Bistable Vibration Energy Harvester Research Articles

Chaotic responses across the potential barrier of bistable vortex-induced vibration energy harvesters

Large-amplitude interwell limit cycle oscillations (LCOs) are regarded as an ideal high-output state of multistable vibration energy harvesters. However, chaotic responses, which result in lower output voltages than interwell LCOs, can be observed in bistable vortex-induced vibration energy harvesters (VIVEHs). In this paper, the chaos in bistable VIVEHs is investigated through numerical simulation, theoretical analyses, and experimental validation. The distribution of the periodic solutions obtained by the incremental harmonic balance (IHB) method and chaos judgment using Lyapunov exponents are elucidated. It is found that the bistable VIVEH shows intrawell periodic solutions at high reduced wind speeds (RWSs) and period-doubling bifurcation appears with the periodic solutions turning into chaos with decreasing RWS. Analyses of the influence of nonlinear parameters on the chaotic responses identify the nonlinear stiffness as the dominant factor contributing to the chaos. Meanwhile, the chaotic responses and interwell LCOs would exist at the same RWS with different initial states. Finally, wind tunnel experiments confirm the occurrence of homologous chaotic responses of the bistable VIVEH which feature aperiodic jumping back and forth motion between two potential wells, in agreement with numerical simulations. Overall, this paper provides a framework for analyzing the chaotic responses of bistable VIVEHs, offering valuable insights for complex response mechanism understanding.

Characterization of magnetostrictive bi-stable rotational vibration energy harvester with integrated centrifugal effect

Rotational machinery is a common presence in dust still production, and the occurrence of operational failures in components like engines and turbine blades necessitates effective measures. To solve this challenge, remote structural health monitoring using energy harvesting and wireless sensors has been widely employed to realize self-powered sensing. This study proposes a magnet-induced bi-stable rotational energy harvester (REH), which utilizes the centrifugal effect to broaden the effective frequency bandwidth, enabling efficient energy harvesting in complex environments. A comprehensive mathematical model has been established to facilitate the dynamic characteristics of the bi-stable system, taking into account the centrifugal effect. The theoretical results demonstrate that the gap distance of magnetic configuration has great effects on the bi-stable system. Additionally, the centrifugal effect decided by the centrifugal radius and rotational speeds also affects the stable high-energy orbit oscillations. Furthermore, experimental results indicate that the proposed REH can effectively operate within the frequency range of 230–290 rpm, with a maximum RMS voltage of 780 mV and corresponding power of 4.35 mW. These findings validate the performance of the bi-stable magnetostrictive REH with the centrifugal effect and indicate its potential to effectively address the power supply challenges for wireless sensors. Overall, this study presents a promising solution for enhancing the energy harvesting performance of REH and also provides insights into the design of high-efficiency REH by magnet-induced nonlinearity and the centrifugal effect.

A comparative analysis of parallel SSHI and SEH for bistable vibration energy harvesters

The present work focuses on ambient vibration energy harvesting. Specifically, this article deals with bistable piezoelectric energy harvesters (PEHs) which exhibits a wider bandwidth than linear oscillators. These complex systems require an energy extraction circuit (EEC) to rectify their voltage to supply power to autonomous sensors. This EEC needs to be optimized in order to increase the harvested power and even the bandwidth of PEHs. Because of the complex dynamics of bistable PEHs, there is a lack of simple and physically-insightful models in the literature that would allow the understanding and optimization of the extraction circuit. To address this issue, the present work derives closed-form models of a bistable PEH coupled to a passive and an active synchronous EEC: respectively the standard energy harvesting (SEH) circuit and the parallel synchronized switch harvesting on inductor (P-SSHI) circuit. Experimental measurements conducted on a custom bistable PEH demonstrate the validity of the proposed models with a relative error lower than 15% on the harvested power and the bandwidth. The proposed models allow to easily understand the influence of the P-SSHI circuit on the dynamics of a bistable PEH. Moreover, a comparison of the performance of the SEH and the P-SSHI circuits, valid for any bistable generator, is proposed. The latter shows that under low electromechanical coupling and low acceleration amplitude the P-SSHI circuit leads to multiply the maximum harvested power up to 4.3 compared to the SEH circuit, and the bandwidth by a factor of 2.3.

