Resonant phenomena in nonlinear vertical rotor systems
DOI:
https://doi.org/10.26577/JMMCS.2021.v112.i4.05Keywords:
Hertz theory, rolling bearings, numerical methods, nonlinear rotary systemAbstract
In this paper, the study of the dynamics of a rotor system mounted on an elastic foundation rotating in rolling bearings is considered. To describe the bearing model, the Hertz theory was used, linking radial loads acting on the bearing and deformation at the points of contact between the movable housing and the bearing rings. When describing the model of rolling bearings, it is assumed that there is no kind of sliding of bodies and moving surfaces. The obtained differential equations of the rotor and the foundation do not have a common solution. Therefore, the study was conducted using numerical methods. In order to simplify the problem and increase the accuracy in solving the obtained differential equations, dimensionless quantities were used. With the increase and decrease of dimensionless quantities, the amplitudes of the rotor and the foundation are constructed. As a result, two resonances were formed: the main resonance and the second resonance. The work is connected with the physical meaning of the process considered in the problem the results obtained are the basis for the application of this mathematical model in the design of a rotary system rotating in rolling bearings.
References
[2] Li, Z., Li, J., Li, M. (2018). Nonlinear dynamics of unsymmetrical rotor-bearing system with fault of parallel misalignment. Advances in Mechanical Engineering, vol. 10(5), p. 1-17, DOI: 10.1177/1687814018772908.
[3] Sun, L. (1995). Active Vibration Control of Rotor-Bearing System. PhD Thesis, University of Melbourn, Melbourn.
[4] Bai, C., Zhang, H., Xu, Q. (2010). Experimental and numerical studies on nonlinear dynamic behavior of rotor system supported by ball bearings. Journal of Engineering for Gas Turbine and Power, vol. 132, no. 8, paper 082502, DOI:10.1115/1.4000586.
[5] Xia, Z., Qiao, G., Zheng, T., Zhang, W. (2009). Nonlinear modelling and dynamic analysis of the rotor-bearing system. Nonlinear Dynamics, vol. 57(4), p. 559-577, DOI: 10.1007/s11071-008-9442-3.
[6] Harris, T.A. (2001). Rolling Bearing Analysis. John Wiley Sons, Inc.
[7] David, P.F., Poplawski, J.V. (2002). Transient vibration prediction for rotors on ball bearings using load-dependent non-linear bearing stiffness. International Journal of Rotating Machinery, vol. 10(6), p. 489-494, DOI: 10.1080/10236210490504102.
[8] Yamamoto, T., Ishida, Y. (2002). Transient vibration prediction for rotors on ball bearings using load- ependent non-linear bearing stiffness. International Journal of Rotating Machinery, vol. 10(6), p. 489-494, DOI: 10.1080/10236210490504102.
[9] Changsen, W. (1991). Analysis of rolling element bearings. Mechanical Engineering Publications Limited.
