| 摘要: | 雙螺桿空壓機是一種廣泛應用於空氣壓縮和工業製程中的關鍵設備，其以穩定、可靠且高效的性能使其成為工業領域中不可或缺的角色。隨著工程領域的研究與發展，為了提高雙螺桿空壓機的性能，轉子的變導程設計將是影響空壓機性能的關鍵因素。因此，本研究針對雙螺桿空壓機，進行不同導程曲線下之空壓機性能分析與比較。首先，本研究在相同齒廓、相同轉子螺旋部長度以及相同轉子包封角的情況下，設計四種不同導程變化曲線，並計算分析不同導程下轉子幾何特徵之差異。接著，本研究建立理論內壓縮過程模型來模擬分析雙螺桿空壓機的壓縮循環過程。其中，模型中將包含空氣之質量守恆方程式、能量守恆方程式、氣體狀態方程式、氣體洩漏方程式與氣體排氣方程式，整體理論內壓縮過程模型包含了6個計算流量的經驗常數。在計算上，本研究使用Runge-Kutta 4th-Order Method演算法進行求解。再來，為了驗證理論模型的準確性，本研究透過實驗量測方式，並使用數值計算軟體Mathematica之最佳化模組Global Optimization最佳化求解6個經驗常數。利用最小平方法將不同轉速下理論與實際之容積排量差值，平方相加作為目標函式，以求出最符合實際排量之經驗常數。經實驗驗證後的理論模型，其容積效率的計算平均誤差均在3%之內，而等熵絕熱效率的計算平均誤差均在2%之內。最後，將不同導程曲線的轉子設計參數套入本研究建立之理論內壓縮過程模型中，探討導程對於空壓機性能之影響，找出導程變化曲線與空壓機性能之關係。;Twin-screw air compressors are key devices extensively used in air compression and industrial processes, known for their stability, reliability, and efficiency, making them indispensable in the industrial sector. As research and development in engineering continue to advance, the design of variable-lead rotors has emerged as a critical factor influencing the performance of these compressors. Consequently, this study focuses on analyzing and comparing the performance of twin-screw air compressors under different lead curve designs. Initially, the study designs four different variable-lead curves while maintaining the same tooth profile, rotor length, and rotor wrap angle, and then analyzes the differences in rotor geometric characteristics under varying leads. Furthermore, this research develops a theoretical internal compression process model to simulate the compression cycle of twin-screw air compressors. This model includes equations for mass conservation, energy conservation, gas state, gas leakage, and gas exhaust, and incorporates six empirical constants for flow calculations. The Runge-Kutta 4th-Order Method is employed for computational solutions. To verify the accuracy of the theoretical model, the study utilizes experimental measurements along with Mathematica′s Global Optimization module to optimize these six empirical constants. The least squares method is applied to aggregate the squared differences between theoretical and actual volumetric displacements at varying speeds as the objective function, aiming to determine the empirical constants that best match actual displacements. The validated theoretical model demonstrates an average error in volumetric efficiency calculations within 3% and an average error in isentropic efficiency calculations within 2%. Finally, the study inserts the rotor design parameters from variable-lead curves into the established theoretical internal compression process model to explore the impact of lead changes on compressor performance, thereby elucidating the relationship between lead variation curves and compressor performance. |
