Gears are crucial elements in mechanical systems and contribute to the overall performance of machinery. As such, optimization of gearbox transmission systems remains a challenging problem faced by researchers and designers for numerous years. In the present work, three objectives viz volume, power output and centre-distance are investigated simultaneously. A two-stage spur gearbox design problem is formulated with eight design variables viz. face-width (stage 1), face-width (stage 2), shaft diameter (stage 1), shaft diameter (stage 2), module, pinion teeth number(stage 1) and pinion teeth number (stage 2) considered. Two geometric and three design constraints are formulated. Pareto frontiers are generated using NSGA-II evolutionary algorithm. The Pareto frontier is investigated using decision tools viz. FUZZY, LINMAP and TOPSIS and the best solutions selected using the deviation index. Validation of results was done using previous reports in the literature and geometric modelling software. Variation and sensitivity studies indicate that module, pinion tooth number and face-width variables had a higher influence on volume as compared to power output and centre-distance. The combined optimization of volume, centre-distance and power output reveals key insights for the design of compact gearboxes.

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Gear transmission systems are very important machine elements and their failure can lead to losses or damage of other mechanical components that comprise a machine or device. Since gears are applied in numerous mechanical devices, there is need to design and subsequently optimize them for intended use. In the present work, two objectives, viz., volume and center distance, are minimized for a rotary tiller to achieve a compact design. Two methods were applied: (1) analytical method, (2) a concatenation of the bounded objective function method and teaching–learning-based optimization techniques, thereby improving the result by 44% for the former and 55% for the latter. Using a geometric model and previous literature, the optimal results obtained were validated with 0.01 variation. The influence of design variables on the objective functions was also evaluated using variation studies reflecting on a ranking according to objective. Bending stress variation of 12.4% was less than contact stress at 51% for a defined stress range.

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