

 

 
-

-
11.6 Compare

+

+
11.6 Compare

 

 

-The three measurements are shown in Figure 26.
+The three measurements are shown in Figure 26.
 

 
-

+

 
apa300ml_meas_freq_compare.png
 

 
Figure 26: Obtained FRF - Comparison

@@ -1550,36 +1550,52 @@ The three measurements are shown in Figure 26.
 

 

 
-

-
11.7 Conclusion

+

+
11.7 Conclusion

 

-
Table 3: Measured maximum stroke
+

+When two flexible joints are fixed at each ends of the APA, the APA is mostly in a free/free condition in terms of bending/torsion (the bending/torsional stiffness of the joints being very small). +

+ +

+In the current tests, the APA are in a fixed/free condition. +Therefore, it is quite obvious that we measured higher resonance frequencies than what is foreseen for the struts. +It is however quite interesting that there is a factor \(\approx \sqrt{2}\) between the two (increased of the stiffness by a factor 2?). +

+ +
++ + + + + @@ -1595,7 +1611,7 @@ The three measurements are shown in Figure 26.

Author: Dehaeze Thomas

-

Created: 2021-05-06 jeu. 16:16

+

Created: 2021-05-06 jeu. 16:27

diff --git a/test-bench-apa300ml.org b/test-bench-apa300ml.org index 5add76e..f242b33 100644 --- a/test-bench-apa300ml.org +++ b/test-bench-apa300ml.org @@ -2469,15 +2469,21 @@ exportFig('figs/apa300ml_meas_freq_compare.pdf', 'width', 'full', 'height', 'tal ** Conclusion +When two flexible joints are fixed at each ends of the APA, the APA is mostly in a free/free condition in terms of bending/torsion (the bending/torsional stiffness of the joints being very small). + +In the current tests, the APA are in a fixed/free condition. +Therefore, it is quite obvious that we measured higher resonance frequencies than what is foreseen for the struts. +It is however quite interesting that there is a factor $\approx \sqrt{2}$ between the two (increased of the stiffness by a factor 2?). + #+name: tab:apa300ml_measured_modes_freq #+caption: Measured frequency of the modes -#+attr_latex: :environment tabularx :width 0.3\linewidth :align lX +#+attr_latex: :environment tabularx :width \linewidth :align lX #+attr_latex: :center t :booktabs t :float t -| Mode | Measured Frequency | -|-----------+--------------------| -| X-Bending | 280Hz | -| Y-Bending | 410Hz | -| Z-Torsion | ? | +| Mode | Strut Mode | Measured Frequency | +|-----------+------------+--------------------| +| X-Bending | 189Hz | 280Hz | +| Y-Bending | 285Hz | 410Hz | +| Z-Torsion | 400Hz | ? | * Bibliography :ignore: #+latex: \printbibliography
Table 4: Measured frequency of the modes
ModeStrut Mode Measured Frequency
X-Bending189Hz 280Hz
Y-Bending285Hz 410Hz
Z-Torsion400Hz ?