Research And Design Of The New Universal Cycloid Gear Tooth Profile

The tooth profile of traditional cycloid gear is formed by a circular cycloidwith the advantages of large contact ratio, fewer number of teeth with noundercutting, less wear and uniform wear, on the increasingly urgent requirementsof small size, light weight, high efficiency in modern production, the advantages ofcycloid gear is concerned, and also the accuracy requirements of cycloid gear can beeasily met by the raising level of processing. However, the cycloid gear does nothave the separability as involute gear, and researches mentioned above lay stress onthe appropriate parameters selecting or method of circle cycloid splicing, makingthe essence is still the traditional cycloid engagement and the application is greatlylimited. The tooth profile described in this article, as is called new universal cycloidtooth profile, is the deformation of traditional circular cycloid tooth profile. Itremains the advantages of cycloid gear, solves the centerline spacing problem andincreases tooth strength.This tooth profile is formed by the deformation of hypocycloid, involute anddeformation epicycloid, whose conjugate tooth profile is generated by principles ofgear. The least teeth number of gear has this tooth profile is6, this meets theconditions of the contact ratio and has no undercutting and greatly reduces thevolume of the gear and reducer. Compared with involute gear, this new universalcycloid gear has small and uniform sliding rate, bigger comprehensive radius ofcurvature and higher strength of tooth caused of the figure of tooth profile. A pair ofmeshing gears degenerate into traditional cycloid gear when the centerline spacingvariation is zero, otherwise, became the new universal cycloid gears. Among them,the closed tooth profile cannot be used in general gear transmission while the moreeffective tooth profile formed by the closed tooth profile can meet the requirementsof the contact ratio with a wider range of application.In this paper, expressions of straight cycloid in the coordinate system of gear isgenerated by coordinates transformation, meshing equation is established byenvelop method and relative motion method, geometric model of straight cycloid’senvelope(the new universal cycloid) is established, the undercutting boundaryequations of straight cycloid envelope is calculated, the region of straight cycloidwhich can be formed into tooth profile is determined, according to the number ofteeth, the geometry of the closed tooth profile and the more effective tooth profilehave been established. According to the theory of gearing, calculating and drawingare shown in this paper of conjugate gear and meshing line, the contact ratio, slidingrate, pressure angle, radius of curvature and comprehensive radius of curvature, pressure on bearings or gears and stress of this two conjugated gears. Through thestudies on the tooth profile of the new universal cycloid gear, the basic parametersof the tooth profile and basic tooth profile are identified, formulas on calculating thevarious parts of the gear, general rules and parameter selecting methods are given,the new universal cycloid gear processing principles are researched, and also theshaping principle of a pair of conjugated cycloid gear are gained. In order to verifythe contents of the research, a set of new universal cycloid gear’s parameters, whichcan meet the meshing condition, are chosen to build a3K-III planetary speedreducer,3-D models are built and the actual reducer are processed. The tooth profilemeshing well and the reducer running smoothly, that proved the tooth profiledesigning is reasonable. However, the serialization and standardization of theparameters, the formula for calculating the geometrical dimensions, the profile errorparameters and the profile error control still need further study.