Application Cases

Experiment Name: Effects of Various Parameters of Unequal-Thickness Beams on Output Voltage

Research Direction: In alignment with the research objectives of the National Natural Science Foundation project, "Study on Magnetically Coupled Assisted Excitation Piezoelectric Vibration Generators Based on Composite Transducers," two types of magnetically coupled piezoelectric vibration energy harvesters with auxiliary cantilever beams for indirect excitation were proposed to enhance the reliability and environmental adaptability of the energy harvester. These designs utilize auxiliary beams to unidirectionally and indirectly excite the piezoelectric oscillator for power generation. The effects of structural parameters of the auxiliary beams, magnet configuration parameters, load resistance, and other factors on the output characteristics of the energy harvester were analyzed. A systematic investigation was conducted from both theoretical simulation and experimental perspectives.

Experimental Objective: To validate the correctness of the theoretical and simulation results, two prototypes—single-magnet coupling and dual-magnet coupling—were designed, and an experimental testing platform was established. Through experimental methods, the effects of structural parameters of equal- and unequal-thickness auxiliary beams (such as length and thickness), magnet configuration parameters (spacing and angle), and excitation parameters (amplitude, frequency, and excitation method) on the output voltage of the two types of magnetically coupled piezoelectric energy harvesters with indirect excitation via auxiliary beams were studied.

Test Equipment: Computer, RC-2000 vibration controller, ATA-309B power amplifier, DC-1000 vibration shaker, accelerometer, digital oscilloscope, and experimental prototypes.

Experimental Procedure: A testing platform, as shown in Figure 4.2, was constructed using a computer, an RC-2000 vibration controller, an ATA-309B power amplifier, a DC-1000 vibration shaker, an accelerometer, a digital oscilloscope, and experimental prototypes. The RC-2000 vibration controller employs an advanced distributed architecture and uses closed-loop control to ensure real-time performance, efficiency, and stability of the control system. The amplitude and frequency of harmonic excitation were set on the computer and transmitted to the vibration controller. The vibration controller, power amplifier, vibration shaker, experimental prototype, and accelerometer formed a closed-loop control system. Finally, the open-circuit voltage output of the piezoelectric oscillator during excitation was collected using the digital oscilloscope.

The study investigated the effects of structural parameters of the auxiliary cantilever beams, configuration parameters of the coupling magnets, and excitation parameters on the voltage characteristics of the energy harvester. For convenience, the following conventions were established:

① Unless otherwise specified, the applied excitation had an amplitude of 1.5 mm and a frequency ranging from 10 Hz to 40 Hz.
② The low-frequency range and high-frequency range refer to excitation frequencies of 10–25 Hz and 25–40 Hz, respectively.
③ The amplitude-frequency characteristics of the upper and lower piezoelectric oscillators under the same conditions were essentially consistent, so only the peak-to-peak open-circuit voltage of the upper piezoelectric oscillator was tested.
④ The effective frequency band refers to the frequency range where the output voltage exceeds 10 V, and the effective bandwidth refers to the width of the effective frequency band.

The auxiliary beam at the fixed end of the flexible beam, as shown in Figure 4.8, was composed of a central beam with a thickness of 0.1 mm and two additional beams with a thickness of 0.2 mm bonded to it. The lengths of the additional beams on both sides were constant at 80 mm, and the length of the flexible beam (the central beam without additional beams) was denoted as l₁.

When L₀ increased from 0 mm to 10 mm, the natural frequency of the energy harvester decreased from 26 Hz to 23.5 Hz, and the maximum voltage decreased from 89.6 V to 88 V. Figure 4.9(b) shows the amplitude-frequency characteristic curves for different values of l₁ under weak magnetic coupling conditions, with a total beam length of L = 100 mm. The results indicate that as l₁ increased from 0 mm to 20 mm, the natural frequency of the energy harvester decreased from 20 Hz to 17 Hz, and the maximum voltage increased from 37.2 V to 41.6 V.

When the auxiliary beam was composed of three rectangular beams, each with a thickness of 0.3 mm, bonded together, the length of the central flexible beam was constant at 90 mm, and the lengths of the additional beams on both sides were both l₂. Additionally, the pre-bent piezoelectric oscillator was measured to have a sliding contact point with the auxiliary beam located 42 mm from the fixed end after installation.

The natural frequency increased with the length of the additional beams, the effective bandwidth broadened as the length increased, and the maximum voltage initially decreased and then increased with increasing length. Comparing the cases where l₂ = 0 mm and l₂ = 55 mm, it was observed that after adding the two additional beams, the maximum voltage of the energy harvester increased from 22 V to 44.8 V (a 2-fold increase), and the effective frequency band expanded from 12.7–14.9 Hz to 18.7–26.3 Hz (a 3.6-fold expansion).

Figure 4.13 shows the structural diagram of an unequal-thickness auxiliary beam with the flexible beam located at an intermediate position (between the contact point of the piezoelectric oscillator and the auxiliary beam and the fixed end). It consists of a central flexible beam with a length of 90 mm and a thickness of h₃, and additional beams with a thickness of 0.3 mm bonded to both sides of the central beam. The length of the flexible beam (the central beam without additional beams) was constant at 10 mm.

Figure 4.14 shows the amplitude-frequency characteristic curves of the single-magnet coupled energy harvester under the conditions of a horizontal coupling distance d₁ = 12.5 mm, vertical coupling distance h₁ = 0 mm, coupling angle α = 0°, excitation amplitude of 3 mm, flexible beam thickness h₃ = 0.3 mm, and different installation distances L₃. When the installation distances were 0 mm, 10 mm, and 20 mm, the natural frequencies of the energy harvester were 16 Hz, 10 Hz, and 10 Hz, respectively, and the maximum voltages were 58.4 V, 32 V, and 28.8 V, respectively. The natural frequency decreased with increasing installation distance L₃, and the maximum voltage also decreased with increasing L₃. Figure 4.15 shows the amplitude-frequency characteristic curves of the single-magnet coupled energy harvester under the conditions of d₁ = 12.5 mm, h₁ = 0 mm, α = 0°, excitation amplitude of 3 mm, and different values of flexible beam thickness h₃ and installation distance L₃. As shown in Figure 4.15, all four groups in the figure exhibited relatively low response frequencies. Among them, when the flexible beam thickness h₃ = 0.2 mm and the installation distance L₃ = 10 mm, the energy harvester exhibited a lower response frequency and a broader effective frequency band.

Test Results:
When the flexible beam was located at the free end and other parameters remained unchanged, reducing the length of the flexible beam increased the natural frequency of the energy harvester, broadened the effective bandwidth, and resulted in better low-frequency response.

When the flexible beam was located at the fixed end and other parameters remained unchanged, increasing the length of the flexible beam L₀ further reduced the natural frequency, while the maximum voltage remained almost unaffected.

In summary, under unchanged conditions, adjusting the length, thickness, and position of the flexible beam can further enhance the power generation capability of the energy harvester.

Recommended Power Amplifier: ATA-309C

Figure: ATA-309C Power Amplifier Specifications

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