Experimental and theoretical analysis of a hybrid vibration energy harvester with integrated piezoelectric and electromagnetic interaction

Shifan HUANG, Weihao LUO, Zongming ZHU, Zhenlong XU, Ban WANG, Maoying ZHOU, Huawei QIN

Research Article

Experimental and theoretical analysis of a hybrid vibration energy harvester with integrated piezoelectric and electromagnetic interaction

Shifan HUANG, Weihao LUO, Zongming ZHU, Zhenlong XU, Ban WANG, Maoying ZHOU, Huawei QIN

School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China

Harvesting vibration energy has attracted the attention of researchers in recent decades as a promising approach for powering wireless sensor networks. The hybridization of piezoelectricity and electromagnetism has proven helpful in the improvement of vibration energy harvesting. In this study, we explore the integration of piezoelectric and electromagnetic parts in one vibration energy harvesting device. Lumped-parameter models of the system are derived considering the different connection topologies of the piezoelectric and electromagnetic parts. Numerical predictions from these models are compared with experimental results to throw light on the nonlinearities in the system. Modifications of the system are also explored to provide insights into opportunities to improve its performance and that of future vibration energy harvesters.

Hybrid energy harvesting; Nonlinear interaction; Magnetic spring; Piezoelectricity; Electromagnetism

1 Introduction

Recent years have witnessed the rapid development of wireless sensor networks and their vast applications in consumer electronics, industrial automation, and environmental monitoring (Kandris et al., 2020; Malik et al., 2020; Priyadarshi et al., 2020). In this process, a major concern has been the power supply of such networks, which currently relies on batteries and suffers from a high cost of maintenance (Priyadarshi et al., 2020). In view of the ubiquitous presence of vibration in the ambient environment, it is feasible in principle to harness available vibration energy and convert it into electricity for sensors. The so-called vibration energy harvester has emerged from this idea and has attracted the attention of numerous researchers (Zhou et al., 2018; Malik et al., 2020; Miller et al., 2020; Yao et al., 2023). According to their underlying mechanisms of energy transduction, several sorts of vibration energy harvesters are found in the literature: electrostatic energy harvesters (Basset et al., 2014; Zhang et al., 2016, 2018), triboelectric energy harvesters (Zhu et al., 2013; Li et al., 2015; Qiu et al., 2020), electromagnetic energy harvesters (Zhang et al., 2015; Saravia, 2019; Shi et al., 2020; Wang W et al., 2022), and piezoelectric energy harvesters (Cao et al., 2015; Zhang and Qin, 2019; Wang ZM et al., 2022; Wu and Xu, 2022). Among these, piezoelectric vibration energy harvesters (PVEHs) have shown superior potential for application due to their high voltage output and simple structure.

Physically, PVEHs operate in resonant mode to achieve high efficiency of energy conversion (Anton and Sodano, 2007; Safaei et al., 2019). One problem with these PVEHs has been their limited working frequency bandwidth. Great efforts have been made to enlarge the bandwidth of PVEHs, including the automatic tuning of their resonant frequencies (Challa et al., 2011), integration of multiple PVEHs with different resonant frequencies (Dechant et al., 2017), combination of PVEHs with other energy transduction mechanisms (Fan et al., 2018c; Liu et al., 2021), and intentional introduction of nonlinearity into PVEHs (Zou et al., 2017; Fan et al., 2018b). Of practical interest here is the combination of piezoelectric and electromagnetic energy harvesters. On the one hand, the frequency bandwidth is broadened due to the different resonant frequencies of piezoelectric and vibration electromagnetic energy harvesters. On the other hand, introduction of magnetic interaction provides an opportunity to further increase the frequency bandwidth with the help of nonlinearity.

