Optimum design of planetary gear set using multi-objective optimization considering mass, power loss and transmission error

In this study, a multi-objective optimal design of a planetary gear set was performed considering mass, power loss, and transmission error. In particular, the results were analyzed from a novel perspective. The implemented multi-objective optimal design methodology minimizes the mass, power loss, and vibration with respect to seven macro-geometry variables. The peak-to-peak static transmission error (PPSTE) of each gear pair corresponds to the excitation source of the planetary gear set, and reducing the PPSTE helps minimize vibration. Thus, the PPSTE was calculated using the time-varying mesh stiffness obtained through an analytical model. The non-dominated sorting genetic algorithm-III (NSGA-III) was implemented as a multi-objective optimization algorithm, and the criteria importance through the inter-criteria correlation method was implemented for quantitative comparison purposes regarding the combination of objective functions. The results showed that obtaining an optimal macro-geometry design for a planetary gear set exhibiting good performance required simultaneous consideration of the mass, power loss, and vibration. Furthermore, the results confirmed that a versatile optimization algorithm, such as NSGA-III, should be used to capture the discontinuous solution distribution owing to various constraints of the planetary gear set.