Development of Kinematic Method of Theory of Gearing to Determine Areas of Tooth Flanks Produced by Jogs of Generating Solids

摘要

The paper describes application of kinematical method of the theory of gearing to determine surfaces and lines produced by generating method related not only to smooth generating surfaces and lines but with the presence of singular points - jogs - in points of adjacent areas. Three types of jogs are considered: jog at the point of intersection of two plane profiles; jog along the line of intersection of two surfaces; jog at the point of intersection of three surfaces. Three types of geometrical images generated by these three types of jogs are proposed: fan, wedge, bunch of normal lines. Efficiency of applying these images when analyzing the process of tooth generation and meshing is shown. Mathematical models are developed and presented for generating processes in the presence of jogs on generating surfaces and lines. Examples of computer modeling with application of these models are given. It is emphasized that the developed method operates much faster than non-differential methods which have been considered to be applicable only when computer modeling the generating processes in the presence of jogs.