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 critically 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 the 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

Predicting the rotating tool-tip dynamics in mechanical micromachining using modal testing

This study presents an experimental methodology to predict the tool-tip dynamics including rotational effects in micromachining. In this approach, the ultra-high-speed spindle dynamics (i.e. the FRF matrix at the spindle tip) at different spindle speeds are obtained experimentally. Since the modal test are performed on a rotating tool, measured response includes unwanted error motions as well as the dynamic response to the excitation. Therefore, a frequency domain filtering algorithm is designed to isolate the dynamic response. Then, the experimentally obtained spindle dynamics are coupled with the tool dynamics calculated using the spectral-Tchebychev technique to predict the tool-tip dynamics. The developed approach/methodology is demonstrated on a micro machine tool incorporating miniature ultra-high-speed spindles (with air bearings), and a tungsten carbide tool blank. The predicted tool-tip dynamics are validated by direct measurements; it is concluded that the presented unified modeling approach can be used to accurately determine the tool-tip dynamics

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