Theoretical modeling and experimental verification of rotational variable reluctance energy harvesters

Highlights

• A new modeling method for variable reluctance energy harvester is proposed.

• A SA-MFD method is presented to accurately calculate air–gap magnetic permeance.

• Numerical and experimental results verify the proposed model to predict voltage.

• The measurement shows that the average power can achieve 46.7 mW under 300 rpm.

Abstract

Energy harvesting has great potential for powering low-power wireless sensor nodes by converting environmental energies into the electricity. It can be widely used for real-time online industrial monitoring. Among different transducers, the variable reluctance energy harvester (VREH) has attracted much attention due to the great performance for the low-speed rotations. However, there is a lack of precise models for performance prediction. In this paper, a new modeling method for VREH is proposed to predict the output voltage. A combined Substituting Angle - Magnetic Field Division modeling method is presented to accurately model the magnetic permeance of the air–gap for the VREH. Then, the magnetic flux change in the magnetic circuit is derived to calculate the voltage response of the coil. The numerical and experimental results of voltage responses verify the effectiveness of proposed model with the maximum error of 4%. The influence of some key factors on voltage response is investigated, including the thickness of air–gap and tooth height. Moreover, power analysis demonstrates that the output power increases from 5.06 mW to 46.7 mW with the rotational speed from 100 rpm to 300 rpm.

Introduction

Wireless sensor networks have been widely used in the field of health monitoring for industrial applications [1], [2]. Due to the small amount of power consumed by these electronic devices, the energy harvesting technology has attracted plenty of attention. Traditionally, a battery-based power supply of electronic devices has some inevitable limitations, such as short-term lifespan, the requirement of periodical charging or replacement. Since there are a variety of energy sources available in the industrial environment, including thermal energy [3], [4], kinetic energy [5], [6], [7], [8], solar energy [9], ocean energy [10] and wind energy [11], such ambient energies provide a foundation for the development of energy harvesting technologies for the sustainable and stable energy supply.

In the last decades, transducers using piezoelectric [12], [13], electromagnetic [14], [15], [16], electrostatic [17] and triboelectric [18], [19], [20] methods were widely employed to achieve energy harvesting from ambient environments. As we know, rotational motion is one of main forms in some key industrial equipment, such as engine, wind turbine, gear box, rolling mill, machine tools and electric generating unit. More importantly, their autonomous health monitoring with energy harvesting is always of significance to reduce the maintenance cost and improve the reliability. Therefore, much effort has been devoted to developing energy harvesting from rotational environments with the use of different piezoelectric and electromagnetic structures [21], [22], [23], [24]. Guan et al. [25] designed a piezoelectric energy harvester for rotational application to obtain the power from the rotating frequencies of 7–13.5 Hz. Gu et al. [26] developed a passive self-tuning rotating piezoelectric beam energy harvester to extract rotational motion by means of centrifugal force. Fu et al. [27] proposed a miniature radial-flow piezoelectric structure to generate energy from the rotational motion of wind turbine driven by airflow. Mei et al. [28] employed a tri-stable configuration for efficiently harvesting energy in the rotating speed range of 240–440 rpm. Zhang et al. [29] proposed an impact-induced piezoelectric structure for harvesting energy from rotational motion driven by wind flow. Additionally, the electromagnetic energy harvester with weighted-pendulum was introduced by Wang et al. [30] to harvest energy from a rotating wheel between 200 rpm and 400 rpm.

However, it is a great challenge to achieve the self-powered online monitoring under low rotational speeds in many industrial environments. Generally, the low rotational motion will cause the incapability of many energy harvesters. To overcome this issue, a large number of advanced magnetic coupling structures have been developed for low frequency rotational environments [8], [31]. Kuang et al. [32] designed a magnetic plucking mechanism to obtain the average output power of 5.8 mW, actuated by knee-joint motion of 0.9 Hz. A methodology for low-speed rotational piezoelectric energy harvesting was proposed by Fu et al. [33] to convert the low frequency rotation ranging from 15 Hz to 35 Hz into high frequency vibration of the piezoelectric beam with the use of magnetic plucking. Although considerable methods were proposed to enhance the performance of the energy harvesting systems, the piezoelectric energy harvesters are not suitable for large scale occasions [29]. For this reason, a variety of electromagnetic structures have been proposed for low frequency rotational environments due to their high power density and easy realization. The circular Halbach electromagnetic energy harvester was developed by Zhang et al. [34], [35] to efficiently harvest the rotational motion of low frequency.

In addition to above configurations, the variable reluctance principle is another effective electromagnetic method for the design of low-frequency rotational energy harvesters due to the simple structure, high power density and high generality. Both traditional electromagnetic energy harvesters and variable reluctance energy harvesters work to generate an electromotive force based on the Faraday law of electromagnetic induction. Traditional electromagnetic energy harvesters normally have a relative motion between the coils and magnets, but it would have a negative impact on the shaft when increasing the size of magnets or coils to enhance performance. However, compared with traditional electromagnetic energy harvesters, variable reluctance energy harvesters are able to make both the magnet and the pickup coil stationary according the variable reluctance theory of magnetic circuit. With the rotational motion, the magnetic flux through magnetic circuit will be varying to provide the voltage as the reluctance changes. This principle can be generally achieved by the simple structure with toothed wheel and m-shaped pole-piece. Hence, this variable reluctance energy harvester can be applied in a robust design with low complexity for power supply. It was found that the VREH has greater potential in optimizing device volume and energy output stability than traditional electromagnetic energy harvesters [36]. Different variable reluctance devices were discussed by Ayala-Garcia et al. [37] for tuning the resonant frequency of a kinetic energy harvester. Their magnetic flux density along the width of the air gap was analyzed in Comsol software. Kroener et al. [38] presented a variable reluctance energy harvester for railroad surveillance system and experimentally demonstrated the power of 5.9 mW with a speed of 81.5 km/h of a train wheel. A wireless wheel speed sensor with the function of energy harvesting was developed by Parthasarathy et al. [39] based on a variable reluctance electromagnetic mechanism, which could extract maximum power of 1 mW at the rotational speed of 300 rpm. An m-shaped VREH was optimally designed by Xu et al. [40], [41] for low-speed rotating application at the speed of 10 rpm to 60 rpm. Their numerical results from COMSOL software were experimentally verified under various structural parameters. Unfortunately, the finite element method among above researches is unfavorable for the performance optimization and parameters analysis due to its time-consuming computational requirements. In fact, the working environment of rotational energy harvesters has always posed the constraint of space dimension and specific power density demand for the VREH. Therefore, it is necessary to develop a theoretical model for predicting the output performance and optimizing the structural parameters of VREHs.

In this paper, a new theoretical model for predicting the magnetic flux change and the output power of the energy harvester is proposed. The combined Substituting Angle – Magnetic Field Division method (SA-MFD) is presented to calculate the magnetic permeance of the air–gap during the rotational motion. According to this model, the magnetic flux can be described and the voltage characteristics including waveform, frequency and amplitude can be predicted accurately. Numerical and experimental results are carried out to verify the effectiveness of the proposed theoretical model for the VREH. The prototype of the variable reluctance energy harvester is implemented for power analysis. It indicates that the proposed method can support the design and optimization of VREH for supplying low-power electronics.

The remainder of this paper is organized as follows. In Section 2, the theoretical model for VREH is proposed; Section 3 depicts the numerical simulation for magnetic flux and voltage responses. Then, the energy harvesting prototype is fabricated and tested under different rotational speeds, and the effectiveness of proposed model is verified by experimental results in Section 4. Some conclusions are drawn in Section 5.