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Number of Points for Roundness Measurement - Measured Results Comparison Paper deals with filtering roundness. It presents experimental results measured for roundness turning and cylindrical grinding. Roundness was measured using Prismo Navigator 5 coordinate measuring machine. Evaluation was done by four methods: Minimum zone reference circles (MZCI), Least squares reference circle (LSCI), Minimum circumscribed reference circle (MCCI) and Maximum inscribed reference circle (MICI). The filters used were: Gauss, Spline and no filter.

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions. The computation and study of Fourier series are known as harmonic analysis. It is a useful way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually, and then recombined to obtain the solution to the original problem or an approximation to it to whatever accuracy is desired or practical. This paper deals with the mathematical basics of Fourier series using trigonometric functions. This is the basic for a discrete Fourier transform. It allows transforming the discrete data to the frequency data or vice versa, i.e. transforming the frequency data to the discrete data. The most important part of the article is the application of the Fourier series and the Fourier transform to metrology, specifically on the roundness profile. The mathematical relationships for the practical use of harmonic analysis and the detailed method of determining the actual phase were described. General relationships do not give accurate results, due to the phase shift quadrant. The results of the harmonic analysis were applied graphically by the authors on a concrete example of a roundness profile. The individual harmonic components are shown in the linear and polar graphs as well as the resulting roundness profile. The Fourier analysis knowledge will contribute to a better analysis of the roundness profiles measured on the drawn tubes that will be investigated in the research project.

The main goal of this publication is to determine the impact of the alignment condition to the repeatability of measured values. In the experimental work were performed four series of measurements, each contains 25 individual measurements on a single component. The component was measured according to the rules for making the comparison of measured values for repeatability. This comparison of measurement results was made by using statistical methods. A given goal was completely fulfilled. Experimental work has shown a dominant impact of the alignment condition on the measured values.

The article deals with simulating superfinishing of single-oscillating grooves. A model of the superfinishing tool was created according to the input information about the tool and the superfinishing process. Using this tool, a simulation of the cutting process was performed. The input parameters for the simulation were the cutting conditions, which determined the paths of individual grains of tools (process kinematics). The simulation is realized by gradual removal of the workpiece material by individual grains of the tool. The result of the simulation is the profile of the superfinished surface at an evaluation length of 1.25 mm. It is possible to determine the surface roughness parameters from the profile. Creating and displaying multiple profiles side by side produces a graphical model of the superfinished surface. The simulation can be used for numerical simulation experiments, where both material and energy are saved. The article presents one such experiment together with the results -the surface roughness was influenced by individual factors. The simulation results (surface roughness parameters and surface appearance) were compared with the real superfinished surface on the outer ring of the bearing. This surface was manufactured under mass production conditions. The comparison confirmed that a simulation is a suitable tool for research of abrasive machining methods. At the end of the article, there is a discussion about a possible improvement of the simulation -considering 3D grains of the tool.