ICSE2010 Proc. 2010, Melaka, Malaysia

Effect of cantilever shape on the power output of a piezoelectric bimorph generator

Akeel Shebeeb and Hanim Salleh Department of Mechanical EngineeringUniversiti Tenaga Nasional (UNITEN)

Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia.akeel_mech@hotmail.com, hanim@uniten.edu.my

Abstract- This paper discusses the effect of the cantilever shape of piezoelectric bimorph bender on the power output. ANSYS® program was used to study the distribution of stress strain in each model design and MATLAB® program was used to simulate the effect of each variable on the output power. Triangular,rectangular and trapezoidal cantilevers were chosen with wide range of frequencies between (50Hz - 150 Hz) with the same input excitation conditions and same volumetric size, to analyze the effect of each design in the power. The result shows that maximum stress-strain value can be produced in the triangular shape with equal distribution on all the surface area. The analytical simulation showed that the maximum value of power of 5 mW at 85 Hz was produced by the triangular cantilever beam.Thus, triangular shape can produce maximum power comparing with the others.

I. INTRODUCTION

The trends of development in the area of electronic technology with respect to recent wireless devices are dependent on the characteristics and applications of these devices [1], which must be characterized by multi functionality, light weight, miniaturization, low cost, short time response, high accuracy and high reliability [2]. These features increase rapidly the demand for portable electronics and wireless sensors. Because these devices are portable, it becomes necessary to possess its own energy supplies, which are in most cases, conventional batteries despite the problems caused by them because of their limited life time [3]. In addition, replacement of the battery sometimes is difficult and may become a tedious process [4].Wireless sensors, may be placed in remote locations such as structural sensors on a high buildings or hanging bridges or in global positioning system (GPS) for tracking devices or animals in the wild or in the sky. Therefore, when the battery life ends, the sensor must be retrieved and the battery must be replaced which becomes a very expensive task or even impossible or unfeasible such as in civil infrastructure applications where it is often desirable to embed the sensor [5].If the surrounding energy of a system could be gained, it could be used to replace or recharge the battery or in the ideal case, it could provide endless energy for the electronic devices lifetimes. One method is to use piezoelectric materials to gain energy due to their ability to obtain energy from vibrations

surrounding a system and convert it into usable electrical energy and vice-versa [6]. For these reasons, many researches have been made and increased in power harvesting area[7]. Vibration sources are numerous and are everywhere in the environment [4]. The increase in demand for mobile communication devices has made this kind of energy harvesting a suitable option to gain a lot of attention. There are many systems that can be powered by a few hundreds of microwatts, which makes their power module as a feature for these systems, and make them autonomous and this power can be gained from the environment surrounding these devices. Particularly, piezoelectric conversion is one of the methods that met a big increase in use for power harvesting to take advantage of the vibrations surrounding a system. However, the vibrations have many ranges and low vibrations generated in the different environments get more attention, such as vibrations generated in the factories, buildings and other [8]. Alist of the sources measured along with the maximum acceleration magnitude of the vibration and frequency at which the maximum occurs is shown in Table I.

TABLE ILIST OF VIBRATIONS SOURCES WITH THEIR MAXIMUM ACCELERATION AND ITS PEAK FREQUENCY [3].

vibration source Peak acceleration

(m/s²)

Peak frequency (Hz)

A/C window unit 1.98 58A/C compressor 2.14 59Microwave oven 0.49 40Household refrigerator 0.14 110Care engine idling 0.56 30Car engine idling 0.52 40Drilling machine 0.81 150Drilling machine 0.93 178Truck engine idling 1.98 37Cloth dryer 4.21 59Washing machine 0.82 62Lathe 1.07 60Lathe 1.36 68Bearing test bed 10.57 200

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ICSE2010 Proc. 2010, Melaka, Malaysia

