DOI: 10.18503/1995-2732-2024-22-1-61-75
Abstract
Problem Statement (Relevance). Turning is one of the main methods of machining bodies of rotation. Vibrations during turning can seriously disrupt the integrity of the surface, and at the same time, along with such process parameters as the state of the cutting edge of the machining tool, the speed of the machining process, feed, and cutting depth, form the morphology of the surface, and, mainly, roughness and waviness of the surface. To determine and predict the waviness parameter, it is necessary to know such vibration parameter as the amplitude of self-oscillations. The amplitude of self-oscillation is a component parameter of the equation of cutting tool durability and can be obtained by solving the differential equation. However, solving this equation requires significant computing resources. In this regard, it is efficient to develop and use analytical approaches to solve the differential equation. Objectives. The research is aimed at developing an analytical approach to determine the value of self-oscillations based on the equation for the coefficient of change in cutting tool durability during finishing turning. Methods Applied. The authors obtained some equations for the amplitude of oscillations depending on cutting speed, the frequency of oscillations and the index of relative durability of the cutting tool, and determined and described their solutions for the amplitude in the form of polynomial roots. Originality. The paper proposes an approach for determining waviness of the surface by analytical estimation of the amplitude of self-oscillations depending on the cutting modes. The proposed approach was experimentally tested on the pulleys of a continuously variable transmission. Result. The paper describes a proposed mathematical relation of the technological quality assurance for the surface layer of the V-belt transmission components formed during turning to predict the height parameters of waviness depending on the change in the spindle speed, feed and cutting speed. Practical Relevance. The research is aimed at improving the quality of machining and forming a microprofile with regular waviness on the surface of the part, contributing to a reduction in machining time by reducing the number of technological operations.
Keywords
coefficient of durability, amplitude, self-oscillations, turning, surface waviness, pulley
For citation
Generalova A.A., Nikulin A.A., Bychkov D.S. Analytical Study on the Characteristics of Tool Durability and Self-Oscillations During Pulley Turning. Vestnik Magnitogorskogo Gosudarstvennogo Tekhnicheskogo Universiteta im. G.I. Nosova [Vestnik of Nosov Magnitogorsk State Technical University]. 2024, vol. 22, no. 1, pp. 61-75. https://doi.org/10.18503/1995-2732-2024-22-1-61-75
1. Drozdov N.A. On the issue of machine vibrations during turning. Stanki i instrument [Machines and Tools]. 1937;(22): 1-25. (In Russ.)
2. Kashirin A.I. Issledovanie vibratsii pri rezanii metallov [Study on vibrations during metal cutting]. Moscow, Leningrad: Academy of Sciences of the USSR, 1944, 132 p. (In Russ.)
3. Sokolovsky A.P. Zhestkost v tekhnologii mashinostroeniya [Rigidity in mechanical engineering technology]. Moscow, Leningrad: Mashgiz in Leningrad, 1946, 207 p. (In Russ.)
4. Gugulothu S., Pasam V.K. Optimizing multi-response parameters in turning of AISI1040 steel using desirability approach. International Journal of Mathematical, Engineering and Management Sciences. 2019;4(4):905-921. DOI: https://dx.doi.org/ 10.33889/IJMEMS.2019.4.4-072
5. Generalova A., Zverovshchikov A., Nikulin A. Surface waviness parameters of continuously variable transmission friction during turning. Journal of King Saud University – Engineering Sciences, 2022. https://doi.org/10.1016/j.jksues.2022.06.001
6. Generalova A.A., Zverovshchikov A.E., Nikulin A.A. The influence of self-oscillations in the turning process on the formation of waviness of pulleys of automobile continuously variable transmissions. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhsky region. Tekhnicheskie nauki [News of Higher Educational Institutions. Volga Region. Technical Sciences]. 2022;(4):108-121. (In Russ.) DOI:10.21685/2072-3059-2022-4-9
7. Lopovok T.S. Volnistost poverkhnosti i ee izmerenie [Surface waviness and its measurement]. Moscow: Publishing House of Standards, 1973, 184 p. (In Russ.)
8. Zharkov I.G. Vibratsii pri obrabotke lezviynym instrumentom [Vibrations when machining with a cutting tool]. Leningrad: Mashinostroenie. Leningrad Branch, 1986, 179 p. (In Russ.)
9. Kedrov S.S. Kolebaniya metallorezhushchikh stankov [Vibrations of metal-cutting machines]. Moscow: Mashinostroenie, 1978, 199 p. (In Russ.)
10. Martinova L.I., Grigoryev A.S., Sokolov S.V. Diagnostics and forecasting of cutting tool wear at CNC machines. Autom. RemoteControl. 2012;73(4):742-749.
11. Johanna M.F. et al. A tool condition monitoring system based on low-cost sensors and an IoT platform for rapid deployment. Processes. 2023;11(3):668. https://doi.org/10.3390/pr11030668
12. Bisu C.D. et al. Displacements analysis of self-excited vibrations in turning. The International Journal of Advanced Manufacturing Technology. 2009;44 (1-2):1-16.
13. Jozef Zajac et al. Prediction of cutting material durability by T = f(vc) dependence for turning processes. Processes. 2020;8:789. DOI: 10.3390/ pr8070789
14. Zapciu M. et al. Dynamic characterization of machining systems. International Journal of Advanced Manufacturing Technology. 2011;(57):73-83. DOI: 10.1007/s00170-011-3277-7
15. Molchanov A., Zaytzev A.N., Alexandrova Yu.P. Identification of the self-oscillating mode in metal-cutting machines in the production of agricultural machinery. VIII International Conference on Advanced Agritechnologies, Environmental Engineering and Sustainable Development. Krasnoyarsk, 2023, vol. 390. https://doi.org/10.1051/e3sconf/202339006009
16. Altintas Y. Manufacturing automation: Metal cutting mechanics, machine tool vibrations, and CNC design. New York, 2000, 286 p.
