Non-linear dynamics and contacts of an unbalanced flexible rotor supported on ball bearings

Abstract

To cite this version:Jean-Jacques Sinou. Non-linear dynamics and contacts of an unbalanced flexible rotor supported on ball bearings. Mechanism and Machine Theory, Elsevier, 2009, 44 (9) AbstractThis study deals with the non-linear dynamic response of a flexible rotor supported by ball bearings. The excitation is due to unbalance force. The finite element rotor system is composed of a shaft with one disk, two flexible bearing supports and a ball-bearing element where the non-linearities are due to both the radial clearance and the Herztian contact between races and rolling elements. A numerical analysis is performed to analyze the non-linear behavior of this bearing rotor by using the Harmonic Balance Method with appropriate condensation located only on the non-linear coordinates of the system in order to minimize computer time. The condensation process reduces the original non-linear rotor system by focusing only on the solution of the non-linear equations of the Fourier coefficients associated with the system's non-linear components. In this study, the procedure is developed for the estimation of the harmonic and super-harmonic responses of the complex rotor system. Consequently, the non-linear unbalance responses and the associated orbits of the bearing rotor will be investigated. Moreover, the transition from contact to no-contact states between rolling elements and races, and the associated restoring contact forces are calculated for different speeds of the unbalanced rotor. Finally, hardening-type nonlinearity or softening-type nonlinearity due to the effects of radial clearance and unbalance mass are examined.

Multi-harmonic measurements and numerical simulations of nonlinear vibrations of a beam with non-ideal boundary conditions

“…The Harmonic Balance Method [5], enables to solve numerically the discrete problem (12), which can be rewritten in the matrix form:Ẅ…”

“…In particular Renson and Kerschen [3] applied a time-integration method with a shooting algorithm [4] to compute the nonlinear vibrations of the SmallSat spacecraft, and focused on internal resonances between linear modes. Sinou [5] applied a Harmonic Balance Method to a nonlinear model of an industrial rotor and computed a multi-harmonic frequency response.…”

Nonlinear vibrations of a mechanical system with non-regular nonlinearities and uncertainties

“…In computational applications, the idea of the AFT method is to use Discrete Fourier Transformation (DFT) to derive the Fourier components of the nonlinear forces for given displacements in the frequency domain. So the generalization of the Alternating Frequency Time process [13,14] to a p-dimensional frequency domain with a p-dimensional DFT is performed to calculate the Fourier coefficients of the nonlinear terms F nl . The following diagram illustrates this procedure:…”

“…As previously explained by Sinou [17,14], if a nonlinear deterministic system consists of a n-degree-of-freedom system with nonlinear forces associated with q of these degrees-of-freedom, it may be of great interest to keep only the q nonlinear degrees-offreedom. The classical procedures of condensation on the nonlinear degrees-of-freedom developed to treat this type of problem are still applicable to the stochastic problem.…”

“…Here, we do not present the condensation procedure used to obtain the Fourier coefficients associated with the nonlinear and linear elements of the complete system. We refer the interested reader to the following paper [14] …”