Title: Frequency tuning design for vibration‐driven electromagnetic energy harvester
Abstract: IET Renewable Power GenerationVolume 9, Issue 7 p. 801-808 Research ArticlesFree Access Frequency tuning design for vibration-driven electromagnetic energy harvester Correction(s) for this article Erratum: Frequency tuning design for vibration-driven electromagnetic energy harvester Volume 9Issue 5IET Renewable Power Generation pages: 539-539 First Published online: July 1, 2015 Byung-Chul Lee, Byung-Chul Lee School of Electrical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan, 680-749 Republic of South KoreaSearch for more papers by this authorGwiy-Sang Chung, Corresponding Author Gwiy-Sang Chung [email protected] School of Electrical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan, 680-749 Republic of South KoreaSearch for more papers by this author Byung-Chul Lee, Byung-Chul Lee School of Electrical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan, 680-749 Republic of South KoreaSearch for more papers by this authorGwiy-Sang Chung, Corresponding Author Gwiy-Sang Chung [email protected] School of Electrical Engineering, University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan, 680-749 Republic of South KoreaSearch for more papers by this author First published: 01 September 2015 https://doi.org/10.1049/iet-rpg.2014.0195Citations: 11AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The common resonant-based vibration energy harvester effectively converts mechanical vibration to electrical power when an ambient excitation frequency matches the specific resonant frequency of the device. The resonant frequencies of energy harvesters are generally fixed during the design process and cannot be changed after fabrication. Therefore frequency tuning technology that allows for operation in a wide frequency range is desirable for a vibration energy harvester. In this study, the authors proposed a novel frequency tuning design of vibration-driven energy harvester, which used electromagnetic conversion. The proposed frequency tuning method uses a rotatable spring in order to adjust the spring constant. Through this tuning method, the resonant frequency of the harvester can be manipulated simply by rotating the spring. The proposed tuning-based energy harvester has been successfully tuned to have a resonant frequency from 23 to 32 Hz. These test results agree with the ANSYS analysis presented. The experimental results demonstrated that the proposed energy harvester can generate a maximum power output of 60 μW with an acceleration of 0.5 g (1 g = 9.81 m/s2). When the proposed harvester was attached to an automobile engine, a maximum open-circuit voltage of 1.78 Vpp was produced at 700 RPM. 1 Introduction Batteries have consistently been used as power supplies for most portable electronics and sensor network devices. However, batteries do have some problems, including a limited lifetime, difficulty of replacement and potential for environmental pollution. To overcome these issues, energy harvesting from ambient sources has become a popular research topic, with the advantages of such technology, including having a semi-permanent lifetime and having a clean generation process. In energy harvesting techniques, electricity can be generated by converting energy from various environmental sources, including solar, wind, thermal, wave, biochemical, radio frequency, vibrations, magnetic fields and others. Of these sources, vibration is an attractive power source for harvesting energy because of its unlimited operating time and the suitability of the generator size for portable applications. With such devices, mechanical oscillations can be converted to electricity using electrostatic, piezoelectric and electromagnetic conversions. Vibration-driven energy harvesters convert energy most effectively when the ambient frequency closely matches the resonant frequency of the device. However, the power output decreases significantly when there is a frequency mismatch of only a few per cent. This phenomenon suggests a need for a harvester design with a resonant frequency that can be adjusted or tuned to match the ambient (driving) vibration across a range of frequencies [1]. The frequencies of ambient vibration sources are time dependent, but the resonant frequency of a device is fixed and has a narrow operating range. To match the ambient frequency, the operating range has to be widened or the resonant frequency has to be tuned. The most commonly used and effective methods to improve the power efficiency are as follows. The first solution is a wideband operation method which is divided into coupled [2] or un-coupled [3] arrays of the harvester, with each one working in different frequencies. It can expand the