An integrated design approach of piezoelectric vibration energy harvesters

Due to its multidisciplinary nature, the power behavior of a piezoelectric vibration energy harvester depends on system properties in multiple domains such as material, mechanical and electrical. This paper presents a dimensionless maximum power equation that integrates these effects into a simple model, which serves as a convenience tool for the design and analysis of piezoelectric vibration energy harvesters. The model is given as a closed-form relationship between the dimensionless maximum power (maximum power normalized by the power limit) and the normalized electromechanical coupling coefficient with respect to the critical coupling coefficient, which is the minimum coupling to reach the power limit of a system. In addition, this integrated design equation can be applied to different energy harvesting interface circuit types such as resistive and standard AC-DC with a simple change of the critical coupling expression in the equation. The application of this equation is illustrated by a detailed design example of a bimorph beam harvester for fixed target natural frequency and length given a base motion excitation. It is found that under the same level of excitation, there is an optimal PZT thickness for maximum power. In addition, overall, it is beneficial to make the system of low damping to yield a larger structural response and more power. However, this also leads to a higher bending stress, which is an important design consideration due to the relatively brittle nature of PZT materials.