在市場競爭的需求下，多檔位的汽車自動變速箱，已成為各大車廠之設計趨勢。但不可避免的，行星齒輪系桿件數增加、控制較複雜與體積變大等現象，皆是檔位數提升的同時，必須面臨之難題。而如何在眾多的行星齒輪系中，完整且有效率地設計出符合設計需求之自動變速箱，仍是重要的研究課題之一。
本文之目的為針對二自由度複式行星齒輪系，經由構造合成、檔位設計與齒數合成等子題之探討，設計可用之七速自動變速箱。在齒輪系構造合成方面，本文以一個單式行星齒輪搭配一個複式行星齒輪，並配合所制定的構造設計規範，合成九桿以下二自由度複式行星齒輪系，共有九個八桿齒輪系與三個九桿齒輪系。在檔位設計方面，先為各個指定輸出桿之複式行星齒輪系，推導減速比公式並製作操作分類表。再依據操作分類表，區分各操作之輸出類型，以組合出作動連續之檔位，並判斷相鄰檔位減速比之大小，以排列出合適的作動連續且減速比遞減之檔位順序組合。在齒輪系齒數合成方面，本文參考現有之專利與文獻，制定一組目標減速比，並以此訂定最佳化設計之目標函數為各檔位所合成之減速比值與目標減速比差值之絕對值總和。接著，依據複式行星齒輪系之幾何構造，建立所有的限制條件與設計變數。然後，以最佳化軟體LINGO進行齒數最佳化。
本文之研究成果，在合成三個低速前進檔、一個直接傳動檔與三個高速前進檔方面，已確定構造合成所得之八桿與九桿複式行星齒輪系，皆無可行之設計。至於合成四個低速前進檔、一個直接傳動檔與二個高速前進檔方面，亦確定本文構造合成之八桿複式行星齒輪系，無可行之設計；然而，本文在兩組九桿複式行星輪系中，順利的合成七組可用之七速自動變速箱設計。

Due to market competition, equipping a multi-speed automatic transmission has become a major trend in automobile design. Inevitably, the arisen problems such as increasing the number of links of planetary gear train, complex control system, and larger volume must be overcome. Therefore, efficiently and completely synthesizing feasible automatic transmission configurations from numerous planetary gear trains is an important research topic.
The purpose of this study is to design seven-speed automatic transmissions with two-degree-of-freedom compound planetary gear trains, including structural synthesis, clutching sequence synthesis, and optimal design of the number of teeth on gears. In structural synthesis aspect, nine eight-link and three nine-link compound planetary gear trains are obtained to satisfy the required structural specifications. In clutching sequence synthesis aspect, the formula of each speed ratio is expressed in terms of the number of teeth on gears for each gear train, and it can be roughly indentified to be an underdrive, an overdrive, a direct drive or a reverse. Under the requirements of a single clutch-to-clutch shift and decreasing speed ratios, all feasible clutching sequences are obtained by combining the usable underdrive sequences with overdrive sequences. In teeth number synthesis aspect, the objective function is defined as the summation of absolute values of the difference between the generated and desired speed ratios for the forward speeds. The optimal number of teeth on gears are then found by using a LINGO software together with the specified geometric constraints for design variables.
The results of this study show that there are no feasible solutions for any eight-link or nine-link planetary gear trains for the speed arrangement consisting of three forward underdrives, one direct drive, and three forward overdrives. As for the speed arrangement consisting of four forward underdrives, one direct drive, and two forward overdrives, there are also no feasible solutions for eight-link planetary gear trains, but seven feasible designs for seven-speed automatic transmissions are synthesized from two nine-link planetary gear trains.

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