Voltage Improvement of a Swing-Magnet-Type Generator for Harvesting Bicycle Vibrations

Abstract

This paper proposes a swing-magnet-type generator that utilizes environment vibration for energy harvesting applications. This device consisted of a liquid, a swing magnet with a float, and a coil, and it was expected to generate electricity using the minute vibration of a bicycle. The vibration of the wide frequency band of the bicycle was converted into a vibration of a low-frequency mover. The yoke size of the permanent magnet affected the linkage flux and swing characteristics. Therefore, we verified the effect of the mover characteristics on the swing moment by structural simulations and vibration experiments using a linear motor. The yoke size changed the torque, which affected the resonant frequency of the swing. The magnetic-field analysis revealed the effect on the flux linkage in the yoke. The output voltage of the generator in the bicycle was 2.1 V, which could power a light-emitting diode.

1. Introduction

Energy harvesting is a sustainable technology that extracts electricity from the energy spent in daily-life activities of people [1,2,3,4,5]. Consumer products with light-emitting diodes (LEDs) attached to shoes and straps have been developed to identify their position in the dark [6,7]. In addition, the number of small devices for measurement and communication has increased with the development of the Internet of Things [8,9,10]. These devices use batteries as power source because the voltage and power required for their operation are small [11]. However, used batteries need to be discarded, which causes a high environmental load. In addition, batteries need to be replaced; thus, maintenance costs tend to increase [12]. The development of energy harvesting technology is important for realizing battery-free devices. The energy sources for energy harvesting include vibration, heat, light, and electromagnetic waves [13,14,15].

Daily environmental vibrations include traffic vibrations resulting from the movement of cars or trains, mechanical vibrations due to the operation of large machines, and floor vibrations in buildings [16,17,18,19]. These vibrations are often discarded. A generator that uses a shock absorber for suspension has been proposed for automobiles [20]. The vibration in the direction of gravity was converted into electric power using a linear electric motor, which led to the recovery of 1-kW on power in a highway truck [21].

The bicycle that is focused on in the present study constantly generates vibrations in the three-dimensional (3D) direction while moving and is expected to be a semipermanent energy source [22,23]. The use of piezoelectric elements as a vibration power generation device is effective for obtaining high voltage [24,25]. A piezo harvester with a cantilever structure that used resonance to increase power generation has been proposed [26]. An energy harvester structure with a liquid chip at the tip of the lever has enabled power generation of approximately 1 mW when mounted on a bicycle [22]. An energy harvester that employed electrostatic induction was also effective for achieving a high voltage output [27]. The contact charging mechanism of a tandem spring-mass structure enabled power generation in a wide frequency band, and an instantaneous output voltage that exceeded 150 V has been confirmed [28]. Electromagnetic induction power generation has been proposed by installing a coil on the handlebar of a bicycle and a reciprocating magnet in the tube [29,30]. This method used the lateral vibration of the bicycle frame to achieve an output power density of 0.1 mW/cm³. In addition, LED lighting devices that used magnets near the metal rims of the wheels have been developed. These devices generated electricity by changing the flux linkage of the coil due to vibration during operation [31].

The present paper proposes a swing-magnet-type wave-power generator, which floats a magnet on a liquid in a container with a coil wrapped around it. The vibration of the bicycle is converted into a liquid wave, which becomes the mechanical input power for the generator. Even a small vibration can lead to swing amplitude above a certain level, and power is generated via electromagnetic induction of the magnet and coil. In addition, the magnet swing that uses liquid can extract the low-frequency-band components from the bicycle vibration in a wide frequency band. Furthermore, the container structure of the cylinder can convert the vibration along the horizontal direction into electrical energy, without employing a complicated structure. A generator comprising a liquid, coil, and magnet provides high structural and electrical reliability.

In Section 2, the proposed swing-magnet-type generator with a cylindrical structure is presented. We report the vibration of a moving bicycle and the swing characteristics of the mover in the proposed generator. In Section 3, the relationship between the specifications of the generator mover and swing characteristics using structural simulation and vibration experiment are explained. In Section 4, the flux linkage of the device obtained using magnetic simulation is presented. We then report the results of the driving of a bicycle test equipped with the proposed device.

