Cross-Edge-Validated Tool Condition Monitoring via Joint Natural-Frequency and Damping-Ratio Tracking of Cutting Vibration

Operational damping and natural-frequency shifts are promising tool-wear indicators, yet many demonstrations use a single cutting edge with an isolated mode. This study evaluates the joint frequency-shift/damping-ratio (Δf_n, ξ_T) feature on two independent cutting edges during AISI 1045 turning (75 passes, flank wear VB ∈ [76, 352] μm), using three single-axis accelerometers and triaxial cutting force as an independent wear channel. The cantilever bending mode anchors the analysis: an adaptive tracker yields the per-pass natural frequency f_n, and a nonlinear least squares fit of the exact single-degree-of-freedom (SDOF) magnitude-squared response to the local Welch spectrum returns the operational damping ratio ξ_T with a median relative standard error of 11%. On the accelerometer aligned with the bending direction, f_n and ξ_T track flank wear with the same sign on both edges (Spearman ρ(f_n)=+0.66+0.74, ρ(ξ_T)=+0.70+0.37; all p ≤ 0.04), and a wear-damping law fitted on either edge predicts the other edge’s productive-wear ξ_T ranking at ρ = +0.73. Cutting-force root mean square independently corroborates wear progression on both edges (ρ ≥ +0.89). The cross-edge result depends on the measurement axis: a secondary spectral feature near the cantilever peak on one axis violates the SDOF assumption, motivating a power spectral density prescreening rule. The study is a proof-of-concept across two edges exercised under different cutting conditions, not a deployment-ready or statistically established result.