A hybrid analytical model for the transverse vibration response of a micro-end mill

As a result of its detrimental effect on tool life and product quality, vibration analyses are crucial if the full potential of micro-milling operation is to be attained. In this paper, a hybrid analytical model (HAM) developed for estimating the transverse response of a micro-end mill is presented. The HAM is a combination of discrete and distributed structural elements. The discrete elements account for the stiffness and damping coefficients of the machining system, while the distributed elements idealize the geometrical representation of the micro-end mill with a novel model of the micro-flute. A number of slot micro-end milling operations, carefully designed with the Taguchi method of design of experiments, are carried out to examine the accuracy of the HAM. The comparison of the response profile from the experiment and the developed model shows reasonably close similarity. The influence of the helix angle is found to be far greater on the response of the micro-end mill than the other geometric variables. By making use of the root mean square of the response, it is further observed that the representation of the micro-flute of the micro-end mill with a less accurate model deteriorates the prediction of the HAM.