Article 12117

Title of the article

APPLICATION OF THE RESIDUE THEORY IN CONSTRUCTING ANALYTICAL MODELS OF THE AUTOCORRELATION FUNCTION OF VIBROACOUSTICAL VIBRATIONS 
IN THE MACHINE TOOL’S DYNAMIC SYSTEM 

Authors

Ignat'ev Aleksandr Anatol'evich, Doctor of engineering sciences, professor, sub-department of automation, control, mechatronics, Yuri Gagarin State Technical University of Saratov (77 Politekhnicheskaya street, Saratov, Russia), atpa@sstu.ru
Samoylova Elena Mikhaylovna, Candidate of engineering sciences, associate professor, sub-department of automation, control, mechatronics, Yuri Gagarin State Technical University of Saratov (77 Politekhnicheskaya street, Saratov, Russia), atpa@sstu.ru
Ignat'ev Stanislav Aleksandrovich, Doctor of engineering sciences, professor, sub-department of automation, control, mechatronics, Yuri Gagarin State Technical University of Saratov (77 Politekhnicheskaya street, Saratov, Russia), atpa@sstu.ru

Index UDK

 681.5

DOI

 10.21685/2072-3059–2017-1-12

Abstract

Background. The dynamic quality of machine tools, greatly influencing the geometric parameters of precision and the physical and mechanical characteristics of the surface layer of parts, is based on the measurement of vibro-acoustic (VA) oscillations. The subsequent treatment thereof is aimed at determining the spectral, correlation and other characteristics, on the basis of which the technical condition of machines and the designated mode of cutting are assessed in terms of quality and productivity of part machining. It is very important to select and substantiate informative characteristics, based on the measurement of the dynamic oscillations of the VA (DS) system of a machine when cutting, which allows to set a suitable processing mode. This mode is set by the maximum margin of DS stability, determined by the transfer function, which, in turn, is determined from the autocorrelation function (ACF), VA oscillation nodes involved in the forming process. The work is topical as the construction of an analytical model of the autocorrelation function (ACF) of VA oscillations of DS is important from the point of view of the subsequent comparison with the experimental ACF, calculated from measurements of vibrations on the machine and used subsequently for determination of the DS stability margin
serving a machine tool’s dynamic quality estimate.
Materials and methods. To calculate the ACF VA oscillations in DS of metalcutting machine tools the authors used its connection with the spectral density of the input “white noise” signal power and the frequency response of the machine tool’s DS.
Results. Analytically, using the theory of residues the authors obtained an expression for the ACF VA oscillations in the machine tool’s DS in the form of a damped cosine curve. The expression was similar to the one identified by experimental data of VA oscillations measurement.
Conclusions. The constructed theoretical model of the ACF VA oscillations of the gridning machine’s DS is adequate to the ACF derived from the experimental data, which makes it possible to prove the feasibility of its use for calculation of the transfer function of the machine tool’s DS with subsequent evaluation of its safety factor.

Key words

 vibroacoustic oscillations, metal-cutting machine tool, dynamic system, autocorrelation function, residue theory.

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References

1. Kudinov V. A. Dinamika stankov [Dynamics of machine tools]. Moscow: Mashinostroenie, 1967, 360 p.
2. Popov V. I., Loktev V. I. Dinamika stankov [Dynamics of machine tools]. Kiev: Tekhnika, 1975, 136 p.
3. Ignat'ev A. A., Gorbunov V. V., Ignat'ev S. A. Monitoring tekhnologicheskogo p otsessa kak element sistemy upravleniya kachestvom produktsii [Technological process monitoring as an element of the product quality management system]. Saratov: SGTU, 20009, 160 p.
4. Risbood K. A., Dixit U. S., Sahasrabudhe A. D. Journal of Material Processing Technology. 2003, vol. 132, pp. 203–214.
5. Ignat'ev A. A., Karakozova V. A., Ignat'ev S. A. Stokhasticheskie metody identifikatsii v dinamike stankov [Stochastic methods of identification in dynamics of machine tools]. Saratov: SGTU, 2013, 124 p.
6. Kozochkin M. P. STIN. 2014, no. 2, pp. 4–9.
7. Vu D., Lyu K. Konstruirovanie i tekhnologiya mashinostroeniya [Construction and mechanical engineering]. 1985, no. 2, pp. 89–100.
8. Dobrynin S. A., Fel'dman M. S., Firsov G. I. Metody avtomatizirovannogo issledovaniya vibratsiy mashin: spravochnik [Methods of computer-aided study of machine vibration: a reference book]. Moscow: Mashinostroenie, 1987, 224 p.
9. Ignat'ev A. A., Konovalov V. V., Ignat'ev S. A. Identifikatsiya v dinamike stankov s ispol'zovaniem stokhasticheskikh metodov [Identification of dynamics of machine tools using stochastic methods]. Saratov: SGTU, 2014, 92 p.
10. Lin Z. H. Int. J. Mach. Tools Manufact. 1988, vol. 28, no. 2, pp. 93–101.
11. Besekerskiy V. A., Popov E. P. Teoriya sistem avtomaticheskogo regulirovaniya [The theory of automatic control systems]. Moscow: Nauka, 1975, 768 p.
12. Korn G., Korn T. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov [Mathematics handbook for researchers and engineers]. Moscow: Nauka, 1984, 832 p.

 

Дата создания: 08.08.2017 15:55
Дата обновления: 09.08.2017 16:17