Study on Design Constraints of Conjugated Straight-Line Internal Gear Pair

Abstract

In order to solve the problem that the design constraints of the conjugated straight-line internal gear pair are unclear, the designing and checking of gear pairs requires repeated trial and error. By analogy with the design of the involute gear pair, the basic design parameters of the conjugated straight-line internal gear pair were clarified. Based on the mathematical model of the gear pair, the constraints on basic design parameters were given according to gear engagement theory and the geometrical relations of the tooth profile. The calculation formula and the constraint of the contact ratio were deduced according to the kinematic relations. Based on Litvin’s undercutting theory, the constraints on avoiding undercutting and end cutting were deduced and their correctness was verified by examples. The judgment method of tooth-overlapping interference and its corresponding numerical calculation flow were presented. The constraint on avoiding radial interference was deduced and analyzed. Based on the above content, the influence laws of design parameters on the design constraints were studied. Last, design examples were given and the effective design flow diagram of the conjugated straight-line internal gear pair was summarized. These research results provide a theoretical basis for the parameter design of conjugated straight-line internal gear pairs, provide guidance to avoid the interference of the gear pair, and promote the design system of the gear pair.