汽車自動變速箱檔位數的提升可以同時帶來減少燃料損耗與提升車輛性能的效益，故各大汽車廠競相配置高檔位數的自動變速箱於車輛上。但提升檔位數隨之而來的是自動變速箱行星齒輪系桿件數增加、控制較複雜與體積增加等問題，因此如何選擇適當的行星齒輪系，完整且有效率地設計出符合設計需求之自動變速箱，為目前重要的研究課題之一。
本文的目的為針對已有的三型兩自由度九桿複式行星齒輪系構造，進行檔位設計與齒數合成，設計出可用之八速自動變速箱。在檔位設計方面，先以複式行星齒輪系中各同軸桿件作為輸出桿，推導其減速比公式，建立操作分類表。其次，判斷相鄰檔位是否作動連續，並依減速比遞減作檔位排序，藉以建立合適之八速作動連續且減速比遞減之檔位順序組合。接著，作桿件干涉及倒退檔存在的篩選，刪除不適用之變速箱構造。在齒數合成方面，以換檔銜接順暢為目標，並且參考現有八速自動變速箱之規格後訂定目標函數。限制條件由太陽齒輪、複式行星齒輪及環齒輪間的嚙合關係，以及行星齒輪系在組裝上所具有的齒數限制所產生。最後，針對指定的首檔與末檔減速比比值，以全域搜尋法在設計限制中，尋找最佳的八速自動變速箱齒數合成結果。
本文之研究成果，在九桿複式行星齒輪系中，順利合成四組四個低速前進檔、一個直接傳動檔與三個高速前進檔可用之八速自動變速箱設計。

The more speed of automatic transmission of vehicle result in more performance and less fuel consumption. Equipping a higher speed automatic transmission becomes one of the main competitions in automobile companies. Nevertheless, the more speed of automatic transmission also results in more links of planetary gear train, complex control system, and larger volume. Therefore, efficiently and completely synthesizing feasible automatic transmission configurations from various planetary gear trains is still an important research topic.
The purpose of this study is to design eight-speed automatic transmissions with two-degree-of-freedom and nine-link compound planetary gear trains, including clutching sequence synthesis and teeth number synthesis. In clutching sequence synthesis aspect, the formula of each speed ratio is expressed in terms of the number of teeth for each gear train, and it can be roughly indentified to be an underdrive, an overdrive or a reverse. Under the requirements of clutch-to-clutch shift, decreasing speed ratios, no interferences, and suitable reverse gears, all feasible clutching sequences are obtained by a systematic method. In teeth number synthesis aspect, for the desired ratio of the first gear over the last gear, an exhaustive searching method is used to find the global optimum solution for the number of teeth on gears under design constraints.
The results of this study show that there are four eight-speed automatic transmission configurations under the speed arrangement consisting of four forward underdrives, one direct drive, and three forward overdrives.

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