Population-Level Assessment of Circumferential Flank Waviness Variability Using a ΔW1 Indicator Derived from CMM Measurements

Long-wavelength flank waviness plays a critical role in the excitation behavior of geared transmissions. While coordinate measuring machine (CMM) exports provide detailed geometric information, conventional evaluations typically focus on individual tooth curves and do not quantify circumferential inhomogeneity across teeth. This study introduces a tooth-to-tooth long-wavelength waviness inhomogeneity indicator (ΔW1) derived directly from Klingelnberg-style MKA plot files and demonstrates its behavior on a large industrial dataset comprising 3375 measured gear parts. Each flank curve was detrended using a second-order polynomial fit, and lobe-based waviness amplitudes (W1–W3) were extracted via sine–cosine projection. The proposed ΔW1 metric was defined as the difference between the maximum and minimum W1 values across measured teeth within the same part. To eliminate measurement edge effects, a mid-section evaluation (10–90% of the face width) was additionally performed. Population-level analysis revealed consistent separation between geometrically homogeneous and inhomogeneous parts, with ΔW1 values in the most critical components exceeding 7–9 µm after mid-section filtering. Unsupervised clustering based on ΔW1 and maximum W1 further distinguished a high-variability subset of parts exhibiting systematic long-wavelength modulation patterns. The results demonstrate that circumferential waviness variability can be quantified using standard CMM outputs without additional hardware or specialized measurement procedures. The proposed indicator provides a practical geometric screening tool for large production batches and establishes a reproducible framework for linking detailed flank geometry to manufacturing consistency assessment. Although acoustic validation is outside the scope of the present work, the metric is intended as an NVH-relevant geometric risk indicator for future vibroacoustic correlation studies.