SIMULATION OF NON-LINEAR CHARACTERISTICS INFLUENCE DYNAMIC ON VERTICAL RIGID GYRO ROTOR RESONANT OSCILLATIONS

Zharilkassin Iskakov

Abstract


The influence of viscous linear and cubic nonlinear damping of an elastic support on the resonance oscillations of a vertical rigid gyroscopic unbalanced rotor is investigated. Simulation results show that linear and cubic non-linear damping can significantly dampen the main harmonic resonant peak. In non-resonant areas where the speed is higher than the critical speed, the cubic non-linear damping can slightly dampen rotor vibration amplitude in contrast to linear damping. If linear or cubic non-linear damping increase in resonant area significantly kills capacity for absolute motion, then they have little or no influence on the capacity for absolute motion in non-resonant areas. The simulation results can be successfully used to create passive vibration isolators used in rotor machines vibration damping, including gyroscopic ones.

Keywords


gyro rotor, resonant amplitude, linear damping, non-linear damping, mathematical simulation

Full Text:

PDF

References


Fujiwara, H., Nakaura, H., & Watanabei K. (2015). The vibration behavior of flexibly fixed rotating machines, Proceedings of the 14th IFToMM World Congress. Taipei, Taiwan.

Gil-Negrete, N., Vinolas, J., & Kari L. (2009). A non-linear rubber material model combining fractional order viscoelasticity and amplitude dependent effects, Journal of Applied Mechanics, 76(1), 9 -11.

Hayashi, C. (1964). Non-linear Oscillations in Physical Systems (Chapters 1, 3 – 6). McGraw – Hill.

Ho, C., Lang Z., & Billings, S. A. (2012). The benefits of non-linear cubic viscous damping on the force transmissibility of a Duffing-type vibration isolator. Proceedings of UKACC International Conference on Control, 479-484. Cardiff, UK.

Iskakov Zh. & Kalybayeva A. (2010, September 14). Kolebaniya i ustoychivost' vertikal'nogo giroskopicheskogo rotora s perekosom diska i disbalansom massy [Oscillations and stability of vertical gyro rotor with disk tilt and mass disbalance]. Trudy I Mezhdunarodnogo simposiuma: “Fundamental’nue i prikladnye problemy” [Proc. of International Symposium “Fundamental and Applied Science Problems”] Moscow pp. 50 – 57. RAS.

Iskakov Zh. & Kunelbayev M. (2018). Centrifuga na baze gyroskopicheskogo rotora [Centrifuge based on gyro rotor]. Invention patent of the Republic of Kazakhstan (19) KZ B (11) 32666 19.02.2018, bulletin № 7.

Iskakov, Zh. (2015, October 25). Resonant Oscillations of a Vertical Unbalanced Gyroscopic Rotor with Non-linear. Characteristics. Proceedings of the 14th IFToMM World Congress. Taipei, Taiwan. DOI Number: 10.6567/IFToMM.14TH.WC.OS14.001.

Iskakov, Zh. (2017a). Dynamics of a Vertical Unbalanced Gyroscopic Rotor with Non-linear Characteristics. New advances in Mechanisms, Mechanical Transmissions and Robotics, Mechanisms and Machine Science, 46, 107–114. Springer International Publishing AG. DOI 10.1007/978-319-45450-4_11.

Iskakov, Zh. (2017b, September 11). Rezonansnyye kolebaniya neuravnoveshennogo vertikal'nogo giroskopicheskogo rotora s nelineynymi kharakteristikami [Resonant oscillations of non-balanced vertical gyro rotor with non-linear characteristics]. Proceedings of the International Symposium of Mechanism and Machine, 240-246. Science, Baku.

Kyderbekuly A.B. (2006). Kolebaniya i ustoychivost' rotornykh sistem i ploskikh mekhanizmov s nelineyno- uprugimi kharakteristikami [Oscillations and stability of rotor systems and plane mechanisms with non-linear rigid characteristics] (Doctor of Engineering Science Dissertation.:01.02.06). Almaty.

Panovko Ya. G. (1971). Vvedeniye v teoriyu mekhanicheskikh kolebaniy [Introduction to mechanical oscillations theory]. Moscow, Nauka.

Peng, Z. K., Mengand Lang, Z. Q., Zhang, W. M., & Chu, F. L. (2012). Study of the effects of cubic non-linear damping on vibration isolations using Harmonic Balance Method. International Journal of Non-Linear Mechanics, 47(10), 1065-1166.

Ravindra, B., & Mallik, A. K. (1994). Performance of non-linear vibration isolators under harmonic excitation. Journal of Sound and Vibration, 170, 325-337.

Richards, C. M., & Singh, R. (1999). Experimental characterization of non-linear rubber isolators in a multi-degree-of-freedom system configuration. The journal of the Acoustical Society of America, 106. 21 - 78.

Szemplinska-Stupnicka, W. (1968). Higher harmonic oscillations in heteronymous non-linear systems with one degree of freedom. International Journal of Non-Linear Mechanics, 3(1), 17-30.

Yablonskiy A.A. (2007). Kurs teorii kolebaniy [Oscillation theory course]. Study guide. BHV - St. Petersburg.




DOI: http://dx.doi.org/10.12955/cbup.v6.1319

Refbacks

  • There are currently no refbacks.


Print ISSN 1805-997X, Online ISSN 1805-9961

(c) 2018 CBU Research Institute s.r.o.

For more information on the conference visit cbuic.cz