Smooth Free-Form Pipe Routing Design in Aero-Engines: A Quartic NURBS-Driven Deep Reinforcement Learning Approach

The layout design of piping systems, particularly for free-form pipes, is crucial for achieving lightweight construction, structural precision, and operational reliability in aero-engine development. Existing routing methods exhibit performance limitations, with generated layouts often lacking the geometric continuity and smoothness required for manufacturability. To address these challenges, this study proposes a novel smooth free-form pipe routing (SFPR) framework, which integrates a proximal policy optimization (PPO) algorithm with a Non-Uniform Rational B-Spline (NURBS) curve parameterization. The SFPR framework optimizes the path smoothness by constraining length, curvature, torsion, and their first-order derivatives. Comparative experiments demonstrate that SFPR achieves robust obstacle avoidance and generates paths up to 24.5% shorter than a heuristic-based method. Further analysis reveals that SFPR reduces curvature and torsion amplitudes by 33.6% and 39.8%, respectively, compared to non-smooth frameworks, while stabilizing their spatial distributions. These advancements enable significant reductions in material consumption, enhanced manufacturability of free-form pipes, and mitigation of mechanical shock on forming dies caused by abrupt geometric transitions.