Enhanced Performance of a Frequency Up-Converted Piezoelectric Energy Harvester for Wideband Vibration

Enhanced Performance of a Frequency Up-Converted Piezoelectric Energy Harvester for Wideband Vibration

Miah A. Halim, Jae Y. Park

Department of Electronic Engineering, Kwangwoon University, 447-1, Wolgye-dong, Nowon-gu, Seoul 139-701, South Korea

Abstract This paper demonstrates enhanced performance of a mechanical impact driven frequency up-converted piezoelectric vibration energy harvester to scavenge energy from a wide range of low frequency ambient vibration. Increased bandwidth of the harvester has been obtained by increasing the stiffness of its power generating elements. The harvester structure comprises a low-frequency flexible driving beam with laterally expanded rectangular tip mass and two high-frequency unimorph piezoelectric generating beams which are struck by the driving beam mass upon excitation, and generate power. This impact mechanism results in a hindrance of the vibration motion of the driving beam, and its frequency response diverges from normal behavior, introducing wideband operation. Increase in generating beams' stiffness causes an increase in the effective stiffness of driving beam after impact which, in turn, allows bandwidth enhancement. Two different sets of unimorph generating beams have been used. Among those, use of relatively stiffer beams, made of stainless steel support layer, offers 60% increased half-power bandwidth (8Hz) and almost 3 times increased peak power (377µW) than the other, made of styrene support layer. It generates significant power within the entire operating frequency range (6Hz to 15Hz) implying its potential to be implemented in human and machine motion applications.

Keywords Effective stiffness; Unimorph beam; Frequency up-conversion; Mechanical impact; Wide bandwidth; Ambient vibration

1. INTRODUCTION

   With the recent advances in wireless and micro- electromechanical system (MEMS) technology, energy harvesting becomes one of the most promising technologies as the alternatives of the conventional batteries. The life of a battery is limited and short compared to the working life of any portable electronics and wireless devices. Sometimes it is inefficient to replace or recharge battery. Therefore, a good number of researchers have been investigating since past few years for the energy harvesting technology as a self-power source of these portable electronics and wireless devices. Ambient vibration is one of the most common and versatile energy sources around our environment [1]. Energy harvesting from ambient vibration is a clean and regenerative means of powering small-scale systems. Vibration energy is typically converted into electrical energy using electrostatic, piezoelectric, electromagnetic, or magnetoelectric transduction mechanisms [2-5]. A vibration energy harvester typically employs spring-mass-damper system having a resonant

   frequency at which the output voltage or power is maximum and significantly drops at other frequencies. In order to achieve maximum power from a vibration energy harvester, the frequency of vibration must match its resonant frequency.

   Ambient vibrations around our environment are characterized by low frequencies (<10Hz for human motion and <100Hz for machine induced motion) having capricious nature with high amplitudes [6]. Energy harvesting from such low frequency vibrations is challenging because (i) different vibration sources produce vibration of different frequencies containing various cyclic movements in different directions which does not allow the resonant oscillator to respond at it resonant frequency [7]; (ii) a low frequency resonator consists of a large mass combined with a compliant spring that undergoes large oscillation even at low level acceleration (<1g) making the harvesting device large for any specific application [8]; (iii) average power flow decreases with the decrease in resonant frequency as the generated power is directly proportional to the cube of the frequency of vibration [9]; (iv) it requires a relatively high electromechanical coupling [10]. Thus, it is quite difficult to produce significant amount of power from low frequency ambient vibration. In order to meet the challenges aforementioned, researchers have reported frequency up-conversion mechanism in low frequency vibration energy harvesting. In a frequency up- converted energy harvester, a low frequency oscillator absorbs the kinetic energy from the ambient vibration and transfers it to one or more high frequency oscillators either by mechanical impact or by magnetic attraction/repulsion which convert the kinetic energy to electrical energy. Impact driven frequency up-converted energy harvesters have been reported in [11-14] whereas those with magnetic attraction/repulsion have been reported in [15-18]. However, reported frequency up- converted harvesters still have the limitations in operating within a wide range of low frequency vibrations which have the random movements in nature (particularly, vibrations below 20 Hz), desiring a wideband operation.

