Synthesis of planetary mechanisms AI type with regard to engagement angles for coupled and uncoupled wheels

Tatiana Heresh, Sergey Kavetsky

Abstract


The subject matter of this article is the processes of synthesis of planetary gear mechanisms of AI type with uncoupled and coupled wheels to solve the problems of gear wheel design. The goal is to develop the synthesis of planetary mechanisms of AI type, considering the possible values of engagement angles and with predetermined quality indicators of gear pairs at the stage of design. The tasks are to develop a methodology of planetary mechanism synthesis of type AI, to find general equations, considering the dependence of the number of teeth on the engagement angles for mechanisms of this type with uncoupled and coupled wheels with additional synthesis parameters, which would give the possibility of performing the synthesis of the planetary mechanism to guarantee the necessary engagement angles of the cogwheels. The methods used are ones for solving the system of linear parametric equations, which is obtained from the general equations of the synthesis of planetary mechanisms. The following results were obtained: the general equations for the mechanism of type AI, which consider the parameters of the geometrical calculation of the gear pairs that make up the mechanism have been obtained. The research on received general equations has been carried out and the area of existence of planetary mechanisms of AI type for different engagement angles of pairs of coupled and uncoupled wheels has been constructed. From the results of synthesis, it can be seen that the range of existence of planetary mechanisms is significantly expanded, which makes it possible to realize a wider range of transmission ratio for each number of satellites and get additional numbers of teeth of the planetary mechanism, which cannot be found using the classical methods. Conclusions. The scientific novelty of the results obtained in the study consists of the following: the considered approach of synthesis with an account of engagement angles makes it possible not only to obtain additional combinations of numbers of teeth of planetary gear but also in further calculations to jointly use the existing locking contours for each pair of wheels, as well as to assess in advance the possibility of cutting the gears whose engagement angles will satisfy the selected parameter at the stage of synthesis of the planetary mechanism.

Keywords


gears; engagement angle; general equations; satellite; gear ratio; planetary mechanism; coupled wheels; uncoupled wheels; synthesis of the planetary mechanism

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DOI: https://doi.org/10.32620/aktt.2022.4.02