A 2DOFvibrational Energy Harvester Exploiting Velocity Amplification: Modeling and Testing

  • Elisabetta BocoEmail author
  • Valeria Nico
  • Declan O’Donoghue
  • Ronan Frizzell
  • Gerard Kelly
  • Jeff Punch
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 579)


A two Degree of Freedom (2DOF) velocity-amplified electromagnetic vibrational energy harvester is presented. The device consists of two masses: a smaller mass which oscillates inside a larger one due to two sets of mechanical springs. The larger mass itself oscillates between two sets of springs. This configuration allows the larger mass to transfer momentum to the smaller mass during impact, which significantly amplifies the velocity of the smaller mass. The smaller mass is designed to disconnect from the larger mass, when input vibrations of sufficient magnitude are present. This leads to significant nonlinearities that increases the bandwidth over which the system can harvest energy. By coupling high strength magnets (placed on the larger mass) and a coil (embedded in the smaller mass), an electric current is induced in the coil through the relative motion of the two masses. This paper characterizes the nonlinear response of a 2DOF velocity-amplified electromagnetic energy harvester using a transfer function analysis. Optimization tools are then presented for designing efficient 2DOF vibration energy harvesters for use at various input frequencies and amplitudes. The first of these tools is a theoretical approach for optimizing the electromagnetic damping that is based on linear approximations. The second approach is a nonlinear model of the 2DOF system that takes into account collisions between the masses and the associated transfer of momentum. In all cases experimental results are used to validate the performance of the design tools. Finally, a performance evaluation using the volumetric Figure of Merit is presented and compared with recent literature, showing the favorable relative performance of the 2DOF system.


Energy harvesting Nonlinearity Multiple degree of freedom Electromagnetic optimization Collision modelling 



The authors acknowledge the financial support of Science Foundation Ireland under Grant No. 10/CE/I1853 and the Irish Research Council (IRC) for funding under their Enterprise Partnership Scheme (EPS). This work was financially supported by the Industrial Development Agency (IDA) Ireland.