bandwidth of the generator. Some drawbacks of this method are that it comes with a lower Q-factor and reduced power density. A larger generator can compensate for lower Q-factor shortcoming, but it is not always a practical solution. On the contrary, the assembled generator has a wide operational frequency range without any decrease in Q-factor, but power density can be reduced. The second solution is a tuning method that is used to tune the resonant frequency of the generator. A tunable generator is able to match the resonant frequency with ambient vibration. Thus, the maximum power can be generated at various frequencies without reducing the Q-factor, achieving a high efficiency per unit volume. This is a superior approach for improving the working frequency range of a vibration-based generator [4]. Attempts to tune the resonant frequency of the generators have been reported in the literature. Zhu et al. [4] presented tunable electromagnetic vibration-based micro-generator by an axial tensile force using additional magnet. The resonant frequency has been successfully tuned from 67.6 to 98 Hz when various axial tensile forces were applied to the structure. Inclusion of additional magnet increased the total volume of the device. Hence, the power density of magnetic force-based tunable energy harvester reduced inevitably. Morris et al. [5] used a tensile axial load for frequency tuning and introduced a mechanism for a tunable frequency where the deformation of the piezoelectric elements was primarily an in-plane extension. Preloading screw adjusts each piezoelectric membrane to shorten and lengthen. This tuning mechanism wildly applies to energy harvesting fields, but only in flexible materials such as polyvinylidene fluoride. Eichhorn et al. developed a tunable piezoelectric energy converter in which the resonant frequency could be tuned by applying mechanical stress to its structure. This tuning mechanism is similar with Leland and Wright [1]. Adjustable screw applies compressive force to the tip of cantilever beam and tensile loads that can be applied in a similar way. An apprehensive point is that the continuous compressive and tensile force can occur a change in spring constant [6]. Peters et al. [7] described a novel, electrically tunable structure that was used as a resonator for vibration-based energy harvesters. Adjustment of the resonant frequency was provided via mechanical stiffening of the structure using piezoelectric actuators. Additional electrical energy was required to supply mechanical stiffening of the structure using piezoelectric actuators. Huang and Lin [8] developed a lead zirconate titanate (PZT)-based self-tuning energy harvester. They used a movable intermediate rigid support which is attached to a beam and can be adjusted to the support's position according to the sensed ambient frequency. Niri et al. introduced a vibration-based piezoelectric energy harvester that was capable of passively tuning itself. This tuning mechanism is similar with Morris et al. [5] and Eichhorn et al. [6]. Adjustable additional stiffness and axial load can change the resonant frequency of the device. However, two oblique springs can hamper the motion of proof mass that can reduce the maximum displacement of the device [9]. Zhu et al. [10] described electrically tunable electromagnetic energy harvesters. Electrical tuning relies on the adjustment of the electrical load. Additionally, the material of the magnets and the magnetic flux guide should be carefully selected. Finally, Aboulfotoh et al. [11] developed a self-tuning resonator for vibration energy harvester. It was designed to automatically adjust its own natural frequency to match the imposed base excitation. Their proposed device consumed more power for tuning than producing. This paper introduces a novel frequency tuning design that uses a rotatable spring. Flame resistant (FR)-4 material (Hatipoglu and Urey [12]) was used in the spring. The proposed tuning method can simply adjust the resonant frequency of the device by rotating the spring. If the resonant frequency of the device does not match the ambient frequency, the position of the spring is changed. The spring position has a relation to the deformed spring length, and therefore the spring constant can be tuned. In addition, the tuning range can be controlled by changing the spring material and design. The proposed energy harvester is excited by external vibrations ranging from 15 to 50 Hz, and the output signals were measured with respect to the frequencies at which the fabricated devices were excited. The effects of the magnetic pole direction, input frequency, acceleration and load resistance were investigated using the ANSYS finite element method. 