Hence, many researchers have tried to construct and investigate hybrid energy harvesters based on piezoelectricity and electromagnetism (HEHPEs) (Xia et al., 2015; Ahmad and Khan, 2021). Magnetic interactions between permanent magnets and conducting coils have been introduced to conventional piezoelectric energy harvesters (Challa et al., 2009). Under the action of base excitation, the piezoelectric beam undergoes elastic vibration. As a result, the permanent magnets oscillate relative to the conducting coil. Electrical output can then be expected from the coil according to the principles of electromagnetism. Different arrangements between the magnets and the coils have been explored, based on spiral coils (Yang et al., 2010; Zhang et al., 2019) or helical coils (Sang et al., 2012; Xu et al., 2017b). Magnetic springs formed by the nonlinear interactions between different magnets have also been used to connect the piezoelectric and electromagnetic parts of the HEHPEs (Xu et al., 2016; Xia et al., 2017). The optimal operation frequency of the HEHPE can be easily tuned by the nonlinear magnetic spring introduced. An interesting approach to integrate the piezoelectric and electromagnetic parts in an HEHPE is to add an electromagnetic energy harvesting unit to the free end of a piezoelectric energy harvesting unit (Shan et al., 2013; Mahmoudi et al., 2014; Li et al., 2016; Liu et al., 2019). In this case, a multi-degree of freedom (DOF) vibration system is formed, increasing the power output of the hybrid system. Other investigations have focused on the introduction of impact or contact to tune the operation frequency of HEHPEs (Fan et al., 2018a, 2018b; Halim et al., 2019; Maamer et al., 2019; Iqbal et al., 2021). Nonetheless, it seems that the full potential of HEHPEs has not yet been revealed. Due to the mismatching characteristics of stand-alone piezoelectric and electromagnetic energy harvesters (Arroyo et al., 2012), nearly all the proposed and investigated HEHPEs disconnect the output of the piezoelectric part from that of the electromagnetic part. Hence, the outputs of these two parts are considered and evaluated separately. Meanwhile, due to the capacitive property of a piezoelectric energy harvester, addition of an external inductor alters the vibration characteristics of the device (Wang B et al., 2022). Noting that coils are typical electrical inductors, the electrical connection between the piezoelectric and electromagnetic parts inside an HEHPE may also alter and enhance the performance of an HEHPE (Huang et al., 2022).

In this study, we investigated the direct integration of piezoelectric and electromagnetic energy harvesting units in one HEHPE. An electromagnetic part based on magnetic springs was attached to the free end of a piezoelectric part in an HEHPE. Lumped-parameter models of the HEHPE were established considering different connection topologies between the piezoelectric and electromagnetic parts. Experimental results were obtained and compared with theoretical predictions considering the nonlinearities in the HEHPE. Modifications of the HEHPE were also explored to provide insights into the potential to improve the performance of HEHPEs and that of future vibration energy harvesters.

2 Structure and working principle

Fig. 2 Different connection topologies: (a) connection topology 1; (b) connection topology 2; (c) connection topology 3; (d) connection topology 4

3 Theoretical model of the HEHPE

3.1 Lumped-parameter representation of the system

As indicated above, the dynamic behavior of the HEHPE is affected by the connection topology between the electromagnetic and piezoelectric parts. Four connection topologies were considered: connection topology 1, connection topology 2, connection topology 3, and connection topology 4.

4 Numerical analysis and experiments

4.1 Experimental setup

Based on the above analysis, a prototype of the studied HEHPE was prepared (as shown in the enlarged inset located in the upper right corner of Fig. 3). Related structural and material parameters are shown in Table 1. The prototype consists of a 3D-printed base made of resin materials, a 3D-printed frame made of transparent resin materials (Future Factory, China), a base beam made of red copper (Taizhou Shunkuo Hardware Products Co., Ltd., China), a ring magnet (Shanghai Strong Magnetic Material Factory, China), an induction coil, a copper bar guide, and some screws and nuts.

Fig. 3 Schematic diagram of the studied HEHPE (PC: personal computer; NI: National Instruments)

The main bimorph beam is composed of two PZT-5H ceramic plates (Baoding Hongsheng Electronics Co., Ltd., China) and the base beam. The two piezoelectric ceramic plates were attached to the base beam in parallel using AB glue. Both surfaces of the piezoelectric ceramic plate are covered with electrodes. The frame is attached to the free end of the base beam with the help of screws and nuts. An induction coil is wound in the middle of the frame. Two ring magnets are fixed at the upper and lower ends of the frame using solid sol. The ring magnets fixed at the upper and lower ends are connected by a thin copper rail, which guides the motion of the moving magnet.

