Seungjae Min

Topology optimization of compliant mechanisms using the homogenization method

A procedure to obtain a topology of an optimal structure considering flexibility is presented. The methodology is based on a mutual energy concept for formulation of flexibility and the homogenization method. A multi-objective optimization problem is formulated as an application of compliant mechanism design. Some examples of the design of compliant mechanisms for plane structures are presented. ( 1998 John Wiley & Sons, Ltd.

Optimal topology design of structures under dynamic loads

When elastic structures are subjected to dynamic loads, a propagation problem is considered to predict structural transient response. To achieve better dynamic performance, it is important to establish an optimum structural design method. Previous work focused on minimizing the structural weight subject to dynamic constraints on displacement, stress, frequency, and member size. Even though these methods made it possible to obtain the optimal size and shape of a structure, it is necessary to obtain an optimal topology for a truly optimal design. In this paper, the homogenization design method is utilized to generate the optimal topology for structures and an explicit direct integration scheme is employed to solve the linear transient problems. The optimization problem is formulated to find the best configuration of structures that minimizes the dynamic compliance within a specified time interval. Examples demonstrate that the homogenization design method can be extended to the optimal topology design method of structures under impact loads.

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.

Optimal Stator Design of Interior Permanent Magnet Motor to Reduce Torque Ripple Using the Level Set Method

Interior permanent magnet (IPM) motor is widely used for many industrial applications and has relatively high torque ripple generated by reluctance torque which results in noise and vibration. Since the configuration of the stator has great influence on reluctance torque, design optimization is necessary to improve the torque performance of IPM motor. In this paper, structural optimization based on the level set method is formulated to reduce torque ripples by minimizing the difference between torque values at defined rotor positions and the constant target average torque value under the constrained material usage. The nonlinear ferromagnetic material boundary of the stator is implicitly represented through an embedded level set function and the movement of the material boundary is driven by the normal velocity derived from optimality and convergence conditions of the level set equation. The proposed method is applied to design the optimal stator configurations of a traction motor of hybrid electric vehicle and presents the improved torque characteristics of IPM motor.

Unified topology design of static and vibrating structures using multiobjective optimization

Abstract Since structural design is usually required to perform in more than one environment, the ability to consider multiple objectives has to be included within the framework of topology optimization. A unified topology design methodology is proposed to generate structures satisfying both static and vibration performance measures using the multiobjective optimization approach. The weighted sum of conflicting objectives resulting from the norm method is used to generate the optimal compromise solutions, and the decision function is set to select the preferred solution. The objective function is defined by the mean compliance and mean eigenvalue to design a flexible structure which meets both the static and vibration requirements. The optimality conditions of the bicriteria problem are derived based on the modified optimality criteria method. To substantiate this approach, illustrated examples are presented both for verification and application.

Design of Magnetic Actuator With Nonlinear Ferromagnetic Materials Using Level-Set Based Topology Optimization

In the practical design of magnetic actuators, the effect of magnetic saturation usually plays an important role. This paper proposes a new computation approach for identifying the optimal configuration of a magnetic actuator to deal with saturation of the ferromagnetic material. A level-set method for topology optimization in magnetic fields is employed to represent the material boundary considering nonlinear B-H characteristics. Design of magnetic actuators is mathematically formulated as a general optimization problem for maximizing magnetic energy in the air gap between armature and yoke under the limited usage of ferromagnetic material. The nonlinear magnetostatic finite element analysis where transient eddy current effects are ignored and the associated design sensitivity analysis are performed. The movement of the implicit boundaries of the ferromagnetic material is driven by the normal velocity derived from optimality and convergence conditions of level-set equation. The validity and effectiveness of the proposed method are illustrated with 2D examples that are widely used in the literature.

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.

Magnetic Actuator Design for Maximizing Force Using Level Set Based Topology Optimization

To obtain weight reduction and high performance, using level set based topology optimization in magnetic fields is promising for the design of magnetic actuators where the precise boundary shape and topological changes are required. This paper addresses a novel scheme to design the optimal configuration of a magnetic actuator for maximizing the actuating force applied at the location where the motion being controlled. Level set function is introduced to represent ferromagnetic material boundaries and material properties of the magnetic reluctivity are determined. The optimization problem is formulated for maximizing the actuating force to a specified direction under limited usage of ferromagnetic material. The topological change analysis is performed to introduce holes and the movement of implicit material boundaries is driven by speed functions that govern the level set propagation. The proposed method is applied to design C-core actuator. It is summarized that the optimal design provides higher magnetic force and less material usage than the initial design.

Optimal Shape Design of Rotor Slot in Squirrel-Cage Induction Motor Considering Torque Characteristics

Induction motors are widely used in various industrial applications with different torque-speed characteristics. Since the configuration of the rotor slot has a great impact on the electromagnetic torque-speed characteristics, a design optimization process is necessary to improve the motor performance of the induction motor. The material boundaries of the rotor slot are represented by a level set function, and a voltage driven time-harmonic field analysis is performed to estimate the characteristics of the induction motor. An optimization problem is formulated to maximize the torque at one speed either a rated or starting condition constrained by the torque at other speeds, starting currents and efficiency. A level set equation with an augmented Lagrangian method is derived to find the optimal design. Optimal results are achieved by updating the sequential changes of the material region driven by the shape derivative. The design flexibility of the proposed method is confirmed to obtain National Electrical Manufacturers Association (NEMA) designs satisfying different torque characteristics.

Low Torque Ripple Rotor Design of the Interior Permanent Magnet Motor Using the Multi-Phase Level-Set and Phase-Field Concept

This paper proposes a new optimization method to design the rotor of interior permanent magnet (IPM) motor which consists of a permanent magnet (PM) and ferromagnetic material (FM) for reducing the torque ripple. To express three different material properties (PM, FM, and air), a multi-phase level-set model representing two level-set functions is introduced and the concept of a phase-field model is incorporated to distribute level-set functions for controlling the complexity of the structural boundaries. The optimization problem is formulated to minimize the torque ripple under the volume constraints of each material. Two level-set functions are updated with their respective design sensitivities. To verify the usefulness of the proposed method, the rotor design example of the IPM motor is performed and a novel configuration is obtained.