Bistable System for Energy Harvesting

M. Majer, M. Husak

Department of Microelectronics, The Faculty of Electrical Engineering, CTU in Prague Technicka 2, 166 27, Prague, Czech Republic

e-mail: majermic@fel.cvut.cz, husak@fel.cvut.cz

This paper presents bistable piezoelectric model of energy harvesting structure. This system can generate higher power in wide frequency band in contrast to resonant monostable structures. The paper presents measuring of transition, and monostable and bistable behavior of loaded buckled beam. Measured generator was created from commercially available components. The measurement compares the monostable and bistable behavior.

1. Introduction

The fundamental characteristic of bistable structures are two stable neutral positions. The system acts in each stable position as a monostable system. In monostable mode structure exhibits resonant behavior. Behavior in this operating mode is similar like at other beam structures [1].

The transition between stable positions occurs in overcoming certain critical force. During the transition quickly releases the energy accumulated in the beam. In the bistable mode depends mainly on the operating force. If the excitation force overcomes the mechanic preload, the buckled beam flips to the second position. This transition occurs even when the beam is exposed to a single external pulse.

The advantage of bistable structure is a wide range of working frequencies and higher output power than the monostable structures. The disadvantage is the threshold force for start of bistable operation.

2. Compressed beam simulation

This structure is a simple beam fixed at both ends. The beam is longitudinally compressed. Because the beam is flat, it may buckle only to one of two neutral positions. The position can be changed by external force. For the simulation were used dimensions and materials of cut of the piezoelectric electroacoustic transducer. The dimensions are: length 20 mm, width 5 mm. Pressing the beam was 0.2 mm.

Figure 1 depicts reactive force of the compressed beam dependency on deflection

Reactive force

-40

-30

-20

-10

0

10

20

30

40

50

-2,5 -2 -1,5 -1 -0,5 0 0,5 1 1,5 2 2,5

deflection d (mm)

forc

e (N

)

Fig. 1 Computed reactive force of the beam

311ASDAM 2012, The Ninth International Conference on Advanced Semiconductor Devices and Microsystems, November 11–15, 2012, Smolenice, Slovakia

of the central point. Two local maxima indicate two stable neutral positions. The characteristic is asymmetric, because the PZT layer is on one side of the supporting beam. This leads to priority of the upper neutral position by compressing the beam. 2. Macromodel measuring

The macromodel is designed as a basic structure of a simple compressed beam. Both ends of the beam are connected to holder by articulated join.

The beam is cut by corundum tool from commercially available piezoelectric electroacoustic transducer. This transducer consists of the supporting brass disc, on which is concentrically glued PZT disc. Piezoelectric material is coated with electrodes. Brass sheet thickness is 0.1 mm, the thickness of the piezoelectric layer is 0.15 mm. Dimensions are: PZT 7 mm � 24 mm and 7 mm � 28 mm supporting plate. In the middle of the beam is placed 16 g load. 2.1 Measuring device

The beam was compressed to achieve deflection of middle of the beam 1 mm. Ends of the beam without PZT layer acts as soft spring. These parts of beam are important to avoid PZT crack. These additive springs also decrease the critical force.

On the side of the module is attached 3-axis accelerometer. In the holder are placed adjustable spring contacts for electric connection of the piezoelectric generator. The PZT generator was electrically loaded with resistance 1 M�. 2.2 Measurement in monostable mode

Figure 3 shows the resonant frequencies of the beam in both states. Frequency difference causes asymmetric structure. Movement of the beam is vertical, so that in the upper position, the weight of load acts against the deflection force of the beam, while in the lower position advances the deflection. The piezoelectric layer is present only on the top side of the supporting beam, which supports the deflection in direction up.

The acceleration was kept at the value of 5 ms-2 peak to peak. Responding force is �40 mN.

Fig. 2 Measuring device

Monostable mode - frequency characteristics

0

0,5

1

1,5

2

2,5

3

3,5

0 50 100 150 200 250

f (Hz)

U (

V) position UP

position DOWN

Fig.3 Frequency characteristics

312

2.3 State transition

Figure 4 shows the output voltage of the beam when flipping from one to second state. At the transition is generated a high voltage pulse, followed by damped oscillations. Frequency read from the waveform is 73 Hz for move up. For move down is read value 80 Hz and oscillations at approximately double frequency. These frequencies also are showed in Figure 3. 2.4 Bistable behavior

The following figures (Fig. 5 and Fig. 6) show the waveform of the output voltage of the beam and acceleration of the excitation generator. To the beam was connected a load resistor 1 M�. The excitation frequency was 30 Hz.

