Mathematical description of a reciprocating compressor taking into account the suspension parameters influence on its output characteristics

The paper presents mathematical model of the piston compressor consisting of a system of the moving solids with the moving center of mass, which leads to vibrations of the suspended compressor housing relative to the stationary base. Suspension elements have dissipative properties and dissipate the energy imparted to them; as a result, portion of the mechanical energy generated by the electric motor is being lost. The piston machines vibrations on the suspension are determined by their vibration rate, which is one of the most important ecologic indicators. Therefore, it is relevant to evaluate and, if necessary, minimize these losses, as well as to study the suspension parameters influence on the compressor output characteristics. The proposed mathematical description is based on the open system thermodynamics methodology and laws of mechanics describing the piston relative movement and the laws that determine motion of the center of mass of the moving elements system, as well as the system motion relative to the center of mass. The mathematical model was tested on the KKh-0.125 household refrigerator compressor. The results obtained confirmed adequacy of the developed mathematical description.

References

[1] Vasilyev A.V. About the experience of research and reduction of vibration of compressor plants. Noise Theory and Practice, 2016, no. 2, pp. 27–34. (In Russ.).

[2] Kozlov A.A., Burakov A.V., Kuznetsov L.G. Reducing vibration of a reciprocating compressor by ensuring the constant sign of the torque diagram. Materialovedenie. Energetika [Materials Science. Power Engineering], 2020, vol. 26, no. 4, pp. 64–74, doi: https://doi.org/10.18721/JEST.26405 (in Russ.).

[3] Naumenko A.P. [Vibroacoustic model of piston compressor diagnostic signal.]. Dinamika sistem, mekhanizmov i mashin. Mat. VII mezhd. nauch.-tekh. konf. Kn. 2 [Dynamics of Systems, Mechanisms and Machines. Proc. VII Int. Sci.-Tech. Conf. Vol. 2.]. Omsk, OmGTU Publ., 2009, pp. 39–44. (In Russ.).

[4] Yamanin A.I. [About criteria of equilibrium of piston machines]. 8-e Lukaninskie chteniya. Problemy i perspektivy razvitiya avtotransportnogo kompleksa. Sb. tr. mezhd. nauch.-tekh. konf. [8th Lukanin Readings. Problems and Prospects of Development of Motor Transport Complex. Proc. Int. Sci.-Tech. Conf.]. Moscow, MAI Publ., 2019, pp. 588–596. (In Russ.).

[5] Maliovanov M.V., Fedina T.O., Khmelev R.N. [On determining the reaction of internal combustion engine supports when taking into account the irregular rotation of the crankshaft]. Avtomobil i tekhnosfera. ICATS ‘2005. Mat. IV mezhd. nauch.-prakt. konf. [Automobile and Technosphere. ICATS ‘2005. Proc. IV Int. Sci.-Pract. Conf.]. Kazan, KGTU, 2005, pp. 165. (In Russ.).

[6] Maliovanov M.V., Khmelev R.N. [Hierarchical system of internal combustion engine models.]. Dvigatel — 2007. Sb. nauch. tr. po mat. mezhd. konf. [Engine — 2007. Proc. Int. Conf]. Moscow, Bauman MSTU Publ., 2007, pp. 113–118. (In Russ.).

[7] Maliovanov M.V., Fedina T.O., Khmelev R.N. [On influence of parameters of a suspension of the internal combustion engine on intra-cylinder processes in it]. Progress transportnykh sredstv i sistem — 2005. Mat. mezhd. nauch.-prakt. konf. [Progress of Vehicles and Systems — 2005. Proc. Int. Sci.-Pract. Conf.]. Volgograd, VolGTU Publ., 2005, pp. 342–343. (In Russ.).

[8] Loytsyanskiy L.G., Lurye A.I. Kurs teoreticheskoy mekhaniki. T. 2. Dinamika [Course of theoretical mechanics. Vol. 2. Dynamics.]. Moscow, Nauka Publ., 1983. 640 p. (In Russ.).

[9] Popov A.N. Issledovanie reaktsiy opor dvigateley vnutrennego sgoraniya na osnove obshchikh teorem dinamiki sistemy s primeneniem ETsVM [Investigation of reactions of internal combustion engine supports on the basis of general system dynamics theorems with the use of computer]. Gorkiy, Izd-vo TPI Publ., 1975. 35 p. (In Russ.).

[10] Maliovanov M.V., Pleshanov A.A., Khmelev R.N. et al. [On determination of reaction of ice supports in view of casing motion, rotation unevenness and partial crankshaft unbalance]. Fundamentalnye i prikladnye problemy sovershenstvovaniya porshnevykh dvigateley. Mat. X MNPK [Fundamental and Applied Problems of Improving of Piston Engines. Mat. X ISPK.]. Vladimir, VlGU Publ., 2005, p. 64. (In Russ.).

[11] Popov I.V., Tolmachev P.V., Khmelev R.N. The virtual stand for removal of static and dynamic characteristics of internal combustion engines. Izvestiya TulGU. Tekhnicheskie nauki [News of the Tula State University. Technical Sciences], 2016, no. 3, pp. 164–170. (In Russ.).

[12] Mamontov M.A. Osnovy termodinamiki tela peremennoy massy [Fundamentals of thermodynamics of a body of variable mass]. Tula, Priokskoe knizhnoe izd-vo Publ., 1970. 87 p. (In Russ.).

[13] Elagin M.Yu. Termodinamika otkrytykh sistem. Prakticheskoe primenenie [Thermodynamics of open systems. Practical application]. Tula, Izd-vo TulGU Publ., 2020. 480 p. (In Russ.).

[14] Elagin M.Yu. Matematicheskoe modelirovanie rabochikh protsessov kompressorov obemnogo printsipa szhatiya [Mathematical modelling of working processes of compressors of volume principle of compression]. Tula, Izd-vo TulGU Publ., 2022. 154 p. (In Russ.).

[15] Vazhnov A.I. Elektricheskie mashiny [Electric machines]. Leningrad, Energiya Publ., 1969. 769 p. (In Russ.).

[16] Rozenblit G.B. Teploperedacha v dizelyakh [Heat transfer in diesel engines]. Moscow, Mashinostroenie Publ., 1977. 216 p. (In Russ.).

[17] GOST 30938–2002. Kompressornoe oborudovanie. Opredelenie vibratsionnykh kharakteristik malykh i srednikh porshnevykh kompressorov i normy vibratsii [State standard GOST 30938-2002. Compresing equipment. Determination of vibration characteristics of few and middle piston compressors and norms vibration]. Minsk, EASS, 2002. 14 p. (In Russ.).

[18] Rozenberg G.Sh., ed. Vibrodiagnostika [Vibrodiagnostics]. Sankt-Petersburg, PEIPK Publ., 2003. 284 p. (In Russ.).

[19] Vidyakin Yu.A., Kondratyeva T.F., Petrova F.P. et al. Kolebaniya i vibratsii v porshnevykh kompressorakh [Oscillations and vibrations in piston compressors]. Leningrad, Mashinostroenie Publ., 1972. 224 p. (In Russ.).