2 Tunable energy harvester 2.1 Theoretical analysis The spring constants are defined according to the force required to produce a unit deformation in a linear structure. A number of authoritative publications are available with respect to the design and analysis of various types of springs. These include helical springs undergoing tension or compression, torsion springs, leaf springs, flat springs, conical springs, spiral springs etc. Different methods are given in the literature in order to design different types of springs for the required force deflection response by determining the work stress level and the energy storage [13]. The equations for the spring constant can be applied to conical springs if the spring is treated as a series of cylindrical springs. Equation (1) determines the spring constants (k) of circular-type beam springs (1)where P represents the load; δ represents the defection; G represents the shear modulus; d represents the beam diameter; D represents the spring diameter; and na represents the number of active spring beam turns. Equation (2) determines the spring constants (k) of a rectangular-type beam spring (2)where b represents the width; t represents the thickness; and K2 represents the correction factor based on the ratio b/t. The spring constant of a planar spiral spring is found by combining these individual rates, according to the series in (3) (3)where k1, k2, k3, …, kn are found using (1) or (2) [14, 15]. When the spring position changed from 1 to 6, the effective spring beam length was continuously decreased. The spring beam length has a direct effect on spring diameter (D) and the number of active spring beam turns (na). The decreased spring diameter and turns result in the spring constant (k) increment. Therefore the resonant frequency of the device can be simply changed by spring beam length. Equations (1)–(3) indicate that the spring constant is a function of the design and the material properties. The spring constant and mass are the main factors that determine the resonant frequency of the device [16]. 2.2 Design of the tunable energy harvester Fig. 1 shows the design of the proposed tunable energy harvester. The harvester is composed of a rotatable spring, stopper, magnets, coil, housing and jig. The spring is located on the stopper, along with magnets. One design consideration of the mechanical resonating spring is the need for it to resonate with high amplitude at a low input vibration. The spring geometry should include a long ‘spiral’ structure to reduce the fatigue and to increase life [17]. For this reason, we designed a two-branch-type planar spiral structure that has a lower spring constant and a higher stability under motion than those that have one or three branches. Total four permanent magnets were used for the spring mass system. At the top position, two small magnets (Φ 2 × 2 mm2) were used for connecting between spring and proof mass using attractive force. Another two magnets were designed in a multipole structure in the centre, which improves the power efficiency with a concentrated magnetic flux density [18, 19]. Table 1 presents detailed design parameters of the proposed energy harvester, including material, diameter, thickness, weight and volume. Table 1. Design parameters of the proposed energy harvester Components Parameters Values spring material FR-4 diameter 17 mm (inner), 33 mm (outer) thickness 0.2 mm beam width 1 mm beam distance 1 mm weight 0.54 g stopper material stainless steel diameter 17 mm (inner), 34 mm (outer) thickness 0.5 mm weight 2.76 g magnet material NdFeB* grade N30 volume Φ 2 × 2 mm2 (2 at top) Φ 12 × 3 mm2 (2 at centre) weight 6.89 g coil material copper outer diameter 26 mm inner diameter 20 mm thickness 12 turns 1000 (approximately) resistance 421 Ω proof mass components defected spring + magnet + bolt + nuts weight 12 g (approximately) housing material teflon jig material teflon generator volume Φ 40 × 50 mm2 weight 85 g *neodymium iron boron Fig. 1Open in figure viewerPowerPoint Design of the proposed tunable energy harvester The proposed tunable device can obtain different resonant behaviours by changing the spring constant, and the adjustment of the spring position with the stopper configures a different deflected spring position where positions 1–6 are, respectively, identified as L1–L6, as shown in Fig. 2. The deflected spring is changed from a spring position and is expressed in red colour, and the maximum deflected spring length is obtained when the spring is set to L1. Fig. 2Open in figure viewerPowerPoint Deflected spring position with rotation a–f Deflected spring lengths L1–L6, respectively 2.3 Analysis of the spring mass system Fig. 3 shows the effect of various materials on harvester resonant frequencies for the proposed design. The spring mass system