Optimization of transmission ratios in a three-stage spur-helical gearbox using an analytical sizing algorithm and differential evolution
Year: 2025
Type: article
Abstract: Designing three-stage gearboxes that combine a high overall transmission ratio with a compact envelope remains a notable challenge for both manufacturers and design engineers. Consequently, the study frames transmission ratio allocation as an objective optimization that (i) uniform contact-fatigue strength across stages, (ii) secures oil-bath lubrication, and (iii) minimises gearbox volume. The solution strategy consists of two sequential steps. First, an Analytical Sizing Algorithm (ASA) is used to delimit the minimum-maximum bounds for the first and second stage transmission ratios. Next, the Differential Evolution (DE) meta heuristic searches those bounds to identify the optimum ratio set that yields the smallest volume. Finally, regression analysis is employed to build surrogate equations for stage ratios, allowing a ready to use lookup table for designers. The study establishes feasible ratio ranges for the high speed and intermediate stages and formulates an objective model whose decision variables are the individual stage ratios. The approach is validated through an industrial case study. Results show that the optimised ratio distribution balances contact stresses between stages and maintains satisfactory lubrication while meeting the minimum volume constraint.
Source: Results in Engineering
Authors: Duy Huu Huynh, Loc Huu Nguyen
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,940
OpenAlex ID: W4415943574