本論文針對車輛雙輸入差速器之動力分析與幾何比例設計優化進行研究，目的是建立一套由機構幾何出發，分析主、輔輸入端與左右輪輸出端之轉速、扭矩、功率流向及效率表現的方法。有別於多數研究著重於控制策略設計，本文首先以方塊圖建立雙輸入差速器之運動與扭矩傳遞模型，藉由梅森增益公式與線性分式轉換法推得整體之轉移函數關係。為降低多個齒輪參數所造成之分析複雜度，進一步導入幾何比例因子x，將齒輪尺寸配置整理為單一設計參數，作為後續功率流向與效率分析之基礎。
利用 MATLAB/Simulink 針對 11 個代表性工況進行分析，計算主輸入端、輔助輸入端與左右輪端之轉速、扭矩、功率及效率。結果顯示，原始尺寸配置下部分工況會使輔助端進入負功率區間，代表系統內部出現功率相抵現象導致效率下降，根據此結果，本文以幾何比例因子x作為尺寸優化依據，提出優化配置以改善輔助端負功率現象，使功率流向更為合理，並提升系統整體效率。此外，本文亦針對原始設計尺寸之機構進行量測分析，以驗證模型與公式推導之合理性。綜合而言，本研究可作為雙輸入差速器前期幾何設計、功率流向分析與效率評估之參考。

This study investigates the dynamic characteristics and geometric design of an active dual-input differential. Unlike previous studies that mainly focus on control strategies, this work analyzes the effects of differential geometry on torque transmission, power flow, and system efficiency. A block-diagram-based model is established to describe the relationships among the primary input, assist input, and left and right output shafts.
To simplify the analysis of multiple gear dimensions, a geometric ratio factor x is introduced as a design parameter. Eleven representative operating conditions are analyzed using MATLAB/Simulink. The results show that the original geometric configuration may cause the assist shaft to operate in a negative-power region, resulting in power cancellation between the primary and assist inputs and increasing the motor power demand.
Experiments using the original differential testbed are conducted to verify the main characteristics of the theoretical model. Based on the analysis, the geometric design is further improved by adjusting the geometric ratio while considering practical gear and installation constraints. A feasible configuration with x≈2.0833 is obtained, which reduces unfavorable power interaction and motor power demand under critical operating conditions.
The proposed method provides a useful approach for the preliminary geometric design and power-flow evaluation of active dual-input differentials.

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