Predicting the dynamic behaviour of the turning tool vibrations using an experimental measurement, numerical simulation and analytical modelling for comparative study

The aim in the present work is studying and predicting the dynamic response of the cutting tool in turning processes through the calculation of the tool tip displacement by an experimental measurement, numerical simulation and analytical modelling study. The first study is based on an experimental measurement method in which the effect of cutting conditions (ap, f and Vc) on the measured cutting force components (F_x, F_y, F_z) and tangential tool tip accelerations are evaluated. Moreover, the study is extended to the numerical simulations based on the finite element method (FEM) utilizing I-deas software to compute the tool tip displacements. For this, the turning tool is designed by two CAD models, such as a cantilever beam and as an approached real tool geometry, both punctually excited at its free end by the measured cutting forces to compute tool acceleration and tool displacement signals. In the following, the analytical modelling formulates the cutting tool in transverse vibrations as a thick cantilever beam based on the Bernoulli beam theory, where the modified effect of rotary inertia term is integrated into the equations of movements in the tangential and axial direction of the cut. However, in the radial direction, the cutting tool is excited axially under longitudinal vibrations. The governing differential equations of movements are resolved using the modal decomposition method and the convolution theorem, taking as impulsive excitations the cutting forces (F_x, F_y, F_z). The general solution corresponding to Duhamel’s integral is evaluated numerically to calculate the tool displacements. For validations, different comparisons are performed, and good agreements are found between all types of results. Thereafter, the presented methodology of cutting tool vibrations contribute to solve some important metal machining troubles, such as chatter machining that affects directly the quality of the surface of parts and reducing the intensity of cutting edge wear rate by monitoring the excessive cutting forces for a long tool life.