OPTIMIZATION OF GEAR DESIGNS OF A 3K TYPE PLANETARY MECHANISM ACCORDING TO THE END OVERLAP CRITERION

The article discusses the optimization methodology for the design of spur cylindrical gear engagements of the 3K type planetary mechanism based on the criterion of end overlap. Optimization of end overlap is performed by selecting the values of the gear shift coefficients from the permissible ranges of variation of their values. Permissible ranges of variation are determined by two limit values – minimum and maximum.. The found permissible ranges of gear shift coefficient values satisfy the conditions of coaxiality of the gear engagements of the 3K type planetary mechanism. The search for permissible ranges of values of the coefficients of gear shifts is performed by analyzing the properties of the functions of the coefficients of the end overlap of gear engagements. Each such function is considered as a function of two quantities – the coefficients of shift of gears that form the corresponding gear engagement. The construction of two-dimensional graphs of these functions allows us to determine the nature of the change in the value of the end overlap coefficient depending on the values of the gear shift coefficients, which are taken as insignificant quantities. Taking into account the condition of ensuring the coaxiality of the gear engagements, the functions of the end overlap coefficients are constructed, depending on one value – the shift coefficient of one of the gears forming the corresponding gear engagement. Analysis of the graphs of these functions allows us to select the optimal values of the gear shift coefficients.