Stability and Stationary Response of a Skew Jeffcott Rotor With Geometric Uncertainty

Abstract

The dynamical behavior of an asymmetrical Jeffcott rotor subjected to a base translational motion is investigated. As the geometry of the skew disk is not well defined, we introduce some randomness. This uncertainty affects a particular parameter in the time-variant motion equations. Consequently, the amplitude of the parametric excitation is a random parameter which leads us to investigate the robustness of the dynamics. The stability is first studied by introducing a transformation of coordinates (feasible in this case) making the problem simpler. Then, far away from the unstable area, the random forced steady state response is computed from the original motion equations. The Taguchi’s method is used to provide statistical moments of the forced response.

Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending

“…These quantities, according to Eqs. (22), (11), and (9a), (9b), further depend on geometric, material and mass unbalance parameters. This indicates that a change in the values of these parameters will give different numerical solutions of Eq.…”

“…(22) quantity b 2 depends on k 3 which represents the effect of an axial dynamic force, see Eq. (11). This implies that if we want to study the dynamics of the system without considering the effect of an axial force we can substitute b 2 = 0 in various constants given in Appendix B.…”

“…Nonlinearities in rotor systems can be due to many reasons [7]. For example, higher order large deformations, rotor-base excitations [8][9][10], geometric nonlinearities [11,12], oil film in journal bearings [13], magnetic bearings [14].…”

Stochastic finite element modeling and response analysis of rotor systems with random properties under random loads

“…Dimentberg and Naess [9] evaluated the nonlinear vibration of a simple Jeffcott rotor with broadband random variations of internal damping. Driot et al [10] investigated the probability of instability and stationary response of a skew Jeffcott rotor with uncertain geometric parameters. However, most of these studies considered simple Jeffcott rotors and employed analytical or the Monte Carlo method.…”

Almost sure asymptotic stability of rotor systems subjected to stochastical axial loads

“…Numerical simulations show that the effects of the random disturbance are significant as the undisturbed response of the cracked rotor system is a quasi-periodic or Mechanism and Machine Theory 58 (2012) 192-201 chaos one. Driot et al [10] investigated the probability of instability and stationary response of a skew Jeffcott rotor with uncertain geometric parameters.…”