Nonlinear analysis of a rub-impact rotor with random stiffness under random excitation

Abstract

Stochastic bifurcation and chaos of a rub-impact rotor system with random stiffness under random excitation are studied in this article. Due to the irrational and fractional expressions existing in the denominator of rub-impact force, the integral process is very complicated. Taylor series expansion is used to expand the irrational and fractional expressions into a series of polynomials. Chebyshev polynomial approximation method is applied to reduce the system equations with random parameter to its equivalent deterministic one, and the responses of stochastic system can be obtained by numerical methods. Numerical simulations show that random parameters have a significant effect on the rub-impact rotor system. It may promote the nonlinear response when the rotational speed is near the 1/2 first-order critical speed and may suppress the nonlinear response when the rotational speed is over the first-order critical speed.

Dynamic Characteristics of a Segmented Supercritical Driveline with Flexible Couplings and Dry Friction Dampers

“…The misalignment effect is more severe in shaft 2 since its eccentricity is smaller than that of shaft 1, but its response characteristics are similar to those of shaft 1. The above characteristics caused by misalignment can also be inferred from Equations (14) and (23). Figure 18 shows subcritical harmonic resonance.…”

“…The impact stiffness directly affects the accuracy of the rub-impact model. The local surface stiffness of the metal stator at the collision point is generally regarded as the impact stiffness, while the remaining position is defined as the rigid body [23]. This stiffness is directly presented with subjectivity in most of the literature, but the process of acquiring it is critical to the accuracy of simulations.…”

Effects of Stator Stiffness, Gap Size, Unbalance, and Shaft’s Asymmetry on the Steady‐State Response and Stability Range of an Asymmetric Rotor with Rub‐Impact

“…Transform equations (16) and (17) into matrix form, the iteration form of arc-length method can be written as…”

“…e effect of rub-impact on the dynamic behavior have been investigated experimentally and numerically, and some results have been summarized by Muszynska [13], Ahmad [14], and Jacquet-Richardet et al [15]. e rub-impact in the rotor-bearing system excited by periodic excitation can induce the quasiperiodic except periodic vibration [16,17]. In order to predict the steadystate response of a rub-impact rotor, Groll and Ewins [18] solved the nonlinear equations of motion in frequency domain by utilizing a harmonic balance method.…”

“…Specifically, the rub-impact can be described as piecewise linear force with a clearance type nonlinearity [21]. In order to obtain the periodic response of such a nonlinear rotor-bearing system, the equations of motion can be solved in a linearized form by adopting the MHB method [22] or numerically through the time-integration method from the initial conditions [16,17]. However, when applying the timeintegration method, a short integration step is needed if the system has strong nonlinearity, which results in a very large computational effort.…”