TECHNICAL PAPER

Ken Sasaki Æ Yuji Osaki Æ Jun Okazaki

Hiroshi Hosaka Æ Kiyoshi Itao

Vibration-based automatic power-generation system

Received: 30 June 2003 / Accepted: 24 October 2003 / Published online: 11 May 2005� Springer-Verlag 2005

Abstract Two types of electric power generator systemsthat automatically extract power from oscillating mo-tion of a human body or vibration of machines andstructures are proposed and studied. The first systemutilizes self-excited rotation of an eccentric rotor thatrotates in one direction in synchronization with the ap-plied oscillating motion. Connecting an electrical load tothe generator increases the damping about the rotoraxis, and numerical analysis shows that there exists anupper limit to this damping to maintain the self-excitedrotation mode. Excessive damping reduces the rotor to aswinging motion, resulting in decreased power output.The second type utilizes resonant vibration of a per-manent magnet unit suspended by a set of springs. Inorder to maximize the output power, a micro controllerchanges the connection of the generator coils, which ineffect changes the electro-mechanical damping, to keepthe vibration amplitude within the allowable stroke.Theoretical analysis and experimental results are pre-sented for both systems.

1 Introduction

Recent progress in microelectronic technology has con-tributed to miniaturization of size and drastic reductionof power consumption of information devices (Itao1996). As the power consumption decreases, generatingelectricity from sunlight, heat, or physical motion, be-comes a realistic alternative to conventional battery cellsthat require replacements. Solar batteries are already inwide use for calculators and watches, and thermoelectricgeneration by Peltier devices or thermocouple is used in

some small electronic devices. Exploiting energy from‘‘motion’’ is, however, still limited to electric generatorsthat require active physical inputs such as squeezing orturning of a handlebar. A rare example of a generatorthat does not require active physical input is ‘‘automaticgenerating system’’ (AGS) developed by SEIKO forwristwatches (Kitahara 1996). It generates electricityfrom transient rotation of a rotor caused by the motionof a wearer’s arm. A speed-up gear train multiplies therotation of the weight approximately 100 times to drivethe generator axis. After being rectified and charged in acapacitor, the generated electricity drives the electronicsand a stepping motor in the movement unit. The averageoutput of AGS is 10 lW. This is sufficient for driving awristwatch, but not enough for driving other smallinformation electronic devices that require power supplyin the order of 10 mW.

This paper investigates two types of electric powergeneration systems that automatically extract powerfrom oscillating motion of a human body or vibration ofmachines and structures in order to develop generatorsystems for wearable information devices. The first sys-tem utilizes self-excited rotation of an eccentric rotorthat rotates in one direction in synchronization with theapplied oscillatory motion. The second type utilizesresonant vibration of a permanent magnet unit sus-pended by a set of springs. In both systems, dynamiccontrol of electro-mechanical damping is necessary tomaximize the output power for arbitrary amplitude ofthe applied oscillatory motion. Dynamic models, pro-totypes, and performance of these generator systems aredescribed in the following sections.

2 Automatic power-generating system using self-excitedrotation

2.1 Self-excited rotation of an eccentric rotor

Figure 1 shows a comparison of motions of an eccentricrotor and the corresponding power output of the

K. Sasaki (&) Æ Y. Osaki Æ J. Okazaki Æ H. Hosaka Æ K. ItaoInstitute of Environmental Studies,Graduate School of Frontier Sciences,The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku,Tokyo 113-8656, JapanE-mail: ksasaki@k.u-tokyo.ac.jpTel.: +81-3-58416452Fax: +81-3-58418551

Microsyst Technol (2005) 11: 965–969DOI 10.1007/s00542-005-0506-8

generator. The center of gravity of an eccentric rotor isset off from its axis of rotation. The generator system‘‘AGS’’ for wristwatches developed by SEIKO generateselectricity from transient rotation of the rotor when theposture of the watch changes. Postural change is themain cause of this transient rotation, rather than theinertial force caused by the acceleration of arm’s motion.If the applied motion is oscillatory, such as walking orrunning of human body, we can increase the poweroutput of the generator by utilizing self-excited rotationof an eccentric rotor (Hosaka et al. 2000). In the self-excited rotation mode, the rotor continues to rotate inthe same direction in synchronization with the appliedoscillatory motion. The mean square of the angularvelocity of the rotor, which is proportional to the poweroutput of a generator, will be approximately ten timeslarger than that of the swinging motion.

