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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + image/svg+xml + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/index.html b/index.html index d4e5f57..a0f2991 100644 --- a/index.html +++ b/index.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Amplifier Piezoelectric Actuator APA300ML - Test Bench @@ -30,8 +30,18 @@

Table of Contents

@@ -47,24 +57,48 @@ This include:
  • Stroke
  • Stiffness
  • Hysteresis
    • -
  • Gain from \(V_a\) to \(d\) (in [m/V]), then it should be possible to compute the gain from \(V_a\) to \(F_a\) using the Simscape model
    • -
  • Gain from \(\delta L\) to \(V_s\) (in [V/m])
    • +
  • Gain from the applied voltage \(V_a\) to the generated Force \(F_a\)
    • +
  • Gain from the sensor stack strain \(\delta L\) to the generated voltage \(V_s\)
    • -
    -

    1 Model of an Amplified Piezoelectric Actuator and Sensor

    +
    +

    1 Model of an Amplified Piezoelectric Actuator and Sensor

    -
      -
    • [ ] Schematic of the APA with values of displacement, voltages, forces, etc.
      • -
    • [ ] Required things to measure
      • -
    +

    +Consider a schematic of the Amplified Piezoelectric Actuator in Figure 1. +

    + +

    +A voltage \(V_a\) applied to the actuator stacks will induce an actuator force \(F_a\): +

    +\begin{equation} + F_a = g_a \cdot V_a +\end{equation} + +

    +A change of length \(dl\) of the sensor stack will induce a voltage \(V_s\): +

    +\begin{equation} + V_s = g_s \cdot dl +\end{equation} + +

    +We wish here to experimental measure \(g_a\) and \(g_s\). +

    + + +
    +

    apa_model_schematic.png +

    +

    Figure 1: Amplified Piezoelectric Actuator Schematic

    +
    -
    -

    2 Test-Bench Description

    +
    +

    2 Test-Bench Description

    -
    +

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

    @@ -79,17 +113,161 @@ Here are the documentation of the equipment used for this test bench:
    -
    +

    test_bench_apa_alone.png

    -

    Figure 1: Schematic of the Test Bench

    +

    Figure 2: Schematic of the Test Bench

    +
    +
    +
    + +
    +

    3 Measurement Procedure

    +
    +
    +
    +

    3.1 Stroke Measurement

    +
    +

    +Using the PD200 amplifier, output a voltage: +\[ V_a = 65 + 85 \sin(2\pi \cdot t) \] +To have a quasi-static excitation between -80 and 150V. +

    + +

    +As the gain of the PD200 amplifier is 20, the DAC output voltage should be: +\[ V_{dac}(t) = 3.25 + 4.25\sin(2\pi \cdot t) \] +

    + +

    +Verify that the voltage offset is zero! +

    + +

    +Measure the output vertical displacement \(d\) using the interferometer. +

    + +

    +Then, plot \(d\) as a function of \(V_a\), and perform a linear regression. +Conclude on the obtained stroke. +

    +
    +
    + +
    +

    3.2 Stiffness Measurement

    +
    +

    +Add some (known) weight \(\delta m g\) on the suspended mass and measure the deflection \(\delta d\). +This can be tested when the piezoelectric stacks are open-circuit. +

    + +

    +As the stiffness will be around \(k \approx 10^6 N/m\), an added mass of \(m \approx 100g\) will induce a static deflection of \(\approx 1\mu m\) which should be large enough for a precise measurement using the interferometer. +

    + +

    +Then the obtained stiffness is: +

    +\begin{equation} + k = \frac{\delta m g}{\delta d} +\end{equation} +
    +
    + +
    +

    3.3 Hysteresis measurement

    +
    +

    +Supply a quasi static sinusoidal excitation \(V_a\) at different voltages. +

    + +

    +The offset should be 65V, and the sin amplitude can range from 1V up to 85V. +

    + +

    +For each excitation amplitude, the vertical displacement \(d\) of the mass is measured. +

    + +

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

    +
    +
    + +
    +

    3.4 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 \(d\). +Use a quasi static (1Hz) excitation signal \(V_a\) on the piezoelectric stack and measure the vertical displacement \(d\). +Perform a linear regression to obtain: +

    +\begin{equation} + d = g_{d/V_a} \cdot V_a +\end{equation} + +

    +Using the Simscape model of the APA, it is possible to determine the static gain between the actuator force \(F_a\) to the induced displacement \(d\): +

    +\begin{equation} + d = g_{d/F_a} \cdot F_a +\end{equation} + +

    +From the two gains, it is then easy to determine \(g_a\): +

    +\begin{equation} + g_a = \frac{F_a}{V_a} = \frac{F_a}{d} \cdot \frac{d}{V_a} = \frac{g_{d/V_a}}{g_{d/F_a}} +\end{equation} +
    +
    + +
    +

    3.5 Piezoelectric Sensor Constant

    +
    +

    +From a quasi static (1Hz) excitation of the piezoelectric stack, measure the gain from \(V_a\) to \(V_s\): +

    +\begin{equation} + V_s = g_{V_s/V_a} V_a +\end{equation} + +

    +Using the simscape model, compute the static gain from the actuator force \(F_a\) to the strain of the sensor stack \(dl\): +

    +\begin{equation} + dl = g_{dl/F_a} F_a +\end{equation} + +

    +Then, the static gain from the sensor stack strain \(dl\) to the general voltage \(V_s\) is: +

    +\begin{equation} + g_s = \frac{V_s}{dl} = \frac{V_s}{V_a} \cdot \frac{V_a}{F_a} \cdot \frac{F_a}{dl} = \frac{g_{V_s/V_a}}{g_a \cdot g_{dl/F_a}} +\end{equation} + +

