目前市面上看到的擺線齒輪，一般製造方式為滾齒切削後在進行研磨，用擠製製程加工擺線齒輪為新的研究領域，雖然製造時間比較短，但是也存在尺寸、精度不易控制的缺點，對實際生產造成了諸多困擾。
為了解決擠製後成品的精度問題，許多人會用分析軟體先進行模擬，分析產品加工後的狀況再加以修正，以利減少廢料產生。但是模擬後產品的輸出圖檔呈現出不規則的三角網格，讓量測者不知該如何著手，目前也沒有一套對這方面完整的量測方式，所以本論文提出DEFORM 3D三角網格齒形誤差評估與補償，以改善此種情況。本論文首先設立了多個數學模型，將擺線齒輪各項物理量及其做動、修形方式均以算式表示。然後藉助這些數學模型，本文會詳細說明經由模擬，胚料（Workpiece）擠製成齒輪樣品後，要如何運用本論文建立的DEFORM 3D三角網格齒形誤差評估與補償，從樣品中提取出單一截面上的數據點並計算其與理論數值的誤差量，再利用敏感度矩陣算出下模(Bottom Die)單齒的左右齒面補償量，從而進行後續的補償修正處理。
之後還建立了一套全新的冷擠製模擬分析流程，特別改良擠製模具中下模的設計更加適用於實際生產製造。本文亦將充分介紹這套流程的設定細節及其實驗結果，以驗證本論文提出的齒輪量測與補償方式的可行性。

At present, the common manufacturing method of cycloidal gears seen on the market is grinding after hobbing. The extrusion processing of cycloidal gears is a new research field. Although the manufacturing time is relatively short, it also has the disadvantage of difficult to control the size and accuracy, which has caused many troubles to the actual production.
To solve the problem of the precision of extruded products, many people will use analysis software to simulate and analyze the situation of products after processing, and then amend it to reduce waste generation. But after simulation, the output drawings of the products show irregular triangular mesh, which makes the surveyors not know how to start. At present, there is no complete measurement method for this aspect. So this paper proposes DEFORM 3D triangular mesh tooth profile error evaluation and compensation to improve this situation. This paper first established several mathematical models, the cycloid gear and do the physical move, modification way equation is expressed. Then, with the help of these mathematical models, this paper will explain in detail how to use DEFORM 3D triangular mesh to evaluate and compensate tooth profile errors after extruding gear samples with simulated Workpiece, extract data points on a single cross-section from the samples and calculate their errors with theoretical values, so as to benefit further. The compensation of the left and right tooth surfaces of the lower die is calculated by the sensitivity matrix, and then the compensation correction is carried out subsequently.
After that, a new cold extrusion simulation analysis process was established, especially the improved design of the lower and middle die of the extrusion die was more suitable for actual production and manufacturing. To verify the feasibility of the gear measurement and compensation method proposed in this paper, the details of the process setting and the experimental results will also be fully introduced in this paper.

中文摘要 I
Abstract II
致謝 III
目錄 IV
符號索引 VI
圖索引 VIII
表索引 XI
第1章 緒論 1
1.1 前言 1
1.2 研究動機與目的 1
1.3 文獻回顧 2
1.4 論文架構 3
第2章 擺線齒輪數學模式及具修形擺線齒輪修形 5
2.1 前言 5
2.2 擺線齒輪齒面數學模式 5
2.3 具修形擺線齒輪齒形修整 9
2.4 數值範例 11
2.5 小結 14
第3章 DEFORM 3D三角網格齒形誤差評估與補償 15
3.1 前言 15
3.2 STL三角網格齒形誤差分析 15
3.3 齒形誤差修形數學模式推導 21
3.4 小結 23
第4章 擠製擺線齒輪齒形DEFORM 3D模擬及其模具下模補償修正步驟說明分析 24
4.1 前言 24
4.2 擺線齒形補償模擬分析 24
4.3 DEFORM-3D擠製擺線齒輪模擬方法 24
4.4 DEFORM-3D擠製擺線齒輪模擬操作步驟 26
4.5 擠製模具下模補償修正步驟說明 31
4.6 小結 38
第5章 擠製擺線齒輪模具齒形多次修正結果 39
5.1 前言 39
5.2 第一次補償之擠製擺線齒輪齒形誤差評估 39
5.3 第二次補償之擠製擺線齒輪齒形誤差評估 44
5.4 第三次補償之擠製擺線齒輪齒形誤差評估 48
5.5 擠製後胚料誤差與補償比較分析 52
5.6 小結 59
第6章 結論與討論 60
6.1 結果與討論 60
6.2 建議與未來展望 61
參考文獻 62

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