振动式压电发电机的理论模型与实验

Mathematical Model and Experiment of Vibration-Based Piezoelectric Generator

为了预测振动式压电发电机的谐振频率和输出功率等参数,Roundy等以悬臂梁末端挠度为自由度,建立了发电机的理论模型,但该模型忽略了质量块中心挠度与悬臂梁末端挠度的差异,在质量块长度较大时有较大误差.为了扩大适用范围,在考虑质量块中心挠度与悬臂梁末端挠度的差异基础上,分别将发电机结构简化为单自由度和二自由度系统,建立了悬臂梁式压电发电机的两个理论模型,其中的单自由度模型以质量块质心挠度为自由度,二自由度模型同时以质量块质心挠度和质量块转角为自由度.为了对模型进行验证,制作了压电发电机并进行了实验.实验结果表明,这两个新模型比Roundy模型的精度更高.

To predict the resonant frequency and output power of a vibration-based piezoelectric generator, Roundy et al established the model of the cantilever piezoelectric generator by using the deflection at the end of the cantilever as the degree of freedom. But this model will cause large errors when the length of the proof mass is large because it neglects the difference between the deflection at the center of the proof mass and that at the end of the cantilever. To extend the applicable range, two models of the cantilever piezoelectric generator were established in this paper by simplifying the generator as a single-degree-of-freedom system and two-degree-of- freedom system respectively, where the difference between the deflection at the center of the proof mass and that at the .end of the cantilever was considered. The degree of the single-degree-of-freedom system were the deflection at the center of the proof mass. The two degrees of the two-degree-of-freedom system were the deflection and the rotation angle at the center of the proof mass. A piezoelectric generator was fabricated and measured to verify the models. The experimental results show that the two new models are far more accurate than Roundy model.