Theoretical modeling and experimental validation of a torsional piezoelectric vibration energy harvesting system

Vibration energy harvesting has been extensively studied in recent years to explore a continuous power source for sensor networks and low-power electronics. Torsional vibration widely exists in mechanical engineering; however, it has not yet been well exploited for energy harvesting. This paper presents a theoretical model and an experimental validation of a torsional vibration energy harvesting system comprised of a shaft and a shear mode piezoelectric transducer. The piezoelectric transducer position on the surface of the shaft is parameterized by two variables that are optimized to obtain the maximum power output. The piezoelectric transducer can work in d ₁₅ mode (pure shear mode), coupled mode of d ₃₁ and d ₃₃, and coupled mode of d ₃₃, d ₃₁ and d ₁₅, respectively, when attached at different angles. Approximate expressions of voltage and power are derived from the theoretical model, which gave predictions in good agreement with analytical solutions. Physical interpretations on the implicit relationship between the power output and the position parameters of the piezoelectric transducer is given based on the derived approximate expression. The optimal position and angle of the piezoelectric transducer is determined, in which case, the transducer works in the coupled mode of d ₁₅, d ₃₁ and d ₃₃.