Tchebychev-based modal-domain coupling (TMDC) for prediction of microtool-tip dynamics

Official URL: https://dx.doi.org/10.1016/j.cirp.2026.04.054

Accurate representation of tool-tip dynamics is essential for predicting stability in micromachining. Frequency-domain coupling approaches amplify measurement noise due to matrix inversions and finite-difference approximations of rotational frequency response functions (FRFs). We propose Tchebychev-based modal-domain coupling (TMDC), which represents measured spindle–artefact mode shapes in a Tchebychev basis, evaluates slopes with spectral differentiation, couples a Tchebychev-based tool-dynamics model, and enforces interface compatibility in modal coordinates. TMDC is validated on two ultra-high-speed spindles, showing agreement with measured FRFs up to 15 kHz and avoiding the artificial antiresonances observed with receptance coupling substructure analysis (RCSA). Predicted tool-tip receptances are then used to predict stability for two micro-endmill geometries.