罗茨转子形状系数最大化设计的啮合角最小化方法  

Engagement-Angle Minimization-Method of Shape-Coefficient Maximization-Design and Its Analytical Innovation for Roots Rotor

作　　者：常利娟[1] 李玉龙 CHANG Lijuan;LI Yulong(Hebi Polytechnic,Hebi 458030,China;Suqian University,Suqian 223800,China)

机构地区：[1]鹤壁职业技术学院,鹤壁458030 [2]宿迁学院,宿迁223800

出　　处：《真空科学与技术学报》2025年第2期164-170,共7页Chinese Journal of Vacuum Science and Technology

基　　金：宿迁市“千名领军人才集聚计划”项目;宿迁市智能制造重点实验室项目(M202108);宿迁市科技计划项目(Z2023139);宿迁学院创新团队项目(2021 td07)。

摘　　要：为解决罗茨转子形状系数最大化设计中的共性问题和简化现有零曲率半径法的应用问题;基于由外定内和由内定外的两种常见轮廓构造;通过分析啮合角和形状系数的因果关系,建立了以啮合角为变量的轮廓坐标方程;通过分析轮廓干涉和干涉坐标异向变动的内在关系,提出了零坐标导数的最小啮合角解析方法;通过最大传动角和极限相位角的内在关系,提出了最大传动角的极限相位角解析方法;最后以渐开线、圆弧和直线转子为例,加以创新方法在两种轮廓构造中的应用论证。结果表明啮合角与形状系数具有直接的因果关系,啮合角越小,形状系数越大;零坐标导数加最大传动角的创新方法等价于现有零曲率半径法,能克服零曲率半径法的应用问题;由内定外轮廓构造中的最小啮合角和极限相位角均为零,而由外定内轮廓构造中最小啮合角均不为零,传动角为不单调函数时极限相位角由零传动角导数确定,单调函数时为端点相位角等。得出以啮合角代替形状系数为轮廓构造变量、零坐标导数和最大传动角代替零曲率半径的方法,逻辑更清晰、方法更简单,解析性更好的重要结论,从而为共轭轮廓的曲线类型创新提供了理论基础。To solve the common problem of calculating maximum shape coefficient of the roots rotor and simplify the application problem of the existing zero curvature-radius method;based on the common two conjugatecontour constructions from the inside to the outside and from the outside to the inside;from analyzing the causality of engagement angle and shape coefficient,the contour coordinate equations with engagement angle as variable are derived;from analyzing the internal relation of contour interference and the interference coordinate,the analytic method with zero coordinate derivative is proposed for the minimum engagement angle;from analyzing the internal relation of the maximum drive angle and the limit phase angle,the analytic method with the maximum drive angle is proposed for the limit phase angle;finally,take the involute,arc and linear rotor as examples to demonstrate the innovative-method application in two contour constructs.All results show that the engagement angle and the shape coefficient are directly causal;the smaller the engagement angle,the larger the shape coefficient;the innovative method of the zero coordinate derivative plus the maximum drive angle is equivalent to the existing zero curvatureradius method,which can overcome the application problem of the existing zero curvature-radius method;the minimum engagement angle and limit phase angle are zero in the conjugate-contour construction from the inside to the outside,but in the conjugate-contour construction from the outside to the inside,the minimum engagement angle is not zero,the limit phase angle is determined by the zero drive angle derivative when the drive angle is not a monotonic function,and the end-point phase angle when the drive angle is a monotonic function,etc.It is concluded that the engagement angle replaces the shape coefficient as the contour construction variable,and the zero coordinate derivative plus the maximum drive angle replaces the zero-curvature radius,with clearer logic,simpler method and better analytics,which provides

关 键 词：罗茨转子 最大形状系数 最小啮合角 零坐标导数 最大传动角 零曲率半径 

分 类 号：B752.26[哲学宗教—外国哲学] TH166[机械工程—机械制造及自动化]