Multi-objective macro-geometry optimization of a compound planetary geartrain for an electric tractor powertrain using NSGA-II

This study presents a multi-objective macro-geometry optimization of a compound planetary geartrain for an electric tractor powertrain. The proposed framework simultaneously minimizes peak-to-peak static transmission error and maximizes gear mesh efficiency under representative agricultural load conditions derived from load duration distribution data. The macro-geometry design variables include normal module, pressure angle, helix angle, and face width for two planetary gear sets integrated into a developed electric tractor prototype. A detailed geartrain model was developed using commercial analysis software, and the optimization was performed using the nondominated sorting genetic algorithm II with strength constraints based on ISO 6336 to ensure durability. The Pareto-optimal solutions were ranked using a criterion importance method based on variability and intercriteria correlation. Compared with the baseline prototype configuration, the optimized designs achieved a 14-16% reduction in transmission error across all gear pairs while maintaining or slightly improving mesh efficiency (up to + 0.16%p). The results demonstrate that macro-geometry refinement within fixed gear ratio and packaging constraints can effectively reduce excitation-related transmission error without compromising efficiency. Experimental validation of the optimized gear sets is planned in future work.