具橢圓形節曲線之魯氏泵研究

A Study on Root's Pumps with Elliptical Pitch Curve

10.29847/JNUU.201112.0009

陳建發(Chien-Fa Chen)；陳翰儀(Han-Yi Chen)；林宜暉(Yi-Huen Lin)；林子揚(Zih-Yang Lin)

橢圓形魯氏泵 ； 轉子線形 ； 過切 ； elliptical Root's pump ； rotor profile ； undercutting

聯大學報

8卷2期（2011 / 12 / 01）

179 - 190

繁體中文

本文根據齒輪原理及創成機構創成具橢圓形節曲線魯氏泵。此橢圓形魯氏泵其轉子之齒冠輪廓為圓弧形，轉子齒根輪廓則為圓弧形齒冠之共軛曲線。首先推導橢圓形魯氏泵之葉輪線形之數學模式，並根據所推導的線形數學模式及微分幾何的觀念探討葉輪線形之過切現象。最後，本文發展出一套電腦設計程式作為橢圓形魯氏泵設計及製造使用。

This study presents the generation of Root's pump with elliptical pitch curve, based on gear theory and generating mechanism. The addendum profile of the rotor is a circular arc, and the dedendum profile of the rotor is a conjugate curve generated by the addendum profile of the rotor. A complete mathematical model of the elliptical Root's pump is developed. According to the developed mathematical model and concept of differential geometry, undercutting is investigated. Furthermore, a computer program is made and computer graphs are also displayed.

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