  1. 1.
    Waters, R.L., Chisum, B., Jazo, H., Fralick, M.: Development of an electro-magnetic transducer for energy harvesting of kinetic energy and its applicability to a mems-scale device. In: Nanopower Forum 2008 (2008)Google Scholar
  2. 2.
    Cottone, F., Vocca, H., Gammaitoni, L.: Nonlinear energy harvesting. Phys. Rev. Lett. 102, 080601-1–080601-4 (2009). American Physical SocietyCrossRefGoogle Scholar
  3. 3.
    Leadenham, A., Erturk, S.: M-shaped asymmetric nonlinear oscillator for broadband vibration energy harvesting: harmonic balance analysis and experimental validation. J. Sound Vib. 333(23), 6029–6223 (2014). ElsevierCrossRefGoogle Scholar
  4. 4.
    Wu, H., Tang, L., Yang, Y., Soh, C.K.: A novel two-degree-of-freedom piezoelectric energy harvester. J. Intell. Mater. Syst. Struct. 24(3), 357–368 (2013)CrossRefGoogle Scholar
  5. 5.
    Wu, H., Tang, L., Yang, Y., Soh, C.K.: Development of a broadband nonlinear two-degree-of-freedom piezoelectric energy harvester. J. Intell. Mater. Syst. Struct. 25(14), 1875–1889 (2012). SAGECrossRefGoogle Scholar
  6. 6.
    Jang, S.J., Rustighi, E., Brennan, M.J., Lee, Y.P., Jung, H.J.: Design of a 2dof vibrational energy harvesting device. J. Intell. Mater. Syst. Struct. 22(5), 443–448 (2011). SAGECrossRefGoogle Scholar
  7. 7.
    Tang, X., Zuo, L.: Vibration energy harvesting from random force and motion excitations. Smart Mater. Struct. 21, 075025:9 (2012)Google Scholar
  8. 8.
    Cottone, F., Frizzell, R., Goyal, S., Kelly, G., Punch, J.: Enhanced vibrational energy harvester based on velocity amplification. J. Intell. Mater. Syst. Struct. 25(4), 443–451 (2014). SAGECrossRefGoogle Scholar
  9. 9.
    Nico, V., O’Donoghue, D., Frizzell, R., Kelly, G., Punch, J.: A multiple degree-of-freedom velocity-amplified vibrational energy harvester part b: Modelling. In: ASME 2014 International Conference on Smart Materials, SMASIS, September 2014Google Scholar
  10. 10.
    O’Donoghue, D., Nico, V., Frizzell, R., Kelly, G., Punch, J.: A novel velocity amplified vibrational energy harvester: experimental analysis. In: ASME 2014 International Conference on Smart Materials, SMASIS, September 2014Google Scholar
  11. 11.
    Muller, S., Massarani, P.: Transfer-function measurement with sweeps. J. Audio Eng. Soc. 49(6), 443–471 (2001). AESGoogle Scholar
  12. 12.
    Mizuno, M., Chetwynd, D.G.: Investigation of a resonance microgenerator. J. Micromech. Microeng. 13, 209–216 (2003). Institute of Physics PublishingCrossRefGoogle Scholar
  13. 13.
    Rebeiz, G.M., Regehr, W.G., Rutledge, D.B., Savage Jr, L.: Submillimeter-wave antennas on thin membranes. Int. J. Infrared Millimeter Waves 8(10), 1249–1255 (1987). SpringerCrossRefGoogle Scholar
  14. 14.
    Bouendeu, E., Greiner, A., Smith, P.J., Korvink, J.G.: Design synthesis of electromagnetic vibration-driven energy generators using a variational formulation. J. Microelectromech. Syst. 20(2), 466–475 (2011). IEEECrossRefGoogle Scholar
  15. 15.
    Poulin, G., Sarraute, E., Costa, F.: Generation of electrical energy for portable devices: Comparative study of an electromagnetic and a piezoelectric system. Sens. Actuators A Phys. 116(3), 461–471 (2004). ElsevierCrossRefGoogle Scholar
  16. 16.
    Wheeler, H.: Formulas for the skin effect. Proc. I.R.E. 30(9), 412–424 (1942)CrossRefGoogle Scholar
  17. 17.
    Wheeler, H.A.: Simple inductance formulas for radio coils. Proc. I.R.E. 16(10), 1398–1400 (1928)CrossRefGoogle Scholar
  18. 18.
    Grasselli, M., Pelinovsky, D.: Numerical Mathematics. Jones & Bartlett Learning, Burlington (2008)zbMATHGoogle Scholar
  19. 19.
    Mitcheson, P.D., Yeatmann, E.M., Rao, G.K., Holmes, A.S., Green, T.C.: Energy harvesting from human and machine motion for wireless electronic devices. Proc. IEEE 96(9), 1457–1486 (2008). IEEECrossRefGoogle Scholar
  20. 20.
    Ashraf, K., Khir, M.M., Dennis, J.O., Baharudin, Z.: Improved energy harvesting from low frequency vibrations by resonance amplification at multiple frequencies. Sens. Actuators A Phys. 195, 123–132 (2013). ElsevierCrossRefGoogle Scholar
  21. 21.
    Ashraf, K., Khir, M.M., Dennis, J.O., Baharudin, Z.: A wideband, frequency up-converting bounded vibration energy harvester for a low frequency environment. Smart Mater. Struct. 22(2), 025018 (2013). IOP PublishingCrossRefGoogle Scholar
  22. 22.
    Galchev, T.V., Cullagh, J., Peterson, R.L., Najafi, K.: Harvesting traffic-induced vibrations for structural health monitoring of bridges. J. Micromech. Microeng. 21(10), 104005 (2011). IOP PublishingCrossRefGoogle Scholar
  23. 23.
    Galchev, T., Kim, H., Najafi, K.: A parametric frequency increased power generator for scavenging low frequency ambient vibrations. Procedia Chem. 1(1), 1439–1442 (2009). ElsevierCrossRefGoogle Scholar
  24. 24.
    Renaud, M., Fiorini, P., van Schaijk, R., van Hoof, C.: Harvesting energy from the motion of human limbs: the design and analysis of an impact-based piezoelectric generator. Smart Mater. Struct. 18(3), 035001 (2009). IOP PublishingCrossRefGoogle Scholar
  25. 25.
    Beeby, S.P., Torah, R.N., Tudor, M.J., Glynne-Jones, P., O’Donnell, T., Saha, C.R., Roy, S.: A micro electromagnetic generator for vibration energy harvesting. J. Micromech. Microeng. 17(7), 1257 (2007). IOP PublishingCrossRefGoogle Scholar
  26. 26.
    Ayala, I.N., Zhu, D., Tudor, M.J., Beeby, S.P.: Autonomous tunable energy harvester. In: PowerMEMS (2009)Google Scholar
  27. 27.
    Berdy, D.F., Srisungsitthisunti, p., Xu, X., Rhoads, J., Jung, B., Peroulis, D.: Compact low frequency meandered piezoelectric energy harvester. In: PowerMEMS (2009)Google Scholar
  28. 28.
    Ching, N.N., Wong, H.Y., Li, W.J., Leong, P.H., Wen, Z.: A laser-micromachined multi-modal resonating power transducer for wireless sensing systems. Sens. Actuators A Phys. 97, 685–690 (2002). ElsevierCrossRefGoogle Scholar
  29. 29.
    Sardini, E., Serpelloni, M.: An efficient electromagnetic power harvesting device for low-frequency applications. Sens. Actuators A Phys. 172(2), 475–482 (2011). ElsevierCrossRefGoogle Scholar
  30. 30.
    Zhu, D., Beeby, S., Tudor, J., Harris, N.: Vibration energy harvesting using the halbach array. Smart Mater. Struct. 21(7), 075020 (2012). IOP PublishingCrossRefGoogle Scholar
  31. 31.
    Kulkarni, S., Koukharenko, E., Torah, R., Tudor, J., Beeby, S., O’Donnell, T., Roy, S.: Design, fabrication and test of integrated micro-scale vibration-based electromagnetic generator. Sens. Actuators A Phys. 145, 336–342 (2008). ElsevierCrossRefGoogle Scholar
  32. 32.
    Yang, B., Lee, C.: Non-resonant electromagnetic wideband energy harvesting mechanism for low frequency vibrations. Microsyst. Technol. 16, 961–966 (2010). SpringerCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Elisabetta Boco
    • 1
    Email author
  • Valeria Nico
    • 1
  • Declan O’Donoghue
    • 1
  • Ronan Frizzell
    • 2
  • Gerard Kelly
    • 2
  • Jeff Punch
    • 1
  1. 1.Stokes InstituteUniversity of LimerickLimerickIreland
  2. 2.Efficient Energy Transfer (ηET) DepartmentBell Labs, Alcatel-LucentDublinIreland

Personalised recommendations