   In this study, we have presented enhancement of both bandwidth and output power of a low frequency driven piezoelectric vibration energy harvester that uses frequency up-conversion of two piezoelectric generating beams by mechanical impact of a mass-loaded flexible driving beam. The generating beams act as one single flexible stopper to the driving beam. The effective stiffness of the driving beam increases after impact on the rigid generating beams,

   introducing its non-linear vibration that allows the system to operate within a wider frequency range. Each of the stiffer generating beams among two different sets of generating beams, generates the maximum allowable power over almost entire operating bandwidth (half-power bandwidth) which are (both generated power and operating bandwidth) significantly higher than the relatively less stiff generating beams set.

2. SYSTEM DESIGN AND MODELING

   1. Wideband Operation by Mechanical Impact

      Fig. 1 illustrates the concept of bandwidth widening by mechanical impact. Generally, when a mass-loaded cantilever beam vibrates freely (no stopper), the stiffness of the beam is constant over its displacement and it shows linear frequency response behavior. But, involvement of any obstruction (stopper) on its way of motion, the vibration motion of the mass-loaded cantilever beam is hampered due to impact on the stopper that changes its effective stiffness and the frequency response diverges from its normal behavior. Fig. 1(a) shows the schematic of an impact model that contains one proof- mass-loaded driving cantilever beam of stiffness k1 and a generating cantilever beam of stiffness k2, (k1<<k2) placed below with a small gap d, acting as a stopper to the driving beam. When vibration with sufficient large amplitude is applied, the mass impacts on the generating beam stopper. As the generating beam mass is negligible as compared to the proof-mass m, both beams vibrate together after impact for a short period (coupled vibration) and then vibrate independently (free vibration) after separation. The coupled vibration changes the effective stiffness of the driving beam to (k1+k2) as shown in Fig. 1(b), introducing its non-linear vibration, allowing resonance to extend over a wider interval, in the vicinity of the it's resonant frequency as shown in Fig. 1(c). This system can be modeled as a single degree of freedom (SDOF) piecewise linear model [19] as shown in Fig. 1(d).

   2. Proposed Device Structure and Its Working

      The structure of the proposed impact based wideband energy harvester has been illustrated in Fig. 2. It cnsists of a proof-mass loaded flexible driving beam having lower stiffness and two similar type rigid generating beams having higher stiffness than the driving beam as shown in Fig. 2(a). The generating beams are placed below the driving beam at the same level with a small gap as shown in Fig. 2(b). The driving beam has a laterally expanded tip at which a rectangular proof-mass (fitted to the expanded tip) is attached whereas each generating beam is composed of a piezoelectric layer mounted over a non-piezoelectric support layer as shown in Fig. 2(c). As seen, two different sets of generating beams with different support layers (Type-1 and Type-2) have been used in order to compare the performance. Type-2 beams are more rigid than Type-1 beams. Moreover, the length ratio of piezoelectric and non-piezoelectric layers are different for two beam types. Details of beam geometry will be discussed in the prototype fabrication section.

      When a low frequency external vibration of sufficiently large amplitude is applied to the harvester, the flexible driving beam starts vibrating and the proof-mass impacts on two rigid generating beams periodically. After impact, both driving and generating beams vibrate together for a short period with system's coupled vibration frequency and then separate. After

      Fig. 2: Structure of the proposed energy harvester: (a) schematic drawing,

      (b) side view, and (c) photographs of driving and generating beams.

      separation, each generating beam vibrates freely with its own resonant frequency which introduces frequency up-conversion mechanism. The piezoelectric layer of each generating beam generates electricity due to the piezoelectric effect.

