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.

Model reduction can greatly reduce complexity and difficulty of control design for spatiotemporal systems (STS) in engineering applications. Empirical eigenfunctions (EEFs) are widely used for the model reduction of spatiotemporal systems, however, truncation of higher modes may describe the behaviours of nonlinear spatiotemporal systems inaccurately. In this paper, modified EEFs are proposed and applied to model reduction of nonlinear spatiotemporal systems. Modified EEFs are obtained via modifying the weights matrix in the method of snapshots, which can be rewritten as linear combinations of initial EEFs. The coefficient matrix for combinations is computed according to the nonlinear temporal dynamics of STSs. Thus, the effects of higher modes are considered into modified EEFs with less computational requirements. The reduced model can give a more accurate description for behaviours of the system. The performance of the proposed method is further proved theoretically, and a numerical example demonstrates the effectiveness of the proposed method.

Condition monitoring performance and diagnosis of rotor-bearing systems depend not only on the methods used, but also on the dynamic complexity of the system itself. Thus, it is important to analyze how changes in parameters under various working conditions impact on dynamic complexity. Most of previous research efforts on this topic have been focused on the analysis of nonlinear dynamics of rotor-bearing systems with different parameters. In this paper, a nonlinearity quantification based analysis method is presented to determine how parameter dynamics impact the complexity of rotor-bearing systems. The dynamic complexity of rotor system is estimated using defined nonlinearity measures. To validate this method, a sliding rotor-bearing system with a loose pedestal is used. The estimates (nonlinearity degrees) and the states of motion are matched with increasing rotational speeds. It is then investigated, how the eccentricities, lubricating oil viscosities, and bearing clearances impacted the dynamic complexity at several critical rotational speeds. These results can guide methodological choices for condition monitoring and diagnosis of rotor systems.