• Title, Summary, Keyword: Shape design sensitivity

### Shape Optimization for Reduction of Cogging Torque in Permanent Magnet Motor by Sensitivity Analysis (영구자석전동기의 코깅토오크저감을 위한 민감도에 의한 형상 최적화)

• 박일한;이범택;한현교;한송엽
• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.12
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• pp.1246-1252
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• 1990
• In order to reduce the cogging torque in a permanent magnet motor, a method to optimize the shape of permanent magnet and iron pole is presented. Sine the cogging torque comes from the irregular system energy variation according to the rotor position, system energy variation is taken as object function and the object function is minimized to optimize the shape. The positions of permanent magnet surface and iron pole surface are chosen as design parameters and sensitivity of object function with respect to the design parameter is calculated. The shape is changed according to sensitivity can be generated by methods that exploit the FEM formulation. A numerical example shows that the cogging torque is reduced to about 10% of the original value.

### Optimal Positioning of Heating Lines in a Compression Molding Die Using the Boundary Element Method (경계요소법을 이용한 압축성형다이 가열선의 최적위치 설계)

• 이부윤;조종래
• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.6
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• pp.1478-1485
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• 1993
• A shape optimization problem is formulated to determine the optimal position of heating lines in a compression molding die. The objective of the problem is that the cavity surface would be maintained by a prescribed uniform temperature. A boundary integral equation for the sensitivity of the temperature in terms of hole position is derived using the method of shape design sensitivity analysis. The boundary element method is employed to analyze the temperature and sensitivity field of the die. The sensitivity calculation algorithm is incorporated in an optimization routine. To demonstrate a numerical implementation, an example problem arising in thermal design of a compression molding die is dealt with, showing that the number of heating lines chosen for the die strongly affects the ultimate uniformity of the cavity surface temperature.

### Shape Optimization of 3D Nonlinear Electromagnetic Device Using Design Sensitivity Analysis and Mesh Relocation Method (설계 민감도법과 요소망 변형법을 이용한 3차원 비선형 전자소자의 형상최적화)

• Ryu, Jae-Seop;Yingying, Yao;Koh, Chang-Seop
• Proceedings of the KIEE Conference
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• pp.124-127
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• 2002
• This paper presents a 3D shape optimization algorithm for electromagnetic devices using the design sensitivity analysis with finite element method. The structural deformation analysis based on the deformation theory of the elastic body under stress is used for mesh renewing. The design sensitivity and adjoint variable formulae are derived for the 3D nonlinear finite element method with edge element. The proposed algorithm is applied to the shape optimization of 3D electromagnet to get a uniform flux density at the air gap.

### Isogeometric Shape Design Optimization of Power Flow Problems at High Frequencies (고주파수 파워흐름 문제의 아이소-지오메트릭 형상 최적설계)

• Yoon, Minho;Ha, Seung-Hyun;Cho, Seonho
• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.3
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• pp.155-162
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• 2014
• Using an isogeometric approach, a continuum-based shape design optimization method is developed for steady state power flow problems at high frequencies. In case the isogeometric method is employed to the shape design optimization, the NURBS basis functions used in CAD geometric modeling are directly utilized to embed the exact geometry into the computational framework so that the design parameterization for shape optimization is much easier than that in the finite element method and consequently provides the enhanced smoothness of design perturbations. Thus, exact geometric models can be used in both the response and the shape sensitivity analyses, where normal vector and curvature are continuous over the whole design space so that enhanced shape sensitivity can be expected. Through numerical examples, the developed isogeometric sensitivity is compared with finite difference one to provide excellent agreement. Also, it turns out that the proposed method works very well in the shape optimization problems.

### Optimum Shape Design of Magnetizing Yoke of 2 Pole PM Motor for Cogging Torque Reduction

• Koh Chang-Seop;Ryu Jae-Seop;Hong Sun-Ki
• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.5B no.2
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• pp.168-172
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• 2005
• A novel cogging torque reduction algorithm is presented for 2-pole permanent magnet DC motor. While the shape of the permanent magnet is changed in the conventional method, the pole shape of the magnetizing yoke is optimized in the presented algorithm. In order to parameterize the shape of the yoke, and the distribution of the residual magnetization of the permanent magnet, the Bezier spline is used. The shape of the magnetizing yoke is optimized using the design sensitivity analysis incorporated with the finite element method and Bezier spline.

