含一控制葉片之旋轉式壓縮機之最佳化設計

Abstract

本文研究設計凸輪轉子機構控制葉片位置之旋轉式壓縮機，並以遺傳演算法之最佳化方法求得特定流量時之最高效率的壓縮機尺寸。由包絡線理論推導葉片之軸承在凸輪盤上運行之軌跡與轉子輪廓，當轉子旋轉時，葉片之軸承沿凸輪盤上之包絡線軌跡運行，控制葉片運動。適當的設計與加工，可使葉片與轉子間無摩擦損失，並利用右凸輪盤與右蓋板之關係形成氣體排氣裝置，取代排氣閥。研究方法為建立壓縮機之數學模型，分析幾何關係，推導凸輪盤與轉子之包絡線，再分析壓縮機之氣體性質與葉片動力模型，並以壓縮機之總效率即機械效率乘以容積效率作為目標函數，進行最佳化設計，根據最佳化結果，製作壓縮機模型並實驗，比較計算與實驗值。在轉速為180rad/s時，計算與實驗分別所得之壓縮比為3.01與2.91，排氣溫度為315.48K與312.25K，容積效率為80.76%與79.71%，機械效率為70.33%與68.53%，總效率為56.79%與54.62%，定義誤差量為計算值減去實驗值除以實驗值，在轉速為50rad/s~200rad/s之間時，壓縮機性能的計算值與實驗值之誤差都在4%以內。當設定體積流量與文獻相同時，本研究與文獻之壓縮機的最大機械效率實驗值分別為69.68%與68.3%，此效率時之轉速分別為14636rad/s與125.6rad/s，本研究之壓縮機機械效率較文獻高1.38%。

A rotary compressor with a controlled sliding vane is designed for a specific flow rate in this study. The genetic algorithms of the optimization method is used with the objective function of the maximum total efficiency, that is the multiplication of the mechanical efficiency and the volumetric efficiency, to determine the dimensions of the compressor. The envelop theorem is used to design the enveloped profiles on the cam plates and the contour of the rotor. When the rotor rotates, the bearings on the vane moves along the envelop profiles on the cam plates to control the motion of the vane. An appropriate design and fabrication of the compressor eliminates friction loss between the vane and the rotor. Utilizing the air outlet formed by the right cam plate and the right cover plate replaces the conventional outlet valve. A mathematical model of the compressor is generated. The geometric relation, the envelopes on the cam plate and the rotor, air properties and the vane dynamic behavior of the compressor are analyzed. The optimum designed compressor is fabricated and tested, and the calculated results are compared with the test data. At the rotor rotational speed of 180 rad/s, the compression ratios are 3.01 and 2.91, the outlet temperatures are 315.48 K and 312.25 K, the volumetric efficiencies are 80.76 % and 79.71 %, the mechanical efficiencies are 70.33 % and 68.53 %, the total efficiencies are 56.79 % and 54.62 % for the calculated results and the test data, respectively. The deviations of the calculated results and test data are within 4 % at the rotor rotational speed from 50 rad/s to 180 rad/s. With the same specific flow rate as an existing compressor, the maximum mechanical efficiencies of the optimum designed compressor and the existing compressor are 69.68 % and 68.3 %, respectively, at the corresponding rotational speeds of 146.6 rad/s and 125.6 rad/s. The mechanical efficiency of the current designed compressor is 1.38 % higher than that of the existing compressor.