Two-Phase Multi-Objective Inverse Design of Rotary Burnishing Regimes and Compliant-Roller Tools: Full-Factorial Grid Enumeration and NSGA-II

The design of regular microreliefs requires process and tool variables that satisfy surface-coverage, lubricant-retention, and residual-depth requirements. This theoretical and computational study formulates the task as a two-objective inverse problem for rigid-ball burnishing of external cylinders and compliant-roller burnishing of internal tubes. The analytical chain maps force or imposed displacement and relative curvature to indentation, elastic recovery, periodic cavity overlap, relative dimple area Fn, and specific oil capacity q. A full-factorial grid generates a discrete catalog of process settings and provides the initial seeds for continuous refinement by the non-dominated sorting genetic algorithm II (NSGA-II). Under a common budget of 648 forward evaluations, the two-phase method achieved 95.9% of the median target-centered hypervolume of pure NSGA-II and produced a higher hypervolume than Latin hypercube sampling (LHS) in eight of ten paired runs. A comparison calibrated at the 200 N data point yielded a held-out axial-width error of −6.5% at 400 N, consistent with the predicted force–width trend under the stated comparison conditions. Morris screening identified imposed displacement as the most influential variable for both objectives, with crown-base thickness also strongly influencing q. The resulting candidates are illustrative model-based solutions that satisfy the stated constraints and lie within the reference machine-coordinate envelope; process-specific calibration and experimental assessment are required before quantitative implementation.