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

LI Yulong; LIU Ping; SONG Anran

doi:10.16578/j.issn.1004.2539.2025.04.004

Abstract：[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 construction-equation 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.