Coordinated Multi-Criteria Optimization Design of Micro Planetary Gearboxes for Downhole Electric Cutters

Abstract Micro planetary gearboxes used in downhole electric cutting tools must achieve compact size, sufficient load-bearing capacity, and high transmission efficiency under high temperature, impact loading, and limited installation space. To address this coupled design problem, this study develops a mixed-integer nonlinear optimization model for a single-stage NGW planetary gearbox. The Analytic Hierarchy Process (AHP) is used to assign weights to material volume, high-temperature safety factor, and transmission efficiency, thereby converting the multi-criteria design problem into a single aggregated optimization objective. To improve the feasibility of integer variables such as gear tooth numbers, an improved particle swarm optimization strategy incorporating a BNB-inspired local discrete feasibility repair mechanism, denoted as IPSO-BNB, is adopted. During each iteration, candidate tooth-number variables are decoded and locally repaired toward feasible integer combinations, so that geometric, assembly, and kinematic constraints can be preserved throughout the search process. This embedded continuous–discrete repair mechanism helps avoid infeasible solutions caused by direct post-optimization rounding.The final discrete tooth-number combination is further checked by exhaustive enumeration within the prescribed design space, confirming the reliability of the obtained integer solution. Compared with the initial empirical design, the optimized gearbox reduces material volume by 18.16 % and improves transmission efficiency by 0.72 percentage points while satisfying the prescribed minimum safety-factor constraint under high-temperature equivalent impact loading. Romax-based simulation further verifies the engineering feasibility of the optimized design in terms of gear strength, bearing life, and tooth-surface contact behavior. The contact-stress results show that crown modification alleviates local face-load concentration and improves the tooth-surface contact state. The results indicate that the proposed engineering optimization framework can support the compact and reliable design of micro planetary gearboxes for downhole electric cutting tools.