17. Yuqing Zhou et al. Synthetic minority oversampling enhanced FEM for tool wear condition monitoring. Processes. 2023;11(6):1785. DOI: 10.3390/pr11061785
18. Zhou Y.Q. et al. Tool wear condition monitoring based on a two-layer angle kernel extreme learningmachine using sound sensor for milling process. Journal of Intelligent Manufacturing. 2022;33:247-258.
19. Korendyasev G. An approach to modeling self-oscillations during metal machining based on a finite-element model with small amount of computing resources. Vibroengineering PROCEDIA. 2020;32:6-12. DOI: 10.21595/vp.2020.21437
20. Omelyanov O. Prospects for the use of vibration during cutting material. Vibrations in Engineering and Technology. 2021;1:10. DOI: 10.37128/2306-8744-2021-1-10
21. Yilmaz B., Karabulut Ş., Cüllü A. A review of the chip breaking methods for continuous chips in turning. Journal of Manufacturing Processes. 2020;49:50-69. DOI: 10.1016/j.jmapro.2019.10.026
22. Leonov S.L., Zinoviev A.T. Osnovy sozdaniya imitatsionnykh tekhnologiy pretsizionnogo formoobrazovaniya [Fundamentals of creating simulation technologies of precision shaping]. Barnaul: Publishing House of Altai State Technical University, 2006, 198 p. (In Russ.)
23. Sokolova I.D., Beckel L.S., Pilipushko A.Y. Mathematical model of changing the combined cutting tool durability. IOP Conference Series: Materials Science and Engineering. 2021;1047(1). DOI: 10.1088/1757-899X/1047/1/012013
24. Vasilkov D., Tarikov I.Y., Nikitin A.V. The dynamics of contact interaction during the cutting process. International Journal of Mathematical, Engineering and Management Sciences. 2019;4(5):1218-1227. DOI: 10.33889/IJMEMS.2019.4.5-096
25. Orgiyan A. et al. Influence of cutting modes on wear resistance of cutters and accuracy of fine boring of steels. Proceedings of Odessa Polytechnic University. 2021;2(64):13-21.
26. Taylor F. On the art of cutting metals. Kindle Edition, 2017, 564 p.
27. Grigoriev S.N. et al. Rezanie materialov. Rezhushchiy instrument: uchebnik dlya srednego professionalnogo obrazovaniya. V 2-kh ch. Ch. 2 [Cutting materials. Cutting tools: textbook for secondary vocational education. In 2 parts. Part 2]. Moscow: Publishing House of Yurait, 2023, 246 p. (In Russ.)
28. Arshinov V.A., Alekseev G.A. Rezanie metallov i rezhushchiy instrument: uchebnik dlya mashinostroit. tekhnikumov [Metal cutting and cutting tools: textbook for mechanical engineering colleges]. Moscow: Mashinostroenie, 1968, 480 p. (In Russ.)
29. Bonfá M.C. et al. Evaluation of tool life and workpiece surface roughness in turning of AISI D6 hardened steel using PCBN tools and minimum quantity of lubricant (MQL) applied at different directions. The International Journal of Advanced Manufacturing Technology. 2019;103:971-984. DOI: 10.1007/s00170-019-03619-z
30. Rashed R. The development of Arabic mathematics: Between arithmetic and algebra. Boston: Springer Science & Business Media, 1994, 600 p.
31. Riley K.F., Hobson M.P., Bence S.J. Mathematical methods for physics and engineering. New York: Cambridge University Press, 2006, 1363 p.
32. Davis P.J. Leonhard Euler’s integral: A historical profile of the gamma function. American Mathematical Monthly. 1959;66(10):849-869. DOI: 10.2307/2309786
33. Pearson K. Historical note on the origin of the normal curve of errors. Biometrika. 1924;16(3):402-404.
34. Kosilova A.K., Meshcheryakov R.K. Spravochnik tekhnologa-mashinostroitelya. V 2-kh t. T. 1 [Handbook of a mechanical engineering technologist. In 2 volumes. Vol. 1]. Moscow: Mashinostroenie, 1986, 656 p. (In Russ.)
35. Fraleigh J.B. A first course in abstract algebra. MA: Addison-Wesley, 2002, 544 p.
36. Mishina A.P. Higher algebra: Linear algebra, polynomials, general algebra. Oxford: Pergamon Press, 1965, 274 p.
37. Gorroochurn P. Some laws and problems of classical probability and how Cardano anticipated them. Chance. 2012; 25(4):13-20. DOI: 0.1080/09332480.2012. 752279
38. Generalova A.A., Nikulin A.A. Increasing the vehicle’s dynamic performance by developing a continuously variable transmission. Journal of Engineering and Applied Sciences. 2019;14:6866-6875. DOI: 10.3923/jeasci.2019.6866.6875
39. Zverovshchikov A.E., Generalova A.A., Nikulin A.A. Ensuring the performance characteristics of a friction V-belt variator. Journal of Physics: Conference Series. 2020;1679. DOI: 10.1088/1742-6596/1679/4/ 042079
40. Generalova A.A., Zverovshchikov A.E., Nikulin A.A. Study on the effect of the microprofile of the friction elements of the continuously variable transmission on the coefficient of friction in the contact zone and efficiency of the transmission. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhsky region. Tekhnicheskie nauki [News of Higher Educational Institutions. Volga Region. Technical Sciences]. 2023;(3):154-172. (In Russ.) DOI: 10.21685/2072-3059-2023-3-12