Improving the off-resonance energy harvesting performance using dynamic magnetic preloading

Piezoelectric stack transducers in d₃₃ mode have a much higher mechanical-to-electric energy conversion efficiency compared with d₃₁ mode piezoelectric harvesters. However, multilayered piezoelectric stacks usually operate in off-resonance due to the higher stiffness and thereby have a lower power output under low-frequency excitations. This paper proposes to apply the dynamic magnetic pre-loading to a piezoelectric stack transducer to significantly increase the power output. The energy harvesting system consists of a multilayered piezoelectric stack with a compliant force amplification frame, a proof mass, and two magnets configured in attraction. The static force–displacement relationship of the magnets is identified from experiments and extended to a dynamic model capable of characterizing the dynamic magnetic interaction. An electromechanical model is developed based on the theoretical derivation and the experimentally identified parameters to predict the voltage outputs under different resistive loads. Approximate analytical solutions are derived by using the harmonic balance method and show good agreements with the numerical and experimental results. The performance of the system is examined and compared with that of the harvester without magnetic pre-loading. The influences of the distance between the two magnets and the electrical resistive loads on the power output are investigated. Results indicate the energy harvesting system with magnetic pre-loading can produce over thousand times more power than the system without magnetic pre-loading at the base excitation of 3 Hz and 0.5 m/s², far below the resonance at 243 Hz.