臺灣博碩士論文加值系統

本研究主要目的乃是針對於無鐵心線性無刷永磁馬達結構分析及設計。利用有限元素法分析軟體COMSOL，模擬線性馬達之二維模型，分析馬達磁路評估其性能，並利用多目標最佳化方法決定無鐵心線性馬達結構之主要設計變數。論文中以馬達結構磁鐵尺寸(磁鐵寬度和磁鐵高度)、磁距、氣隙高度、線圈尺寸(繞線寬度及高度)與線徑等七個參數為所求之設計變數，而以推力最大化、溫度最小化以及體積最小化等，以此多目標最佳化問題，同時以設計變數範圍做為本最佳化問題之限制條件。
本論文利用反應曲面法有效預測無鐵心線性馬達參數與各目標之間的反應數學模型。並利用以量子粒子群演算法配合突變運算子，避免落入局部區域解以提高全域搜索。運算過程中，利用擁擠距離、非支配排序法及菁英策略，以增加解的正確性與多樣性，最後所得到之柏拉圖最佳解前沿，利用有限元素法分析軟體，驗證反應曲面法所建構之線性馬達多目標模型之準確性，可以提供設計者更多無鐵心線性馬達結構的設計方案選擇。

The main purpose of this study was focusing on the analysis and design of the structure of air-core linear brushless permanent magnet motor (LBPMM). To analyze magnetic circuit and evaluate performance of motor, two-dimensional model of the linear motor was simulated by using the finite element method (FEM) through analysis software, COMSOL Mutiphysics (COMSOL). Multi-objective optimization also had been used to come up with the main design variables of an air-core LBPMM. The seven variables, magnet dimensions (magnet width and magnet height), Magnet Distance, airgap, coil winding dimensions (coil width and coil height), and wire diameter were chosen as the design variables in this study. The maximal thrust, minimal temperature, and minimal volume were taken as the multi-objective optimization problems, while the design variables were being setting as the restrictive conditions of the optimization problems
This study adopted response surface methodology (RSM) to develop a mathematical prediction for the variables of air-core LBPMM and the response surface model for each of the objectives. In addition, a quantum particle swarm optimization (QPSO) with a mutation operator was used to avoid falling into the local solution and optimize the full searching. In the calculating process, the crowding distance, non-dominated sorting, and elitism were used to improve the accuracy and diversity of the solutions.
Finally, the result showed the Pareto-optimal front solutions, and COMSOL had been used to verify the accuracy of multi-objective model of the linear motor constructed by RSM, which can provide more effective design methods for designers.

目次
摘要 I
Abstract II
謝誌 III
目次 V
表目錄 VII
圖目錄 VIII
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 研究目的 3
1.4 論文架構 4
第二章 無鐵心線性馬達特性及理論基礎 5
2.1 無鐵心線性馬達簡介 5
2.2 無鐵心線性馬達定子設計分析 7
2.3 無鐵心線性馬達的動子繞組設計 8
2.4 無鐵心線性馬達的氣隙磁通密度的計算 10
2.5 無鐵心線性馬達推力計算 18
2.6 線性馬達之熱分析 20
2.7 建構線性馬達模型及參數設定 23
第三章 反應曲面法 26
3.1反應曲面法設計概念 26
3.2 反應曲面法設計步驟 27
3.3反應曲面之優點 29
第四章 菁英策略多目標混合量子粒子群最佳化演算法 30
4.1傳統粒子群演算法(Particle Swarm Optimization，PSO) 31
4.2 混合量子粒子群演算法(HQPSO) 32
4.3懲罰函數(Penalty Function) 35
4.4 多目標最佳化(Multi-Objective Optimization) 36
第五章 模擬分析實例應用 39
5.1 建立無鐵心線性馬達之反應曲面 41
5.2 懲罰函數求解方法 48
5.3 執行EMOHQPSO進行無鐵心線性馬達最佳化 48
5.3有限元素分析 57
第六章 結論與展望 77
參考文獻 80

表目錄
表1 原始無鐵心線性馬達參數表格 25
表2設計變數範圍表(mm) 42
表3無鐵心線性馬達推力的二階模型迴歸系數 42
表4無鐵心線性馬達推力的反應曲面二階模型變異數分析 43
表5無鐵心線性馬達溫度的二階模型迴歸系數 44
表6無鐵心線性馬達溫度的反應曲面二階模型變異數分析 45
表7無鐵心線性馬達體積的二階模型迴歸系數 46
表8無鐵心線性馬達體積的反應曲面二階模型變異數分析 47
表9 原始線馬及EMOHQPSO柏拉圖最佳解前沿的馬達結構參數 49
表10 EMOHQPSO演算法之參數設定 56
表11 反應曲面模型EMOHQPSO最佳解與有限元素分析結果比較 74
表12 反應曲面EMOHQPSO最佳解之預測誤差率 75
附錄A.1中央合成實驗設計方法152組變數組合及目標反應值 84

圖目錄
圖1 無鐵心式線性馬達動子與定子 6
圖2 佛來明左手定則 6
圖3 無鐵心式線性馬達動作原理圖 6
圖4 三相繞組的位置分佈及繞線方向平視圖 8
圖5 三相繞組位置表示圖 9
圖6 電流向量表示圖 9
圖7 三相電流設定 10
圖9 無鐵心線性馬達實體模型3D示意圖 21
圖10 無鐵心線馬設計變數2D視圖 22
圖11 傳統粒子群演算法位置更新示意圖 32
圖12 擁擠距離示意圖 37
圖13菁英策略示意圖 38
圖14 EMOHPSO結合反應曲面法流程圖 38
圖13 NSGAII柏拉圖前沿曲面擬合 48
圖14 MOPSO柏拉圖前沿曲面擬合 48
圖15 EMOHQPSO柏拉圖前沿曲面擬合 48
圖16 NSGAII之柏拉圖前沿 51
圖17 MOPSO之柏拉圖前沿 52
圖18 EMOHQPSO之柏拉圖前沿 53
圖19 三種演算法之柏拉圖前沿圖形疊加 54
圖20 三種演算法之柏拉圖前沿比較於原始尺寸更佳族群的圖形疊加 55
圖21 原始尺寸馬達之磁通密度分佈圖B(T) 58
圖22 原始尺寸馬達之溫度場分佈圖(℃) 59
圖23 原始尺寸馬達之推力鏈波(N) 59
圖24 EMOHQPSO第1個最佳解之線性馬達結構參數 60
圖25 EMOHQPSO第2個最佳解之線性馬達結構參數 61
圖26 EMOHQPSO第3個最佳解之線性馬達結構參數 62
圖27 EMOHQPSO第4個最佳解之線性馬達結構參數 63
圖28 EMOHQPSO第5個最佳解之線性馬達結構參數 64
圖29 EMOHQPSO第6個最佳解之線性馬達結構參數 65
圖30 EMOHQPSO第7個最佳解之線性馬達結構參數 66
圖31 EMOHQPSO第8個最佳解之線性馬達結構參數 67
圖32 EMOHQPSO第9個最佳解之線性馬達結構參數 68
圖33 EMOHQPSO第10個最佳解之線性馬達結構參數 69
圖34 EMOHQPSO第11個最佳解之線性馬達結構參數 70
圖35 EMOHQPSO第12個最佳解之線性馬達結構參數 71
圖36 EMOHQPSO第13個最佳解之線性馬達結構參數 72
圖37 EMOHQPSO第14個最佳解之線性馬達結構參數 73
圖38 EMOHQPSO第1個最佳解之推力鏈波 74

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