Meshing Characteristics of Profile Shifted Cylindrical Quasi-Involute Arc-Tooth-Trace Gears. Part 1. Theoretical Base

A mathematical model of profile shifted quasi-involute arc-tooth-trace gears is obtained. The model includes functional relationships between the geometric-kinematic meshing characteristics and parameters of the generating surface as well as conditions which allow to prevent teeth undercutting and tip pointing. A short analysis of meshing characteristics value along the tooth trace is done for pressure angle value of 20º. This value of the angle was chosen as it is the most common one for general-duty gears, although the basic rack profile angle in the model is a variable quantity. The model can be used in the design and analysis of geometric-kinematic meshing characteristics of profile shifted quasi-involute arc-tooth-trace gears, cut by Gleason-type cutters with different profile angle value.