Nonlinear Dynamic Analysis of Rotor‐Bearing System with Cubic Nonlinearity

Abstract

Nonlinear dynamic characteristics of a rotor-bearing system with cubic nonlinearity are investigated. The comprehensive effects of the unbalanced excitation, the internal clearance, the nonlinear Hertzian contact force, the varying compliance vibration, and the nonlinear stiffness of support material are considered. The expression with the linear and the cubic nonlinear terms is adopted to characterize the synthetical nonlinearity of the rotor-bearing system. The effects of nonlinear stiffness, rotating speed, and mass eccentricity on the dynamic behaviors of the system are studied using the rotor trajectory diagrams, bifurcation diagrams, and Poincaré map. The complicated dynamic behaviors and types of routes to chaos are found, including the periodic doubling bifurcation, sudden transition, and quasiperiodic from periodic motion to chaos. The research results show that the system has complex nonlinear dynamic behaviors such as multiple period, paroxysmal bifurcation, inverse bifurcation, jumping phenomena, and chaos; the nonlinear characteristics of the system are significantly enhanced with the increase of the nonlinear stiffness, and the material with lower nonlinear stiffness is more conducive to the stable operation of the system. The research will contribute to a comprehensive understanding of the nonlinear dynamics of the rotor-bearing system.

Investigation of Nonlinear Forced Vibrations of the “Rotor-Movable Foundation” System on Rolling Bearings by the Jacobi Elliptic Functions Method

“…In this paper, rolling bearings with a non-linear characteristic act as elastic supports. The neglect of nonlinear properties in the study of the dynamics of vibrations of mechanical systems usually leads to overestimated amplitudes and frequencies, which, accordingly, worsens qualitative and quantitative results, and causes unnecessary additional costs in the design of rotor systems [18][19][20]. In the linear theory of the dynamics of rotary machines, damping and elastic properties of bearings are not accurately specified, which is especially important when it is necessary to study high-speed and high-frequency processes.…”

“…Often, Hertz's contact theory is used to analyze and describe the restoring forces of a rolling bearing. It connects the deformation at the points of contact between the rolling element of the bearing with the loads acting on the bearing in the radial direction, without taking into account the slippage of the rolling elements or rolling surfaces [19,20,28]. To describe the nonlinear properties of the restoring force of rolling bearings, the cubic power series approximation [4,18,28,29] is used, since this approximation is in good agreement over a wide range of deformation.…”

Analytical Study of Nonlinear Vibration in a Rub-Impact Jeffcott Rotor

“…It was found that the viscous internal damping has a contribution to improving the stability of the synchronous full annular rub solution, the rub-impact delays the change in phase difference and the gyroscopic moment has an influence on the increase in the phase difference. Nan et al [19] investigated the nonlinear dynamics of a rotor-bearing system with cubic nonlinearity, internal clearance, nonlinear Hertzian contact force and nonlinear stiffness of support material. By means of rotor trajectory diagrams, a Poincaré map and bifurcation diagrams, the effects of nonlinear stiffness, mass eccentricity and rotating speed on the dynamic behavior of the system were analyzed.…”