本論文發展一套適用於個人電腦上操作之旋轉圓盤之電腦輔助設計軟體，提供友善的面板式操作介面，並藉由所選用之圓盤的數值分析方法，以取代一般使用有限元素法進行圓盤之應力分析與外形設計所需之繁複程序，讓使用者能輕易而迅速地獲取可靠的計算結果以供參考利用。
在發展此電腦輔助設計軟體時，整個流程架構大致可區分成三部份：（一）、旋轉圓盤公式推導部份：將旋轉圓盤橫剖面切割成有限個圓環疊加，由彈性力學中軸對稱變形及平面應力應變關係式，推導得到圓盤內任一半徑距離之壓力方程式，以及計算徑向應力與切向應力之數值計算公式。（二）、數值計算部份：本文是利用Matlab軟體發展所需之電腦程式，並且以最佳化搜尋法中的梯度法與黃金分割法為整個迭代計算流程之主要架構，在相同目標函數及限制條件下，將公式推導部份所得之方程組與最佳化方法相結合，以求得旋轉圓盤剖面之最佳厚度變化。（三）、使用者介面部份：利用Matlab軟體之圖形使用者介面（GUI）來整合數值計算電腦程式以及輸入與輸出之圖形視窗，使操作者可以經由個人電腦視窗的圖形介面進行圓盤之設計工作。
本文另外探討圓盤之設計參數（如轉速與輪轂壓力）對於圓盤剖面厚度變化之影響，其結果如下：（一）、輪轂壓力為零時，圓盤剖面之厚度變化與轉速無關；（二）、輪轂壓力不為零時，轉速愈高，遠離輪轂處之圓盤厚度愈大；（三）、轉速一定，則輪轂壓力愈大，在接近輪轂處之圓盤厚度將略微增加。

A computer-aid design software operated on personal computers was developed for rotating disks in this thesis. It provides a user-friendly operating interface. Instead of tedious and complicated processes when using finite element methods for stress analysis and shape design of rotating disks, the user can quickly obtain useful results of disks by the numerical method applied in this thesis.
In developing the computer-aided design software, the process includes three stages: (1). Derive the necessary equations for numerically computing the pressure distribution, radial stress, and tangential stress for rotating disks. (2). Develop the computer programs by using Matlab software to obtain the optimum cross-section-thickness variation of rotating disks. In this stage, the gradient method and golden section method are optimization methods used to search the optimum thickness and numerical equations derived in the first stage are combined into the optimization search process. (3). Develop the user interface by using Matlab GUI ( Graphic User Interface ) tool to integrate the input and output figures as well as the computer programs developed in the second stage so that the design of rotating disks can be easily implemented.
The effect of design parameters such as rotating speed and hub fitting pressure on the variation of disk thickness is also studied in this thesis. The results are as follows: (1). The speed has no effect on the disk thickness variation if the pressure is equal to zero. (2). The more the speed is, the more the disk thickness increases in the cross section slightly away from the hub if the pressure is not equal to zero. (3). The disk thickness close to the hub is little increased if the speed is fixed and the pressure is increasing.

摘要iii
誌謝v
圖目錄viii
表目錄xi
符號說明xii
第一章 緒論1
1.1 前言1
1.2 論文架構3
第二章 旋轉圓盤模型建立與分析6
2.1 旋轉圓盤的理論探討6
2.1.1 靜態壓力6
2.1.2 旋轉離心力9
2.2 圓盤模型建立與數值分析12
第三章 旋轉圓盤的最佳化設計19
3.1 最佳化方法19
3.1.1 梯度法21
3.1.2 黃金分割法22
3.2 旋轉圓盤最佳化數學模型24
3.3 電腦計算流程與實例說明27
第四章 電腦輔助設計流程30
4.1 圖形使用者介面（GUI）簡介30
4.2圖形使用者介面應用33
4.2.1 主畫面系統33
4.2.2 輸入畫面系統35
4.2.3 輸出畫面系統39
第五章 結果與討論47
5.1 圓盤轉速的影響（輪轂壓力為零）48
5.2 圓盤轉速的影響（輪轂壓力不為零）53
5.3 輪轂壓力之影響58
5.4 圓盤之切向應力比較62
第六章　結論65
參考文獻67

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