Analysis of conditions for selecting the number of teeth of planetary gearboxes

Abstract

The issues of selecting the number of teeth for 2k-h type A mechanisms based on the study of the known conditions for their assembly used in the development of planetary gearboxes of various shipboard both deck and main power ship installations are highlighted in the paper. Considering the design practice, when selecting the number of teeth, it is important to maintain a given gear ratio, ensure the alignment of the mechanism gears, withstand the condition of the neighborhood of satellites, ensure the assembly condition and the absence of interference of internal gearing. These conditions are expressed in terms of the number of teeth of gears and impose restrictions on the parameters of 2k-h mechanisms. Checking the interference condition of internal gearing at the stage of selecting the number of teeth in existing methods is usually not done, but it is performed at the stage of checking the quality of gearing according to geometric conditions. With this approach, the selection of tooth numbers is considered as a problem solved by the method of successive approximations: selection of tooth numbers — calculation of geometric dimensions — checking the quality of gearing — selection of a new combination of tooth numbers, etc. The condition of interference of internal gearing obtained in the work is represented by a closed formula, which eliminates the use of the iteration method, which requires a large amount of computational work and allows it to be tested at an early stage of product development. The neighborhood condition is expressed by an equation in which the design parameter is associated with the maximum possible number of satellites and a guaranteed gap between their initial circles. It makes it possible to theoretically explain well-known constructions that do not agree with the theoretical views existing at that time. The alignment condition allows for both an even and an odd difference in the number of teeth of the central wheels. Thus, the results obtained make it possible to solve the problems of creating a mechanism with the maximum possible number of satellites for reducing the size of a planetary mechanism as a unit completing a marine gearbox of any complexity, to expand the set of possible combinations of the teeth numbers that provide a given design and require less computational work.