Practical asymmetry and its effects on power and bandwidth performance in bi-stable vibration energy harvesters

Scavenging energy from ambient vibrations using piezoelectric bi-stable energy harvesters (BEHs) has been a research focus in recent years. The typical assumption that BEHs have perfectly symmetric potential profiles is hardly attainable in practice. Unlike previous works which model asymmetry as a quadratic restoring force term, we present a physically quantifiable concept of practical asymmetry degree γ which can be utilized in both theory and experiment. Also, we optimize the nondimensional method by normalizing to the inherent parameters, which guarantees consistent and comparative model analysis. Based on above, a comprehensive study of practical asymmetry’s effect on BEH’s performance is experimentally validated. Results show that for stable inter-well oscillation, asymmetry increases BEH’s output power due to enlarged phase orbit space, but decreases BEH’s bandwidth due to elevated potential barrier. Compared with symmetric BEH, asymmetric BEH improves power by 57.56 % and 26.93 % but reduces bandwidth by 73.81 % and 57.38 % in simulation (γ = 4.08) and in experiment (γ = 4.11), respectively. Initial position in the shallow well improves both power and bandwidth of the asymmetric BEHs. Compared with deep well initial position, shallow well initial position exhibits 41.72 % power improvement and 50.00 % bandwidth increase in experiment (γ = 4.11). Sufficiently large excitation level is required to reach above conclusions, as asymmetric BEHs under small excitations might not reach optimal performance. These results provide instructive insights for designing practical BEHs with improved power and bandwidth performance.

Correction to: Probabilistic maps on bistable vibration energy harvesters

Correction to: Probabilistic maps on bistable vibration energy harvesters

Correction to: Probabilistic maps on bistable vibration energy harvesters

Correction to: Probabilistic maps on bistable vibration energy harvesters

Resonance provocation of improved energy orbit in bi-stable vibration energy harvesters for power enhancement

Bi-stable vibration energy harvesters are advantageous for a wide bandwidth in low frequency ranges, but are confronted with the issue of limited output power. Bi-stability traditionally contains two low- and high-energy orbits; however, this paper reports resonance provocation of the improved energy orbit, which is much higher than the traditional two energy orbits and can be utilized for power enhancement. Theoretically, the enhanced energy orbit is provoked due to an increase in the system’s kinetic energy, achieved by modifying the bi-stable potential energy function from quartic function to quadratic function to utilize the linear resonant restoring force. Experimental results demonstrate that the provocation of the improved energy orbit is frequency selective, and the root mean square voltage is increased by 63.6% in the upward sweep and 188.5% in the downward sweep. For optimal load, the improved energy orbit increases the maximal root mean square voltage by 2.10 times and the maximal average output power by 4.37 times. Meanwhile, the device’s bi-stable bandwidth remains almost unchanged. These results prove that the resonance provocation of the improved energy orbit can refine the power while not sacrificing bandwidth, which is a promising solution to the overall performance improvement for vibration energy harvesters.

Gravity-induced bistable 2DOF piezoelectric vibration energy harvester for broadband low-frequency operation

Gravity-induced bistable 2DOF piezoelectric vibration energy harvester for broadband low-frequency operation

Bi-stable electromagnetic generator with asymmetrical potential wells for low frequency vibration energy harvesting

