Autors: Sinapov, P. V.
Title: Forced Vibrations of an Elastically Supported Rigid Rotor at Different Types of Unbalance
Keywords:

Abstract: This paper studies forced vibrations of a rigid rotor mounted on a balancing machine. The dynamic model is with two degrees of freedom and the rotor is unbalanced. The d'Alembert's principle for a mechanical system (dynamic equilibrium) is used to produce the differential equations of motion. Small displacements for the rotor axis are studied. Vector equations are projected along certain coordinate axes to obtain equations without the involvement of reaction forces. Differential equations are non-linear. Three cases of unbalance are examined and the differential equations of motion are solved using MATLAB (Simulink) software. The values of the parameters were determined on the basis of an existing stand for balancing.

References

  1. H. Schneider, Rotor Balancing, Fundamentals for Systematic Processes (Springer-Vieweg, 2020).
  2. Y. Ishida, T. Yamamoto, Linear and Nonlinear Rotordynamics (Wiley-VCH Verlag & Co.KGaA, 2012).
  3. R.E.D. Bishop, “The vibration of rotating shafts”, Journal of Mechanical Engineering Science 1(1), pp.50-65 (1959).
  4. J. Taghipour, M. Dardel, M. H. Pashae, “Nonlinear vibration analysis of a flexible rotor shaft with a longitudinally dispositioned unbalanced rigid disc”, Communications in Nonlinear Science and Numerical Simulation 97, 105761 (2021).
  5. B. Kirchgäßner, “Finite elements in rotordynamics”, Procedia Engineering 144, pp. 736-750 (2016).
  6. D.J. Rodrigues, A.R. Champneys, M.I. Friswell, R.E. Wilson, “Automatic two-plane balancing for rigid rotors”, International Journal of Non-Linear Mechanics 43(6), pp. 527-541 (2008).
  7. L. Sperling, F. Merten, H. Duckstein, “Self-synchronization and automatic balancing in rotor dynamics”, International Journal of Rotating Machinery 6(4), pp. 275-285 (2000).
  8. L. Sperling, B. Ryzhik, Ch. Linz, H. Duckstein, “Simulation of two-plane automatic balancing of a rigid rotor”, Mathematics and Computers in Simulation 58, pp. 351-365 (2002).
  9. W. Liu, P. Bättig, P. H. Wagner, J. Schiffmann, “Nonlinear study on a rigid rotor supported by herringbone grooved gas bearings: Theory and validation”, Mechanical Systems and Signal Processing 146, 106983 (2021).
  10. E. Iseli, J. Schiffmann, “Experimental and numerical investigation of the unbalance behavior of rigid rotors supported by spiral-grooved gas journal bearings”, Mechanical Systems and Signal Processing 174, 109080 (2022).
  11. B. Nayek, A. S. Das, J. K. Dutt, “Model based estimation of inertial parameters of a rigid rotor having dynamic unbalance on Active Magnetic Bearings in presence of noise”, Applied Mathematical Modelling 97, pp. 701-720 (2021).
  12. P. Kumar, R. Tiwari, “Dynamic analysis and identification of unbalance and misalignment in a rigid rotor with two offset discs levitated by active magnetic bearings: a novel trial misalignment approach”, Propulsion and Power Research 10, pp. 58-82 (2021).
  13. P. Singh, H. Chaudhary, “Optimum two-plane balancing of rigid rotor using discrete optimization algorithm”, World Journal of Engineering 16(1), pp. 138-146 (2019).
  14. J. A. Genov, I. M. Kralov, “A linear quadratic regulator synthesis for a semi-active vehicle suspension part 1 - Modeling of the dynamical system”, AIP Conference Proceedings 2172, 110006 (2019).
  15. V. Tsonev, N. Kuzmanov, B. Borisov, K. Penkov, “System for materials testing at static loading”, IOP Conf. Ser.: Mater. Sci. Eng. 618, 012048 (2019).

Issue

AIP Conference Proceedings, vol. 3129, 2024, , https://doi.org/10.1063/5.0202838

Copyright AIP Conference Proceedings

Вид: публикация в международен форум, публикация в реферирано издание, индексирана в Scopus