Tool-tip dynamics in micromachining with arbitrary tool geometries and the effect of spindle speed

Mechanical micromachining has become a leading approach to fabricating complex three-dimensional microscale features and miniature devices on a broad range of materials. To satisfy the accuracy and productivity demands of various micromachining applications, the tool-tip dynamics, i.e., the dynamic behavior of the tool-ultra high-speed spindle assembly as reflected at the cutting edges of a microtool, should be well-understood. However, existing techniques for predicting tool-tip dynamics pose strict limitations in frequency bandwidth and do not capture the effect of the spindle speed on tool-tip dynamics. In addition, those techniques cannot be applied broadly to predict tool tip dynamics for a myriad of microtool geometries. This paper presents a systematic approach to predicting the tool-tip dynamics accurately in micromachining when using ultra-high-speed (UHS) spindles and for arbitrary microtool geometries. The speed-dependent dynamics of the UHS spindle are obtained using an experimental approach. The dynamics of microtools are obtained analytically using the spectral Tchebychev technique, such that any microtool geometry can be modeled accurately and does not require new testing. The tool-tip dynamics are then predicted by combining (coupling) the spindle and microtool dynamics using a novel modal-Tchebychev domain coupling technique. This technique enabled accurate coupling/decoupling of substructure dynamics within a broad frequency bandwidth (up to 15 kHz) and at different spindle speeds (up to 120,000 rpm). Furthermore, an empirical model for the mode-splitting effect is derived to capture the effect of spindle speeds on tool-tip dynamics. The overall approach is demonstrated and experimentally validated on a UHS spindle with microtool blanks and micro endmills at operational speeds. We conclude that the presented methodology can be used to determine the tool-tip dynamics accurately.