has same dimension and simulated by ANSYS modal analysis with three material properties (Young's modulus, Poisson's ratio and density). The desired resonant frequency of the device should be considered when choosing the spring material. For example, in the electromagnetic energy harvester, the magnet is an essential component. Therefore magnetic materials (steel, nickel etc.) cannot be used for spring because of the magnetic attractive force between spring and magnet. This phenomenon will hamper the motion of magnet. Additionally, material flexibility, fabrication process, durability, application field and the cost should also be considered. Among of various spring materials, the FR-4 is suitable for our proposed device. The FR-4 is composed of a woven fiberglass cloth with an FR epoxy resin binder, and the spring mass system made with the FR-4 has the lowest resonant frequencies at each resonant mode as a result of the specific mechanical properties of the material (Table 2) [20]. Table 2. Material properties for the spring Materials Young's modulus, GPa Poisson's ratio Density, g cm−3 silicon 130–188 0.064–0.28 2.33 aluminium 70 0.35 2.7 titanium 116 0.32 4.51 copper 110–128 0.34 8.94 FR-4 15–20 0.12–0.14 1.85 Fig. 3Open in figure viewerPowerPoint Effect of various materials on harvester resonant frequencies for the proposed design Fig. 4 shows the meshed model and modal analysis results of the proposed spring mass system. The meshed model along with the boundary conditions is shown in Fig. 4a. The outside of the spring beam was fixed by displacement limit. In the spring mass system, permanent magnets and screws were used as a proof mass, and the first two modes (Figs. 4b and c) were torsional motion with frequencies of 6.8 and 7.3 Hz, respectively. The vertical deflection (z-axis) is shown in the third resonant mode at 24.5 Hz. In the voltage induction, the maximum output was found at crossing motion between magnet and coil. At the first and second resonant modes, flux linkage was induced very weakly in the coil. However, at the third resonant mode, the spring showed the maximum deflection with connected magnet, and it induced maximum flux linkage in the coil. Fig. 4Open in figure viewerPowerPoint Meshed model and modal analysis results of the proposed spring mass system a Meshed model b First mode c Second mode d Third mode Fig. 5 shows the harmonic analysis of the spring mass system with spring positions. The displacement of the spring mass system strongly depends on the external vibration frequency. The displacements were dropped rapidly above and below the each resonant frequency. The harmonic analysis was carried out within the frequency range between 15 and 50 Hz. The calculated damping ratio was 0.022, and the maximum displacement was ∼4.78 mm at spring position 1. Each spring position showed different maximum displacements and resonant frequencies. The maximum displacement decreased with the increment of resonant frequency for each spring position (1–6). Fig. 5Open in figure viewerPowerPoint Harmonic analysis of the spring mass system Fig. 6 shows the magnetostatic analysis of the spring mass system. The magnetic density is shown in Figs. 6a and b with N-S : N-S and N-S : S-N magnet arrangements, respectively. The magnets used were cylindrical and ring-type permanent magnets arranged with magnetisations along the vertical axis. In addition, the centre magnet inside the housing was wrapped with copper wire. The N-S : S-N magnet arrangement concentrates higher effective magnetic flux density than the N-S : N-S in the centre, as a result of the repulsive magnetism. The maximum magnetic flux density was 1.2 T, and the large range of the effective magnetic flux density was shown in N-S : N-S magnet arrangement. Fig. 6Open in figure viewerPowerPoint Magnetostatic analysis of the spring mass system a N-S : N-S magnet arrangement b N-S : S-N magnet arrangement 2.4 Fabrication of the tunable energy harvester Fig. 7 shows (a) the fabricated planar spiral FR-4 spring and stopper, (b) spring mass system, (c) assembled spring mass system with a stainless steel stopper, (d) wound copper coil and (e) the complete tunable energy harvester. The planar spiral FR-4 spring is fabricated via a desktop computer numerical control three-dimensional modelling machine, with detailed information shown in Table 1. The spring mass system consists of NdFeB multipole magnets (N 30; Br = 1.08–1.12 T), a planar spiral FR-4 spring and stainless steel bolt and nuts. The assembled spring mass system is placed over the stopper, which is fixed in the cylindrical Teflon housing. Enamelled copper wire with a diameter of 0.1 mm is used for the coil and is wrapped around the Teflon housing, forming the primary element for magnetic induction