   3. Electromechanical Modeling

   According to the piecewise linear model, the impact behavior of the proposed system is similar to an inelastic collision because the effective mass of each generating beam is negligible as compared to that of the proof-mass attached to the driving beam tip [11]. When the system is externally excited by a harmonic acceleration a, it allows the proof-mass to move relative to the base as z. If z < d, then there is no impact on the generating beams. Only the mass-loaded driving beam vibrates independently. If z d (while excited with sufficient large acceleration), the proof-mass impacts on the generating beams. They stick and vibrate together for a short period with an increased stiffness (k1+2k2) which transforms the proof-mass motion from linear to non-linear. This enables the resonance of the driving beam to extend over a wider frequency range [19]. The tendency of non-linearity in driving beam motion increases as the effective stiffness during coupled vibration period increases which, in turn, enhances the bandwidth significantly. Therefore, the piecewise linear equation of driving beam motion can be expressed as

   mz c1z k1z masin(at) ; z d

   (1a)

   Fig. 1: Concept of bandwidth widening by impact: (a) schematic view, (b) typical stiffness variation, (c) typical frequency response, and (d) SDOF piecewise linear model.

   mz (c1 2c2 )z (k1 2k2 )z 2k2d masin(at) ;

   z d

   (1b)

   TABLE I: MATERIAL PARAMETERS AND GEOMETRY OF

   where c1 and c2 are the damping constants of driving beam and each generating beam, respectively. a is the frequency of applied excitation. Since the coupled vibration period is over, the proof mass moves away from the generating beams and each generating beam vibrates at its own resonant frequency with exponentially decayed amplitude, while the driving beam reverts to its original linear motion behavior until it impacts the generating beams during the next cycle. It is assumed that the vibration of each generating beam decays fully and stays at position d, before the next impact cycle approaching.

   Let us consider, each unimorph generating beam of effective length L and width w has a piezoelectric layer of thickness tp and a non-piezoelectric support layer of thickness ts. When an impact force Fimp is applied at the tip by the driving beam proof-mass, the average stress on the surface of the piezoelectric layer can be given as [20]

   THE PROPOSED ENERGY HARVESTER

   n p

   Fimp Ep t t

   1 t 2

   (2)

   p

   wD 2

   Parameter	Driving Beam	Generating Beam
   		Type-1	Type-2
   Effective length of the beam	55 mm	15 mm	15 mm
   Width of the beam	4.8 mm	3.5 mm	3.5 mm
   Thickness of the beam	1 mm	0.8 mm	0.4 mm
   Length of piezoelectric layer	–	15 mm	25 mm
   Thickness of piezoelectric layer	–	0.3 mm	0.3 mm
   Support layer thickness	–	0.5 mm	0.1 mm
   Proof-mass	4.36 gm	–	–
   Young's modulus of styrene	3 GPa	3 GPa	–
   Young's modulus of stainless steel	–	–	200 GPa
   Young's modulus of PMN-PT*	–	20 GPa	20 GPa
   Dielectric constant of PMN-PT*	–	5200	5200
   Piezoelectric strain coefficient*	–	2000 pC/N	2000 pC/N
   Capacitance of PMN-PT*	–	9.85 nF	13.5 nF

   in which Ep is the Young's modulus of the piezoelectric layer, D is the bending modulus per unit width of the beam and tn is the position of the neutral plane from the bonding plane. Therefore, the generated open circuit voltage can be expressed in terms of average stress and the material properties of the piezoelectric layer, such as

   *Piezoelectric (PMN-PT) material parameters were provided by the supplier.

3. PROTOTYPE FABRICATION

   In order to verify the performance of the proposed energy harvester, a macro prototype was assembled on an Aluminum base structure. The driving beam was made of a flexible styrene strip with laterally expanded tip of area 14×10 mm2.