2.2 Dynamics of self-excited vibration of an eccentricrotor

Equation of motion of an eccentric rotor when oscilla-tory motion is applied is derived using a dynamic modeldepicted in Fig. 2. Let A be the amplitude, and x be theangular frequency of the applied oscillatory motionalong the x axis. Let a be the distance between the centerof gravity of the eccentric rotor and its axis of rotation,and m be the mass, J be the moment of inertia about thecenter of gravity, h be the rotation angle of the rotor,and g be the gravitational acceleration. The electro-mechanical damping caused by the electric current in thegenerator’s coil is represented by c. The value of c de-pends on the electrical impedance of the output load and

the DC resistance of the coil. Mechanical friction anddamping are ignored. The equation of motion will be asfollows:

ma2 þ J� �

€hþ c _h ¼ maAx2 sin h sin xt � mga cos h: ð1Þ

The system maintains self-excited rotation under thefollowing initial conditions:

_h�� ��

t¼0> x ð2Þ

2cAmax

\1: ð3Þ

Although the effect of gravity was ignored in the deri-vation process of these conditions, it does not affect thequalitative indications of the conditions. Equation 2indicates that the initial angular velocity of the rotormust be larger than that of the applied oscillatory mo-tion in order to initiate self-excited rotation. Equation 3gives the conditions for electro-mechanical damping ofthe generator system, amplitude and angular frequencyof the applied motion, mass of the rotor, and radius ofeccentricity of the rotor. Results of numerical analysisand experiments are given in the next section.

2.3 Numerical analysis and experiments

Figure 3 shows a relationship between the amplitude ofthe applied oscillation and the power output of thegenerator. Other parameters in Eq. 3 are kept constant.The solid line indicates numerical analysis based onEq. 1, and the dots indicate experimental results. AsEq. 3 implies, there is a minimum value for the ampli-tude of the applied oscillation in order to maintain theself-excited rotation.

Equation 3 also indicates that there is a minimumfrequency of the applied motion to maintain the self-excited rotation. Figure 4 shows an example of thiscondition. When the frequency of the applied motion is1 Hz, the acceleration is not sufficient to overcome thedamping of the rotor to maintain self-excited rotationand the motion reduces to swinging motion, resulting inlow power output. When the frequency is 2 Hz, thesystem maintains the self-excited rotation, which yieldslarger power output.

Figure 5 shows a relationship between the electro-mechanical damping and the power output of the

Fig. 1 Comparison of motions of an eccentric rotor

Fig. 2 Dynamic model of an eccentric rotor

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generator, which is proportional to the mean square ofthe angular velocity. The applied oscillatory motion iskept constant. The graph shows that the power output

increases proportionally to the electro-mechanicaldamping, up to a point where damping torque becomestoo large to maintain the self-excited rotation mode. Therotor’s motion changes to a swinging motion, and thepower output decreases abruptly. This indicates that weneed to control the electro-mechanical damping tomaintain the self-excited vibration mode.

3 Automatic power-generating system using resonantvibration

3.1 Dynamics of automatic power-generating systemusing resonant vibration

Automatic power-generating system using resonantvibration consists of a permanent magnet unit sus-pended by a set of springs (Okazaki et al. 2002). Thevibration of the magnet unit, which is caused by theoscillatory motion applied to the base of the system,generates electricity in the coils. When the frequency ofthe applied force or motion is equal to the resonantfrequency in forced vibration of a harmonic system, themechanical impedance of the system is at its minimumand the efficiency of energy transfer from the appliedmotion to the system is at its maximum. This means thatthe resonant frequency of the generator system shouldbe adjusted to the frequency of the applied motion.

The transferred energy dissipates through mechanicaldamping and electro-mechanical damping. Electro-mechanical damping corresponds to the sum of the en-ergy consumption of the electrical load and the heatdissipation in the generator coils. The design goal is tomaximize the generator output under given constraintson dimension and weight. We assume from hereafterthat the frequency of the applied motion is always equalto the resonant frequency of the generator system.

Equation of motion is derived using the model shownin Fig. 6. Let A be the amplitude and x be the angularfrequency of the externally applied motion. LetM be themass, x be the displacement, A0 be the amplitude, andAmax be the allowable amplitude of the vibrating mag-net. Let K be the spring coefficient of the suspensionspring, cm be the mechanical damping, and ce be theelectromechanical damping that corresponds to the

Fig. 4 Effect of the frequency of the applied motion to the motionof an eccentric rotor

Fig. 5 Relationship between the electro-mechanical damping andthe generator output

Fig. 6 Dynamic model of a generator utilizing resonant frequency

Fig. 3 Relationship between the amplitude of the applied motionand the generator output

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generator output. Equation of motion of the generatorsystem is as follows:

M€xþ ðcm þ ceÞ _xþ Kx ¼ MAx2 sin xt: ð4Þ

The average generator output power is given by thetotal generator output of one cycle divided by the period

P ¼ 1

T

ZT

0

ce _x � _xdt ¼ ceA2M2x4

2 cm þ ceð Þ2: ð5Þ

Ignoring the mechanical damping yields

P ¼ A2M2x4

2ce: ð6Þ

Equation 6 indicates that the output power increasesinverse proportionally to the electro-mechanical damp-ing. This is, however, applicable only when the ampli-tude is not limited. The amplitude A0 is given by

