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Analysis and Design of Minigenerator

P. Fiala and T. Jirku

Department of Theoretical and Experimental Electrical EngineeringFaculty of Electrotechnical Engineering and Communication, Brno University of Technology

Kolejni 2906/4, Brno 612 00, Czech Republic

Abstract The paper presents results of the analysis of the vibrational generator. The paperdeals with the design of a vibrational generator that is used as a power supply for independentelectric circuits. The vibrational generator can be used in the various areas, e.g., traffic, electron-ics, special-purpose machines, and robotics. The proposed design employs magnetic dampingof the core movement. It was numerically evaluated and it was shown that it was possible toobtain significantly larger output voltage and output power than in experimental settings usedpreviously [1].

1. INTRODUCTION

The development of any new device always lays strong requirements on its reliability. The ar-eas where reliability demands are of particular importance are transport, robotic and automotiveapplications.

One of the ways to increase the sensor reliability is their supplying from autonomous powersources. Sensors used in industry and automotive systems can be placed at critical points, withoutsupply and data transmission systems. These sensors monitor important quantities during thesystem operation. In the course of the revision, the operator just scans the device under test, andby using wireless transmission the needed data are retrieved from all sensors. These data can bethen compared with those from a previous system operation and all other data available.

This paper presents the results of a vibrational mini-generator (MG) analysis. The MG isintended to provide power for the above sensors. The principle of its operation is based on the uti-lization of changes of the external mechanical forces, which can be described by Faradays law [1, 2].

The required output parameters are: output voltage between 35 V in the ideal case, output power2001000 W. The value of output power depends on the type of the sensor used.

Figure 1: The basic arrangement of the investigateddevice.

i(t)

Earths surface

x y

zo

gz

spring

MG core

g(t)

MG body

u(t)

permanent magnet

moving

Figure 2: The principle of a vibrational minigenera-tor.

The basic arrangement of the vibrational generator is in Fig. 1. The MG body is tightly con-nected with the source of vibration the fuselage, and thanks to the oscillation of the wholesystem the MG core starts moving with respect to the fuselage. The mechanical part of the MG isdesigned such that the MG core driven by external vibrations performs non-damped oscillations.

The design of the MG allows oscillations of the MG core within quite a wide spectrum of externaloscillation frequencies. The operation of the MG is based on Faradays law as follows from Fig. 2.

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The core containing ferromagnetic parts and permanent magnets (with high density of the storedenergy, e.g., FeNdB, SmCo) that moves with respect to the winding connected to the shell inducesin it a voltage and the external current connected to it starts carrying a current. Both the inducedvoltage and current in the external circuit are generally complex functions of time. Typical oscilla-tion frequencies of the vibration source that were measured at two places of one investigated device(aircraft) are, for an illustration, shown in Fig. 3. The graphs express the square of amplitudeof the movable parts on external oscillation frequencies (the amplitudes are, moreover, related toquantity g = 9.81m/s2).

0 50 100 150 200 250 300 3500

10

20

30

40

50

60

70

Flight 63 APU - Power spectrum

frequency [Hz]

Vibrationsamplitude[g/Hz]

Figure 3: Squared relative amplitudes of vibrations versus external frequency of oscillations (measured attwo different places of an aircraft).

2. MATHEMATICAL MODEL

The mathematical model of the problem consists of a partial differential equation describing thedistribution of electromagnetic field in the device and two ordinary nonlinear differential equationsdescribing the behavior of external electric circuit and mechanical movement the movable parts ofthe generator. The electromagnetic and mechanical phenomena strongly influence one another. Thegenerator (Fig. 4(a)) whose volume is denoted by letter contains several important subdomains(Fig. 4(b)) of different physical parameters. These subdomains are denoted as Fe ferromagneticparts of the magnetic circuit, p permanent magnets, w windings. Other subdomains are,for example, spring, shell and air. The electromagnetic part of this coupled model may be describedby the reduced Maxwell equations:

