Application Cases

Experiment Name: Displacement Response of Piezoelectric Stack Actuators

Research Direction:
A novel active flow control method—biomimetic flow control—was selected to reduce flow resistance on wing surfaces. Based on requirements such as short response time, high output force, and significant displacement for wing flow control, the BCS3-05051 piezoelectric stack actuator was chosen among commonly used smart materials. An experimental system for flexible moving walls was integrated to simulate the state of dolphin skin during high-speed motion. Drag reduction characteristics were observed through displacement measurement and numerical simulation. During displacement measurement of the moving wall experimental system using a laser displacement sensor, a frequency doubling phenomenon was observed in the surface-generated standing waves. This phenomenon was attributed to the phase difference in the driving voltage, signal distortion after amplification, and the inherent hysteresis effect of the piezoelectric stack. To address this, methods such as real-time monitoring with an oscilloscope, adjusting amplification factors, and modifying the driving voltage through nonlinear hysteresis models were proposed to eliminate the frequency doubling phenomenon.

Experiment Objective:
To verify the drag reduction effect of standing wave motion in the moving wall experimental system through displacement measurement and numerical simulation. The results indicate that the drag reduction mechanism involves the generation of a stable vortex array on the surface of the flexible moving wall by standing wave motion. The frequency of the standing wave motion has a greater impact on drag reduction than its amplitude.

Testing Equipment:
Function signal generator, ATA-4315 high-voltage power amplifier, laser vibrometer, digital storage oscilloscope, etc.

Experimental Procedure:
The physical image of the BCS3-05051 piezoelectric stack is shown below. The outer layer is an insulating plastic film, with positive and negative leads marked in red and black, respectively, and extending 75 mm outward. During operation, the piezoelectric stack is often subjected to voltages of varying amplitudes and frequencies. According to the working principle of piezoelectric stacks, their displacements differ under different conditions. The displacement response under alternating voltages with different parameters was measured.

The schematic diagram of the displacement measurement setup for the piezoelectric stack actuator is shown below. The piezoelectric stack is bonded to a rigid support platform using silicone rubber, with the bottom considered a fixed boundary condition and the top as a completely free boundary condition without any additional load. Due to the small displacement of the piezoelectric stack, the rigid support platform is fixed on a vibration isolation table to minimize the impact of external vibrations on measurements. The desired driving voltage is generated by a function signal generator, amplified by a power amplifier, and then connected to the piezoelectric stack via the positive and negative terminals for actuation. The displacement of the piezoelectric stack surface is measured using a laser vibrometer. To enhance laser reflectivity, a reflective film is attached to the surface. The distance measured by the laser vibrometer is converted into changes in voltage signals, recorded by an oscilloscope, and multiplied by the corresponding sensitivity to obtain the displacement of the piezoelectric stack.

After applying the driving voltage to the piezoelectric stack, the surface displacement is measured using a single-point laser vibrometer. The laser vibrometer operates on the principle of laser Doppler measurement, directing an output laser beam onto the target and collecting the reflected laser light. Interference generates a Doppler frequency shift signal proportional to the target’s velocity, which is processed by a decoder embedded in the controller to output the velocity and displacement values of the measured object. The core components are the high-performance controller and the non-contact, high-sensitivity optical head, as shown in the figure. A standard optical head is used here, capable of measuring at distances ranging from 0.5 meters to 100 meters, with extremely high measurement resolution and a wide dynamic measurement range—from atomic-level weak vibrations to impacts of hundreds of thousands of g. At a bandwidth of 1 Hz, its velocity resolution can reach 0.02 μm/s, and its displacement resolution can be as high as 0.15 nm, fully meeting the measurement requirements for micrometer-level displacements of piezoelectric stacks.

The signal from the laser displacement sensor is transmitted to the digital storage oscilloscope via a BNC cable. The oscilloscope has four channels, can store 100 kpts of data, and has a maximum update rate of 50,000 waveforms per second. The oscilloscope can simultaneously record the voltage signal from the laser displacement sensor and the signal generated by the function generator. Through digital processing, these are output as electrical signals, from which the relationship between the specific displacement of the piezoelectric stack and the applied excitation source can be derived.

Experimental Results:
From the working principle of piezoelectric stacks described above, the displacement response of a piezoelectric stack under DC voltage is generally proportional to the voltage. However, in practical applications, the driving voltage often changes in real time according to requirements, meaning the voltage amplitude applied to the piezoelectric stack is not constant. Under varying voltage amplitudes, the adhesive layers connecting the piezoelectric stack, which have stiffness significantly different from that of the piezoelectric ceramic sheets, deform at different rates compared to the ceramic sheets. Therefore, it is necessary to study the relationship between displacement response and voltage.

