Rotary Burnishing of Internal Tube Surfaces with a Preloaded Compliant Crown: A Force–Geometry–Compliance Model and Parametric Sensitivity Analysis

A reduced model of internal rotary burnishing couples Hertz–expanding-cavity indentation, Euler–Bernoulli crown bending and loading-chain compression through incremental equilibrium from preload. The resulting residual geometry supplies an in-service contact model. In the reference numerical case with a steel crown and an Al–Cu–Mg tube, 20 μm of additional travel from a 20 N preload gives a total force of 408 N, a maximum penetration of 14.1 μm and an edge-to-centre residual sag of 2.70 μm. Indentation, crown bending and loading-chain compression account for 60.9%, 19.7% and 19.4% of this travel, respectively. The two process-derived cells have texture area fractions of 0.03–0.04 and specific cavity volumes of 0.05–0.07 μm. In a separate 1×1 mm periodic-contact benchmark at 5 MPa, the directly integrated rough-land approach is 1.07 μm, compared with a smooth-contact rigid-plane offset of 2.85 nm. Global sensitivity identifies yield strength as the leading input for residual sag (total-order Sobol index STi=0.57); total-force sensitivity is greatest for preload, followed by crown thickness. With the Hertz–expanding-cavity transition markers fixed, the prescribed calibration-uncertainty distributions give Monte Carlo 5th–95th percentile intervals of 2.2–3.3 μm for residual sag and 387–426 N for total force. Variance reductions obtained by fixing individual inputs in this calibration scenario identify yield strength as the main calibration priority for residual geometry, and loading-chain stiffness and local crown thickness as priorities for force transfer.