Efficient energy harvesting from low and broadband frequency has always been a challenging problem. This paper proposes a solution in the form of an electromagnetic bi-stable vibration energy harvester (BVEH) with asymmetric potential barriers, in which the vibrator is attracted to the top magnet and repelled from the bottom magnet. By combining a magnetic spring and a mechanical spring, the BVEH achieves bi-stability with asymmetric potential barriers, enabling large amplitude vibration as the vibrator travels between the two potential wells. The traditional magnetic force model is modified to establish an electromechanical coupling model that accurately predicts the output of the BVEH. Numerical simulation results solved by the Runge-Kutta method show good agreement with experimental results. In addition, a prototype is fabricated and the system parameters are adjusted to achieve high-energy oscillation at the lowest frequency of 4 Hz. Under a sinusoidal excitation with an amplitude of 4 mm, the BVEH's bandwidth is expanded to 6 Hz, and the maximum power can reach 72.76 mW. Finally, the feasibility of the BVEH is demonstrated by powering different electrical appliances. The study provides a new technical approach for energy harvesting under low and broadband frequency vibration excitation.

Development of Bi-Stable Vibration Energy Harvesting System Using Duffing-Type Motion Model

Vibration power generation is an important issue in development of renewable energy. If a vibration system with a maximum possible amplitude is designed, it can be advantageous in improving the vibration power generation efficiency. In this study, we propose a Duffing-type bi-stable vibration energy harvesting system that utilizes the stochastic resonance phenomenon, which can significantly expand the vibration amplitude. We designed the motion rail shape of the bistable vibration model using the Duffing function, and created a Duffing-type wave-shaped motion rail using an acrylic plate. An electromagnetic motor was installed in place of the four rotating wheels below the mass block that moves on the wave-shaped motion rail. When the mass block moves on the rail, it can output a voltage directly from the electromagnetic motor. To verify the performance of the proposed bi-stable vibration energy-harvesting system, a vibration experiment was conducted by combining a random excitation signal that simulates an actual natural environment and intentional periodic excitation signal. Using the experimental results, the stochastic resonance phenomenon and vibration power generation performance of the bi-stable vibration energy-harvesting system were investigated. The stochastic resonance phenomenon can be reliably generated using the bi-stable vibration system proposed in this study, and a large amplitude expansion effect can be obtained in the response vibration of the mass block. In addition, using random signals simulating the natural environment and periodic signals as stimulus signals, vibration experiments were conducted separately for two measurement cases: single excitation and joint excitation. The measurement results showed that under the same input excitation energy, the simultaneous excitation of the two signals generated 82.99% more power than that generated by separate excitation of the two signals. The generation of the stochastic resonance phenomenon by exciting two signals simultaneously has a significant effect on the improvement of the power generation efficiency of the bi-stable vibration energy harvesting system.

Comparative Study of Bistable Vibration Energy Harvester Using Different Elastic Boundary

This paper demonstrates a novel bistable energy harvester coupled with a nonlinear elastic boundary (NEB-BVEH). The nonlinear elastic boundary changes the dynamic response of the bistable vibration energy harvester and improves its performance by providing additional support for the inclined spring through coupled dynamics. This work considers the performance of bistable vibration energy harvesters using different elastic boundary under different excitation amplitudes, including bistable energy harvester with linear elastic boundary (LEB-BVEH) and NEB-BVEH with different horizontal spring stiffness. The comparative results show that the performance of NEB-BVEH and LEB-BVEH is approximately the same under small excitation amplitude. However, NEB-BVEH with adding horizontal springs can significantly improve performance compared to LEB-BVEH under larger excitation amplitude. Results of the investigated case show that the bandwidth of NEB-BVEH is increased by 89.31%. The output power is increased by more than 25%. A comparative study demonstrates the superiority of NEB-BVEH, which is very beneficial for energy harvesting.

The Influence of the Piezoelectric Non-conservative Effect on the Bi-stable Vibration Energy Harvester

The Influence of the Piezoelectric Non-conservative Effect on the Bi-stable Vibration Energy Harvester

Small excitation self-powered sensing energy harvester for rail traffic condition monitoring

A small excitation bistable vibration energy harvester for railway transportation is developed for self-powered condition monitoring utilizing low-frequency vibration of key train components. Analyze operational vibration data collected from trains to determine design requirements. A free sliding magnet is placed in a tube with a top fixed magnet and two limit springs, using gravity, magnetism, and spring force to provide two stable positions for the movable magnet. This structure can enter the bistable operating region under small excitation amplitude and has a wide operating bandwidth. Build and test prototypes using conditions similar to real train operating conditions. A wide operating bandwidth (7 Hz-46 Hz) is obtained due to the bistability. Peak output power is 3.17mW measured into a 900 Ω resistive load at 30 Hz and 1.4g.