with the magnet. The tunable energy harvester has a diameter of 40 mm, a height of 50 mm and a weight of 85 g. Fig. 7Open in figure viewerPowerPoint Fabricated a FR-4 spring and stopper b Spring mass system c Assembled spring mass system with stopper d Copper coil e Energy harvester 3 Results and discussion Fig. 8 shows the experimental setup used to test the proposed energy harvester. A Bru˝el & Kjaer vibration generator is used to supply mechanical vibrations to the energy harvester, and an amplifier (LDS PA25E-CE) incorporated with a controller (LAS-200, SCO-02P) is used to drive the shaker. The proposed energy harvester is glued to the top of the vibrator (LDS-V201-M4) with an IEPE accelerometer (8341 model) attached to the vibrator in order to measure the input acceleration. A LeCroy oscilloscope (WaveAce 214) is connected to the energy harvester coils to measure the induced output voltage along with the frequencies, acceleration and load resistances. The performance of the generator is measured using a sine wave signal and a frequency sweeping process with a specific acceleration [20]. Fig. 8Open in figure viewerPowerPoint Experimental setup for testing Fig. 9 shows the waveforms of the open-circuit output voltages with the N-S : N-S and N-S : S-N magnet arrangements at a resonant frequency of 23 Hz and acceleration of 0.5 g with spring L1. For the N-S : N-S magnet arrangement, the maximum open-circuit output voltage was found to be 440 mVrms. The N-S : S-N magnet arrangement shows a maximum open-circuit output voltage of 1.12 Vrms when the wave frequency is half that of the N-S : N-S arrangement. It shows that N-S : S-N has a higher amplitude as a result of the higher concentration of magnetic flux in the centre. This result demonstrates that the N-S : S-N magnet arrangement can improve the efficiency of the power output. Fig. 9Open in figure viewerPowerPoint Waveforms of open-circuit output voltages with the N-S : S-N and N-S : S-N magnet arrangements The open-circuit output voltage of the tunable energy harvester with various input frequency is shown in Fig. 10. In the experiment, the vibration equipment has a 5 s sweep time from 15 to 50 Hz. The proposed harvester has different resonant frequencies and output voltages associated with spring positions L1–L6, as shown in Fig. 10a. The maximum open-circuit output voltage and quality factor are 1.12 Vrms and 11.2, respectively, at L1, with an input frequency of 23 Hz and acceleration of 0.5 g. The harvester starts to resonate at 21 Hz, and the output voltage of the harvester increases rapidly afterwards. Finally, the tunable energy harvester with L1 jumps down at 24 Hz and becomes quiet. The other spring positions (2–6) also show similar results with different start- and jump-down frequencies. Total frequency sweep time is for 180 s. However, there was no specific information over 150 s. When the frequency sweep, acceleration level can be automatically changed by accelerometer. Therefore the constant acceleration can maintain during the frequency sweep. Fig. 10Open in figure viewerPowerPoint Open-circuit output voltage with various input frequencies a Waveforms b Measured values The proposed prototype was successfully tuned between 23 and 32 Hz. As shown in Fig. 10b, the induced output voltage depends strongly on the external vibration frequency. The resonant frequencies of the different spring positions slowly switched to higher frequencies. The maximum output voltage occurs at each resonant frequency, and decreases significantly when the vibration deviates from this frequency range. The displacement is also strongly influenced by the frequency and the acceleration at low frequencies. Fig. 11 shows the open-circuit output voltage with various input accelerations. The induced output voltages increased with acceleration increasement. A higher acceleration led to a higher displacement at the same frequency (23 Hz), and as a result, when the acceleration of the vibrator increased, the proposed energy harvester generated a higher output voltage, displaying a linear relationship. However, the maximum displacement of the spring is limited because of fatigue failure. Therefore the output voltage and enhancement rate are slowly saturated when over a specific acceleration level [21]. Fig. 11Open in figure viewerPowerPoint Open-circuit output voltage with various input accelerations Fig. 12 shows the output voltage and power of the proposed energy harvester with various load resistances. The bridge rectifiers with Schottky diodes are used here to convert AC into DC. The prototype of the rectifier circuit consists of four HITACHI HRP 22 Schottky barrier diodes and a 1000 μF SAMWAH SG capacitor to remove the ripple. During testing, the output voltage increased in