   OC L n p p

   V 1 d31 Fimp E p t t 1 t 2

   2 wD 2

   (3)

   An iron (Fe) proof-mass was attached with the driving beam tip to lessen its resonant frequency. Four generating beams

   r 0

   where -d31 is the piezoelectric strain constant, r and 0 are the dielectric constant of the piezoelectric layer and the permittivity of free space, respectively. According to the piecewise linear dynamics of the periodic impact vibration model described earlier, the instantaneous output voltage of each generating beam connected to a matched load as a function of time t can be written as [12]

   were prepared. Two of those (Type-1) were made by mounting PMN-PT single crystal piezoelectric layers with gold (Au) electrodes (supplied by Ibule Photonics, South Korea) on the styrene strip support layers by silver epoxy (Eccobond 56CJ; Emerson & Cuming). Another two (Type-2) were made of stainless steel support layers in the similar way. The clamp area of Type-1 generating beam was not covered with piezoelectric layer; length of piezoelectric layer was equal to

   V OC e

   Tct sin( t);

   n 2 t n 1 3

   the effective length of the generating beam. Two similar type generating beams (either Type-1 or Type-2) were placed at

   V (t) V

   4

   t

   3 a

   2c

   ()

   both sides of the driving beam, below it, 7 mm apart, at the

   c

   OC e

   4

   T g sin t

   ;

   n 1 3 t n 12

   2c a

   same level so that the proof-mass attached to the laterally expanded driving beam tip can impact on both generating

   g

   2

   where n = 0,1,2,3,….. is the number of impact, T is the total (sum of mechanical and electrical) damping ratio, g is the resonant frequency of each generating beam, and c is the frequency of the coupled vibration which can be calculated assuming that the driving beam mass and the generating beams never separate after impact, as c k1 2k2 m .

   beams' free ends at the same time, during its vibration. The vertical gap between the proof-mass and both generating beams was kept so small (in this case, 0.5 mm) that the mass can impact on the generating beams' free ends within its displacement over an interesting frequency range. However, the gap should not be zero because the higher resonant

   The peak power, generated from each generating beam, delivered to load can be written as

   V 2 R

   Ppeak OC L

   2

   RS RL

   (5)

   When the applied load resistance RL matches the source resistance RS, then maximum power is achieved. The source resistance is estimated as RS = 1/(rC), where r (= g) is the resonant frequency and C is the capacitance of the piezoelectric layer.

   Fig. 3: Schematic of experimental setup and photographs of the prototype energy harvester under vibration exciter test.

   Fig. 4: Measured open circuit voltage of one single generating beam of

   Type-1 and Type-2 under 6 ms-2 acceleration within low frequency range.

   frequency of the coupled vibration limits the driving beams' ability to respond to a lower frequency excitation at typical acceleration amplitudes. Table I presents the material parameters and geometry of the proposed energy harvester.

4. EXPERIMENTAL RESULTS AND DISCUSSION

   1. Experimental Setup

      We measured the performances of the fabricated energy harvester with two different types (Type-1 and Type-2) of generating beams in order to prove the concept of enhancing bandwidth by impact under low frequency vibration. Fig. 3 illustrates the schematic of the complete experimental setup and the photograph of the fabricated prototype under test. The fabricated energy harvester prototype was mounted on a

   2. Results and Discussion

   Frequency response of the device was carried out by sweeping the applied vibration frequency from 5 Hz to 16 Hz, keeping the acceleration fixed at 6 ms-2. Fig. 4 shows the generated peak-peak open circuit voltages of one single generating beam of Type-1 and Type-2. A maximum 12.96 volt was obtained at 12.5 Hz resonant frequency from Type-1 beam while Type-2 beam generated maximum 28.16 volt at 14 Hz resonant frequency. The higher stiffness of Type-2 generating beam produces larger strain on the Piezoelectric layer during impact, resulting in higher output voltage. The impact results in a hindrance of the vibration motion in driving beam, and the frequency response diverges from its normal behavior enabling the resonance to extend over a wide range. The resonant peak shifts slightly towards higher frequency for Type-2 beam due to increased effective stiffness of the driving beam during coupled vibration after impact which, in turn, increases the -3dB bandwidth (5 Hz) as compared to that (1 Hz) of Type-1 beam.

