The Effect of Unbalance Mass on the Necessary Conditions of the Double-Support Rotor Autobalancing Stability

Authors: Gorbenko A.N., Shmelev S.Kh., Strautmanis G. Published: 22.04.2019
Published in issue: #2(125)/2019  

DOI: 10.18698/0236-3941-2019-2-71-82

Category: Mechanical Engineering and Machine Science | Chapter: Machines, Units and Technological Processes  
Keywords: rotor, unbalance, autobalancing stability, critical speeds, anisotropy

The analysis of necessary conditions for autobalancing stability of rotor, which performs spatial oscillations, was carried out in this paper taking into account the influence of unbalance and autobalancer masses. It was found that the using of traditional models, where unbalance and autobalancer masses are assumed small, could lead to significant errors in the dynamics analysis of spatially moving rotor. The influence of this factor leads to the doubling of the critical rotational speeds spectrum. Moreover, the system motion between the split critical frequencies is unstable. There may be one or two onset areas of autobalancing mode motion depending on the dynamic rotor type, its location relative to the supports, the unbalance mass and other system parameters. It was found that rotors, that are long type or close to the spherical type, are the most sensitive to this factor. On the other hand, rotors of the short type are weakly sensitive. It is shown that the most preferred case is when the unbalance and autobalancer location plane passes through the common mass center of the composite rotor. The quantitative criterion is formulated for the necessity of taking into account (or not taking into account) the influence of this factor when analyzing the system dynamics


[1] Gusarov A.A. Avtobalansiruyushchie ustroystva pryamogo deystviya [Automatic balancing devices of direct action]. Moscow, Nauka Publ., 2002.

[2] Fіlіmonіkhіn G.B. Zrіvnovazhennya і vіbrozakhist rotorіv avtobalansirami z tverdimi koriguvalnimi vantazhami [Balancing and vibration protection of rotors by autobalancers with solid corrective weights]. Kіrovograd, KNTU Publ., 2004.

[3] Gorbenko A.N. On the stability of self-balancing of a rotor with the help of balls. Strength Mater., 2003, vol. 35, no. 3, pp. 305–312. DOI: 10.1023/A:1024621023821

[4] Rodrigues D.J., Champneys A.R., Friswell M.I., et al. Automatic two-plane balancing for rigid rotors. Int. J. Non-Linear Mech., 2008, vol. 43, no. 6, pp. 527–541. DOI: 10.1016/j.ijnonlinmec.2008.01.002

[5] Bykov V.G. Compensating of statically and dynamically unbalanced rotor by single-plane auto-balancing device. Vestnik Sankt-Peterburgskogo universiteta. Ser. 1. Matematika. Mekhanika. Astronomiya [Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy], 2009, no. 4, pp. 67–76 (in Russ.).

[6] Strautmanis G., Mezitis M., Strautmane V., et al. Impact of dimensions of the compensating mass of the automatic balancer on its acceleration. VP, 2017, vol. 12, pp. 1–5. DOI: 10.21595/vp.2017.18449

[7] Filimonikhin G., Filimonikhina I., Yakymenko M., et al. Application of the empirical criterion for the occurrence of auto-balancing for axisymmetric rotor on two isotropic elastic supports. Eastern-European J. Enterprise Technologies, 2017, vol. 2, no. 7, pp. 51–58. DOI: 10.15587/1729-4061.2017.96622

[8] Filimonikhin G.B., Gorbenko A.N. Effect of the balls mass of the autobalancer on structure of the motion equations of the rotor on two supports. Automation of production processes in mechanical and instrument engineering: Ukr. interdepart. sci.-tech. coll. National University Lviv Polytechnic, 2011, vol. 45, pp. 478–488 (in Russ.).

[9] Gorbenko A.N. Mass-inertial characteristics and dimensionless equations of two-bearing rotor motion with auto-balancer in terms of compensating body mass. Nauka i obrazovanie: nauchnoe izdanie [Science and Education: Scientific Publication], 2015, no. 12 (in Russ.). DOI: 10.7463/1215.0827773

[10] Gorbenko A.N. Auto-balancer influence on the critical speeds of rotor on two supports. Nauka i obrazovanie: nauchnoe izdanie [Science and Education: Scientific Publication], 2016, no. 10, pp. 143–167 (in Russ.). DOI: 10.7463/1016.0847756

[11] Gorbenko A.N., Shmelev S.Kh. Necessary self-balancing robustness conditions for a two-bearing rotor taking unbalance mass into account. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Mashinostr. [Herald of the Bauman Moscow State Tech. Univ., Mechan. Eng.], 2018, no. 5, pp. 36−50 (in Russ.). DOI: 10.18698/0236-3941-2018-5-36-50

[12] Dimentberg F.M., Kolesnikov K.S., eds. Vibratsii v tekhnike. T. 3. Kolebaniya mashin, konstruktsiy i ikh elementov [Vibrations in the technique. Vol. 3. Oscillations of machines, constructions and their elements]. Moscow, Mashinostroenie Publ., 1980.