On the Theory and Methods of Calculating the Critical Regimes of Elastic Rotor Rotation

V. V. Eliseev, T. V. Zinovieva, S. A. Abid

Abstract


The foundations of the theory of critical regimes and balancing of elastic rotors have been considered. A rotating reference frame was used with translational motion inertia forces and Coriolis forces introduced. For the case of small relative thickness, one-dimensional rod models were proposed, namely, classical and shifted. The emergence of negative stiffness due to centrifugal forces was shown. With speed increase, there ap-peared critical regimes that could be removed by balancing. Eigenvalue problems were presented for calculating critical speeds and corresponding forms. Formulas for the balancing weight mass were deduced. A method was developed for calculating critical speeds and parameters of thin rotor balancing using computer mathematics

Full Text:

PDF

References


Goldin A.S. Vibratsiya rotornykh mashin [Vibration of rotary machines], Moscow, Mashinostroyeniye, 2000, 344 p. (in Russ.)

Gusarov A.A. Dinamika i balansirovka gibkikh rotorov [Dynamics and balancing of flexible rotors], Moscow, Nauka, 1990, 152 p. (in Russ.)

Kelzon A.S., Tsimansky Yu.P., Yakovlev V.I. Dinamika rotorov v uprugikh oporakh [Dynamics of rotors in elastic supports], Moscow, Nauka, 1982, 280 p. (in Russ.)

Poznyak E.L., Dntmentberg F.M., Kolesnikov K.S., eds. Vibratsii v tekhnike. V 6 t. Tom 3. Kolebaniya mashin, konstruktsiy i ikh elementov. Kolebaniya rotorov [Vibration in engineering. In 6 vol. Vol. 3. Vibrations of machinery, structures and their elements. Rotor oscillations], Moscow, Mashinostroyeniye, 1980, pp. 130-189. (in Russ.)

Kolesnikova K.S., ed. Mashinostroenie: entsiklopedya. V 40 t. T.1-3. Dinamika i prochnost' mashin. Teoriya mekhanizmov i mashin. V 2 kn. Kn. 2 [Mechanical engineering: encyclopedia. In 40 vol. Vol. 1-3. Dynamics and strength of machines. Theory of mechanisms and machines. In 2 books. Book 2], Moscow, Innovative Mechanical Engineering, 1995, 624 p. (in Russ.)

Nazarenko Yu.B. Novoe v dinamike rotorov gazoturbinnykh dvigateley i problemy mezhrotornogo podshipnika dvigatelya [New in the dynamics of rotors of gas turbine engines and the problems of the inter-rotor engine bearing], Moscow, Mega-art, 2014, 110 p. (in Russ.)

Pasynkova I.A. Dinamika pretsessionnogo dvizheniya neuravnoveshennogo rotora [Dynamics of the precession motion of an unbalanced rotor, St. Petersburg, Publishing House of St. Petersburg State University], 2014, 238 p. (in Russ.)

Genta G. Dynamics of Rotating Systems, New York, Springer, 2005, 658 p.

Yamamoto T., Ishida Y. Linear and Nonlinear Rotordynamics: A Modern Treatment with Applications, New York, Wiley Interscience, 2001, 348 p.

Eliseev V.V. Mekhanika deformiruemogo tverdogo tela [Mechanics of a deformable solid], St. Petersburg, Publishing house of Polytechnic. University, 2006, 231 p. (in Russ.)

Kiryanov D.V. Mathcad 14, St. Petersburg, BHV-Petersburg, 2007, 704 p. (in Russ.)

Eliseev V.V. Dynamics, critical velocities and balancing of thermoelastic rotors [Dinamika, kriticheskie skorosti i balansirovka termouprugikh rotorov], Sovremennoe mashinostroenie. Nauka i obrazovanie [Modern machine building. Science and education], 2013, no.3, pp. 311-317. (in Russ.)

Yeliseyev V.V. Dynamics, critical speeds and balancing of thermoelastic rotors, Lecture Notes in Control and Information Sciences, 2015, vol.22, pp. 129-136. DOI: 10.1007/978-3-319-15684-2_15

Bykov V.G., Melnikov A.E. Mathematical model of a flexible rotor on the basis of generalized Lagrange coordinates [Matematicheskaya model' gibkogo rotora na osnove obobshchennykh lagranzhevykh koordinat], Vestnik Sankt-Peterburgskogo universiteta. Seriya 1. Matematika. Mekhanika. Astronomiya [Bulletin of St. Petersburg University. Series 1. Mathematics. Mechanics. Astronomy], 2010, no.4, pp. 110-118. (in Russ.)

Voronkov V.S., Denisov G.G. The method of balancing the rotor in two radial thrust bearings [Metodika balansirovki rotora v dvukh radial'nykh upornykh podshipnikakh], Problemy mashinostroeniya i nadezhnosti mashin [Problems of machine building and machine reliability], 2006, no.4, pp. 32-40. (in Russ.)

Eliseev V.V., Avksentiev A.I. Models of elastic rods in the dynamics of flexible rotors [Modeli uprugikh sterzhney v dinamike gibkikh rotorov], Sovremennoe mashinostroenie [Modern machine building], 2014, no.4, pp. 335-343. (in Russ.)

Polushkin O.O. System regularity of mechanics and rotor balancing [Sistemnye zakonomernosti mekhaniki i balansirovki rotorov], Vestnik Donskogo gosudarstvennogo tekhnicheskogo universiteta [Bulletin of Don State Technical University], 2011, vol.11, no.6, pp. 842-849. (in Russ.)

Prokopev V.N. Dynamics of rotors on bearings with floating bushings [Dinamika rotorov na podshipnikakh s plavayushchimi vtulkami], Problemy mashinostroeniya i nadezhnosti mashin [Problems of machine building and machine reliability], 1995, no.5, pp. 37-42. (in Russ.)

Solomin O.V. Morozov A.A. Numerical methods for solving the equations of motion in problems of the dynamics of rotor systems with support for liquid friction [Chislennye metody resheniya uravneniy dvizheniya v zadachakh dinamiki rotornykh sistem s oporami zhidkostnogo treniya], Izv. vuzov: Mashinostroenie [Journal of Proc. of the higher educational institutions. Engineering], 2006, no.11, pp. 16-26. (in Russ.)

Sperling L., Ryzhik B., Linz C., Duckstein H. Simulation of two-plane automatic balancing of a rigid rotor, Mathematics and Computers in Simulat., 2002, no.58, pp. 351-365. DOI: 10.1016/S0378-4754(01)00377-9

Eliseev V.V. Towards a Nonlinear Dynamics of Elastic Rods [K nelineynoy dinamike uprugikh sterzhney], Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics], 1988, vol.52, no.4, pp. 635-641. (in Russ.)

Eliseev V.V. Defining equations for elastic prismatic rods [Opredelyayushchie uravneniya dlya uprugikh prizmaticheskikh sterzhney], Izvestiya Akademii nauk SSSR. Mekhanika tverdogo tela [Mechanics of Solids], 1989, no.1, pp. 70-75. (in Russ.)




DOI: http://dx.doi.org/10.24892/RIJIE/20170302

Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 V. V. Eliseev, T. V. Zinovieva, S. A. Abid

© Russian Internet Journal of Industrial Engineering. ISSN 2310-0818

E-mail: indust.engineering.ru@gmail.com

Another version of the web site: http://indust-engineering.ru