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.

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This article is part of a longer research-analytical work, because it outlines the results and conclusions of the study according to the main topic of the research and the applies method. The central theme of the research is the dynamic stiffness of machine tools and the various methods for their determination. The first such (finite element) method is modal analysis, which allows for an analytical test. The purpose of this article is to approach this study from the practical side through a specific example.

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This article concerns a thermovision analysis of a DMU40 5-axis CNC milling machine [1] using a thermal camera. First I specify the measuring instrument and I present the layout of the measurement. Before this measurement I created a thermal model of machine tool and I analysed it by finite element method. After evaluating simulation results I make the thermovision analysis. Finally I compare measured and simulated results with each other and I draw up some conclusions about thermal analysis.