自由分子流域下轉子間隙的洩漏分析

Abstract

為了解真空幫浦抽氣於自由分子流狀態下，轉子間隙因壓力差所產生的洩漏量，本研究中利用類似於熱輻射學中視因子(View factor)的觀念來計算自由分子流的流量。研究中針對螺旋式真空幫浦，依照其轉子和外殼的幾何形狀，找出可能產生洩漏的地方來計算間隙流量。我們透過數值方法解氣體分佈密度之聯立積分方程式，以算出壁面上的氣體密度分佈(單位時間內碰撞單位壁面面積的氣體質量)。已知氣體密度分佈後可進而求出各進(出)口端的淨流量。本文中我們探討間隙尺寸、壓力差和間隙幾何外形對於洩漏量的影響；分析顯示，間隙尺寸越大時洩漏量越大，壓力差增加洩漏量也隨之增加；另，間隙尺寸變化對流量的影響關係中，可知這兩者之間為近似線性的變化關係，而且當壓力差增加時曲線斜率亦增加，間隙尺寸變化對流量的影響越明顯。最後我們發現三個產生洩漏的間隙，其間隙尺寸變化對流量的影響皆為近似線性關係，和間隙幾何外形無關。

To understand the mass transfer processes of the free-molecule flow in vacuum pump, we utilize the concepts of view factors introduced from the field of thermal radiation to analyze the leakage flow rate produced by the pressure differences within the gap. We investigate the flow rates from leakage gaps regarding to the geometric shape of the rotors and shell of the screw vacuum pump. We numerically solve the associated integral equations for the gas density distributions（the gas mass collided on per unit area per unit time）at the walls. And then we solve the net flow rate at the inlets and outlets. We examine the effects of gap size, pressure difference and gap geometry on the leakage. Results show that the leakage increases as the gap size increases also, as the pressure differences become large, the leakage becomes large. From the influences of gap sizes on flow rate, we find that the relationships of the flow rate with the gap size are linear. While the pressure differences are larger, the influences are distinct. Finally, the effects of the gap sizes on the variation of flow rates are similar for all three types of gaps geometric.