Study of rigidity and frequency response of an end mill on a vertical milling center

The study covers the problem of early elimination of tool resonant vibrations through preliminary mathematical modelling. In particular, the problem is considered for the case of milling with an end mill on a vertical milling centre. The paper presents processed experimental data and results of mathematical modelling containing information on the rigidity of the FKC 4257 mill, its natural frequencies on the spectrum and vibration modes. The constructed finite element mathematical model covers the mill itself, the gripping collet and the collet chuck attachment. The model describes the static rigidity of the mill with an error of 2.2 %, and the position of its natural frequencies on the spectrum – with an error of about 7 % relative to the experimental results. By constructing the amplitude-frequency characteristic and conducting a modal analysis, it is shown that the first two vibration modes (80 and 112 Hz) are the most critical for the mill, both in terms of the amplitude of vibrations and in terms of their shape. The vibration shapes in the first modes are bending. During the modal analysis, the vibration shapes in the remaining modes are considered and estimated. To improve the convergence of the frequency analysis results, it is proposed to introduce the coefficient Kk1=0.9, which takes into account the lower rigidity of a real mill in comparison with an idealized mathematical model, when applying which the convergence is improved to 2.5 %. Thanks to the applied technique, it is possible to obtain reliable data on the frequency zones of instability used in practice to avoid resonance phenomena. In the future, based on such data, taking into account the correction factors, it is possible to train neural network models predicting the tool response under specific processing conditions and solving the inverse problem of selecting rational tool geometry for specific tasks.