Proposal of “specific cutting displacement coefficient” concept and its operational identification in milling - Part 1: General formulation and simulation-based validation

In general, the specific cutting force and the dynamic/static compliance are measured separately for analyses of vibration/displacement problems such as chatter/forced vibration and static displacement. However, these measurements are usually impractical, e.g., the former requires a high-cost dynamometer. In Part 1 of this paper, a novel concept, namely “specific cutting displacement coefficient”, is proposed, which is the product of the specific cutting force and the structural compliance. Additionally, a method to identify its dynamic matrix for milling (D-matrix) is also proposed, where cutting tests are conducted so that the harmonics of the varied tooth-passing frequencies of the cutting force excite the compliant structure and generate forced vibrations. By measuring only the forced vibrations, the D-matrix can be extracted utilizing the measured vibrations and the known cutting/tool conditions; the measurements by the dynamometer and the impact hammer can be eliminated which are conventionally required for identification of the specific cutting force and the dynamic compliance, respectively. Moreover, this realizes the measurement which automatically reflects the operational state of the tool-holder-spindle system. Formulation/identification of the D-matrix is conducted, and the matrix is applied to the stability lobe analysis in this study as a typical example. It is shown that the lobes can be generated solely from the forced-vibration measurements.