For piezoelectric stacks, to investigate the linear relationship between voltage amplitude and displacement response, it is essential to ensure that the voltage amplitude increases linearly, i.e., applying a triangular wave to the piezoelectric stack. However, driving voltages are typically composed of smooth trigonometric functions. Thus, for two different waveform types, it is first necessary to study how the function form affects the displacement response of the piezoelectric stack. Using an arbitrary function generator, triangular waves and the most common sinusoidal waves are applied to the piezoelectric stack, with both waveforms having the same frequency (as low as possible, close to DC conditions) and the same peak-to-peak voltage, as shown in Figure 2.7(a). The displacement of the piezoelectric stack under these two voltage waveforms is measured using a laser displacement sensor, as shown in Figure 2.7(b). The figure shows that the displacement forms of the piezoelectric stack actuator under the two waveforms are similar, with errors between displacements at the same voltage not exceeding 5%. This indicates that triangular and sinusoidal waveforms have no significant effect on the displacement response of the piezoelectric stack. Subsequently, by adjusting the amplification factor of the power amplifier, voltages of different amplitudes are applied to the piezoelectric stack to observe its displacement response. As shown in Figure 2.8, when the driving voltage decreases from 60 V to half (30 V), the maximum displacement decreases by more than half, and the width of the hysteresis curve significantly narrows. This indicates that the hysteresis effect of the piezoelectric stack is weaker at lower voltages.

Additionally, in Figure 2.7, when the applied voltage increases from zero to the maximum value and then decreases back to zero, it is evident that during the voltage loading process, the displacement of the piezoelectric stack is largely linear with respect to the voltage. However, during the voltage unloading process, the displacement of the piezoelectric stack exhibits significant nonlinearity, not returning along the original linear curve but showing a displacement lag. This lag is represented in the figure as the gap between the loading and unloading curves. This hysteresis phenomenon is very similar to magnetic hysteresis. The piezoelectric ceramic sheets constituting the piezoelectric stack undergo polarization under high voltage and high temperature during manufacturing, endowing them with spontaneous polarization capability. Under an external electric field, the direction of the electric dipole moment in the piezoelectric ceramic sheets changes. The change curves of electrode polarization intensity $P$ and electric field intensity $E$ during this process closely resemble the hysteresis loop of ferromagnetic materials, a phenomenon known as the ferroelectricity of piezoelectric ceramics. Piezoelectric ceramics with ferroelectricity share many physical properties with magnets, such as the similarity between the electric hysteresis loop during voltage changes and the magnetic hysteresis loop of ferromagnetic materials, and the correspondence between electric domains in ferroelectrics and magnetic domains in magnets. Under alternating external voltages, the relationship between electrode polarization intensity and the external electric field in ferroelectric piezoelectric ceramics is nonlinear, a phenomenon known as electric hysteresis. This occurs because piezoelectric crystals possess a certain degree of asymmetry, with lattice constants along the x-axis and z-axis being unequal. Even after polarization treatment, piezoelectric ceramics still contain some electric dipoles oriented at 90° to the polarization direction. The displacement of piezoelectric ceramics under relatively low voltages is primarily due to the polarization of electric dipoles in the piezoelectric crystals by the external electric field. This change in polarization direction, i.e., the inverse piezoelectric effect, results in linear displacement of the piezoelectric ceramics. However, when piezoelectric ceramics are subjected to higher voltages, electric domains oriented at 90° to the polarization direction gradually begin to move. Due to the unequal lattice constants along the x-axis and z-axis, the rotation along these two axes causes the displacement change along the polarization direction to become nonlinear with respect to the voltage. Additionally, there are two types of electric domains oriented at 90° to the polarization direction: one returns to the 90° direction after voltage unloading, while the other is irreversible, remaining in the polarization direction even after voltage unloading. Therefore, after the external electric field is removed, the displacement of the piezoelectric ceramics cannot fully replicate the loading process, and the nonlinearity of displacement further increases, resulting in the electric hysteresis phenomenon of piezoelectric stacks.

In addition to waveform and amplitude, frequency is another important parameter of the external excitation voltage for piezoelectric stack actuators. Due to the capacitive nature of piezoelectric stacks, the application of an external voltage causes internal charge movement to the surfaces of the positive and negative electrodes. This charge movement requires a certain amount of time. If the external voltage changes too rapidly, charges may not move completely, leading to incomplete polarization of the piezoelectric ceramic sheets and correspondingly different displacements. Therefore, sinusoidal alternating voltages of different frequencies are applied to the piezoelectric stack to measure changes in displacement. As shown in Figure 2.9, a 30 V sinusoidal alternating voltage is applied to the piezoelectric stack actuator at frequencies of 1 Hz, 10 Hz, and 100 Hz. Results from the laser vibrometer show that the maximum displacement of the piezoelectric stack is inversely proportional to the frequency of the sinusoidal alternating voltage. As frequency increases, maximum displacement decreases, with the maximum displacement at 100 Hz being 10.48% smaller than at 1 Hz.

Furthermore, as the frequency of the sinusoidal alternating voltage is gradually increased, the phase of displacement is compared with the phase of the input voltage. As shown in Figure 2.10, the dynamic displacement phase of the piezoelectric stack is largely consistent with the driving voltage, with a phase difference of 3° at 1000 Hz. Since one end of the piezoelectric stack in this experiment is under free boundary conditions, the frequency of the applied voltage cannot be too high. At low frequencies, the phase of the piezoelectric stack is almost independent of voltage frequency. This is a favorable characteristic for wing flow control, as the displacement phase of the piezoelectric stack actuator does not change with frequency variation, providing some flexibility for active control.

Recommended Power Amplifier: ATA-4315

Figure: Specifications of the ATA-4315 High-Voltage Power Amplifier