Theoretical, Numerical and Experimental Investigations of Overhang Effect on a Cutting Tool Natural Frequencies

In the turning process, the cutting forces acting on the workpiece become reaction forces on the cutting tool. Due to the elasticity of the cutting tool, the forces acting on it will cause its deformation and its removal from the surface to be processed. The forces being variable in time and traces left on the surface of the piece, by the cutting forces, will have different depths. The values of these forces depend on the rotation speed of the chuck, the radial cutting depth, the axial cutting depth, the feed rate, but also on the mechanical characteristics of the turning material. It is known that in the turning process the best results are obtained for small values of overhang. The overhang is defined as the length of the cutting tool relative to the end of the support. For certain machining given by the workpiece geometry, but especially in the case of inner turning, the overhang may have a longer length. This involves increasing the vibration amplitudes of the cutting tool. By keeping the overhang to a minimum, low vibrations, well-finished surfaces, increasing the life of the cutting tool, increasing the processing and feed speed and, consequently, increasing productivity can be obtained. These are the reasons why this paper aims at the analytical, numerical and experimental analysis of the natural frequencies of a cutting instrument in relation to its overhang. From an analytical point of view, the cutting tool will be considered as Euler Bernoulli beam with a square cross section. The Finite Element Method (FEM) coupled with the Modal Analysis (MA) from the ANSYS module was used for the numerical analysis. These gave both natural modes and corresponding frequencies. Experimentally, the analysis of a vibration signal obtained by applying a mechanical impulse on the cutting tool is made. The acquisition of the signal is done by means of Laser Doppler Vibrometer (LDV), and the processing isgiven by software based on the Pronv Series Method (PSM).