II. STRESS AND STRAIN DISTRIBUTION SIMULATION

The piezoelectric has been chosen as the basic device as the design base and modeling of piezoelectric generator based on the low frequencies of the most potential vibration sources and also the high stiffness of the piezoelectric. Bimorph bender type has the advantage because of its lower stiffness that caused mean higher value of strain can be produced with a given force input also the bimorph bender preferred it can easily be designed (rephrase please) [4]. A mass held on the end of cantilever beam with two tiny piezoelectric materials on both surfaces has been chosen for two reasons. The first reason is related to the cantilever mounting results in the lowest stiffness for a given size, and even with the use of bending elements it is difficult to design for operation at about 120 Hz in less than 1 cm³ [4]. The second reason is because of the converted power is closely related to the average strain in the bender. Moreover, for a given force input, the cantilever configuration results in the highest average strain for a given force input [3]. ANSYS® program version 12 was used to study the stress strain distribution for three different cantilever shapes (rectangular, triangular, trapezoidal) which represent the shapes of cantilevers to be used. The simulation was done by using the same excitation conditions. The results of stress/strain distribution showed in the Figures 2, 3 and 4. The maximum stress-strain value of rectangular shape increased to reach maximum value at the fixed end of the cantilever. The stress-strain distribution in trapezoidal shape was bettercompared to the rectangular because the strain effect in surface area was larger than in rectangular. In contrast, it decreased towards the free end of the cantilever which was exactly zero also at the free end. However, the triangular shape had equal distribution for stress-strain, which was maximum value at any point on the surface area of this shape. In addition, this led to the triangular shape of bimorph cantilever can be used to generate maximum power between the three shapes.

Fig. 1-a stress distribution for rectangular cantilever

Fig. 1-b strain distribution for rectangular cantilever.

Fig. 2-a stress distribution for trapezoidal cantilever

Fig. 2-b strain distribution for trapezoidal cantilever.

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ICSE2010 Proc. 2010, Melaka, Malaysia

Fig.3-a stress disribution for triangular cantilever

Fig. 3-b strain distribution for triangular cantilever

III. POWER OUTPUT SIMULATION

A commercial product, PSI-5H 4E bimorph bender (T-220-A4-303X) was selected from Piezo Systems Inc [9], as the piezoelectric transducer by miniaturizing the prototype based on the available commercial products. MATLAB program version R2008a was used to study and analyze the effect of these dimensions on the power output. The are many variablesaffecting the output power of the piezoelectric bimorph bender. Optimization of the dimensions were also done in order to reach the maximum value of power can be extracted. Using the result from the optimization simulation, the selected parameters given in Table II were used to simulate the power output. The power output calculated was based on the equation (1) presented by X. Gao [3] for the triangular shape and the

equation (2) presented by shad Roundy [4] for the rectangularshape. ⃒ ⃒= { ²/ ( ²+ ²) } ·⃒ in⃒. (1)

( )= ̶ 4 pz 31 pz ⁄ (2)

( )= ͈²/( )‒( ⁄ )+2 ͈) ² (3)

( )= ( ͈²( + ²)+2 ͈⁄( )‒ ²) (4)

= + (5)

= ₃₁² / (6)

Where the power equation of rectangular shape is: = × 2 ₃₁ c2 2 ᴘℇ in2( n2b ̶ ( b +2 n))²+( n2 (1+ ₃₁2)+2 n b − ²)

(7)Where:

P is the power output.R is the load resistance.Cp is the capacitance of piezoelectric bimorph.

31 is the strain coefficient.is the frequency of input vibration. n is the natural frequency of piezoelectric bimorph.k31 or k is the coupling coefficient. is the dielectric constant .

is the damping ratio.pz is the young modulus of piezoelectric bimorph.

s is the capacitance of storage capacitor.Pz is the thickness of single layer of piezoelectric bimorph.

TABLE IIRELEVANT PARAMETERS

Parameter Value UnitL 25 Mm

Hpz 0.19 * 10⁻³ MmHsh 0.13 * 10⁻³ Mmd31 320 * 10⁻¹² m/VYpz 5.4 * 10¹⁰ N/m²ℇ 3800* 8.85*10⁻¹² F/mCs 1 * 10⁻⁶ Fk31 0.13Ain 10 m/s²

Table III shows the corresponding proof mass and volume for each natural frequency. The volume calculated is the total generator volume measured with holder clamping volume.