   V

   2

   Fig. 5 plots the measured peak-peak output voltage across various load resistances and the peak power delivered to the load at 12.5 Hz, under 6 ms-2 acceleration. Results show that, a maximum peak power of 129.15 µW was delivered to a matched load resistance of 200 K from each Type-1 generating beam. On the other hand, each Type-2 beam delivered a maximum 355µW peak power to 180 K optimal load. This optimal load resistance values match the frequency of the coupled vibration of the driving and generating beams rather than that of the free vibration of the generating beam, because most of the output was obtained during the coupled vibration. The values of peak power were calculated by

   vibration exciter (B&K 4809) connected to a function

   generator (Agilent 33250A) in conjunction with a power

   L 4RL

   ; where VL is the peak-peak voltage across the load

   amplifier (B&K 2718) which provides sinusoidal excitation of various frequencies and accelerations to the harvester prototype. The amplitude of the input vibration was measured by using a reference accelerometer (B&K 8305) attached to the base of the vibration exciter along with the harvester prototype, connected to a measuring amplifier (B&K 2525). A digital storage oscilloscope (Tektronix TDS5052B) was connected to the harvester outputs to measure and record its output response.

   Fig. 5: Measured peak-peak load voltages (dashed lines) and peak output powers (solid lines) against various load resistances generated by one single generating beam of Type-1 and Type-2 at 12.5 Hz frequency under 6ms-2 acceleration.

   resistance RL.

   The characteristics of instantaneous voltage waveforms generated by Type-1 and Type-2 beams are shown in Fig. 6. They show similar characteristics. The generated voltage amplitude decays exponentially with time as predicted but not perfectly exponential because of imperfect bonding of piezoelectric layer with the support layer. It is almost zero over half of the cycle because of the longer time interval between two consecutive impacts. It can be minimized by reducing the time interval between two consecutive impacts by applying multiple impacts during a single cycle of the

   Fig. 6: Instantaneous output voltage waveforms generated by one Type-1 (bottom) and one Type-2 (top) generating beams across respective optimum load resistances at 12.5 Hz frequency under 6 ms-2 acceleration.

   TABLE II: DAMPING RATIO, Q-FACTOR AND ENERGY CONVERSION EFFICIENCY OF THE DEVICE

   Parameter	Device with………
   	Type-1 beams	Type-2 beams
   Mechanical damping ratio, m	0.013	0.018
   Total damping ratio, T	0.072	0.116
   Electrical damping ratio, e	0.059	0.098
   Mechanical Q-factor, Q	38.46	27.78
   Energy conversion efficiency,	81.9%	84.5%

   driving beam vibration. Each highest peak corresponds to an impact between the proof-mass of the driving beam tip and the generating beams. By using Fast Fourier Transform (FFT), it has been observed that the frequencies of the system's coupled vibration and free vibration of the generating beam were 119 Hz and 346 Hz, respectively for Type-1 beam and, 198 Hz and

   731 Hz, respectively for Type-2 beam. This clearly illustrates

   Fig. 8: Comparison of different output responses of the device with Type-1

   and Type-2 generating beams measured at different accelerations.

   2

   the frequency up-conversion behavior of the device even though the applied frequency was 12.5 Hz.

   In order to determine the mechanical Quality factor, Q and

   lna1 a2

   1

   4 2 [lna

   a ]2

   (8)

   energy conversion efficiency, of the proposed system, we measured the damping ratio (both mechanical and electrical) by flick test which are related as [8, 21]

   where a1 and a2 are the consecutive peak amplitudes in the plot. A number of impulse responses were recorded and an average value of the damping ratio was taken. Open circuit impulse response (without load) gives the mechanical

   Q 1 2 m

   e

   m e

   00%

   (6)

   (7)

   damping ratio m whereas load connected impulse response gives the total damping ratio T. Electrical damping ratio e was obtained as e =(T – m). Table II summarizes the values of damping ratio, Q-factor and energy conversion efficiency of the device with Type-1 and Type-2 generating beams.

