螺旋轉子三維嚙合模擬與間隙計算方法研究

Three-dimentional meshing simulation and clearance evaluation of screw rotors

黃詣超(Yi-Chao Huang)

指導教授 ： 賴景義

國立中央大學/工學院/機械工程學系/博士(2011年)

摘要

螺旋式壓縮機具有多項優點，因此，在過去數十年間廣泛的應用於各領域中。螺旋式壓縮機的核心為一對公母轉子，藉由轉動的容積變化產生壓縮空氣。在理論設計時，公、母轉子為嚙合條件及設計參數下所創生的理論齒形，並可形成完美的接觸線密封氣體防止洩漏。但實際上，轉子因加工誤差、組裝偏擺、運轉時的熱膨脹、以及應力變形等因素，容易發生轉子干涉或咬死的情況，因此，轉子的設計流程中會將間隙加入齒形中，但間隙會造成接觸線中斷及洩漏降低效率，雖然間隙會造成諸多缺點，但間隙對於轉子是必要的。所以，適當的間隙設計是影響壓縮機效率的主要因素之一。然而，傳統間隙的量測方式耗費人力與時間，並且需仰賴特定方式或機台進行量測，同時受限於分析軟體的功能限制，無法有效的計算實際間隙，因此，本研究主要目的為發展嚙合模擬與間隙計算的方法，以預測實際組裝的情況。

本研究所發展的各項技術具體說明如下：轉子嚙合模擬技術，以轉子的幾何造型搭配角度疊代方法，主要目的為計算轉子實際嚙合的位置。接觸線間隙計算方法，藉由嚙合模擬後的轉子結合接觸線資料，以多截面疊代方法計算轉子在接觸線附近的間隙分佈。點對曲面搜尋最近點方法，建立以網格為基礎的搜尋方法，搭配計算初始值及數值疊代計算點到曲面的最近點。透過此三項技術的結合，不論齒形資料的類型或輸入的模擬條件，均可正確的計算嚙合位置及間隙分佈，與過去模擬方法最重要的不同點在於考量整根轉子而非單一截面，能夠近似實際轉子以多溝嚙合的情況。本研究除了與商用軟體計算結果以佐證本研究的正確性，同時，以實際量測間隙的結果進行比較，以驗證本方法對於間隙預測的準確性。

關鍵字

螺旋轉子 ； 嚙合模擬 ； 間隙計算

並列摘要

Twin screw compressors are for decades widely used in industry owing to advantages over other types of compressors. Due to machining imperfections, thermal expansion, pressure deformation, and assembly misalignment, these deviations from the theoretical profile often causes interference between the rotors. To compensate such deviations, it is necessary to apply clearance between the main and the gate rotors which will still provide minimum clearance to reduce the interference. However, the clearance may result in a change of the meshing conditions, such as imperfect contact, discontinuity of the sealing line, backlash and decreasing efficiency caused by the leakage of gas from a high-pressure region to a low-pressure region. Although the clearance may also lead to the above drawbacks, it is still necessary to design clearance between the rotors. Thus, the appropriate clearance between the rotors should be design carefully. Conventionally, clearance measurement must depend on the specific machines and spend lots time and effort. Also, the analysis software has limits for simulate the clearance. So, the aim of this study is to develop a new meshing simulation and clearance evaluation method to predict the real condition after assembly.

The methods developed in this study can be classified into the following three issues. The meshing simulation method is proposed to define the real meshing position for rotors by the geometry of rotor profile and angle iteration method. The clearance evaluation method is to calculate the clearance along the sealing line by the method of multiple transverses iteration. The procedure for searching the closest point between massive points and surface is based on the triangular mesh of surface and iterative method in order to comptute more rapidly. By the combination of the above methods, the meshing position and clearance can be computed correctly regardless the data type of rotor profiles or the variation simulation conditions. Specifically, the difference between this study and past researches is that the simulation method in this study considers the all lobes but not the single lobe at the same time for the purpose of approximate real meshing. Computer simulations are compared with commercial software to demonstrate the accuracy of the proposed method. Also, experimental results are presented to verify the feasibility for clearance prediction.

並列關鍵字

meshing simulation ； clearance evaluation ； screw rotors

參考文獻

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