레벨셋법과 하이브리드 해석기법을 이용한 정자계 내 다중 컴포넌트 레이아웃 최적설계

Abstract

Magnetic devices such as solenoid-type magnetic actuators and permanent magnet motors are widely used in various industrial applications due to their simple structure, easy control, and zero emission aspect. Since the driving conditions of such magnetic device are dominated by magnetic flux paths, it is important to find optimal layouts for magnetic components, including the ferromagnetic material (FM) and the permanent magnet (PM). A design optimization method is therefore often applied to the development process for magnetic devices. Parametric optimization, which uses simple parameters to represent geometrical shapes and the properties of magnetic materials, is commonly applied to magnetic design problems and it can provide optimal designs that achieve various design targets. However, when using parametric optimization, the selection of particular design variables that affect the design target may be difficult, and the obtained optimal designs are strongly dependent on the initial design. Topology optimization, which guarantees a high degree of freedom with respect to changes in material distribution, was employed to overcome these limitations. Design optimization using a topological design variable, such as the material density, a homogeneous property, and the use of the level set function, can result in innovative structural designs and the utility of such approaches has been confirmed in copious previous research. Unfortunately, since most magnetic devices are formed as multi-component systems, manufacturing the shape designs obtained from topology optimization is often problematic. Further studies are therefore needed so that design optimization methods can be more effectively employed in real-world development processes. This thesis presents a practical design method for optimizing multi-component layouts in a magneto-static field. A level set-based shape optimization method is employed to obtain clear boundaries in the optimal FM distribution that affects the magnetic flux paths in the magnetic device. However, since PM boundaries may cause manufacturing and magnetization problems if they are excessively complex, a parametric design method is also applied to obtain the optimal size and position of the PM while maintaining a simple shape. The magnetic properties of the PM and FM, such as the nonlinear magnetic relative permeability and the direction of the remanent magnetic flux, are calculated using both geometrical parameters and the sign of the level set function. The optimization problem is formulated with an objective function and design constraints for the magnetic performance and the use of the magnetic materials, and the sensitivities of the design variables are obtained by the finite difference method and adjoint variable method. To make the proposed design method more practical and increase the scope of its applicability, a new design methodology that can provide a detailed optimal layout of a magnetic device through the use of only a few system parameters at the conceptual design stage, is also proposed in this thesis. The concept of a hybrid analysis method that incorporates both the equivalent circuit method and the finite element method is introduced to predict the driving performance of the magnetic device. The coupling boundary condition between two different types of analysis domain can be derived from the relationship between the circuit flux and the magnetic potential. Two optimization problems are formulated using the proposed method, to determine the optimal value of the circuit parameter and to obtain a detailed structural design that satisfies an optimal circuit value, by using the distribution of the level set function. The target magnetic potential, calculated using the optimal circuit flux and parameters, creates the target magnetic flux in the finite element domain and the topological sensitivity can be approximately calculated using field measurements. Several design examples, including a simple C-core magnetic actuator and a surface-mounted permanent magnet (SPM) motor, are provided in this thesis to verify the effectiveness of the proposed method. Optimization for single and multiple level set models, a multi-component layout design optimization using both parametric variables and the level set function, and a hybrid analysis-based design optimization, are performed to obtain an optimal core design for a magnetic actuator that maximizes the magnetic force. The advantages and disadvantages of the presented methods are verified through the optimal results. The design optimization of the SPM motor is performed to minimize the PM volume while subject to design constraints for the target torque and the torque ripple. It is confirmed that the proposed hybrid analysis-based design method helps to reduce the otherwise large computational demand and facilitates obtaining design candidates for the SPM motor that are meaningful in an engineering sense. The effect of the material nonlinearity is also verified for the optimal designs.