內葉輪幫浦之特性研究

Abstract

內葉輪幫浦為旋轉式幫浦其中之一種形式，目前已被廣泛地使用在工具機、飛行器、汽車、印刷機、變速箱……等本身具有液壓系統的設備上，用來提供該液壓系統之流體動力來源。同時，內葉輪幫浦具有構造簡單、體積小、壽命長、流量穩定、噪音低等優點，已逐漸取代傳統漸開線型齒輪幫浦在工業上的應用。 藉由內、外轉子之間的共軛運動，內葉輪幫浦可以達成推送管線中流體的目的。因此，欲進行內葉輪幫浦之特性研究，必須從內、外轉子之幾何外形著手。本論文係以齒輪原理為基礎，以解析法來求得轉子外形曲線之數學模式。同時，利用所推得之轉子外形曲線數學模式，可以建立內葉輪幫浦各種特性分析所需之模型。 在本論文中，分別推導出圓弧線型與橢圓線型為基本線型之轉子數學模式，並依據所推得之數學模式進行內葉輪幫浦的轉子外形過切分析，並舉實例說明過切現象發生之位置與改善過切現象之方法。另外，根據轉子外形曲線之數學模式，進行內、外轉子的接觸分析，其中包括了接觸點的探討與接觸應力的分析。有了內、外轉子嚙合過程中接觸點的資料後，進一步從事流體進出口的設計工作。 其次，內葉輪幫浦在高速運轉的狀態之下，將會產生溫升的現象，致使轉子外形幾何發生變化。所以，在本論文中利用轉子外形曲線之數學方程式，建立有限元素熱變形分析所需之轉子幾何模型，以進行轉子熱膨脹的模擬。同時，依據有限元素法商用分析軟體ANSYS模擬的結果，針對內、外轉子外形曲線數學方程式進行修正的工作。 最後，以面積效率的觀點來探討具不同基本線型之內葉輪幫浦在面積效率上的差異，以及不同的設計參數對於面積效率的影響程度。

An internal lobe pump, which is used primarily as a source of fluid power in hydraulic systems, is one type of the rotary pumps. It is widely used in the machine tool, aircraft, automotive, press, transmission, and mobile equipment applications. The advantages of the internal lobe pump are simple structure, small volume, long working life, steady flow and low noise. Therefore, applications of the conventional involute gear pump in many branches of industry have been replaced by internal lobe pumps gradually. In the operation of an internal lobe pump, the conjugate motion between the inner and outer rotors forces liquid forward. Therefore, in order to investigate the characteristics of an internal lobe pump, the first step is to develop the geometry of inner and outer rotors. In this thesis, mathematical models of the inner and outer rotors of the internal lobe pump have been developed based on the theory of gearing. Based on the developed mathematical models various characteristic analyses of internal lobe pumps can be performed. First, mathematical models of two different types of the rotor's profile, the circular lobe profile and the elliptical lobe profile, are developed in this thesis. The investigations on the profile undercutting for inner rotors are studied according to the developed mathematical models. Also, based on the theory of tooth contact analysis, the contact analysis for lobe contact points at any instant and the contact stress analysis for internal lobe pumps are studied. According to the location of contact points, we can design the inlet and outlet ports of the internal lobe pump. Second, the geometry of the rotors' profile will change because of the raised temperature while the pump is in operation. In this thesis, the simulation for thermal expansion of the rotor is performed by the commercial FEM software, ANSYS. According to the results of the thermal expansion simulation, we can modify the mathematical model of the rotors' profile to avoid the interference between the inner and outer rotors. Finally, further discussions on the pumping performance are presented based on the area-efficiency of the pumps. A comparison on the pumping performance for pumps with circular lobe profile and elliptical lobe profile is also studied. The influence of different design parameters on the pumping performance of an internal lobe pump is also investigated.