Fully Coupled Nonlinear Equivalent Circuit Model for Magnetostrictive Vibration Energy Harvester
Huang Wenmei1,2, Liu Zequn1,2, Guo Wanli1,2, Xue Tianxiang1,2, Weng Ling1,2
1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment Hebei University of Technology Tianjin 300130 China; 2. Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province Hebei University of Technology Tianjin 300130 China
Abstract：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 1 310 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 1 483 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 ηpp =3.58%, ηrms =2.47%. When the F=755 N, f=1 Hz and the external loads are R=10 kΩ, R=200 Ω, R=50 Ω and R=10 Ω 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 errors η of Upp and Urms 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.
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2023, Vol. 38 
