Numerical Investigation on the Relationship Between Pitch Angle Variance and Milling Stability with Waveform Parameter Variations

Wave-edge milling tools can suppress chatter by introducing periodic harmonic variations along the cutting edge, which change the tooth-passing time delays between adjacent teeth. However, their stability is affected by coupled waveform parameters, such as amplitude, wavelength, and phase, making it difficult to screen suitable parameter combinations efficiently. This numerical/modeling-based study uses a previously validated multi-delay dynamic model to investigate the probabilistic relationship between pitch angle variance (PAV) and stability region area (SRA). A large number of feasible waveform-parameter combinations are generated under geometric constraints, and a PAV-based stratified sampling strategy is used to retain 54 representative parameter sets from six PAV layers for stability lobe diagram construction and SRA calculation. The results show that PAV has weak pointwise predictive capability for individual SRA values, with Pearson = 0.4234, Spearman = 0.4720, and R² = 0.179. However, the stratified statistical results reveal a clear layer-wise probabilistic tendency: the mean SRA increases from 17.962 to 20.996 in units of rpm·m, and the probability of obtaining an above-median SRA increases from 11.1% to 88.9%. The high-value tail case with PAV > 0.06 further indicates that a higher PAV does not necessarily guarantee a larger SRA for an individual parameter set. Therefore, PAV should not be used as a deterministic predictor or stand-alone tool-selection criterion, but can serve as a low-cost auxiliary probabilistic pre-screening descriptor before high-fidelity SLD/SRA evaluation.