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|Title:||A novel fast remesh-free finite element method for optimal design of electric machines||Authors:||Zhao, Yanpu||Degree:||Ph.D.||Issue Date:||2015||Abstract:||In this thesis, a novel fast remesh-free finite element method (FEM) for optimal design of electric machines and other electromagnetic (EM) devices is investigated to accelerate the process of optimal design of EM devices. Both two-dimensional (2D) and three-dimensional (3D) engineering optimal design problems can be solved using the proposed algorithms which are also developed into software packages in C++. This work is aiming to accelerate the solution of optimal shape design problems of EM devices, and the contribution of this work includes fast remesh-free mesh deformation techniques for 2D and 3D meshes, a novel adaptive degrees-of-freedom (DoFs) finite element algorithm and a low-frequency approximation to the Maxwell equations simultaneously considering inductive and capacitive effects. The remesh-free mesh deformation method, FEM and global optimization algorithms are combined to tackle several engineering optimal shape design problems. In this research of accelerating the optimal design process of EM devices, the 2D Delaunay parameterized mesh generation and refinement method and 3D remesh-free mesh deformation method are first proposed and applied to practical problems. To solve the magnetic field accurately with minimal effort, a novel error estimator is proposed to obtain the numerical error of the computed magnetic field with multiple materials in the problem domain. Besides, an adaptive DoFs FEM is proposed and applied to static nonlinear problems and transient field computation in time-domain. To solve the quasi-magneto-static field inside high-speed moving conductors presenting thin eddy-current layers accurately, the adaptive discontinuous Galerkin method (DGM), characteristic Galerkin method (CGM) and operator splitting method (OSM) are proposed and proved to be effective in use. For 3D EM field computation, a low-frequency approximation to the Maxwell equations simultaneously considering inductive and capacitive effects is proposed. All the proposed algorithms are implemented into computer code in C++, which is then applied to optimize the performance of several EM devices, such as electromagnet, permanent magnet motor, and magnetic gear.
In this thesis, the following work has been done: (1) 2D parameterized mesh generation and mesh refinement algorithms, including edge bisection, element trisection and regular mesh refinement methods; 2D parameterized mesh deformation technique for small shape modification and large mesh deformation; 3D fast remesh-free mesh deformation technique and its application to practical optimal design problems. (2) 2D finite element solver with second-order triangular finite element basis functions for the approximation of the magnetic vector potential (MVP); To analyze the EM fields in electric machines, nonlinear material, rotational movement and circuit-coupling are all taken into account. Adaptive mesh refinement is allowed using several optional error estimators. The Newton-Raphson iteration method is adopted for handling nonlinear magnetic material. For transient eddy-current field analysis, the backward-Euler time stepping scheme with slave-master technique for handling of rotational movement is adopted. (3) A novel adaptive DoFs FEM and its application to each Newton iteration step for nonlinear problems and each time-step for transient eddy-current field analysis. Only one set of mesh is needed in the method, the DoFs can be dynamically adjusted to adapt to the variation of the solution, both mesh refinement and mesh coarsening are processed implicitly. (4) 3D finite element solver with Whitney edge element to discretize the MVP and first-order nodal element to discretize the electric scalar potential (ESP). A low-frequency approximation to the Maxwell equations simultaneously considering inductive and capacitive effects is proposed. The magnetostatic, transient eddy-current, and nearly full-wave EM fields with external circuit-coupling can be solved with the developed code. Benchmark TEAM Workshop problems are used to validate the accuracy of the developed program. (5) An adaptive DGM, CGM and OSM are applied to eddy-current problems with high-speed moving conductors which present thin eddy-current layers. The advantages of these proposed methods are compared with traditional FEM. The major contributions of this work can be summarized as: - A novel parameterized mesh generation, refinement and deformation method for 2D and 3D optimal design problems. - A novel adaptive DoFs FEM which can reduce the computational time for both static and transient problems. A novel error estimator which is convenient to be used to estimate the local error distribution of the finite element solution. - The DGM, CGM and OSM are used to capture the thin eddy-current layers for problems with high-speed moving conductors. - Second-order 2D finite element and first-order 3D edge element programs are developed to solve EM field computation problems with nonlinear material, mechanical movement and external circuit. - A low-frequency approximation to the Maxwell equations simultaneously considering inductive and capacitive effects in the time-domain is proposed and validated using a numerical example. - Practical engineering optimal design problems are solved using the proposed methods and evolutionary optimization algorithms for several types of EM devices.
|Subjects:||Electric machinery -- Design and construction.
Hong Kong Polytechnic University -- Dissertations
|Pages:||xvii, 185 pages : illustrations (some color)|
|Appears in Collections:||Thesis|
View full-text via https://theses.lib.polyu.edu.hk/handle/200/8113
Citations as of Jun 4, 2023
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