Analysis and improvement of design diagrams and mathematical models of vibratory lapping machines

https://doi.org/10.23939/ujmems2019.03-04.044
Received: August 19, 2019
Revised: October 03, 2019
Accepted: December 28, 2019

V. Zakharov, I. Kuzio, V. Korendiy, P. Dmyterko, "Analysis and improvement of design diagrams and mathematical models of vibratory lapping machines", Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 5, no. 3-4, pp. 44-56, 2019.

1
ISKRA PJSC
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
Lviv Polytechnic National University

Problem statement. The development of energy-efficient and high-performance vibratory lapping machines demands the improvement of their design diagrams and calculation techniques. Purpose. The main objectives of this research consist in detailed analysis of existent design diagrams and mathematical models of vibratory lapping machines; designing the three-mass hanger-type structures of such machines providing circular oscillations of laps; derivation of differential equations describing the motion of their oscillatory systems. Methodology. The technique of the research is based on fundamental concepts of engineering mechanics, strength of materials and theory of mechanical vibrations. Findings (results). The improved design diagrams of vibratory lapping machines with circular oscillations of laps are proposed and the corresponding differential equations describing the motion of the working elements are derived. Originality (novelty). The mathematical model of circular oscillations of the three-mass mechanical oscillatory system of vibratory lapping machine is developed. The possibilities of performing the double-side lapping of cylindrical and prismatic parts are considered. Practical value. The results of the performed investigations can be used during creating new designs and improving existent structures of vibratory finishing machines for lapping flat surfaces of cylindrical and prismatic parts. Scopes of further investigations. In further investigations, it is necessary to perform the numerical modelling of the system’s motion using the derived differential equations, and to compare the obtained theoretical results with the results of experimental investigations.

[1] O. S. Lanets, Ya. V. Shpak, and Yu. P. Sholovii, “Mizhrezonansni vibratsiini prytyralni mashyny z elektromahnitnym pryvodom, rozrobleni na osnovi efektu “Nulovoi zhorstkosti”” [“Inter-Rezonant Vibratory Lapping Machines with Electromagnetic Drive Designed on the Basis of the Effect of "Zero-Stiffness”], Avtomatizacìâ virobničih procesìv u mašinobuduvannì ta priladobuduvannì [Industrial Process Automation in Engineering and Instrumentation], vol. 41, pp. 41–48, 2007. [in Ukrainian].

[2] R. I. Silin, V. V. Tret’ko, and A. I. Gordeev, “Dinamicheskaja model' i ee realizacija v rezonansnom vibracionnom stanke dlja dovodki ploskih izdelij” [“Dynamic model and its implementation in resonant vibration machine for flat articles grinding”], Vektor nauki Tol'jattinskogo gosudarstvennogo universiteta [Vektor Nauki of Togliatti State University], vol. 3–1 (33–1), pp. 123–128, 2015. [in Russian]. https://doi.org/10.18323/2073-5073-2015-3-123-128

[3] V. F. Makarov, and K. R. Muratov, “Analiz oborudovanija dlja finishnoj abrazivnoj obrabotki ploskih precizionnyh poverhnostej izdelij” [“Equipment analysis for finishing abrasive processing of flat precision surfaces of products”], Vestnik Permskogo nacional'nogo issledovatel'skogo politehnicheskogo universiteta. Mashinostroenie, materialovedenie [Bulletin of Perm National Research Polytechnic University. Mechanical engineering, materials science], vol. 19, no. 1, pp. 170–187, 2017. [in Russian]. https://doi.org/10.15593/2224-9877/2017.1.11

[4] O. S. Lanets, O. V. Havrylchenko, Ya. V. Shpak, and V. M. Zakharov, “Vibratsiina vykinchuvalna mashyna z elektromahnitnym pryvodom” [“Vibratory finishing machine with electromagnetic drive”], UA Patent 93891, October 27, 2014. [in Ukrainian].

[5] O. S. Lanets, O. V. Havrylchenko, V. M. Zakharov, and V. M. Korendiy, “Vibratsiina vykinchuvalna mashyna z elektromahnitnym pryvodom” [“Vibratory finishing machine with electromagnetic drive”], UA Patent 132950, March 25, 2019. [in Ukrainian].

[6] I. V. Kuzio, O. S. Lanets, O. V. Havrylchenko, V. M. Zakharov, and V. M. Korendiy, “Vibratsiina vykinchuvalna mashyna z elektromahnitnym pryvodom” [“Vibratory finishing machine with electromagnetic drive”], UA Patent 141765, April 27, 2019. [in Ukrainian].

[7] I. V. Kuzio, V. M. Zakharov, V. M. Korendiy, and O. V. Havrylchenko, “Vibratsiina vykinchuvalna mashyna z elektromahnitnym pryvodom” [“Vibratory finishing machine with electromagnetic drive”], UA Patent 142743, June 25, 2019. [in Ukrainian].

[8] O. V. Havrylchenko, V. M. Korendiy, and V. M. Zakharov, “Formuvannia matematychnykh modelei try- i chotyrymasovykh kolyvnykh system vibrovykinchuvalnykh verstativ” [“Formation mathematical model three and four mass oscillatory systems of vibrating finishing machines”], Visnyk Natsionalnoho universytetu “Lvivska politekhnika” [Bulletin of Lviv Polytechnic National University], no. 866, pp. 3–12, 2017. [in Ukrainian].

[9] V. Korendiy, and V. Zakharov, “Substantiation of Parameters and Analysis of Operational Characteristics of Oscillating Systems of Vibratory Finishing Machines”, Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 3, no. 2, pp. 67–78, 2017. https://doi.org/10.23939/ujmems2017.02.067

[10] I. Kuzio, V. Zakharov, and V. Korendiy, “Substantiation of inertial, stiffness and excitation parameters of vibratory lapping machine with linear oscillations of laps”, Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 4, no. 2, pp. 26-39, 2018. https://doi.org/10.23939/ujmems2018.02.026

[11] I. V. Kuzio, V. M. Zakharov, and V. M. Korendiy, “Modelling the process of dressing the laps of vibratory finishing machine”, Avtomatizacìâ virobničih procesìv u mašinobuduvannì ta priladobuduvannì [Industrial Process Automation in Engineering and Instrumentation], no. 52, pp. 32–42, 2018. https://doi.org/10.23939/istcipa2018.52.032