A0 ¼AMx

ce: ð7Þ

By rearranging Eq. 7 and replacing A0 with Amax, weget the electro-mechanical damping that lets the systemto vibrate at its allowable amplitude

ce ¼AMxAmax

: ð8Þ

Substituting Eq. 8 into Eq. 6 gives the maximumpower output Pmax for given amplitude and frequency ofthe oscillatory motion, and mass and the allowableamplitude of the magnet unit

Pmax ¼AmaxAMx3

2: ð9Þ

3.2 Controlling electro-mechanical damping for maxi-mum generator output

In the previous section, it has been shown that theelectro-mechanical damping should be adjusted to thevalue given by Eq. 8 to obtain maximum generatoroutput. The electromagnetic force acting on the gener-ator coil is given by

F ¼ IBL � 2N ¼ _xBL � 2NRc þ Rload

� BL � 2N ¼ 2NBLð Þ2

Rc þ Rload� _x;

ð10Þ

where F is the electromagnetic force, I is the current, B isthe magnetic flux density, L is the coil width, N is thenumber of turns of the coil, Rc is the DC resistance ofthe coil, and Rload is the resistance of the electrical loadconnected to the generator. By comparing Eq. 10 withF ¼ ce � _x; we immediately get

ce ¼2NBLð Þ2

Rc þ Rload: ð11Þ

Since the amplitude of the applied oscillatory motionvaries, we need to change the value of ce in order tomaximize the generator output. There are several waysto change the value of ce. One is to change the loadresistance Rload by regulating the sink current to a reg-ulator that controls the charging of batteries or supplyto external circuits. Although such regulators are tech-nically feasible, fabrication of complex circuitry will becostly. Changing the magnetic field is unrealistic. Wehave decided to change the combination of connectionsamong multiple generator coils, and thus changing theimpedance of the coils, in order to change the value of ceto maximize the vibration amplitude.

Figure 7 shows the schematic diagram of the proto-type system. A permanent magnet is suspended by a setof springs. The resonant frequency of the system is 6 Hz.Three generator coils whose number-of-turns are 200,400, and 400 were attached on the base. The DC resis-tance is 50, 100, and 100 X respectively. By changing theconnections among the coils, we obtain five differentnumber-of-turns, 200, 400, 600, 800, and 1,000. Amicrocomputer controls a set of relays to change theconnections. The power consumptions of the micro-computer and the relays were less than 1 mW in total.The external load was 100X.

A microcomputer monitors the output voltage andsearches the best combination of coils by changing thenumber-of-turns sequentially from 1,000 down to 200.Figure 8 shows this sequence. In this case, 400 turns wasselected as optimal.

Figure 9 shows the results of this adjusting algorithmfor input amplitude of 0 mm to 5.5 mm (peak to peak).The graph shows that the proposed impedance controlalgorithm always selects the best number-of-turns formaximum generator output.

4 Conclusion

Two types of electronic power generation systems thatautomatically extract power from oscillating motion of ahuman body or vibration of machines and structures

Fig. 7 Schematic diagram of the prototype system

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were proposed and studied. The first system utilizes self-excited rotation of an eccentric rotor. Power output byself-excited rotation was ten times larger than that of theswinging motion of the rotor. Theoretical analysis andexperiments have verified that the electro-mechanicaldamping, which is equivalent to the generator output,needs adjustment in order to initiate and maintain theself-excited rotation. The second system utilizes resonantvibration. In order to adapt to different amplitude of theinput motion, a microcomputer selects the connectionsof the multiple generator coils to change the impedanceof the coils to maximize the vibration amplitude of the

generator within the allowable stroke. Experimentsusing the prototype system have verified the usability theproposed impedance control algorithm. The first systemis suitable for generating electricity from low frequencyoscillatory motion with relatively large amplitude, suchas human body motion of walking or running, and thesecond system is suitable for higher frequency vibrationwith small amplitude, such as vibration of heavymachineries, buildings and bridges.

References

Hosaka H, Shikama K, Kanao R, Yamada I, Itao K (2000) Studyon automatic power generators for wireless communicationdevices utilizing mechanical and human movements. In: Pro-ceedings of the 11th annual symposium on information storageand processing systems, Santa Clara University, California

Itao K (1996) Wearable information network nowadays. Optron-ics, pp 3–25

Kitahara J (1996) Development of small AGS (automatic power-generator for a wristwatch). Horol Inst Jpn 157:33–42

Okazaki J, Shikama K, Hosaka H, Yamakawa H, Itao K (2002)Design of automatic power generator using mechanical vibra-tion. Micromechatronics 46(1):27–35

Fig. 8 Search algorithm forselecting optimal number-of-turns of the generator coils

Fig. 9 Generator output by impedance control

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