2. Proposal for a Swing-Magnet-Type Generator

2.1. Bicycle Vibration Characteristics

Figure 1 shows the measurement results of the acceleration when the bicycle ran on an asphalt road at a constant speed of 10 km/h. Figure 1a shows the bicycle direction when it ran along on the x-axis, Figure 1b shows the direction along and perpendicular to the moving direction on the y-axis, and Figure 1c shows the acceleration in the direction perpendicular to the ground on the z-axis. Figure 1d shows the sensor position of the bicycle and the axes in each direction. The acceleration was measured at a period of 5 ms using a small wireless recorder (Microstone Co., Ltd., Saku-city, Japan, MVP-RF10-AC). These results were filtered from 1 Hz to 100 Hz to eliminate the effects of high-frequency noise and gravitational acceleration. Vibration was constantly generated on all axes due to the bicycle run. Acceleration occurred in the x and y-axis directions due to the bicycle’s motion.

Figure 2 shows the frequency distribution obtained by Fourier transformation of the acceleration generated during the bicycle run. The frequency component of the acceleration of each axis was dispersed in a wide frequency range. Acceleration components appear not only on the z-axis but also on the x-axis in the direction of bicycle’s motion.

2.2. Structure of the Swing-Magnet-Type Generator

Figure 3a–c shows the external, plan, and cross-sectional views, respectively, of the swing-magnet-type generator proposed in this paper. The container used a bush vial with an outer diameter of 35 mm and contained a liquid. This study used water as the liquid in the container. The mover inside the container was composed of a floating body and a permanent magnet, which floated on the liquid. A coil was wound around the container. The bicycle vibration caused the mover to swing through the liquid, which generated an induced electromotive force in the coil.

The mover used a polystyrene cylinder as a floating body inside the ring magnet for buoyancy. The dimensions of the ring magnet were 19 mm inner diameter, 31 mm outer diameter, and 3-mm thick (Figure 4). The permanent magnet used N40 (Arnold Magnetic Technologies Corporation) which has the following magnetic characteristics: remanence B_r = 1.27 T, coercivity H_c = 923 kA/m, and maximum energy product BH_max = 318 kJ/m². The yoke used in this study is a steel plate cold commercial (SPCC). Mount the yoke symmetrically on permanent magnet can improve the coil flux linkage and enhance the swing effect.

The coil conductor diameter was 0.1 mm, and it was wound 1872 times around a bobbin with an inner diameter of 35 mm. The winding diameter and number of turns were set based on the forward voltage of the diode. The internal resistance of the coil was 0.5 kΩ. The large number of coil turns increased the induced electromotive force, and the internal resistance of the coil, whereas it reduced the output current. The number of coil turns must be set by considering the required output voltage. A ring magnet was installed in the middle of the two coils.

The input power to the generator due to the vibration of the liquid is expressed by the wave height, group velocity and vibration frequency. The generator size needs to be considered with respect to the input power. Large input energy requires an increase in generator size. The mass and moment of inertia can be used to determine the mover of the generator with respect to the resonance frequency, as shown in Section 3.3. The number of turns and size of the coil are determined by considering the voltage required for output.

2.3. Characteristic of the Swing-Magnet-Type Generator

The swing characteristics of the mover were evaluated using the tilt angle measurement of the mover. The tilt angle was measured using motion-analysis software Kinovea ver. 0.9.5 by Joan Charmant (Bordeaux, France) [32,33]. The mover movement was recorded using a smartphone at a frame rate of 240 frames per second and a resolution of 1920 × 1080 px. The video is captured by the software. The coordinate value was extracted from the motion trajectory of the mover, by tracking an arbitrary point on the screen. The tilt angle of the mover was measured by tracking two points in the mover and one point as reference in the container, as shown in Figure 5. The bicycle-mounted container was completely fixed to the basket support. The tilt angle was measured relative to the bicycle basket support.

Figure 6a shows the fixed position of the generator near the front basket. The bicycle-mounted container is completely fixed to the basket support. Figure 6b shows the tilt angle definition, which indicated the tilt from the balanced state (θ = 0). Figure 6c shows the tilt angle characteristics of the proposed generator mounted on a bicycle while being operated. The mover swung at a maximum tilt angle of approximately 15° and frequency of approximately 2 Hz when the bicycle was moving. Figure 6d shows the result of the Fourier transformation of these tilt angle characteristics. Most of the high-amplitude components were concentrated in low frequencies below 5 Hz. The proposed generator demonstrated a low-frequency vibration compared with the vibration characteristics generated during the bicycle operation presented in Section 2.1. The bicycle vibration over a wide frequency range could be converted into a vibration in a specific frequency using the proposed generator. The mover hardly swung by the vibration along the z-axis direction; the primary component of swing moment was external vibrations along the x- and y-axis directions.

