Rotational dynamics of micro-scale cutting tools

The dynamics of micro-scale cutting tools used during micromachining is critical to attainable process precision. Forced and self-excited vibration behavior of a micromachining process depend significantly on the dynamic response of the microtools. As these micro tools are rotated at very high speeds (40,000 to 250,000 rpm) the rotational effects can play a critical role in their dynamic response. However, their complex, multi-dimensional, and pre-twisted geometry causes a coupled dynamic response, thereby rendering the prevailing simplified one-dimensional (1D) modeling approaches inaccurate. Towards addressing this modeling challenge, in this work, we present an application of spectral-Tchebychev (ST) method to predict the three-dimensional (3D) coupled dynamics of microtools including the rotational (gyroscopic) effects. To capture the dynamics of the sectioned geometry of microtools efficiently, a unified modeling approach is followed in the modeling, merging 1D-ST models for the sections having circular cross sections, and 3D-ST models for the fluted section, which exhibits coupled three-dimensional motions due to the complex geometry. The presented solution technique is applied to predict and understand the dynamics of rotating micro-endmills and micro-drills. Natural frequencies, mode shapes, and the frequency response functions (FRFs) obtained from the unified 1D/3D-ST model are shown to have an excellent agreement with those from a commercial finite element (FE) software. The unified 1D/3D-ST model is then used to analyze the accuracy and limitations of reduced-order modeling approaches that could be used to model the rotational dynamics of microtools. Finally, the effect of rotational speed on radial throw arising from the rotational dynamics is investigated.