   Fig. 7 shows the peak output powers delivered from one

   where m and e are the mechanical and electrical damping ratio, respectively. Flick test was done by applying a high amplitude impulse (pulse period 30ms, pulse width 500µs, and acceleration amplitude 30.3 ms-2) to the generating beams and monitoring the decay of the generated output voltage amplitude over time without and with load to the terminals. The corresponding damping ratio, then, be calculated from the decay plot using the following relationship

   Fig. 7: Measured peak output powers delivered to respective optimum load resistances of one single Type-1 and Type-2 generating beams against applied frequency under 6ms-2 accelerations.

   generating beam to the respective optimal load resistances of the device with Type-1 and Type-2 beams against operating frequencies at 6 ms-2 acceleration. A maximum peak power of

   129.15 µW was delivered by Type-1 beam at 12.5 Hz while Type-2 beam generated maximum 377.21 µW peak power at 14 Hz frequency. In case of Type-2 beam, the resonant peak shifts slightly towards higher frequency (as also seen in the frequency response curve) because increased effective stiffness of the driving beam which also introduces increased half-power bandwidth. The half-power bandwidth of the device with Type-1 beams is 5 Hz (from 9 Hz to 14 Hz) and that with Type-2 beams is 8 Hz (from 7 Hz to 15 Hz). The experimental results clearly shows that use of much rigid generating beam stoppers not only increases (2.92 times) the output power but also increases (60%) the half-power bandwidth than relatively less rigid generating beam stoppers. It is capable of generating significant power (more than 227

   µW peak power) within 89% of its operating frequency range (from 6 Hz to 15 Hz). This has made the great innovation of our proposed impact based system in low frequency energy harvesting. Besides, use of two similar generating beams increases the power density of the device.

   The output responses of the proposed device with two different sets of generating beam type were measured under various accelerations as illustrated in Fig. 8. As seen from the figure that voltage, power and half-power bandwidth increases with the increase in the acceleration for both types of beams. The impact force increases with the acceleration, resulting in increased stress on the PMN-PT surfaces which, in turn,

   increases the output voltages and powers. Moreover, the resonant peaks slightly shifts towards higher frequency in both cases as the acceleration increases (indicated by vertical texts within the columns in the bottom graph). Higher impact force results in the retardation of the driving beams' vibration amplitude and increases the effective stiffness after impact. Higher effective stiffness increases the effective resonant frequency of the driving beam, enabling the resonance to enhance over a wide interval of the applied frequency spectrum.

5. CONCLUSIONS

Enhancement of operating bandwidth along with the output power of a mechanical impact driven frequency up- converted piezoelectric energy harvester has been investigated for improving the performance at very low ambient vibration frequencies. A macroscale prototype was fabricated by assembling a flexible driving beam with a proof-mass attached at its expanded tip that impacts on two piezoelectric generating beams at the same time, placed below it at the same level, while externally excited. Two different sets of generating beams were used to compare the performance of the device.. The device with stainless steel supported generating beams showed the improved performance than those with styrene support layers. It generates 2.92 times increased output power offering 60% increased half-power bandwidth (8 Hz) which is 89% of the operating frequency band (6 Hz to 15 Hz) of the proposed device. Results indicate the potential of the proposed idea to be implemented in harvesting energy from human and machine motion. There are still rooms for improving its output performances. Future work will include more optimized design and micro fabrication using MEMS process.

ACKNOWLEDGMENTS

The authors are grateful to acknowledge the support from the research grant of Kwangwoon University in 2014, the Basic Science Research Program (2013R1A1A2A10064810) and the Pioneer Research Centre Program (2010-0019313) through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning, Korea.

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