The aim is to derive an expression to calculate the natural frequencies and plot the mode shapes of a simply-supported beam with an overhang with an end overhang point mass by using the Euler-Bernoulli theory in the case of free transverse vibrations. The results are validated by finite element analysis. The importance of the system presented is that it can represent machine tool spindles or even machining tools like boring bars. The results are in good agreement with the results from the finite element analyses. The derived expression can be used in optimizing the value of the point mass and optimizing the support location for better performance of the system without the need to perform complex analysis to obtain the values of the natural frequencies and to plot the mode shapes.

The goal of this study is to dynamically simulate a turning-centre main spindle system utilizing the systems receptance coupling technique to determine the spindle system's first three resonant frequencies in the event of transverse vibrations. The findings are then confirmed using the finite element technique using ANSYS software. The significance of analysing the spindle system described in this study is that it can be utilized to optimize the spindle system in terms of resonance frequencies for improved performance in terms of spindle vibration while the turning centre is in operation.

Chatter is a self-excited vibration that takes place during turning operations. It is either to be avoided or reduced for its negative impact on the machine-tool, the workpiece surface finish, and the cutting tool life. A lot of research has been carried out in this domain to understand this phenomenon, which leads to finding ways to detect, identify, avoid, reduce, and control chatter in turning processes. In this paper, chatter research related to turning processes is reviewed and summarized. The main goal of this review paper is to compare different chatter prediction, suppression, and avoidance techniques to find out the most effective technique, so a scope of a work related to turning processes chatter is defined.