Acceleration measurement results indicated that irregular vibrations occurred in the moving bicycle. The generator extracted only the vibrations in a specific low-frequency range in the horizontal direction from a wide vibration range. Bicycle vibrations generated a liquid wave of a particular frequency, which made the tilt angle of the mover sine-wave.

3. Swing Characteristics of the Mover

Section 2 indicated that the directions of external vibrations that strongly affect the vibration of the mover are the x-and y-axes. In this section swing characteristics are identified using numerical simulations (i.e., structural finite element method (FEM) analysis) and experimental tests (i.e., horizontal vibrations excited by a linear motor).

3.1. Equation of Motion of the Mover

The generator container is fixed to the external structure. Figure 7 shows the rotational moment that acts on the tilted mover, which assumes that the generator is mounted vertically on the bicycle driving flat ground along the gravity’s direction. Gravity and buoyancy act on the center of gravity and buoyancy of the mover, respectively [34]. When the center of gravity and buoyancy are aligned, the mover has a stable position (Figure 7a). Figure 7b shows the tilted state of the mover due to liquid waves caused by external vibrations. The tilted angle of the mover shifts the position of the centers of gravity and buoyancy. The tilt of the float makes its volume in the water fluctuates, resulting in movement in the float position. The deviation in the line of action between the center of gravity and buoyancy causes a moment of rotation [35]. This deviation exerts a restoring force on the mover and causes the oscillating moment to return to the stable state. The distance between these two points (defined as restoration length L_r) affects the magnitude of the moment [36]. The equation of rotational motion of the mover is Equation (1), which is the same as that of a capsizing ship. J and m represent the moment of inertia and mass of the mover, respectively. L_r denotes the restored length of the mover that floats on the water, which indicates the vertical distance between the center of gravity of the magnetic rocker and center of buoyancy. θ and θ″ denotes the tilt angle and angular acceleration of the mover, respectively. Viscous damping and external acceleration are considered in the rolling motion of large ships [37]. The simplified Equation (1) was used in this study, assuming that the size of the mover is small and these effects can be neglected. The equation related to the rolling motion of the ship can improve the simulated accuracy of the mover’s motion.

$$J{\theta }^{″}=mg{L}_r=T$$

(1)

3.2. Swinging Moment of the Mover

The simulation that uses the SolidWorks software (ver.2018, by Dassault Systèmes SolidWorks Corporation, Waltham, MA, USA) reveals the effect of the yoke size attached to the mover on the swing moment. The center of gravity and buoyancy are obtained via mass characteristic analysis using the 3D model of the mover, which clarifies the relationship between the yoke size and restoration length L_r [38]. Figure 4 shows that the yoke is arranged using a 0.6-mm-thick cold-rolled steel plate with mounting angles of θ_m = 180, 90, 45, and 0°.

Figure 8 shows the relationship between the tilt angle and restoration length. A large tilt angle extends the restoration length, and the action of the oscillating moment is strong. In addition, the larger the mounting angle of the yoke is, the larger is trend of the restoration length even at the same inclination angle.

Figure 9 shows the contour diagram based on Equation (1) on the relationship among yoke mounting angle θ_m, inclination angle θ, and torque T in the rotational direction. The moment of inertia and mass are derived using SolidWorks software (ver. 2018, by Dassault Systèmes SolidWorks Corporation) by considering permanent magnets, floats, and yokes [39]. The conditions for structural analysis are listed in

Table 1. Conditions for structural analysis.

Item	Contents
Software	SolidWorks Ver. 2018
Analysis method	Mass characteristic calculation
Material density	Permanent magnet (ρ = 7.5 g/cm3), Yoke (ρ = 7.87 g/cm3), Floating (ρ = 0.15 g/cm3), Liquid (ρ = 1 g/cm3)

. The magnitude of the tilt angle contributes to torque T in the rotation direction. A large value of yoke mounting angle θ_m increases torque T in the rotational direction. The size of mounting angle θ_m affects moment of inertia J and the torque T in the rotation direction. The larger the value of mounting angle θ_m is, the stronger is the effect of the increase on the torque, which leads to large acceleration. A large swing occurs with the in-crease in the yoke mounting angle under the conditions in this study.