Horizontal Bi-Stable Vibration Energy Harvesting Using Electromagnetic Induction and Power Generation Efficiency Improvement via Stochastic Resonance

In this study, a vibration energy-harvesting system is developed by first proposing a horizontal bi-stable vibration model comprising an elastic spring and a mass block and then applying an electromagnetic induction power generation device composed of a magnet and a coil. Subsequently, based on a weight function that considers the mutual positional relationship between the magnet and conducting coil, a set of simultaneous governing equations that consider the elastic force of the elastic spring and the Lorentz force of electromagnetic induction is derived. Additionally, a numerical analysis method employing the Runge–Kutta method is utilized to obtain a numerical solution for the vibration response displacement and vibration power generation voltage simultaneously. Experiments are performed to verify the results yielded by the proposed bi-stable vibration energy-harvesting system. The results shows that the measured vibration response displacement and the vibration power generation voltage are consistent with the analytical results. Moreover, issues including the identification of damping coefficients that consider the mutual effects of normal kinetic friction and electromagnetic induction damping forces, as well as the effects of electromagnetic induction damping on the vibration response displacement, are discussed comprehensively. Simultaneously adding random and periodic signals to the bi-stable vibration model results in stochastic resonance and improves both the vibration amplification effect and vibration power generation.

A bistable vibration energy harvester with spherical moving magnets: Theoretical modeling and experimental validation

In recent years, battery-free self-powered sensing has attracted much attention. However, effective energy harvesting over wide frequency bandwidth is still a great challenge. This paper explores a bistable vibration energy harvester. The harvester uses a spherical magnet as a moving magnet, combining the restoring force of limit spring, attractive magnetic force and gravity to achieve bistability to increase power output and bandwidth. A prototype of the harvester is constructed and characterized experimentally. The nonlinear dynamic model of the harvester is formulated and validated using the experimental data. The impedance matching experiment is carried out at a fixed frequency. The working frequency range is 12–43 Hz at 4.5 g. The maximum peak to peak output voltage is 18.9 V. At 40 Hz and with a 900 Ω load, the output power reaches 11.5 mW.

Performance and dynamics of a novel bistable vibration energy harvester with appended nonlinear elastic boundary

This paper proposes a novel bistable energy harvester coupled with a nonlinear elastic boundary (BEH-NB) to enhance energy harvesting performance. The analytical model of BEH-NB is derived and verified experimentally. Then the performance of the bistable energy harvester with different boundary conditions is investigated, including the bistable energy harvester with linear elastic boundary (BEH-LB), the bistable energy harvester without elastic boundary (BEH), and a linear energy harvester (LEH). The compared results show that the performance of BEH-NB is better than that of its counterparts. Results of the studied case show that the average power of BEH-NB can be improved by 42.05%, and the operational bandwidth is significantly widened by 93.18%, which is highly beneficial for energy harvesting. To identify the optimal parameters set for energy harvesting from ambient excitation, bifurcation analyses are performed. It is found that small changes in parameters can profoundly alter the system’s steady-state response. The initial conditions also have a significant effect on the type of the system’s response. Therefore, the basin of attraction of BEH-NB is calculated to reveal the influence of the initial conditions and to quantify the occurrence probability of the different types of motion. The results of this paper provide a novel perspective in the structural design of the system and offer a practical application design guidelines to improve the system’s performance.

