Main Tasks of Classical Theory of Gearing and Problems of Optimization Synthesis of Tooth Surface

Abstract

The classical theory of gearing (by Faydor Litvin) includes two main tasks: 1) Task of Synthesis: the tooth surface of one gearwheel is known, the tooth surface of the second gearwheel is to be determined. 2) Task of Analysis (reverse task): the tooth surfaces of two moving members are known, the law of motion is to be determined. It is proposed to add the third task to two main tasks of the theory of gearing: tooth surface synthesis according to the assigned surface of meshing. From mathematical point of view, this task is different significantly as compared to two common ones. It is not reduced to the Task of Synthesis by Litvin. It is solved by integrating the differential equation of meshing by numerical methods. One of the reasons of innovation is the perspective of optimization synthesis of the tooth surface based on analysis of quality indicators in all possible contact points (by Sergey Lagutin - in all space of meshing). Within such a synthesis, the line or surface of meshing is firstly synthesized: they are drawn in areas with the most favorable or assigned values of the chosen criterion of the load capacity. Surfaces of contacting teeth are determined after synthesis of the line (surface) of meshing. Certain problems are considered, that appear at optimization synthesis based on analysis of features of the space of meshing: the dualism of the task of gear synthesis when using the reduced radius of curvature in the target function, the problem of the target function degeneration and oth. For eliminating some of these problems, the local quality criteria is required that estimates the local positive effect and simultaneously influences the global indicator (first of all, the contact ratio). It is proposed and substantiated to apply the specific work of surfaces AF as such a criterion.