The mathematical model of engagement and analytical description of tooth profile of waveform edge kinematic reducer

Abstract

The problem of creating a waveform edge kinematical reducer with multi-pair gearing brings to the fore a range of issues in the field of geometric-kinematic gearing theory, which are considered in this work. The synthesis of multi-pair gearing for a waveform edge kinematical reducer, which ensures the constancy of their transfer function, provides for: development of a mathematical model of gearing taking into account the peculiarities of the interaction of teeth during special-spherical motion; description of the profile of the teeth by a system of equations for a spherical surface and for a normal section of teeth for internal gearing; identification with the help of the MathCAD 2010 Professional program of a mathematical experiment and determination of the area of existence of 100 % multi-pair mating of teeth by comparing the shape of their profile with the nature of the analytical function of multi-pair engagement.