磁致伸缩振动能量收集器的全耦合非线性等效电路模型

Fully Coupled Nonlinear Equivalent Circuit Model for Magnetostrictive Vibration Energy Harvester

磁致伸缩材料具有应变大、响应速度快、稳定性好、频带宽的特点,是制作振动能量收集器的理想材料。当前磁致伸缩振动能量收集器建模主要利用线性压磁方程,此模型未能从材料自身耦合和磁路结构进行输出分析,导致输出预测误差较大。该文首先搭建了磁致伸缩材料磁特性测试装置,测试分析了磁致伸缩材料Galfenol合金在不同压应力尤其是大幅值应力下的磁特性;然后基于Gibbs自由能推导了Galfenol材料的全耦合非线性本构方程,进而构建了考虑漏磁、非线性、机磁耦合及饱和效应的振动能量收集器的等效电路模型,并对等效电路模型进行了非线性数学表征和参数识别;最后基于Galfenol材料设计了一个可以承受大幅值振动力的双棒型振动能量收集器样机,通过实验研究了收集器输出电压在不同力幅值、力频率、负载阻值等工况下的变化规律。实验结果与模型的计算结果对比分析表明,所建立的全耦合非线性等效电路模型可以准确预测振动能量收集器的输出电压特性。

Magnetostrictive vibration energy harvester(MVEH)uses the Villali effect of magnetostrictive rod or sheet to convert energy from mechanical vibrations to electrical energy.MVEH has obvious advantages in output stability,strain capacity and electromechanical coupling.In areas where power is not readily available,such as wildlife sanctuaries,MVEH can convert the abundant animal kinetic energy into electrical energy to power some sensing devices.However,multiple bidirectional coupling of mechanica-magnetic-electric and nonlinear characteristics occur in the process of energy conversion.In previous studies,the prediction models for the output characteristics of MVEH were mostly based on linear piezomagnetic equations,which do not allow for good prediction of the output voltage characteristics of the harvester due to the neglect of nonlinearities of materials.In order to solve the problem of large errors in the prediction of the output voltage characteristics of the linear model.This paper constructs a mechanical-magnetic-electric three-port fully coupled nonlinear equivalent circuit model based on the Gibbs free energy.The model takes into account the effects of different compressive stresses,bias magnetic fields and leakage magnetism,et al.The core material chosen for the MVEH studied in this work is Fe81.6Ga18.4,which has excellent electromagnetic,mechanical and magnetostrictive properties.A magnetostrictive materials test platform has been built to analyse the main magnetic properties of Galfenol.Firstly,the M-H curves of the rod are tested in the compressive stress range of 0~70 MPa to obtain the trend of the magnetisation intensity of the Galfenol rod at different compressive stresses and bias magnetic fields.Secondly,based on the Gibbs free energy within the material and using a modified hyperbolic function to characterise the M-H curve clusters.A final machine-magnetic coupling model of the magnetostrictive Galfenol rod is constructed.To further simplify the analysis of the MVEH equivalent output model,the mechanical,magnetic and electrical aspects of the global system of MVEH are interlinked with their equivalent circuits using a specific electromechanical analogy to construct a three-port fully coupled nonlinear equivalent circuit model.In order to verify the accuracy of the predicted results of the equivalent circuit model,an experimental test system consisting of a pneumatic stamping press and an air compressor is built.It can provide MVEH with vibration forces varying in amplitude from 115 N to 1310 N and in frequency from 0.5 Hz to 2 Hz to simulate the vibrations generated by animal movements in a practical application.In addition,a double-rods MVEH which can withstand large vibration force is designed.After several sets of experiments,the maximum actual output voltage of MVEH can reach 1483 mV.Two groups of different vibration force input conditions and different external load resistance values are selected as comparison conditions.By comparing the peak-to-peak value of output voltage Upp and output voltage RMS Urms obtained from the actual test with the data predicted by the equivalent circuit model.The results show that when the vibration force amplitude F=350 N,frequency f=1 Hz,and external load R=10 kΩ,the relative errors are η_(pp)=3.58%,η_(rms)=2.47%.When the F=755 N,f=1 Hz and the external loads are R=10 kΩ,R=200Ω,R=50Ω and R=10Ω respectively,ηpp are 3.79%,3.00%,3.82%and 3.07%respectively.ηrms are 1.10%,3.71%,2.49% and 3.52%respectively.The relative errorsηof U_(pp) and U_(rms) predicted by the model and experimentally tested are less than 4%,proving the effectiveness of the equivalent circuit model for predicting output voltage.In addition,the MVEH also ensures structural and output stability while withstanding large amplitude vibration forces.This study can provide some theoretical guidance for the construction of nonlinear fully coupled models of MVEH and the prediction of output voltage characteristics.