conjunction with the load resistance, and if the load resistance value can be adaptively changed to match the source impedance, high-power extraction efficiency can be achieved at the resonant frequency [22]. The resulting power () is plotted in Fig. 12 where it can be seen that the output power of the generator reached its maximum value and then decreased slowly. The proposed energy harvester shows a maximum output power of 60.3 μW at a voltage of 320 mVDC when the load resistance is ∼1.3 kΩ. Fig. 12Open in figure viewerPowerPoint Output voltage and power with various load resistances Fig. 13 indicates the fast Fourier transform (FFT) results and output voltages with respect to different spring positions on an automobile engine. To confirm the applicability of the power supply system to harvest energy from environmental vibration, the proposed tunable energy harvester is tested while attached to a stationary automobile (SsangYong Motor's Rexton-II) with the engine running (Table 3). The real-world test showed an output voltage of 1.78 Vpp AC at L6 with the engine running at 700 RPM. The output voltages increased with spring tuning. FFT results showed that the majority of the excitation happens around 32–35 Hz range, and agreement with the experiment results in Fig. 13b. Unfortunately, the resonant frequency of the engine was slightly higher than the expected frequency of 32 Hz. Table 3. Overview of the previous reported tunable energy harvesters References Conversion method Tuning mechanism Frequency range, Hz [4] electromagnetic magnetic force 67–98 [5] piezoelectric adjustable preloading 80–235 [6] piezoelectric compressive and tensile force 292–380 [7] electromagnetic mechanical stiffening 65–89 [8] piezoelectric movable support 85–149 [9] piezoelectric adjustable loading 6–61 [10] electromagnetic electrical load 90.5–95.5 [11] electromagnetic magnetic force 4.7–9 this work electromagnetic spring rotating 23–32 Fig. 13Open in figure viewerPowerPoint Frequency analysis and application of automobile engine a FFT results b Output voltage with spring positions The previously reported work used an additional magnet or a mechanical force to tune the frequency, whereas the suggested design uses a rotation of the spring. The proposed energy harvester can use this method to tune the resonant frequency from 23 to 32 Hz. The output power can be reduced by changing of spring position, as shown in Table 4. L1 produced the highest output power of 60.3 μW (at 23 Hz) and L6 produced an output power of 41.4 μW (32 Hz) with same acceleration level (0.5 g). The maximum power reduction was ∼18.9 μW. Additionally, half power bandwidth and qualify factor results included. Table 4. Resonant frequency and output power of the proposed energy harvester with spring positions Spring positions Resonant frequency, Hz Output power, μW Half power bandwidth, Hz (qualify factor) 1 (L1) 23 60.3 2.15 (11.2) 2 (L2) 24 56.5 1.35 (17.7) 3 (L3) 25 51.6 2.57 (9.72) 4 (L4) 27 48.9 2.32 (11.6) 5 (L5) 29 46.8 1.75 (16.5) 6 (L6) 32 41.4 2.48 (12.9) 4 Conclusions Vibration energy harvesting is an attractive technique with potential as a power supply for low-power devices. A key characteristic of a vibration energy harvesting device is the resonant frequency at which it operates. The resonant frequency of the proposed device can be adjusted before or during operation, and the proposed tuning method is a novel approach that allows for simple manipulation. As the spring rotated from L1 to L6, the deformed length of the spring could be shortened, and as a consequence, the spring constant values of the device changed. The experimental results also clearly showed that the proposed energy harvester could tune its resonant frequency within a range from 23 to 32 Hz, and that it was able to produce 41.4–60.3 μW of power over that range when excited at a constant acceleration level of 0.5 g. In addition, we installed the proposed device on an automobile engine and generated a maximum open-circuit voltage of 1.78 V. The proposed tuning design may have potential applications in self-powered devices where an auto-tuning capability is desired. A feedback loop could control the spring position, and hence the resonant frequency of the device, by altering the deformed spring length to optimise the amount of energy generated. If the energy supply required to adjust the spring position and to monitor the frequency is higher than the total amount of energy that can be produced by the device, then the tuning system would not be efficient. However, the development of a control and monitoring systems for the auto-tunable energy harvester is beyond the scope of this paper, and is therefore the subject of future work of our group. 