A Free Interface Component Mode Synthesis Approach for Determining the Micro-End Mill Dynamics

Abstract

The prediction accuracy of the stability boundary in the machining process depends upon accurate estimation of cutting tool-tip dynamics. Note that the experimental modal analysis using direct impact at miniature end mill (typically 50–500 μm in diameter) is not feasible as it can result in tool failure. Consequently, alternative techniques such as experimental modal analysis using reciprocity theory and frequency-based receptance coupling substructure analysis (RCSA) have been used extensively for determining tool-tip dynamics. The experimental approach based on reciprocity theory assumes that the structure is symmetric (cross frequency response functions (FRFs) are same between two points of interest in a structure). RCSA requires a very fine frequency resolution and matrix inversion, which can lead to computational complexities. In addition, RCSA takes into account the FRFs only at the interface and free end, which can induce errors. Owing to these issues with existing approaches, this paper proposes a free-interface component mode synthesis (CMS) approach for estimation of micro-end mill dynamics. The effect of machine tool compliance including the collet–tool interface has been included for estimation of micro-end mill dynamics via a free-interface CMS approach wherein the experimental and analytical mode shapes are coupled. The predicted micro-end mill dynamics have been compared with RCSA and experimental modal analysis using reciprocity theory. Finally, the stability lobe diagrams for high-speed micromilling of Ti6Al4V has been made using the tool-tip dynamics from CMS, RCSA, and experimental technique using reciprocity theory and validated against experimental measurements for onset of instability.