Research Papers

Nonlinear H-Shaped Springs to Improve Efficiency of Vibration Energy Harvesters

[+] Author and Article Information
Sebastien Boisseau

e-mail: sebastien.boisseau@cea.fr

Ghislain Despesse

e-mail: ghislain.despesse@cea.fr

Bouhadjar Ahmed Seddik

Minatec Campus,
Grenoble 38000, France

Manuscript received October 10, 2012; final manuscript received February 28, 2013; accepted manuscript posted March 6, 2013; published online August 21, 2013. Assoc. Editor: Marc Geers.

J. Appl. Mech 80(6), 061013 (Aug 21, 2013) (9 pages) Paper No: JAM-12-1470; doi: 10.1115/1.4023961 History: Received October 10, 2012; Revised February 28, 2013; Accepted March 06, 2013

Vibration energy harvesting is an emerging technology aimed at turning mechanical energy from vibrations into electricity to power the microsystems of the future. Most current vibration energy harvesters (VEH) are based on a mass-spring structure: this introduces a resonance phenomenon that enables an increase of VEH output power (compared to nonresonant systems); however, the working frequency bandwidth is limited. Therefore, these devices are not able to harvest energy when ambient vibrations’ frequencies shift. To solve this problem and to increase the frequency band where power can be harvested, one solution consists in using nonlinear springs. This paper introduces H-shaped nonlinear springs, their model, and their benefits to improve VEH output powers. Simulations on real vibration sources show that the output power can be higher in nonlinear devices (up to +48%) compared to linear systems.

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Roundy, S., Wright, P. K., and Rabaey, J., 2003, “A Study of Low Level Vibrations as a Power Source for Wireless Sensor Nodes,” Comput. Commun., 26, pp. 1131–1143. [CrossRef]
Despesse, G., Jager, T., Chaillout, J. J., Léger, J. M., Vassilev, A., Basrour, S., and Charlot, B., 2005, “Fabrication and Characterization of High Damping Electrostatic Micro Devices for Vibration Energy Scavenging,” Proceedings of the DTIP, Montreux, Switzerland, June 1–3.
Anton, S. R., and Sodano, H. A., 2007, “A Review of Power Harvesting Using Piezoelectric Materials (2003–2006),” Smart Mater. Struct., 16, pp. R1–R21. [CrossRef]
Beeby, S. P., Tudor, M. J., and White, N. M., 2006, “Energy Harvesting Vibration Sources for Microsystems Applications,” Meas. Sci. Technol., 17, pp. R175–R195. [CrossRef]
Cook-Chennault, K. A., Thambi, N., and Sastry, A. M., 2008. “Powering MEMS Portable Devices—A Review of Non-Regenerative and Regenerative Power Supply Systems With Special Emphasis on Piezoelectric Energy Harvesting Systems,” Smart Mater. Struct., 17, p. 043001. [CrossRef]
Saadon, S., and Sidek, O., 2011, “A Review of Vibration-Based MEMS Piezoelectric Energy Harvesters,” Energy Convers. Manage., 52, pp. 500–504. [CrossRef]
Nguyen, S., and Halvorsen, E., 2011, “Nonlinear Springs for Bandwidth-Tolerant Vibration Energy Harvesting,” JMEMS Lett.20, pp. 1225–1227. [CrossRef]
Ahmed Seddik, B., Despesse, G., BoisseauS., and Defay, E., 2012, “Strategies for Wideband Mechanical Energy Harvester,” Small Scale Energy Harvesting, Intech, New York, Chap. 10. [CrossRef]
Tang, L., Yang, Y., and Soh, C. K., 2010, “Toward Broadband Vibration-Based Energy Harvesting,” J. Intell. Mater. Syst. Struct., 21, pp. 1867–1897. [CrossRef]
Amri, M., Basset, P., Cottone, F., Galayko, D., Najar, F., and Bourouina, T., 2011, “Novel Nonlinear Spring Design for Wideband Vibration Energy Harvesters,” Proceedings of the PowerMEMS 2011, Seoul, Korea, November 15–18.
Ando, B., Baglio, S., Trigona, C., Dumas, N., Latorre, L., and Nouet, P., 2010, “Nonlinear Mechanism in MEMS Devices for Energy Harvesting Applications,” J. Micromech. Microeng., 20, p. 125020. [CrossRef]
Cottone, F., Vocca, H., and Gammaitoni, L., 2009, “Nonlinear Energy Harvesting,” Phys. Rev. Lett., 102, p. 080601. [CrossRef] [PubMed]
Ferrari, M., Ferrari, V., Guizzetti, M., Ando, B., Baglio, S., and Trigona, C., 2009, “Improved Energy Harvesting From Wideband Vibrations by Nonlinear Piezoelectric Converters,” Proceedings of the Eurosensors’09, Lausanne, Switzerland, September 6–9, pp. 1203–1206.
Quinn, D., Triplett, A., Bergman, L., and Vakakis, A., 2011, “Comparing Linear and Essentially Nonlinear Vibration-Based Energy Harvesting,” J. Vib. Acoust., 133, p. 011001. [CrossRef]
Mann, B. P., and Owens, B. A., 2010, “Investigations of a Nonlinear Energy Harvester With a Bistable Potential Well,” J. Sound VIb., 329, pp. 1215–1226. [CrossRef]
Miki, D., Honzumi, M., Suzuki, Y., and Kasagi, N., 2010, “Large-Amplitude MEMS Electret Generator With Nonlinear Springs,” Proceedings of the IEEE 23rd International Conference on Micro Electro Mechanical Systems (MEMS’10), pp. 176–179.
Nguyen, D. S., and Halvorsen, E., 2010, “Analysis of Vibration Energy Harvesters Utilizing a Variety of Nonlinear Springs,” Proceedings of the PowerMEMS’10, Leuven, Belgium, November 30–December 3, pp. 331–334.
Stanton, S. C., and Mann, B. P., 2010, “Engaging Nonlinearity for Enhanced Vibratory Energy Harvesting,” 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Orlando, FL, April 12–15, AIAA Paper No. 2010-3067. [CrossRef]
Triplett, A., and Quinn, D., 2009, “The Effect of Nonlinear Piezoelectric Coupling on Vibration-Based Energy Harvesting,” J. Intell. Mater. Syst. Struct., 16, pp. 1959–1967. [CrossRef]
Kaajakari, K., Mattila, T., Oja, A., and Seppa, H., 2004, “Nonlinear Limits for Single-Crystal Silicon Microresonators,” J. Microelectromech. Syst., 13, pp. 715–724. [CrossRef]
Landau, L. D., and Lifshitz, E. M., 1999, Mechanics, 3rd ed, Butterworth-Heinemann, Oxford, UK.
Legtenberg, R. A., Groeneveld, W., and Elwenspoek, M., 1996, “Comb-Drive Actuators for Large Displacements,” J. Micromech. Microeng., 6, pp. 320–329. [CrossRef]
Marzencki, M., Defosseux, M., and Basrour, S., 2009, “MEMS Vibration Energy Harvesting Devices With Passive Resonance Frequency Adaptation Capability,” J. Microelectromech. Syst., 18, pp. 1444–1453. [CrossRef]
Lobontiu, N., and Garcia, E., 2005, Mechanics of Microelectromechanical Systems, Springer, New York.
Roundy, S. J., 2003, “Energy Scavenging for Wireless Sensor Nodes With a Focus on Vibration to Electricity Conversion,” Ph.D. thesis, The University of California, Berkeley, Berkeley, CA.
Reilly, E. K., Miller, L. M., Fain, R., and Wright, P., 2009, “A Study of Ambient Vibrations for Piezoelectric Energy Conversion,” Proceedings of the PowerMEMS, Washington, DC, December 1–4, pp. 312–315.
Erturk, A., and Inman, D. J., 2008, “Issues in Mathematical Modeling of Piezoelectric Energy Harvesters,” Smart Mater. Struct., 17, p. 065016. [CrossRef]
Boisseau, S., Despesse, G., and Ahmed Seddik, B., 2012, “Electrostatic Conversion for Vibration Energy Harvesting,” Small-Scale Energy Harvesting, Intech, New York.
Williams, C. B., and Yates, R. B., 1996, “Analysis of a Micro-Electric Generator for Microsystems,” Sens. Actuators, A, 52, pp. 8–11. [CrossRef]
Senturia, S. D., 2000, Microsystem Design, Springer, New York.
Duffing, G., 1918, Erzwungene Schwingungen bei Veränderlicher Eigenfrequenz, F. Vieweg u. Sohn, Braunschweig, Germany.
Wiggins, S., 1990, Application to the Dynamics of the Damped, Forced Duffing Oscillator, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York.
Holmes, P., and Rand, D., 1980, “Phase Portraits and Bifurcations of the Non-Linear Oscillator: x¨+(α+γx2)x˙+βx+δx3=0,” Int. J. Nonlinear Mech., 15, pp. 449–458. [CrossRef]
Ueda, Y., 1980, “Explosion of Strange Attractors Exhibited by Duffing’s Equation,” Nonlinear Dynamics, R. H. G.Helleman, ed., Annals of the New York Academy of Sciences, New York, pp. 422–434.
Burrow, S. G., Clare, L. R., Carella, A., and Barton, D., 2008, “Vibration Energy Harvesters With Non-Linear Compliance,” Procedings of the SPIE, Vol. 6928, Active and Passive Smart Structures and Integrated Systems. [CrossRef]