3.3. Resonance Frequency of the Swing of the Mover

Tilt angle θ and restoration length L_r are almost proportional to each other, as shown in Figure 8. The equation of motion i.e., Equation (1), is transformed into Equation (2) using resonant coefficient $K_{\mathrm{g}}$ (= mgL_r/θ). This equation is formulated in the same form of a spring–mass system equation. Therefore, resonant frequency of the swing f_r is expressed by Equation (3). Figure 10 shows the relationship between the yoke mounting angle and resonant frequency. The resonant frequency increases as the mounting angle of the yoke increases because the increase in the restoration length is larger than that in the mass and moment of inertia of the mover. Resonant frequency f_r depends on the yoke mounting angle. Further, resonance frequency f_r represents the factor that causes the vibration in the wide frequency band of the bicycle to be concentrated in the low-frequency range.

$$J{\theta }^{″}=K_{\mathrm{g}}\theta$$

(2)

$$f_{\mathrm{r}}=\frac{1}{2\pi }\sqrt{\frac{K_{\mathrm{g}}}{J}}$$

(3)

3.4. Vibration Experiment Using a Linear Motor

This section presents the relationship between the yoke mounting angle and resonance frequency by applying a horizontal vibration to the generator using a linear motor, as shown in Figure 11. The tilt angle of the mover is measured via vibration using a linear servomotor (Linear servo system DT030; Sanyo Denki Co., Ltd., Ueda-city, Japan). Yoke mounting angle θ_m is set to 0 and 45° according to the floatability of the mover. The experiments in this section are fixed on the lower side to avoid the influence of the field magnet of the linear motor. The container of the generator is completely fixed to a support or a structure forming a rigid body. Therefore, the vibration given to the generator is transmitted to the liquid inside without moving the container itself.

Figure 12 and Figure 13 show the tilt angle characteristics of the mover at mounting angle θ_m 0 and 45°, respectively. These results are compared with the vibration at frequencies f_i = 1.0, 1.5, 2.0, 2.5, 3.0 Hz to observe the effect of resonance. The mover keeps tilting at f_i = 1.5 and 2.0 Hz, whereas the vibration is small at f_i = 1.0 Hz. The movement of the mover stops beyond f_i = 2.5 Hz at θ_m = 0°. The mover continues to stably swing even at f_i = 2.5 Hz, whereas the vibration is small at f_i = 1.0 and 1.5 Hz. The vibration does not substantially continue at f_i = 3.0 Hz, at θ_m = 45°. The continuation frequency of the vibration in the experimental results tends to be slightly lower than the resonant frequency predicted by the simulation, as presented in Section 3.3. However, a large value of yoke mounting angle θ_m increases the vibration continuation frequency, which tends to be the same as that in the simulation. As described in Section 3.3, the resonant frequency changes according to the specifications of the mover, this indicates the existence of the vibration continuation frequency.

The external vibration frequency f_i close to specific frequencies due to floating structure brings tilt angle changes to a stable sine wave, increasing its amplitude. The factor that makes the vibration in the wide frequency band of the bicycle to concentrate at the low-frequency range is largely influenced by the resonant frequency due to the mover specifications. Adjusting the resonant frequency by setting the mover specifications based on the frequency spectrum of the external vibration is important to increase the swing.

4. Output Voltage Characteristics of the Generator

This section presents the effect of the yoked mover on the increase in the flux linkage using simulation. In addition, the output voltage of the generator due to the bicycle’s motion was measured.

4.1. Relationship between the Yoke and Flux Linkage

The yoke could concentrate the magnetic flux of the permanent magnet and increase the flux linkage to the coil, which led to the increase in the output voltage of the generator. The coil flux linkage was calculated via 3D magnetic field analysis using JMAG-Designer (x64) Ver.19.1 (JSOL Corporation, Japan). The conditions for the magnetic field analysis are listed in

Table 2. Conditions for magnetic field analysis.

