同一凸转子上节圆内、外工作轮廓间的互求机制  

Mutual tectonics mechanism of working outlines between inner and outer of node-circle based on the same convex-rotor

作　　者：李玉龙 刘萍[1] 宋安然 LI Yulong;LIU Ping;SONG Anran(School of Mechanical and Electrical Engineering,Suqian University,Suqian 223800,China)

机构地区：[1]宿迁学院机电工程学院,宿迁223800

出　　处：《机械传动》2025年第4期25-29,共5页Journal of Mechanical Transmission

基　　金：宿迁市智能制造重点实验室(M202108);江苏省智能制造装备关键技术工程研究中心资助;宿迁市“千名领军人才集聚计划”项目;宿迁学院高层次人才引进项目;宿迁学院创新团队项目(2021td07);宿迁市科技计划项目(Z2023139)。

摘　　要：【目的】凸转子轮廓因具有直接决定产品性能的特点而一直备受关注,但其构造也因需借助两个转子轮廓的共轭操作而相对复杂。为此,提出一种基于单一转子的简单构造方法,以期有效降低轮廓构造的难度。【方法】首先,针对由两个完全相同转子组成的转子副,基于其轮廓在节点啮合时简单的节点对称关系及其同步的共轭旋转规律,演绎出转子副非节点啮合时的共轭轮廓关系;其次,由简化到同一转子上节圆内、外工作轮廓间的互求关系,揭示出同一转子上节圆内、外工作轮廓间具有节点轴和瞬切轴先后对称的双轴对称机制;最后,以节圆的转角为直接变量,共轭的法向长度和传动角为间接变量,快速构建出工作轮廓的量纲一方程及其双轴对称矩阵。【结果】以圆弧工作轮廓为例的结果表明,双轴对称关系极便于转子轮廓的高效构造,真正实现了将两个转子轮廓间复杂的共轭关系,转化成同一转子上节圆内、外工作轮廓间简单的互求关系。量纲一方程及其双轴对称矩阵正确可靠,具有普适于圆柱齿轮、转子轮廓构造上的应用价值,从而为后续进一步的推广应用奠定基础。[Objective] The convex-rotor outline has attracted much attention because of its characteristics that directly determine the product performance;whereas the structure of it is also relatively complex due to the conjugate operation of the two rotor outlines.Therefore,a simple construction method based on a single rotor is proposed to effectively reduce the difficulty of outline-construction.[Methods] Firstly,for the rotor-pair consisting of two identical convex-rotor,from the simple nodal symmetry relationship of rotor-pair outlines when the node was conjugated and its synchronous conjugate rotation law,the conjugate outline relationship of the rotor-pair was derived when the node was non-conjugated.Secondly,from the simplified reciprocal relation between the inner and outer working outlines of node-circle on the same convex-rotor,the bi-axial sequential symmetry mechanism of the node-axis and the instantaneous-center tangent-axis between the inner and outer working outlines of node-circle was revealed.Finally,with the rotation-angle of node-circle as a direct variable,the conjugated normal-length and transmission-angle as two indirect variables,the dimensionless construction-equation of the inner and outer working outlines of node-circle and its bi-axial symmetry matrix were quickly constructed.[Results] The results of circular-arc as working outline show that the bi-axial symmetry relationship facilitates the efficient construction for convex-rotor outline,which makes the complex conjugate-relationship between the two convex-rotor outlines be transformed into the simple mutual relationship between inner and outer working outlines of node-circle based on the same convex-rotor.The dimensionless constructionequation and following bi-axial symmetry matrix are correct and reliable.The bi-axial sequential symmetry mechanism has the application-value for any profile-construction of convex cylindrical-gear and cylindrical-rotor,so as to provide a foundation for subsequent further popularization and application.

关 键 词：凸转子 轮廓构造 量纲一构造方程 双轴对称矩阵 法向长度 传动角 

分 类 号：TH137.3[机械工程—机械制造及自动化] TH166TH325