### Optimum Design of Electrical Apparatus Using Design Variable Parametrization (설계변수 매개화를 이용한 전기기기 최적설계)

• Lee, Hyeong-Beom;Park, Il-Han;Han, Song-Yeop
• The Transactions of the Korean Institute of Electrical Engineers B
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• v.50 no.11
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• pp.546-555
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• 2001
• ln this paper, the optimum design of electrical apparatus using design variable parametrization is presented. For analysis and design, the finite element method and the design sensitivity method is used, respectively. By applying the parametrization of the design variables, the obtained designed shape is continuous and smooth. For the parametrization the Bezier spline is used. The designed shape with parametrization is characterized by the control points. By delivering control points to the commercial CAD packages or NC machines, the exact designed shape can be realized in the manufacturing the electrical apparatus. The designed results with and without parametrization are compared and the validity of the parametrization is verified.

### SHAPE DESIGN FOR DISC OF A DOUBLE-ECCENTRIC BUTTERFLY VALVE USING THE TOPOLOGY OPTIMIZATION TECHNIQUE (위상최적설계 기법을 이용한 이중편심 버터플라이 밸브의 디스크에 대한 형상설계)

• Yang, S.M.;Baek, S.H.;Kang, S.
• Journal of computational fluids engineering
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• v.17 no.1
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• pp.61-69
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• 2012
• In this paper, the shape design process is briefly discussed emphasizing the use of topology optimization in the conceptual design stage. The basic idea is to view feasible domains for sensitivity region concepts. In this method, the main process consists of two steps: as the design moves further inside the feasible domain using Taguchi method, and thus becoming more successful topology optimization, the sensitivity region becomes larger. In designing a double-eccentric butterfly valve, related to hydrodynamic performance and disc structure, are discussed where the use of topology optimization has proven to dramatically improve an existing design and significantly decrease the development time of a shape design. CFD analysis results demonstrate the validity of this approach.

### Die Shape Optimal Design in Bimetal Extrusion by The Finite Element Method (유한요소법에 의한 이중 금속봉 압출 공정의 금형 형상 최적설계)

• 변상민;황상무
• Transactions of Materials Processing
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• v.3 no.3
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• pp.302-319
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• 1994
• A new approach to die shape optimal design in bimetal extrusion of rods is presented. In this approach, the design problem is formulated as a constrained optimization problem incorporated with the finite element model, and optimization of the die shape is conducted on the basis of the design sensitivities. The combinations of the core and sleeve materials.

### A study on the improvement of shape design sensitivity in eigenvalue problems using semi-analytical method (반해석적 방법을 이용한 고유치 문제의 형상 설계 민감도 향상에 관한 연구)

• 김현기;조맹효
• Proceedings of the Computational Structural Engineering Institute Conference
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• pp.159-166
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• 2001
• Structural optimization often requires the evaluation of design sensitivities. The Semi Aanalytic method(SAM) for computing sensitivity is popular in shape optimization because this method has several advantages. But when relatively large rigid body motions are identified for individual elements, the SA method shows severe inaccuracy. In this paper, the improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes. Moreover, the error of the SA method caused by numerical difference scheme is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms. Finally, this paper shows that the refined SA method including the iterative method improves the results of sensitivity analysis in dynamic problems.

### Design Sensitivity Analysis and Topology Optimization of Piezoelectric Crystal Resonators (압전 수정진동자의 설계민감도 해석과 위상 최적설계)

• Ha Youn-Doh;Cho Seon-Ho;Jung Sang-Sub
• Proceedings of the Computational Structural Engineering Institute Conference
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• pp.335-342
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• 2005
• Using higher order Mindlin plates and piezoelectric materials, eigenvalue problems are considered. Since piezoelectric crystal resonators produce a proper amount of electric signal for a thickness-shear frequency, the objective is to decouple the thickness-shear mode from the others. Design variables are the bulk material densities corresponding to the mass of masking plates for electrodes. The design sensitivity expressions for the thickness-shear frequency and mode shape vector are derived using direct differentiation method(DDM). Using the developed design sensitivity analysis (DSA) method, we formulate a topology optimization problem whose objective function is to maximize the thickness-shear component of strain energy density at the thickness-shear mode. Constraints are the allowable volume and area of masking plate. Numerical examples show that the optimal design yields an improved mode shape and thickness-shear energy.