Item	Contents
Software	JMAG-Designer (x64) Ver. 19.1
Analysis method	Three-dimensional magnetic field transient response analysis (FEM)
Mesh size	Mover: 0.5 mm, Coil: 0.5 mm, Air: Auto
Time interval	4 ms
Step number	21
Material	Permanent magnet: (Arnold: N35), Yoke: (JSOL: SPCC), Air: (μr = 1)

. Tilt angles θ ranged from 0° to 20°. The flux linkage attached to the entire surface of the magnetic pole was compared at θ_m = 0°, 45°, and 180°.

Figure 14 shows the relationship between tilt angle θ and the number of magnetic fluxes for each yoke mounting angle θ_m. The amounts of change in the number of flux linkage between 15° and 0° were compared based on the tilt angle characteristics of the bicycle, as shown in Figure 6. The difference in the flux linkage between tilt angles of 15° and 0° was 15.0, 12.4 and 10.5 mWb at θ_m = 180°, 45° and θ_m = 0°, respectively. The maximum flux linkage improved to 104.0 mWb at θ_m = 180°. The coil flux linkage was increased by using a yoke attached to the permanent magnet. The output voltage was obtained using the time derivative of the number of flux linkage. The presence of the yoke also increased the rotational torque as mentioned in Section 3.3, and the change in the number of flux linkage was larger, which was expected to increase the output voltage. However, a large yoke mounting angle increases the mass, which could not float on the liquid. The mounting range of the yoke was determined at 0° and 45°, considering the floating on the liquid.

4.2. Bicycle Motion Experiment

The output voltage was measured at a constant speed (approximately 10 km/h) by attaching a generator to the front basket of the bicycle. The yoke was set at θ_m = 45° and 0° (without yoke) based on the floating range. Figure 15 shows the output voltage characteristic where the maximum voltage without yoke was 0.8 V and that with yoke was 2.1 V. In addition, the LED at the generator output was intermittently lighted. The power due to the vibration of a liquid is expressed using the wave height, group velocity, and vibration frequency [40]. The mechanical input of this experiment is estimated to be approximately 10 mW. Considering that several mWs are required to light the diode, the vibration energy could be converted into electrical energy. The current and output of the LED were 0.7 mA and 1.3 mW, respectively, considering the coil resistance and the reverse voltage of the LED. Turning on the LED more brighter needs improvement of the generator output. However, the lighting time was only approximately 20% of the total moving time. Increasing the container size and the vibration frequency or inserting a capacitor in the output circuit is effective to keep the LED on longer time. Continuous lighting is difficult because of shorter time on output voltage exceeding LED threshold voltage. Increasing the output voltage amplitude to exceed the LED threshold voltage results in periodic blinking.

The output voltage increased with the attachment of the yoke to the mover within the levitation range. The voltage improvement was due to the effect of the mover swing characteristics described in Section 3 and that of increasing the flux linkage described in Section 4. When driving at a constant speed, pedaling causes the bicycle to vibrate and generate power. Acceleration is expected to have a stronger pedaling effect than that at a constant speed, resulting in a large amount of power generation.

5. Conclusions

This study has proposed a swing-magnet-type generator for energy harvesting applications from vibration. The mover is shaken by external vibration via the liquid in a container, which leads to power generation in the coil. The vibration of a bicycle in a wide frequency band (>10 Hz) is converted into a 2 Hz mover swing using liquid.

The output voltage of the generator depends on the coil flux linkage and tilt angle characteristics of the mover. The tilt angle characteristics, which depend on the mover specifications, are investigated using either simulations or experiments. The mass and moment of inertia depend on the yoke size to increase the connecting flux. The larger the yoke mounting angle is, the larger the restoration length at the same tilt angle. If mounting angle θ_m of the yoke is large, the rotational torque of the mover increases. Furthermore, the simulation results reveal that the resonant frequency related to the mover swing is 2.5 Hz. Vibration experiments using a linear motor also indicates that a resonant frequency of approximately 2 Hz is observed. The specifications of the mover significantly influence its swing characteristics.

The magnetic-field analysis reveals that the fluctuation in the number of flux linkage with the inclination improves by 18% at yoke mounting angle θ_m = 45°. The bicycle vibration experiment proves that the output voltage of the generator with a yoke is 2.1 V, which indicate the effect of the yoke. The proposed generator prototype is able to power a LED.