Inverse identification of tool-tip modal parameters in milling from cutting test

Regenerative chatter is a major limiter of productivity in milling: it degrades surface quality, shortens tool life, and forces conservative cutting. Stability lobe diagrams (SLDs) are a proven way to avoid chatter by selecting favourable spindle speeds, yet their adoption on the shop floor is hindered by the need for tool-tip modal parameters, which typically require impact testing, special equipment, and expert setup. This work presents a practical, low-cost way to obtain the required modal properties directly from simple cutting tests and chatter sound. We investigate two complementary identification routes. (i) ZOA-NLSO: a direct inverse formulation based on the Zero-Order Approximation (ZOA), where identified chatter frequencies and stability limits at several speeds are fitted via nonlinear least squares to extract tool-tip modal parameters in x and y directions. The method is fast and easy to deploy, but ZOA’s modelling simplifications can miss certain lobes, reducing accuracy in some regimes. (ii) SDM-ML: a semi-discretization-informed machine-learning approach. Offline, SDM is used to generate a dataset linking modal parameters and cutting conditions to stability outcomes; a supervised regressor is then trained to invert this mapping from measured features (speed, axial limit, chatter frequency) to modal parameters. However, SDM is computationally time-consuming; embedding SDM in an NLSO loop is impractical, so a machine-learning surrogate is preferred. It is more accurate and gives almost real-time results, but only within the trained data range. In our milling tests, both approaches recover modal parameters with sufficient accuracy to reconstruct SLDs consistent with observed stability boundaries. The proposed workflow eliminates instrumented impact tests, enabling rapid, industry-friendly SLD deployment for process planning and on-machine optimization.