Table 1 Parameters of the experimental prototype HEHPE

sandsare the width and thickness of the base beam, respectively;pandpare the width and thickness of the piezoelectric plates, respectively;oandiare the outer diameter and inner diameter of the magnets, respectively;andmare the thicknesses of fixed magnets and moving magnets, respectively

The test rig of the HEHPE is shown in Fig. 3. A vibration exciter is used to provide periodic base excitation, and its waveform and frequency are adjusted by a vibration controller, the control computer, and a power amplifier. The experimental prototype is fixed on the vibration exciter by screws. Two acceleration sensors are fixed to the base, one for detecting feedback signal and the other for monitoring the vibration controller. Voltage generated by the prototype is collected by the computer through a data acquisition card.

4.2 Comparisons of the models and the experiments

Since the lumped-parameter model described in the ESM is based on the first resonant vibration mode of the studied HEHPE, in subsequent analysis we use only the experimental data collected for the first-order harmonic. Under different connection topologies and given external load resistance, the output voltages of the piezoelectric and electromagnetic parts, if available, are normalized with respect to the amplitude of base excitation accelerations. Results were also obtained using the lumped-parameter model with parameters tuned to match the experimental results.

Fig. 4 Comparison of the frequency responses of RMS voltage and average power of the HEHPE obtained with different connection topologies: (a) and (b) for connection 1 and (c) and (d) for connection 2

For condition 3, the piezoelectric and electromagnetic parts of the HEHPE were electrically disconnected from each other. The external load resistance of the piezoelectric part was 70 k?, while that of the electromagnetic part was 150 ?. The normalized output RMS voltage and average power of the piezoelectric part are shown in Figs. 5a and 5b, respectively, and those of the electromagnetic part in Figs. 5c and 5d, respectively. For both the piezoelectric and electromagnetic parts, two resonant peaks are present at the base excitation frequencies of 6.4 and 9.6 Hz, respectively. For the piezoelectric part, the normalized RMS voltages for the two resonant peaks were 2.624 and 10.850, respectively, while those for the average power were 0.91 and 1.68, respectively. For the electromagnetic part, the normalized RMS voltages for the two resonant peaks were 0.733 and 0.892, respectively, while those for average power were 3.585 and 5.300, respectively.

Fig. 5 Comparison of the frequency responses of RMS voltage and average power of the piezoelectric part (a and b) and electromagnetic part (c and d) obtained with connection topology 3

Note that although the experimental results obtained are in good qualitative agreement with the numerical predictions from the developed models, there are quantitative errors. One reason for this is the oversimplification of the 3D motion of the HEHPE 1D linear motion. Rotational elastic vibration of the piezoelectric cantilever beam is ignored. The swing of the electromagnetic part and revolution of the moving magnetic with respect to the copper guide rail are also neglected. A second concern is the simplified expression of the magnetic force and electromagnetic damping shown before. Moreover, although the copper guide rail was made as smooth as possible before the experiment, friction and collision between the moving magnet and the copper guide rail contribute to the differences.

where

Fig. 6 Comparison of the frequency responses of RMS voltage (a) and average power (b) of the HEHPE obtained with connection topology 4

Fig. 7 Schematic diagram of the resistor-capacitor-inductor (RCL) circuit in the energy harvester device

As stated previously (Huang et al., 2022), the complex coupling between the electrical resonator, the piezoelectric part, and the electromagnetic part is seen to have the most influence on device performance. Calculations show that in our situation, the electrical resonant frequency was around 631 Hz. As this frequency is far outside the considered frequency range, the effect of the electrical resonance is not shown in our experiments. However, extra tuning of the external load circuits can help tune the output performance of HEHPEs (Huang et al., 2022). Because of the limited choice of piezoelectric and electromagnetic materials, the effect of electrical resonance has not been fully recognized. Further research is needed urgently, and this will be a topic of future investigations.

As a final characterization, considering the HEHPE in connection topology 3, different external load resistances were applied to the piezoelectric part (1–1000 k?) and electromagnetic part (10–5000 ?), respectively. The RMS voltage and average power of the HEHPE are shown in Fig. 8. With increasing load resistance, the output voltage amplitude gradually increases, and finally approaches a limit (Figs. 8a and 8c). The average output power first reaches the maximum value at the optimal load, and then decreases monotonically with the further increase of load resistance (Figs. 8b and 8d). The predictions from our lumped-parameter models are also shown.

