On the Improved Modeling of the Magnetoelastic Force in a Vibrational Energy Harvesting System
On the Improved Modeling of the Magnetoelastic Force in a Vibrational Energy Harvesting System
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DOI：
10.1007/s42417-019-00159-4
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发表时间：
2019-06
影响因子：
2.7
通讯作者：
M. Noll;L. Lentz;U. von Wagner
中科院分区：
文献类型：
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作者：
M. Noll;L. Lentz;U. von Wagner
振动能量收集系统由悬臂梁和压电陶瓷层组成，其效率可以通过有意引入非线性来提高。这些非线性通常以靠近梁的自由端的永磁体的形式实现。这些磁铁的影响通常被假定为一个单一的横向力，取决于立方的梁尖的位移。一个相应的单自由度模型的系数往往被发现explanistically，没有明确的建模的magnetoelasticforces.MethodsIn本文中，我们提出和评估的程序的有效性，以确定作用在梁上的磁弹性力的磁场与相应的参数的物理定律。本文概述了方法本身，最初描述如何通过有限元模拟计算磁场。在第二步中，梁上的总横向力通过麦克斯韦应力张量的数值计算由磁场确定。简要地讨论了一个合适的多项式力近似的数值所需的最低程度。该模型的有效性，然后被认为是通过调查其分叉行为相对于单，双，和三稳态不同的磁铁之间的距离和比较的结果，由experiments.ResultsWhile该模型的预测的平衡位置的数量为任何磁铁的距离一般是在良好的协议与实验结果，在平衡点的精确位置上会有偏差。关于这些发现，一个二维的磁场建模只有线性材料models.ConclusionThe的局限性，本文得出结论，这里概述的方法是一个步骤，推导一个详细的模型的基础上的物理定律的磁场与相应的参数取代简单的启发式多项式磁力定律。
ObjectiveThe efficiency of vibrational energy harvesting systems that consist of a cantilever beam with attached piezoceramic layers can be increased by intentionally introducing nonlinearities. These nonlinearities are often implemented in the form of permanent magnets near the beam’s free end. The influence of these magnets is typically assumed to be a single transverse force that depends cubically on the displacement of the beam tip. The coefficients of a corresponding single degree of freedom model are often found heuristically, without an explicit modeling of the magnetoelastic force.MethodsIn this paper, we present and assess the validity of a procedure to determine the magnetoelastic forces acting on the beam from physical laws of the magnetic field with corresponding parameters. The paper outlines the method itself, describing initially how the magnetic field is computed by a Finite Element simulation. In the second step, the total transverse force on the beam is determined from the magnetic field by means of a numerical evaluation of the Maxwell stress tensor. The required minimum degree of a suitable polynomial force approximation of the numeric values is discussed briefly. The validity of this model is then considered by investigating its bifurcation behavior with respect to mono-, bi-, and tristability for different distances between the magnets and comparing the findings to results found by experiments.ResultsWhile the model’s predictions of the number of equilibrium positions for any magnet distance are generally in good agreement with results of experiments, there are deviations when it comes to the exact positions of the equilibria. With respect to these findings, the limitations of a two-dimensional magnetic field modeling with only linear material models are addressed.ConclusionThe paper concludes that the method outlined here is a step toward the deduction of a detailed model based on physical laws of the magnetic field with corresponding parameters replacing simple heuristic polynomial magnetic force laws.