Simple analytical models and analysis of bistable vibration energy harvesters

In order to scavenge the energy of ambient vibrations, bistable vibration energy harvesters constitute a promising solution due to their large frequency bandwidth. Because of their complex dynamics, simple models that easily explain and predict the behavior of such harvesters are missing from the literature. To tackle this issue, this paper derives simple analytical closed-form models of the characteristics of bistable energy harvesters (e.g. power-frequency response, displacement response, cut-off frequency of the interwell motion) by mean of truncated harmonic balance methods. Measurements on a bistable piezoelectric energy harvester illustrate that the proposed analytical models allow the prediction of the mechanical displacement and harvested power, with a relative error below 10%. From these models, the influences of various parameters such as the inertial mass, the acceleration amplitude, the electromechanical coupling, and the resistive load, are derived, analyzed and discussed. The proposed models and analysis give an intuitive understanding of the dynamics of bistable vibration energy harvesters, and can be exploited for their design and optimization.

Theoretical and experimental studies on bistable vibration energy harvester with levitation magnet couple

To improve the efficiency of vibration energy harvesting, a levitation magnet couple is introduced to the bi-stable energy harvester (BEH) to create a desired potential energy, by which the harvester’s response and output can be increased greatly. Compared to the classical BEH, the novel harvester has a lower potential barrier and a flatter bottom of its potential well, which can help increase the response and outputs. The experimental results show that the introduction of levitation magnet couple effectively extends the working frequency bandwidth of the harvester. The inter-well jump can be executed easily under weak stochastic excitations and the amplitude is larger than the classical one, even in the case of executing the same kind of intra-well oscillation. The experiments prove that the output voltage of the novel harvester outperforms the classical BEH over the whole intensity range. This study may provide a good guidance to improving the performance of bistable energy harvester.

Power generation performance of a bistable speed bump vibration energy harvester

A model of a bistable speed bump vibration energy harvester (BSVEH) is designed by combining the buckling beam, rack and pinion, one-way clutch and speed bump with rotor alternator. One-way clutches are used to ensure the input shaft of rotor alternator to rotate unidirectionally during the up-and-down vibration of the speed bump. The coupled mechanical model of the speed bump energy harvester is established to study the power generation performance subjected to various structural parameters, that is, types of speed bump, types of vehicles, geometrical parameters of the buckling beam, speed increasing ratio and moment of inertia. Simulations show that the output power of the BSVEH (such as 148 J in 1 second) is larger than that of the speed bump energy harvester with linear spring (86 J in 1 second). Compared with the vehicle passing over speed bump energy harvester with linear spring, the vertical and pitch accelerations of a vehicle are decreased 9.3% and 16.5%, respectively when it passes over the BSVEH. Riding quality is also improved. The effect laws of the type and speed of the vehicle speed on the output power of the BSVEH are obtained. The maximum output power of SBVEH is 14.8 W at the vehicle speed 24 km/h. The maximum energy-efficiency of the BSVEH can reach 43.9%. And the maximum average electrical power can arrive at 12.7 W. The optimal parameters favoring the output power of BSVEH are determined. The advantages of power generation and riding quality, correctness of mechanical models and effectiveness of BSVEH are verified by simulation results.

A Magnet-Coil-Type Bistable Vibration Energy Harvester for Random Wave Environment

In this study, a new bistable vibration energy harvesting system is developed by originally proposing a bistable vibration model comprising a spring and a mass block and then applying a vibration generator composed of a coil and a magnet. The nonlinear equations of motion for this vibration energy harvesting system are developed and the static potential energy distribution is analyzed. The bistable vibration characteristics and the method for prediction of the periodic excitation frequency at which stochastic resonance is likely to occur are investigated theoretically, and the electromagnetic induction-based bistable vibration energy harvesting system is then developed. We predicted the excitation value that the stochastic resonance phenomenon is most likely to occur at 1.543 Hz. We also conducted experiments at 1.15 Hz, 1.50 Hz, and 1.85 Hz, which are centered on the predicted value. As a result, stochastic resonance occurred in all experimental cases. The power generation efficiency was improved by 125.03%, 149.05%, and 95.39%, respectively.