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Fig. 1

Generic model of vibration energy harvesters

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Fig. 2

Clamped-guided beam

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Fig. 3

Nonlinear effects in clamped-guided beams

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Fig. 4

Boundary conditions for FEA

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Fig. 5

Successive derivatives of FK(x) with respect to x: (a) FK, (b) FK (c) FK, (d) FK

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Fig. 6

H-shaped spring design

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Fig. 7

(a) Model of the new spring and equivalent behavior in (b) linear domain and (c) nonlinear domain

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Fig. 8

Finite element analyses results. Deformation and Von Mises stresses σ in Pa for various x and for (L, b, e, l1, l2, a) = (3 mm, 1 mm, 100 μm, 100 μm, 100 μm, 1 mm) (a) x = 50 μm, (b) x = 100 μm, (c) x = 250 μm, and (d) x = 500 μm.

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Fig. 9

Relative position (x) as a function of time (t) for nondamped oscillators

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Fig. 10

Variation of the normalized natural frequency feq/f0 of the energy harvester as a function of the normalized displacement amplitude xmax/e (f0 = 100 Hz, e = 100 μm)

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Fig. 11

Simulink model of VEH (a) linear and (b) nonlinear

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Fig. 12

(a) Relative displacement and (b) output power of a nonlinear energy harvester as a function of α (A = 1 m s−2) for e = 100 μm

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Fig. 13

Output powers of (a) a linear energy harvester and (b) a nonlinear energy harvester as a function of A (α = 1)

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Fig. 14

Vibrations on a “car engine at 3000 rpm”: (a) temporal, (b) zoom between 8 s and 8.02 s, and (c) spectrum

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Fig. 15

(a) Relative displacement and (b) zoom; (c) output power of the linear energy harvester for m = 1 g and (d) zoom

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Fig. 16

(a) Relative displacement and (b) zoom; (c) output power of the nonlinear energy harvester for m = 1 g and (d) zoom




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