Amplifier Piezoelectric Actuator APA300ML - Test Bench
-Table of Contents
- --The goal of this test bench is to extract all the important parameters of the Amplified Piezoelectric Actuator APA300ML. -
- --This include: -
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- Stroke -
- Stiffness -
- Hysteresis -
- 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 \(V_s\) -
- Dynamical behavior -
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Figure 1: Picture of the APA300ML
-1 Model of an Amplified Piezoelectric Actuator and Sensor
--Consider a schematic of the Amplified Piezoelectric Actuator in Figure 2. -
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Figure 2: Amplified Piezoelectric Actuator 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 \(g_s\). -
- --The block-diagram model of the piezoelectric actuator is then as shown in Figure 3. -
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Figure 3: Model of the APA with Simscape/Simulink
-2 Test-Bench Description
--Here are the documentation of the equipment used for this test bench: -
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- Voltage Amplifier: PD200 -
- Amplified Piezoelectric Actuator: APA300ML -
- DAC/ADC: Speedgoat IO313 -
- Encoder: Renishaw Vionic and used Ruler -
- Interferometer: Attocube IDS3010 -
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Figure 4: 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. -
-3.7 Dynamical Behavior
--Perform a system identification from \(V_a\) to the measured displacement \(d\) by the interferometer and by the encoder, and to the general voltage \(V_s\). -
- --This can be performed using different excitation signals. -
- --This can also be performed with and without the encoder fixed to the APA. -
-3.8 Compare the results obtained for all 7 APA300ML
--Compare all the obtained parameters for all the test APA. -
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