    +Alternatively, we could impose an external force to add strain in the APA that should be equally present in all the 3 stacks and equal to 1/5 of the vertical strain. +This external force can be some weight added, or a piezo in parallel. +

    +
    +
    + +
    +

    3.6 Capacitance Measurement

    +
    +

    +Measure the capacitance of the 3 stacks individually using a precise multi-meter. +

    Author: Dehaeze Thomas

    -

    Created: 2020-12-15 mar. 23:33

    +

    Created: 2020-12-16 mer. 11:07

    diff --git a/index.org b/index.org index f23d600..67136b4 100644 --- a/index.org +++ b/index.org @@ -48,13 +48,28 @@ This include: - Stroke - Stiffness - Hysteresis -- Gain from $V_a$ to $d$ (in [m/V]), then it should be possible to compute the gain from $V_a$ to $F_a$ using the Simscape model -- Gain from $\delta L$ to $V_s$ (in [V/m]) +- Gain from the applied voltage $V_a$ to the generated Force $F_a$ +- Gain from the sensor stack strain $\delta L$ to the generated voltage $V_s$ * Model of an Amplified Piezoelectric Actuator and Sensor -- [ ] Schematic of the APA with values of displacement, voltages, forces, etc. -- [ ] Required things to measure +Consider a schematic of the Amplified Piezoelectric Actuator in Figure [[fig:apa_model_schematic]]. + +A voltage $V_a$ applied to the actuator stacks will induce an actuator force $F_a$: +\begin{equation} + F_a = g_a \cdot V_a +\end{equation} + +A change of length $dl$ of the sensor stack will induce a voltage $V_s$: +\begin{equation} + V_s = g_s \cdot dl +\end{equation} + +We wish here to experimental measure $g_a$ and $g_s$. + +#+name: fig:apa_model_schematic +#+caption: Amplified Piezoelectric Actuator Schematic +[[file:figs/apa_model_schematic.png]] * Test-Bench Description @@ -70,3 +85,85 @@ Here are the documentation of the equipment used for this test bench: #+name: fig:test_bench_apa_alone #+caption: Schematic of the Test Bench [[file:figs/test_bench_apa_alone.png]] + +* Measurement Procedure +** Stroke Measurement + +Using the PD200 amplifier, output a voltage: +\[ V_a = 65 + 85 \sin(2\pi \cdot t) \] +To have a quasi-static excitation between -80 and 150V. + +As the gain of the PD200 amplifier is 20, the DAC output voltage should be: +\[ V_{dac}(t) = 3.25 + 4.25\sin(2\pi \cdot t) \] + +Verify that the voltage offset is zero! + +Measure the output vertical displacement $d$ using the interferometer. + +Then, plot $d$ as a function of $V_a$, and perform a linear regression. +Conclude on the obtained stroke. + +** Stiffness Measurement + +Add some (known) weight $\delta m g$ on the suspended mass and measure the deflection $\delta d$. +This can be tested when the piezoelectric stacks are open-circuit. + +As the stiffness will be around $k \approx 10^6 N/m$, an added mass of $m \approx 100g$ will induce a static deflection of $\approx 1\mu m$ which should be large enough for a precise measurement using the interferometer. + +Then the obtained stiffness is: +\begin{equation} + k = \frac{\delta m g}{\delta d} +\end{equation} + +** Hysteresis measurement + +Supply a quasi static sinusoidal excitation $V_a$ at different voltages. + +The offset should be 65V, and the sin amplitude can range from 1V up to 85V. + +For each excitation amplitude, the vertical displacement $d$ of the mass is measured. + +Then, $d$ is plotted as a function of $V_a$ for all the amplitudes. + +** 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 $d$. +Use a quasi static (1Hz) excitation signal $V_a$ on the piezoelectric stack and measure the vertical displacement $d$. +Perform a linear regression to obtain: +\begin{equation} + d = g_{d/V_a} \cdot V_a +\end{equation} + +Using the Simscape model of the APA, it is possible to determine the static gain between the actuator force $F_a$ to the induced displacement $d$: +\begin{equation} + d = g_{d/F_a} \cdot F_a +\end{equation} + +From the two gains, it is then easy to determine $g_a$: +\begin{equation} + g_a = \frac{F_a}{V_a} = \frac{F_a}{d} \cdot \frac{d}{V_a} = \frac{g_{d/V_a}}{g_{d/F_a}} +\end{equation} + +** Piezoelectric Sensor Constant + +From a quasi static (1Hz) excitation of the piezoelectric stack, measure the gain from $V_a$ to $V_s$: +\begin{equation} + V_s = g_{V_s/V_a} V_a +\end{equation} + +Using the simscape model, compute the static gain from the actuator force $F_a$ to the strain of the sensor stack $dl$: +\begin{equation} + dl = g_{dl/F_a} F_a +\end{equation} + +Then, the static gain from the sensor stack strain $dl$ to the general voltage $V_s$ is: +\begin{equation} + g_s = \frac{V_s}{dl} = \frac{V_s}{V_a} \cdot \frac{V_a}{F_a} \cdot \frac{F_a}{dl} = \frac{g_{V_s/V_a}}{g_a \cdot g_{dl/F_a}} +\end{equation} + +Alternatively, we could impose an external force to add strain in the APA that should be equally present in all the 3 stacks and equal to 1/5 of the vertical strain. +This external force can be some weight added, or a piezo in parallel. + +** Capacitance Measurement + +Measure the capacitance of the 3 stacks individually using a precise multi-meter.