Figure 5 shows the output voltage of the beam and acceleration of the holder excited by vibration with acceleration under bistability (approximately 4 m.s-2) and under resonant frequency.

Figure 6 shows the situation, where was the control unit of vibration exciter adjusted to

corresponding value of acceleration 5 m.s-2 to use the beam in bistable mode. The bistable behavior causes significantly higher values of acceleration visible in the picture.

At the beginning of the transition the inertia force of the mass acts against the excitation force. After overcoming critical position of the beam to the transition states, the beam with load rapidly moves to the opposite position. Its reactive force is added to excitation force. This additive force increases the acceleration. Therefore, the measured acceleration exceeds 10 ms-2.

Monostable function

-15,00

-10,00

-5,00

0,00

5,00

10,00

15,00

0 50 100 150 200

time t (ms)

outp

ut v

olta

ge U

(V

)

-30,00

-20,00

-10,00

0,00

10,00

20,00

30,00

acce

lera

tion

a (

m.s

-2)

Bistable function

-15,00

-10,00

-5,00

0,00

5,00

10,00

15,00

0 50 100 150 200

time t (ms)

outp

ut v

olta

ge U

(V

)

-30,00

-20,00

-10,00

0,00

10,00

20,00

30,00

acce

lera

tion

a (

m.s

-2)

Fig. 5, 6 Output voltage and acceleration in monostable and bistable mode

State transition

-4

-3

-2

-1

0

1

2

3

4

5

-100 -50 0 50 100 150 200

time t (ms)

outp

ut v

olta

ge U

(V)

Transition UPTransition DOWN

Fig. 4 Output voltage waveform in transition

313ASDAM 2012, The Ninth International Conference on Advanced Semiconductor Devices and Microsystems, November 11–15, 2012, Smolenice, Slovakia

3. Conclusions

The measured waveform shows that this generator can be used as a monostable resonant generator for operating with small acceleration. For larger acceleration, which leads to two stable states flipping, the structure generates much higher power (Tab. 1). The beam can be flipped by one force impulse. If the bistable generator is used near its monostable-mode resonant frequencies or whole number fraction of the resonant frequency, the resonant behavior keeps the beam in bistable mode even if the excitation force decreases under critical force. Tab. 1 Generated power Behavior mode monostable bistable Maximal output voltage 0.6 V 12 V Maximal output power 0.36 �W 144 �W Energy generated in one period 0.0045 �J 1.1 �J

The generator works with a wide band of excitation frequencies. The bistable system is due to this band suitable for MEMS technology, where is the problem to reduce the resonant frequency of the monostable structures to the band of considered vibrations. Acknowledgement

This research has been supported by the Czech Science Foundation project No. 102/09/1601 "Intelligent Micro and Nano Structures for Microsensor Realized Using Nanotechnologies" and partially by CTU project No. SGS11/156/OHK3/3T/13 „Development of Smart Devices and Systems in the Field of Microelectronics, Nanoelectronics and Optoelectronics.“ References

[1] S. Priya, D. J. Inman, Energy Harvesting Technologies, Springer Science+Business Media, New York, 2009.

[2] D. N. Betts, H. A. Kim, C. R. Bowen, D. J. Inman, Appl. Phys. Lett. 100, 114104, 2012. [3] Q C Tang, Y L Yang, Xinxin Li, Smart Mater. Struct. 20, 125011, 2011. [4] B. Ando, S. Baglio, C. Trigona, N. Dumas, L. Latorre, P. Nouet, J. Micromech. Microeng.

20, 125020, 2010. [5] H. Vocca, I. Neri, F. Travasso, L. Gammaitoni, Applied Energy 97, 771–776, 2012. [6] F. Cottone, L. Gammaitoni, H. Vocca, M. Ferrari, V. Ferrari, Smart Mater. Struct. 21,

035021, 2012. [7] B. Ando, S. Baglio, G. L’Episcopo, C. Trigona, J. Microelectromech. Sys. 21, 779-790,

2012. [8] A. F. Arrieta, P. Hagedorn, A. Erturk, D. J. Inman, Appl. Phys. Lett., 97, 104102 , 2010.

314