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ICSE2010 Proc. 2010, Melaka, Malaysia

TABLE IIINATURAL FREQUENCIES, PROOF MASS AND VOLUME

Model Fn(Hz)

Proof mass (g)

Volume (mm³)

RectangularTriangular

85 2.2 346.96295 1.7 288.162105 1.4 285.062115 1.1 216.762

Figure 4 shows the comparison of extracted power with increasing the value of natural frequency for triangular and rectangular shapes. It shows that the triangular shape had the ability to generate higher value of scavenged power with the comparison to the rectangular shape. The reason was due to the stress strain distribution on the triangle surface area aspresented in section II. In other words, any applied load at the end of the triangular cantilever and all the cantilever area were under the maximum and had same value of stress and strain at all the points on this cantilever. On the other hand, the maximum value of stress and strain for rectangular shape was just near the holding edge. High value of strain showed that high ability to harvest power in piezoelectric cantilever since the output power was related to the value of strain [10]. MATLAB program was used to analyze the effect of changing cantilever dimensions and proof mass dimensions in producing power in order to make a tuning between these parameters which led to maximum power. The four designated natural frequencies which were 85Hz, 95Hz, 105Hz and 115Hz. The peak power value for triangular shape was 5128 μW (5.128 mW) with 85Hz as a natural frequency and total volume of 0.336 cm³ for the piezoelectric cantilever and proof mass. While the highest value of produced power for rectangular shape was 1200 μW at the same input excitation conditions and generator volume. The results also showed that the decreased in extracted power caused the increased in the value of natural frequency as shown in Figure 4.

Fig.4: Power produced by triangular and rectangular piezoelectric bimorph bender.

IV. CONCLUSION

The triangular, rectangular, trapezoidal piezoelectric bimorph bender designs are proposed, simulated, and evaluated experimentally in order to improve extraction of energy from the environmental vibration. Simulation results illustrated that the single triangular beam can be used to generate highest output power value after compared with the other shapes. Under the same volumetric condition and vibration excitation, the simulation results showed that the triangular cantilever shape had the ability to generate 5128 μW at 85 Hz which was the highest value of produced power compared to the rectangular shape. The resonant frequency can be tuned by changing the geometry of proof mass, and the increase of natural frequency can lead to the decrease of the harvested power.

REFERENCES

[1] G. K. Ottman, H. F. Hofmann, A. C. Bhatt, and G. A. Lesieutre, "Adaptive piezoelectric energy harvesting circuit for wireless remote power supply," Power Electronics, IEEE Transactions on, vol. 17, pp. 669-676, 2002.

[2] N. S. Shenck and J. A. Paradiso, "Energy scavenging with shoe-mounted piezoelectrics," Micro, IEEE, vol. 21, pp. 30-42, 2001.

[3] R. X. Gao and Y. Cui,“Vibration- based sensor powering for manufacturing process monitoring ”, Transaction of the north American Manufacturing Research Institution ,Society of Manufacturing Engineers , Vol. 33,pp.335-342, May, 2005.

[4] S. Roundy, E. S. Leland, J. Baker, E. Carleton, E. Reilly, E. Lai, B. Otis, J. M. Rabaey, P. K. Wright, and V. Sundararajan, "Improving power output for vibration-based energy scavengers," Pervasive Computing, IEEE, vol. 4, pp. 28-36, 2005.

[5] S. L. Seung, R. P. Ried, and R. M. White, "Piezoelectric cantilever microphone and microspeaker," Microelectromechanical Systems, Journal of, vol. 5, pp. 238-242, 1996.

[6] S. Meninger, J. O. Mur-Miranda, R. Amirtharajah, A. Chandrakasan, and J. H. Lang, "Vibration-to-electric energy conversion," Very Large Scale Integration (VLSI) Systems, IEEE Transactions on, vol. 9, pp. 64-76, 2001.

[7] S. Roundy, P. Wright, and J. Rabaey, "A study of low level vibrations as a power source for wireless sensor nodes," Computer Communications, vol. 26, pp. 1131-1144, 2003.

[8] Bartosz Pekoslawski , “ Application of Vibration Energy Harvesters for Powering of Wireless Sensors Nodes in Large Rotary Machines Diagnostic System”, X International PhD. Workshop OWD′2008, 18-21October 2008.

[9] Piezo Systems Products Catalog describing PZTpiezoceramic materials,www.piezo.com 22/5/2008.

[10] J. Baker, S. Roundy, and P. Wright, " Alternative geometries for Increasing power density in vibration energy scavenging for wireless sensor networks," 2005, pp. 959–70.

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