臺灣博碩士論文加值系統

在蝸桿加工中，為了獲得更精確的蝸桿廓形，通常在粗加工後進行精磨加工，而在精加工中，輪磨加工可以達到最高的精度。本研究針對ZC型蝸桿進行深入探討。相較於其他類型蝸桿，ZC型蝸桿的刀具廓形是相對較為複雜的，是由一個盤型並具有圓弧廓形之刀具所成形而得。本研究將對ZC型蝸桿的全齒部齒廓進行三次曲線修形，透過調整節點之壓力角、節點處的曲率半徑及齒頂與齒底的反向翹曲程度，分別對應一階、二階和三階參數的修形，以獲得新的蝸桿齒廓。此外，本研究也將曲線修形的方法延伸應用於齒形修正上，透過將齒形調整方程式擴展至多階多項式，並利用最小平方法進行反向補償，求得逼近誤差的修正曲線以修正齒形。除此之外，我們還對齒廓的齒頂及齒底部份進行導圓處理，並得出ZC型蝸桿的全齒部齒面數學模式，利用嚙合理論求出相應成形輪磨所需之砂輪廓形。通過數值範例驗證所推導的數學模式，並利用嚙合理論推導出被成形蝸桿。隨後，將被成形蝸桿與原生蝸桿進行廓形比對，以分析砂輪的安裝角變化以及修砂後的砂輪所成形之蝸桿的齒形誤差。本研究還利用微軟的C#設計一泛用五軸成形輪磨機的前加工程式，包含機台加工作動、砂輪廓形修整以及刀具補正等作動程式，適用於調整過的加工模擬，以節省時間成本及降低人員失誤。最後，通過加工模擬軟體驗證程式所生成的加工動作，確認機台運作時是否存在碰撞或加工邏輯不佳等問題，避免實際加工中可能出現的問題，驗證程式撰寫及加工模擬軟體的機台設定是否正確。

In worm machining, to achieve a more precise worm profile, precision grinding is typically performed after rough machining, and among precision machining methods, form grinding can achieve the highest accuracy. This study delves into the ZC-type worm. Compared to other types of worms, the tool profile for the ZC-type worm is relatively complex, formed by a disc-type tool with an arc-shaped profile. This study applies cubic curve fitting to the entire tooth profile of the ZC-type worm. By adjusting the pressure angle at the nodes, the radius of curvature at the nodes, and the reverse warping degree at the tooth tip and root—corresponding to first, second, and third-order parameters respectively—a new worm tooth profile can be obtained. Additionally, this study extends the curve fitting method to tooth profile correction. By extending the tooth profile adjustment equations to multi-order polynomials and using the least squares method for inverse compensation, a correction curve that approximates the error can be obtained to adjust the tooth profile. Furthermore, the tooth tip and root areas undergo filleting, resulting in a complete mathematical model of the ZC-type worm's tooth surface. Using meshing theory, the corresponding grinding wheel profile required for form grinding can be determined. Numerical examples will verify the derived mathematical model. Additionally, meshing theory is used to derive the formed worm. Subsequently, a comparison between the formed worm and the original worm profiles is conducted to analyze the installation angle changes of the grinding wheel and the tooth profile errors formed by the dressed grinding wheel. This study also uses Microsoft's C# to design a front-end program for a general-purpose five-axis form grinding machine, including machine operations, grinding wheel profile trimming, and tool compensation programs, suitable for adjusted machining simulations. This approach saves time and reduces human error. Finally, machining simulation software is used to verify the generated machining actions, ensuring there are no collisions or logical issues during machine operation. This step prevents potential problems during actual machining, verifying the correctness of the program writing and the machine setup in the simulation software.

摘要......................................i
Abstract.................................ii
誌謝.....................................iii
目錄.....................................iv
表目錄....................................v
圖目錄....................................vi
第一章 緒論................................1
1.1 研究動機與目的.....................1
1.2 研究流程...........................2
1.3 文獻回顧...........................3
第二章 ZC型蝸桿齒面及廓形修形之數學模式......4
2.1 原生砂輪之輪面數學模式..............4
2.2 ZC型蝸桿之齒面數學模式..............6
2.3 齒廓修形之數學模式..................8
2.4 齒形誤差修正.......................12
2.5 修形後之全齒部齒面數學模式..........14
2.6 參數計算及齒形修形之數值範例........18
2.7 齒形修正之數值範例.................22
第三章 成形砂輪之齒面數學模式...............25
3.1 五軸成形機台之機台配置..............25
3.2 成形輪磨之機械設定.................26
3.3 成形砂輪之輪面數學模式..............27
3.4 數值範例...........................30
第四章 被成形之修形後ZC型蝸桿齒面數學模式.....36
4.1 被成形蝸桿之齒面數學模式.............36
4.2 數值範例以及被成形蝸桿之剖面之齒形誤差比對...37
第五章 蝸桿成形輪磨加工模擬...................47
5.1 機台之軸向及修砂器之定義..............48
5.2 輪磨加工流程.........................51
5.3 數值範例 ............................52
第六章 結論與未來展望.........................54
6.1 結論................................54
6.2 未來展望............................54
參考文獻....................................56
Extended Abstract...........................58

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