Probability-of-existence of vibro-impact regimes in a nonlinear vibration energy harvester

Abstract

This paper reports on the characterization of high-energy vibro-impacting regimes in a vibration energy harvester with softening Duffing nonlinearity, by mathematical modelling and numerical analysis with experimental validation. The harvester is implemented as a base excited permanent-magnet/ball-bearing arrangement, where oscillations by the ball-bearing induce a change in magnetic flux in a wire coil, which in turn generates a voltage. Symmetric rigid aluminum stops in the harvester structure restrain the amplitude of the ball-bearing motion (within gap Δ) and thus produce vibro-impact behaviour under certain operating conditions—leading to wideband operation. These operating conditions are analysed by means of an event-driven equation switching algorithm, implementing a base-driven Duffing oscillator with conditional hyster–Hertz impact mechanics. In considering the ‘probability-of-existence’ of impact regimes, predictions about the frequency bandwidth of the high-energy impact state are made and compared to the experimental prototype. A trade-off between operating bandwidth and output power is noted. For the non-optimized harvester arrangement examined in this paper, with a gap Δ = 14.7 mm the bandwidth was predicted to be ∼1.3 Hz, and was measured at 0.7 Hz with an output power of 7.4 mW rms. With a gap size Δ = 2.9 mm the bandwidth was predicted to be ∼7.2 Hz, and was measured at 6.1 Hz with an output power of 54 μW rms. The authors believe that the probability-of-existence approach may be useful for characterizing the conditions required for exciting high-energy states of other nonlinear vibration energy harvesting systems.