curlH= J in , divB = 0 in , curlE= dBdt

in w (1)

whereH is the magnetic field strength vector, B the magnetic flux density vector and J the currentdensity vector, material relations are represented by relations

divJ= 0 in w, B = 0rH in Fe, B = 0rH+ 0M in p, J = E in (2)

where E is the electric field strength vector, where 0 is the permeability of vacuum, r the relativepermeability, M the remnant intrinsic magnetisation vector of permanent magnet, the specificelectric conductivity and any from the above subregions with nonzero electrical conductivity.After introducing magnetic vector potential by equations

curlA = B, divA = 0, E= graddAdt

, (3)

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4. RESULTS OF NUMERICAL ANALYSIS

The modules of vector functions of magnetic flux density B and field strength H are shown inFig. 5.

The model is fully 3D. No symmetries were used in the model. This is due to the convergenceevaluation and error estimation [6, 7].

5. EXPERIEMNTAL REALIZATION OF VIBRATIONAL GENERATOR

Several prototypes of mini-generators of different constructions were realized. Fig. 6 shows theprototype of a minigenerator of output Pout = 10 100 mW. The prototypes were tested on avibrational bench during their development. The non-harmonic periodical voltage transients wereobtained by measurement for vibration displacement within the range x < 0.1, 0.4 > mm. Thevibration bench measurements were performed for various bench displacements (see Tab. 1). Thetheoretical values of generator output parameters are listed in Tab. 1. This is necessary to verifyby experiment.

Table 1: Measured values of generator output voltage.

x (mm) Upp (V) f(Hz) Umaxp (V) a (ms2)/g fcent (Hz)

0.4 26 27-38 46 0.586149 36-370.2 14 27-38 36 0.293074 38

0.1 8 27-38 18 0.146537 38

0.05 4 28-38 7 0.073269 31

fcent peak of the resonant curve, g is Earth gravitational acceleration.

Figure 6: Functional sample of a generator version (10100) mW.

6. CONCLUSION

The paper represents a part of an introductory study of the vibrational MG design. It is intendedas a preparation for a proposal of the 6th General European Project.

The paper presents results of the distribution of magnetic and electric field strengths and fluxdensities. In order to get voltage of required time dependence it is possible to suitably modify theshape of the winding (the details are discussed in [4]). The time domain simulations were performedusing the lumped equivalent circuit in the MATLAB program. This approach is not very accuratein comparison with FEM capabilities. However, this approach is substantially faster. The resultsof the analysis serve as a foundation for the design of the minigenerator.

ACKNOWLEDGMENT

The paper was prepared within the framework of the research plan MSM 0021630516 of the Ministry

of Education, Youth and Sports of the Czech Republic, WISE Wireless Sensing STREP 6FPProject No. FP6-2003-AERO-1.

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1. Li, W. J., Z. Wen, and P. K. Wong, A micromachined vibration induced power generator forlow power sensors of robotic systems, World Automation Congress, Maui, Hawai, July 1116,2000.

2. Stratton, J. A., Theory of Electromagnetic Field, SNTL, Prague, Czech Republic, 1961.3. Fiala, P., T. Vojtek, and I. Behunek, Analysis and test of vibrational minigenerators, Proc.

IC SPETO 2006, Vol. 1, 155158, Gliwice-Ustron, Poland.4. Fiala, P., Conception of vibrational microgenerator, 102, Research report UTEE FEKT VUTin Brno, UTEE FEKT in Brno, Czech Republic, Jan. 30, 2003.

5. ANSYS, Users Manual for Revision 5.18.0, Vol. 14, Swanson Analysis System, Inc., Hous-ton, USA, 19942003.

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7. Fiala, P., Solution of electric field at a bushing support from distribution frame, ResearchReport No. 1/96, Laboratory of Modeling and Optimization of Fields in ElectromechanicalSystems, FEI VUT Brno and ABB EJF, a.s. Brno, 24.7.1996.

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