Fig. 8 Outputs of the HEHPE with connection topology 3 at excitation frequencies of 6.0, 7.5, and 9.0 Hz: RMS voltage (a) and average power (b) for the piezoelectric part; RMS voltage (c) and average power (d) for the electromagnetic part

Note that when the base excitation frequency is far from the resonant frequencies (here we aimed for a resonant frequency of around 6.4 Hz), the numerical predictions are in good agreement with the experiment results. However, when the base excitation frequency is close to the resonance, numerical predictions deviate from experimental results. This is consistent with our model assumption that the electromagnetic and piezoelectric parts weakly interact with each other. Close to resonance, however, the interaction between these two parts is strong with dramatic energy exchange, which is not accounted for in the simplified model. Nonlinearity and mutual coupling in the HEHPE need extra attention in future investigations.

4.3 Modifications of the electromagnetic part

Results from previous experiments gave us the impression that a moving magnet in the electromagnetic part does not move far from its balanced position. As a consequence, the RMS output voltage of the electromagnetic part shown in Fig. 8 is far from satisfactory. A direct cause is that the magnetic force is too strong for the moving magnet to move easily. To strengthen the motion of the moving magnet, we replaced the upper fixed magnet in the electromagnetic part with an elastic spring. A schematic diagram of the modified system is shown in Fig. 9. The main idea is that when the moving magnet oscillates, it will collide with the elastic spring. Non-smooth nonlinearity is introduced into the system and the oscillating amplitude of the moving magnet can be increased (Xu et al., 2017a).

Fig. 9 Diagram of the structure of the modified HEHPE with the upper fixed magnet replaced with a fixed spring

To begin with, we were concerned about the distancebetween the elastic spring and the moving magnet (Fig. 9). Its influence upon device performance was explored. The values ofwere set to 0, 2, and 4 mm, respectively. Under connection topology 3, the RMS voltages of the piezoelectric part and the electromagnetic part were as shown in Figs. 10a and 10b, respectively, versus the base excitation frequency. Under connection topology 4, the RMS voltage of the HEHPE was as shown in Fig. 11.

In Figs. 10a and 11, with increasing, the RMS voltage for the first resonant peak decreases gradually, while that for the second peak increases, while in Fig. 10b, the RMS voltage of both resonant peaks decreases with increasingand gradually approachs that of the original HEHPE prototype. Note that replacement of the upper fixed magnet with an elastic spring increased the output performance of the device for nearly all connection topologies. Besides, due to the introduction of collision between the moving magnet and the elastic spring, up-conversion of the frequency is apparent in Figs. 10 and 11.

Fig. 10 Output performance of the modified HEHPE with different d with connection topology 3: (a) RMS voltage of the piezoelectric part; (b) RMS voltage of the electromagnetic part

Fig. 11 Output voltage of the modified HEHPE with different d with connection topology 4

Since the mathematical model of the modified HEHPE is not well established, detailed discussions are postponed. In future investigations, a search for an optimal value ofcould be of primary interest to improve device performance. In addition, the stiffness of the elastic spring was not carefully tuned in our small-scale experiments. Future investigations should be done to elucidate its effects.

5 Conclusions

With increasing attention being paid to PVEHs, researchers are attempting to increase their working bandwidths through the integration of piezoelectric and electromagnetic energy transduction mechanisms in a single HEHPE.

This study focused on the nonlinear interaction in an HEHPE. Mathematical models of the proposed HEHPE were established considering different connection topologies. Prototypes were prepared and tested. Input and output signals of the HEHPE were firstly analyzed to stress the insufficiently understood features of containing multi-frequency components. Methods for characterizing such signals are put forward and discussed. With regard to different connection topologies, the RMS voltage and average power of the HEHPE were investigated and compared with numerical predictions based on a developed model. Good agreement was found. We also found that the electrical connection between the electromagnetic and piezoelectric parts in the HEHPE serves to tune the frequency characteristics of the device and alter its output performance. Nonlinearity due to the magnetic force introduced also changes the energy distribution between the electromagnetic and piezoelectric parts. Once system parameters are well tuned, better device performance in terms of working bandwidth and output power can be expected.

