Multiscale Finite Element Analysis of Linear Magnetic Actuators Using Asymptotic Homogenization Method

Abstract

This work presents the multiscale finite element analysis of linear magnetic actuators. Here, the actuators includes unidirectional fiber reinforced magnetic composites as a back-iron core component. The composite is employed in actuators to enhance the magnetic force. However, the direct computation of actuators including heterogeneous composite structures requires high computation cost. To overcome this problem, multiscale computational technique for the analysis of a magnetic actuator is proposed in this work. First, the effective magnetic permeability of the composite is calculated at various fiber volume fractions and orientation angles. For this, the asymptotic homogenization method is applied to the composite unit cell model in microscopic coordinate system. Next, the obtained homogenized effective permeability is utilized for the macroscopic magnetostatic analysis of actuator model. Subsequently, the magnetic force acting on a actuator plunger is calculated using the Maxwell stress tensor method. To validate the accuracy and computational benefit of the proposed multiscale approach, a actuator numerical example is provided. For the accuracy validation, the magnetic force and magnetic field distribution obtained from the proposed multiscale approach are compared with those from the direct calculation. In addition, the computation time consumed for the mutiscale approach and direct calculation is compared to validate the benefit of the proposed analysis process.

Multiscale Analysis of Heterostructured Electropermanent Magnet in Magnetic Actuators

“…Using the asymptotic expansion and the chain rule, the cell problem equations are derived from Eqs. (11) and (12) in the microscopic coordinate system y 1 y 2 . It is written as:…”

“…Using this method, homogenized effective material properties describing macroscopic material behavior can be calculated in a highly heterogeneous medium. In [12], multiscale analysis of anisotropic magnetic composite using asymptotic homogenization was studied. The composite in [12] consists of high and low permeability ferromagnetic materials, which requires the calculation of anisotropic effective magnetic permeability.…”

“…In [12], multiscale analysis of anisotropic magnetic composite using asymptotic homogenization was studied. The composite in [12] consists of high and low permeability ferromagnetic materials, which requires the calculation of anisotropic effective magnetic permeability. On the contrary, the EPM in this work is composed of hard ferromagnetic (i.e., PM) material and soft ferromagnetic (i.e., iron) materials.…”