Jeonghoon Yoo

Design of a Halbach Magnet Array Based on Optimization Techniques

We have designed a Halbach magnet array by using a numerical optimization method based on finite-element analysis. The magnetization direction of each element is defined as the design variable. The optimal magnet arrays composed of two and three linear magnet layers can then be investigated to increase the attractive, repulsive, and tangential magnetic forces between magnet layers. We have applied a magnet array maximizing the tangential force to a torsional spring composed of two- and three-magnet rings. The two-dimensional finite-element analysis incorporates optimization techniques such as the sequential linear programming and the adjoint variable method.

Structural optimization in magnetic devices by the homogenization design method

The homogenization design method (HDM) is extended to obtain an optimal topology of magnetic fields. This is accomplished by maximizing the magnetic mean compliance in a given region of the device. HDM is applied to a three-dimensional case, taking into account the saturation effect of the material. Results show that HDM is valid to maximize the vector potential and the magnetic energy. This method can also be applied to increase the performance of motors and antennas.

Optimal structural design considering flexibility

A topology optimization method based on the homogenization method (the homogenization design method) has been successfully applied to a variety of optimization problems such as the stiffness maximization problem and the eigen-frequency maximization problem. In this study, a methodology to obtain the optimal structure design considering flexibility is developed as a new extension of the homogenization design method. First, flexibility is formulated using the mutual energy concept. Second, a new multi-objective function is proposed to obtain optimal solutions incorporating flexibility and stiffness. Next, the topology optimization procedure is constructed using the homogenization method and sequential linear programming (SLP). Finally, some examples are presented to confirm that the methodology presented here can provide flexible structures satisfying the problem specifications.

Optimization of Magnetization Directions in a 3-D Magnetic Structure

This study introduces a design method for determining the optimized magnetization directions in 3-D magnetic systems. Based on a modified topology optimization method, discrete magnetizations are investigated in six directions . The finite-element method is used for the 3-D magnetostatic field analysis. The proposed method is applied to the design of a magnet pattern having ¿one-sided flux¿ and the design results show that the optimized magnet pattern appears as one or two Halbach arrays according to the shape of the design domain. The optimization process is accomplished by using sequential linear programming and the adjoint variable method.

Structural Topology Optimization of Magnetic Actuators Using Genetic Algorithms and ON/OFF Sensitivity

In genetic algorithm (GA) based topology optimization problems, characteristics of an initial population are important for the rapid and stable convergence. This paper introduces an algorithm generating randomly an initial population with superior hereditary characteristics. To avoid the generation of small structural spots, the blurring technique is proposed. The connectivity of seed elements considerging the magnetic flux flow in the design domain is focused. Differently from the classical GA by linear strings, this study deals with two-dimensonal chromosomes and the geographic crossover method to increase the diversity of offspring. The proposed design algorithm is applied to the yoke optimization of magnetic actuators.

Optimal Design of an Electromagnetic Coupler to Maximize Force to a Specific Direction

This study suggests a concept design for an electromagnetic (EM) coupler, using the topology optimization method. To maximize the force generated by magnetic flux, the magnetic energy generated must be differentiable, at the location where the force is acting, in a prescribed force direction. This study proposes a topology optimization scheme for maximizing the force in a specific direction, using a commercial analysis program, ANSYS, to provide the force value. We use ANSYS for obtaining the resultant force as well as analyzing the magnetic field. We adopt a density calculation method called SIMP (solid isotropic material with penalization), and compute the sensitivity of the objective function according to the density change of each finite element in the design domain. As a result, optimal shapes of the core and the armature of the coupler are obtained and the performance is verified.

Magnetic Actuator Design Using Level Set Based Topology Optimization

This paper presents a novel design methodology for optimum structural design of magnetic actuators using a level set based topology optimization method where the level set method can represent the precise boundary shape of a structure and also deal with complex topological changes during the optimization process. The distribution of ferromagnetic material is represented by introducing a level set function into the definition of the magnetic reluctivity. The optimization problem is defined to obtain optimal configurations that maximize the magnetic energy of actuators under a minimum bound of total volume. The movement of the implicit moving boundaries of the structure is driven by a transformation of design sensitivities of the objective and the constraints into speed functions that govern the level set propagation. The proposed method is applied to the structural design of magnetic actuators, and is confirmed to be useful for achieving optimal configurations that deliver higher performance and lighter weight designs.

Shape Design of the Surface Mounted Permanent Magnet in a Synchronous Machine

This paper deals with how to obtain the optimal shape of a permanent magnet of surface mounted permanent magnet brushless synchronous machine using the level set based topology optimization method. Two types of the flux linkage calculation method are formulated; one is a modified method based on traditional flux linkage calculation through transient analysis and the other is the mono-tooth method newly introduced in this study. The mono-tooth method makes it possible to avoid time-consuming transient analysis because it requires only magnetostatic field analysis and may deal with infinite design points. The level set based topology optimization method is combined with both types of flux linkage calculation method. The optimization problem for shape design of a surface mounted permanent magnet synchronous machine is defined focused on the permanent magnet shape design and optimization results by two different approaches are compared. The performance of the optimal model is also compared with that of a conventional magnet shape model.

Topology optimization for reduction of vibration caused by magnetic harmonic excitation

We apply the homogenization design method (HDM) to reduce the vibration level of a structure excited by magnetic harmonic force. We do this by obtaining the optimal material distribution of the structure to minimize the frequency response. We first use the Maxwell stress method to compute the magnetic force and then apply HDM for the optimization. Results show that the HDM can be used to minimize the frequency response. This method can also be applied to other rotary electrical devices such as motors and generators.

Modified method of topology optimization in magnetic fields

This paper reports on a modification of the ordinary density method for solving problems of structural optimization in magnetic fields. The method uses the homogenization design concept. A simple hole is assumed in an element, and the element density is determined according to the size of the hole. The report compares the results based on the modified density method with the results obtained by the homogenization design method (HDM), with special focus on changing the penalization parameter in the density method. The results show different tendencies in magnetic optimization problems compared to those in elastic optimization problems. The results are also discussed according to the global/local definition of the design domain using the density method as well as HDM.