The Influence of Slowly Varying Mass on Severity of Dynamics Nonlinearity of Bearing‐Rotor Systems with Pedestal Looseness

Abstract

Nonlinearity measure is proposed to investigate the influence of slowly varying mass on severity of dynamics nonlinearity of bearing-rotor systems with pedestal looseness. A nonlinear mathematical model including the effect of slowly varying disk mass is developed for a bearing-rotor system with pedestal looseness. The varying of equivalent disk mass is described by a cosine function, and the amplitude coefficient is used as a control parameter. Then, nonlinearity measure is employed to quantify the severity of dynamics nonlinearity of bearing-rotor systems. With the increasing of looseness clearances, the curves that denote the trend of nonlinearity degree are plotted for each amplitude coefficient of mass varying. It can be concluded that larger amplitude coefficients of the disk mass varying will have more influence on the severity of dynamics nonlinearity and generation of chaotic behaviors in rotor systems with pedestal looseness.

Rub‐Impact Detection in Rotor Systems with Pedestal Looseness Using a Nonlinearity Evaluation

“…Computation of ϕ ω N in equation (13) can be extremely complicated, because the minimization must be performed over all linear operators G in the set G. Due to the computation requirement for engineering applications, it is appropriate to use a simple definition of nonlinearity quantification. In some situations [35,36], Taylor expansions are used to obtain the linear approximations on the vicinity of the equilibrium position. Linearizing the nonlinear terms on the static equilibrium position allows for a linear system L(ω) to be derived to calculate the dynamical differences between the outputs.…”

“…e equation 14is a special case of the definition of nonlinearity measure, which is used to assess the pedestal looseness of rotor systems in References [35,36]. However, different linear model will influence on the nonlinearity quantification on a real rotor system by using the directly measured data.…”

“…e parameter values used for the nonlinearity measure and simulations are given in Table 1 of Appendix B, while the values of the parameters for oil film bearings and rub-impact used in the numerical examples are given in Tables 2 and 3, respectively. Some parameters used in the simulations are chosen as the same as Tables 1 and 2 in References [35,36].…”

An analysis method to determine how changes in dynamic complexity impact on rotor-bearing systems

“…14 Additionally, the influences of looseness clearances and rotating speeds on dynamic characteristics have been studied under two loading conditions. Jiang 15,16 proposed a nonlinearity measures based method for pedestal looseness of a rotor-bearing system and analyzed the influence of slowly varying mass on the severity of the dynamics.…”

“…How slowly varying mass influences the severity of dynamics has only been considered for rotorbearing systems with constant rotational speeds. 16 This paper analyzed how certain parameters impact the complexity of nonlinear dynamics in rotorbearing systems. Nonlinearity measures are employed to estimate the dynamic complexity of rotor systems, and their definitions are introduced in detail.…”