本研究將現有之雙級式史特靈冷凍機內的二級移氣器分離，建立理論模型並撰寫程式以進行數值模擬。本研究中冷凍機動力模型分為兩種，第一種為將一、二級移氣器相位角設為給定的變數，第二種為將一、二級移氣器之間以彈性元件連接，其相位角由彈性元件和振動特性決定。首先給定初始條件以求得活塞及一、二級移氣器位置，接著計算各腔室之熱力性質，透過代入熱損失至能量方程式中，求得各腔室及各級製冷頭之溫度變化。另外也透過參數分析，找出能使冷凍機無負載溫度最低的一、二級移氣器間相位差，並且探討不同操作條件下的相位差表現和彈簧系統中製冷頭溫度表現。透過數值模擬的結果，在給定相位角的雙級史特靈冷凍機中，於工作流體為氦氣、填充壓力為7 bar、馬達轉速為1800 rpm、第二級移氣器領先第一級移氣器140°的操作條件下，第一、二級製冷頭分別可獲得152.1 K及100.3 K之無負載溫度；在此操作條件下，於第二級製冷頭加上0.5 W之熱負載，此時一、二級製冷頭的溫度分別為152.8 K及104.8 K，冷凍機整體的COP為 0.09，約為卡諾循環COP的16.8%。在以彈簧系統連接、二級移氣器的雙級史特靈冷凍機中，填充壓力為1 bar、馬達轉速為1600 rpm時，未碰撞的彈簧系統參數組合最佳值為阻尼比 η=1.0、彈簧常數 k=400 N/m，在此參數組合下，第一級製冷頭的穩態溫度為228.73 K，第二級製冷頭的穩態溫度為163 K。若在第二級製冷頭加上0.5 W之熱負載，則第一級製冷頭之溫度升為229.78 K，第二級製冷頭之溫度升為167.97 K。

In this study, a two-stage Stirling cooler with different phase angles between displacers is analyzed by a theoretical model. Pressure, volume and mass in working chamber can be predicted by using the instantaneous position of piston, first stage and second stage displacer. The cold head temperature is calculated by the law of conservation of energy, which contains three kinds of thermodynamic losses: shuttle loss, pumping loss and pressure drop loss. Coefficient of performance can be determined by applying a heat load on the second stage cold head. The results of simulation shows the cold head temperature can reach 152K at the first stage cold head and 100K at the second stage cold head when the operating speed is 1800 rpm, the charging pressure is 7 bar and the second stage displacer leads the first stage displacer 140 degrees. When the heat load is 0.5W at 105 K, the coefficient of performance is 0.09. If a mass spring damper system is used to determine the motion of the second stage displacer, the temperature of the best case of the first stage and the second stage cold head are 228.73 K and 163 K respectively.

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