5 References 1Leland, E.S., Wright, P.K.: ‘Resonance tuning of piezoelectric vibration energy scavenging generators using compressive axial preload’, Smart Mater. Struct., 2006, 15, pp. 1413– 1420 (doi: https://doi.org/10.1088/0964-1726/15/5/030) 2Sari, I., Balkan, T., Kulah, H.: ‘An electromagnetic micro power generator for wideband environmental vibrations’, Sens. Actuators A, 2008, 145–146, pp. 405– 413 (doi: https://doi.org/10.1016/j.sna.2007.11.021) 3Foisal, A.R.M., Hong, C., Chung, G.S.: ‘Multi-frequency electromagnetic energy harvester using a magnetic spring cantilever’, Sens. Actuators A, 2011, 182, pp. 106– 113 (doi: https://doi.org/10.1016/j.sna.2012.05.009) 4Zhu, D., Robertsb, S., Tudora, M.J., Beeby, S.P.: ‘Design and experimental characterization of a tunable vibration-based electromagnetic micro-generator’, Sens. Actuators A, 2010, 158, pp. 284– 293 (doi: https://doi.org/10.1016/j.sna.2010.01.002) 5Morris, D.J., Youngsman, J.M., Anderson, M.J., Bahr, D.F.: ‘A resonant frequency tunable, extensional mode piezoelectric vibration harvesting mechanism’, Smart Mater. Struct., 2008, 17, p. 65021 (doi: https://doi.org/10.1088/0964-1726/17/6/065021) 6Eichhorn, C., Goldschmidtboeing, F., Woias, P.: ‘Bidirectional frequency tuning of a piezoelectric energy converter based on a cantilever beam’, J. Micromech. Microeng., 2009, 19, p. 94006 (doi: https://doi.org/10.1088/0960-1317/19/9/094006) 7Peters, C., Maurath, D., Schock, W., Mezger, F., Manoli, Y.: ‘A closed-loop wide-range tunable mechanical resonator for energy harvesting systems’, J. Micromech. Microeng., 2009, 19, p. 94004 (doi: https://doi.org/10.1088/0960-1317/19/9/094004) 8Huang, S.C., Lin, K.A.: ‘A novel design of a map-tuning piezoelectric vibration energy harvester’, Smart Mater. Struct., 2012, 21, p. 85014 (doi: https://doi.org/10.1088/0964-1726/21/8/085014) 9Niri, E.D., Salamone, S.: ‘A passively tunable mechanism for a dual bimorph energy harvester with variable tip stiffness and axial load’, Smart Mater. Struct., 2012, 21, p. 125025 (doi: https://doi.org/10.1088/0964-1726/21/12/125025) 10Zhu, D., Roberts, S., Mouille, T., Tudor, M.J., Beeby, S.P.: ‘General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters’, Smart Mater. Struct., 2012, 21, p. 105039 (doi: https://doi.org/10.1088/0964-1726/21/10/105039) 11Aboulfotoh, N.A., Arafa, M.H., Megahed, S.M.: ‘A self-tuning resonator for vibration energy harvesting’, Sens. Actuators A, 2013, 201, pp. 328– 334 (doi: https://doi.org/10.1016/j.sna.2013.07.030) 12Hatipoglu, G., Urey, H.: ‘FR-4 based electromagnetic energy harvester for wireless sensor nodes’, Smart Mater. Struct., 2010, 19, pp. 15022– 15032 (doi: https://doi.org/10.1088/0964-1726/19/1/015022) 13Roser, S.: ‘ Analysis of a planar spiral displacer spring for use in free-piston sterling engines’. MSc dissertation, College of Engineering and Technology, Ohio University, USA, 1991 14Joseph, E.S., Charles, R.M.: ‘ Standard handbook of machine design’ ( McGraw-Hill, 1986) 15Wu, M.H., Hsu, W.Y.: ‘Modelling the static and dynamic behavior of a conical spring by considering the coil close and damping effects’, J. Sound Vib., 1998, 214, pp. 17– 28 (doi: https://doi.org/10.1006/jsvi.1997.1511) 16Robert, D.B.: ‘ Formulas for natural frequency and mode shape’ ( Krieger Publishing Company, Malabar, FL, 2001) 17Ching, N.N.H., Wong, H.Y., Li, W.J., Leong, P.H.W., Wen, Z.: ‘A laser micro-machined multi-modal resonating power transducer for wireless sensing systems’, Sens. Actuators A, 2002, 97–98, pp. 685– 690 (doi: https://doi.org/10.1016/S0924-4247(02)00033-X) 18Sara, C.R., O'Donnell, T., Wang, N., McCloskey, P.: ‘Electromagnetic generator for harvesting energy from human motion’, Sens. Actuators A, 2008, 147, pp. 248– 253 (doi: https://doi.org/10.1016/j.sna.2008.03.008) 19Munaz, A., Lee, B.C., Chung, G.S.: ‘A study of an electromagnetic energy harvester using multi-pole magnet’, Sens. Actuators A, 2013, 201, pp. 134– 140 (doi: https://doi.org/10.1016/j.sna.2013.07.003) 20Lee, B.C., Rahman, M.A., Hyun, S.H., Chung, G.S.: ‘Low frequency driven electromagnetic energy harvester for self-powered system’, Smart Mater. Struct., 2012, 21, p. 125024 (doi: https://doi.org/10.1088/0964-1726/21/12/125024) 21Kim, H., Tadesse, Y., Priya, S.: ‘ Piezoelectric energy harvesting’ Energy Harvesting Technologies, 2009, 1, pp. 3– 39 22Kong, N., Ha, D.S., Erturk, A., Inman, D.: ‘Resistive impedance matching circuit for piezoelectric energy harvesting’, J. Intell. Mater. Syst. Struct., 2010, 21, pp. 1293– 1302 (doi: https://doi.org/10.1177/1045389X09357971) Citing Literature Volume9, Issue7September 2015Pages 801-808 FiguresReferencesRelatedInformation
Publication Year: 2015
Publication Date: 2015-04-22
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 15
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot