新型椭圆弧型罗茨转子的几何理论及其性能分析

摘要

The idea of designing a novel elliptical arc profile for the roots rotor is proposed. And the mathematical model for generating the elliptical arc rotor profile is established,then the equations of profile as well as the range of angle parameter for roots rotor are obtained. Conditions of undercutting and carryover in the elliptical arc rotor are studied,and a program for calculating the roots rotor of non-undercutting and non-carryover is designed using Matlab. The influence of parameter varia-tion on the area utilization coefficient of the elliptical arc rotor is analyzed,where the elliptical arc rotor is compared with the traditional circular rotor and involutes rotor,respectively.The results show that the area utilization coefficient of the elliptical arc rotors is inversely proportional to the pitch radius and elliptical axial ratio(a shorter axis divided by a larger axis)when the rotor radius is a constant;and the area utilization coefficient of the elliptical arc rotor with the same structure is higher than that of the circular rotor and involutes rotor.%提出一种新型椭圆弧型罗茨转子型线,建立椭圆弧型转子型线生成的数学模型,得到转子中各段曲线的解析方程和角度的取值范围.研究椭圆弧型转子产生根切和余隙容积的条件,并利用Matlab设计无根切、无余隙容积的罗茨转子程序.分析椭圆弧型转子的参数变化对其面积利用系数的影响,并与传统的圆弧型、渐开线型转子进行对比.结果表明:在外圆半径不变时,椭圆弧型转子的面积利用系数与节圆半径、椭圆弧段短半轴与长半轴比值成反比;在相同结构尺寸下,椭圆弧型转子的面积利用系数高于圆弧型、渐开线型转子.