Applicability of Selected Groups of Roughness Parameters for Description of Surface Layer of Flat - Top “Plateau” Structures

Kowalski, Maciej; Wiśniewska, M.; Karolczak, Paweł; Stančeková, Dana

doi:10.12913/22998624/65110

Cited by 5 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, it is necessary to know the mathematical basics of harmonic analysis and apply it to the measured profiles. The har- monic analysis can be applied in the area of surface macrogeometry (geometric tolerances) but also in the area of surface microgeometry (surface roughness [10,19]). The article focused on applying the harmonic analysis to a roughness profile that belongs to the area of geometric tolerances.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Application of Fourier Series for Evaluation of Roundness Profiles in Metrology

Görög¹,

Görögová²

2019

Adv. Sci. Technol. Res. J.

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

confidence: 99%

“…(a n cos(nx) + + b n sin(nx)) (10) This series is called "Fourier series" and the constants a 0 , a 1 , a 2 , ... a n , b 1 , b 2 , ... b n are called Fourier coefficients.…”

Section: Fourier Seriesmentioning

confidence: 99%

Application of Fourier Series for Evaluation of Roundness Profiles in Metrology

Görög¹,

Görögová²

2019

Adv. Sci. Technol. Res. J.

View full text Add to dashboard Cite

show abstract

“…These finishing methods no longer reshape the overall geometry but only refine the resulting properties. Therefore, the grinding process must ensure the correct profile of the geometric parameters [ 11 ].…”

Section: Introductionmentioning

confidence: 99%

Research on the Oscillation in Centerless Grinding Technology When Machining Bearing Steel

et al. 2022

View full text Add to dashboard Cite

In today’s engineering industry, technical diagnostics presents many advantages for improving the management of machining centers and automated production lines. As the fourth industrial revolution is currently being implemented, which includes machine diagnostics, the idea of adding information from the field of vibrodiagnostics was born. The vibration of the workpiece or machine tool negatively affects the geometric parameters of the machined surfaces of the workpiece. Through vibrodiagnostics, the influence of cutting parameters on the oscillation of a bearing steel workpiece during centerless grinding is investigated. The presented publication deals with the vibration of the mechanical parts of a centerless grinding machine. The oscillations are recorded by acceleration sensors, which are also placed on the support ruler in which the workpieces are guided, and the recorded data are input parameters for statistical processing of acceleration values in the form of statistical characteristics (minimum, lower quartile, median, upper quartile, maximum). In this paper, this procedure was applied for the selection of the optimum cutting parameters (for the speed of the support wheel), where the machining parameters at which the minimum oscillation values occur were selected based on the above-mentioned statistical characteristics. This optimization procedure revealed increased vibration values which reached the highest amplitude on the ruler, namely accelerations of 11 m/s2, the origin of which was subsequently detected by STFT because the occurrence of resonance events or the excitation of natural frequencies of the machine were suspected. The STFT analysis identified a resonant region at machine start-up determined by the spindle speed which excites the resonance on the machine. The speed range between 1950 and 2150 rpm, which corresponds to the built-up resonance, was provided to the technologists to ensure that the machine was not operated around this resonance region at 400 and 760 Hz until the undesired phenomenon was eliminated. The results of the individual measurements provided information on the ideal setting of the cutting parameters and the current state of the machine.

show abstract