Lightweight Design of Screw Rotors via an Enhanced Newton–Raphson-Based Surrogate-Assisted Multi-Objective Optimization Framework

Traditional solid screw rotors suffer from excessive weight, structural redundancy, low material utilization, and high energy consumption, conflicting with the growing demand for efficient, sustainable manufacturing. To address these challenges, this study proposes a lightweight design method for hollow, internally supported male screw rotors that simultaneously enhances stiffness and static–dynamic performance. A parameterized structural model with four key design variables was established, and multi-physics simulations integrating fluid flow, heat transfer, and structural mechanics were conducted to obtain mass, maximum deformation, and first-order natural frequency. Based on these simulation results, a surrogate-assisted multi-objective evolutionary optimization framework was employed: an enhanced Newton–Raphson-based optimizer (SNRBO) was used to tune the extreme gradient boosting surrogate (XGBoost 1.5.2), and the tuned surrogate then guided the Nondominated Sorting Genetic Algorithm III (NSGA-III) to perform multi-objective search and construct the Pareto front. Compared with a conventional solid rotor, the optimized design reduces mass by 64.43%, decreases maximum deformation by 4.41%, and increases the first-order natural frequency by 82.14%. These findings indicate that the proposed method provides an effective pathway to balance lightweight design with structural safety and dynamic stability, offering strong potential for green manufacturing and high-performance applications in energy, aerospace, and industrial compressor systems, and providing robust support for further advances in this field.