Also, the original HEHPE was modified by replacing the upper fixed magnet with an elastic spring. An obvious performance improvement was witnessed and considerable frequency tuning observed. Changing the distancebetween the spring and the moving magnet was shown to greatly affect device behavior.

Nonetheless, several points need attention in future research. The base beam in the piezoelectric part should be longer and thicker, to make it easier to match the resonant properties of the piezoelectric and electromagnetic parts. Besides, tuning of the resonant frequency due to the electrical connection between the piezoelectric part and the electromagnetic should be optimized. In addition, a detailed study of the modified HEHPE is needed to provide a thorough understanding of the effect of the introduced nonlinearity on device performance.

Acknowledgments

This work is supported by the Zhejiang Provincial Natural Science Foundation of China (No. LY22E050013) and the China Postdoctoral Science Foundation (No. 2021M690545), and is also supported in part by the Zhejiang Provincial Natural Science Foundation of China (No. LZY22E050001) and the National Natural Science Foundation of China (No. 51805124).

Author contributions

Shifan HUANG, Zhenlong XU, and Maoying ZHOU designed the research. Shifan HUANG and Weihao LUO processed the corresponding data. Shifan HUANG wrote the first draft of the manuscript. Weihao LUO, Zongming ZHU, Ban WANG, and Huawei QIN helped to organize the manuscript. Maoying ZHOU and Shifan HUANG revised and edited the final version.

Conflict of interest

Shifan HUANG, Weihao LUO, Zongming ZHU, Zhenlong XU, Ban WANG, Maoying ZHOU, and Huawei QIN declare that they have no conflict of interest.

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Electronic supplementary materials

Sections S1 and S2

題目：壓電-電磁混合振動俘能器的實驗與理論分析

作者：黃世帆，羅偉昊，朱宗明，徐振龍，王班，周茂瑛，秦華偉

機構(gòu)：杭州電子科技大學，機械工程學院，中國杭州，310018

目的：振動俘能器作為一種富有前景的無線傳感器網(wǎng)絡(luò)供電方法，壓電與電磁的耦合有助于提高振動俘能器的輸出性能。本文旨在探討壓電和電磁在混合振動俘能器中的集成，考慮壓電和電磁不同的連接拓撲，并對該混合振動俘能器的優(yōu)化結(jié)構(gòu)進行探索，提出改進其性能的方法。

創(chuàng)新點：1. 將壓電和電磁兩種能量收集裝置集成在一個系統(tǒng)中進行分析；2. 分析壓電與電磁之間不同的連接拓撲，建立其集總參數(shù)模型；3. 提出該混合振動俘能器的優(yōu)化結(jié)構(gòu)。

方法：1. 首先對壓電-電磁混合振動俘能器的輸入和輸出信號進行分析，強調(diào)對其包含多頻成分的特征理解不夠充分，提出并討論表征這類信號的方法。2. 通過實驗分析壓電和電磁混合振動俘能器四種連接拓撲方式的輸出性能，推導出他們的集中參數(shù)模型。3. 將這些參數(shù)模型的數(shù)值預測結(jié)果與實驗結(jié)果進行比較（圖4～6），揭示系統(tǒng)中的非線性。4. 對優(yōu)化的混合振動俘能器進行了實驗分析探索，提出改進其性能的方法。

結(jié)論：1.針對不同的連接拓撲，通過實驗研究的混合振動俘能器的均方根電壓和平均功率與所建立模型的數(shù)值預測結(jié)果一致。2. 電磁和壓電部件之間的電氣連接可以調(diào)節(jié)俘能器的頻率特性并改變其輸出性能。3. 用彈性彈簧取代原混合振動俘能器的上部固定磁鐵，性能得到了明顯的改善，并觀察到了相當大的頻率調(diào)整；改變彈簧和移動磁鐵之間的初始距離會極大地影響俘能器的輸出性能（圖10和11）。

關(guān)鍵詞：混合能量收集；非線性；磁彈簧；壓電；電磁

https://doi.org/10.1631/jzus.A2200551

https://doi.org/10.1631/jzus.A2200551

? Zhejiang University Press 2023

Nov. 20, 2022;

Jan. 6, 2022;

June 21, 2023;

Aug. 1, 2023