Nonparametric Stochastic Modeling of Uncertainty in Rotordynamics—Part II: Applications

Abstract

In the first part of this series, a comprehensive methodology was proposed for the consideration of uncertainty in rotordynamic systems. This second part focuses on the application of this approach to a simple, yet representative, symmetric rotor supported by two journal bearings exhibiting linear, asymmetric properties. The effects of uncertainty in rotor properties (i.e., mass, gyroscopic, and stiffness matrices) that maintain the symmetry of the rotor are first considered. The parameter λ that specifies the level of uncertainty in the simulation of stiffness and mass uncertain properties (the latter with algorithm I) is obtained by imposing a standard deviation of the first nonzero natural frequency of the free nonrotating rotor. Then, the effects of these uncertainties on the Campbell diagram, eigenvalues and eigenvectors of the rotating rotor on its bearings, forced unbalance response, and oil whip instability threshold are predicted and discussed. A similar effort is also carried out for uncertainties in the bearing stiffness and damping matrices. Next, uncertainties that violate the asymmetry of the present rotor are considered to exemplify the simulation of uncertain asymmetric rotors. A comparison of the effects of symmetric and asymmetric uncertainties on the eigenvalues and eigenvectors of the rotating rotor on symmetric bearings is finally performed to provide a first perspective on the importance of uncertainty-born asymmetry in the response of rotordynamic systems.

Nonparametric Stochastic Modeling of Structural Uncertainty in Rotordynamics: Unbalance and Balancing Aspects

“…[12] (see Fig. [3] was considered to exemplify the concepts introduced in the preceding section. [3] was considered to exemplify the concepts introduced in the preceding section.…”

“…Shown in Fig. [3], owing to a recently discovered mistake in the code. 3(a)) and in the rotating one (see Fig.…”

“…In practice, however, this is not the case and uncertainty/ variability in those properties does exist, as is well exemplified by the occurrence of unbalance, and a few, mostly recent, investigations [1][2][3][4][5][6] have focused on the introduction of such uncertainty in rotordynamic analyses. In practice, however, this is not the case and uncertainty/ variability in those properties does exist, as is well exemplified by the occurrence of unbalance, and a few, mostly recent, investigations [1][2][3][4][5][6] have focused on the introduction of such uncertainty in rotordynamic analyses.…”

“…Of particular interest here is the work of Murthy et al [2,3], which has provided an extension of the nonparametric methodology used extensively in other structural dynamics applications in which uncertainty must be modeled. This methodology is based on first developing a reduced order (modal) model of the "mean" system, i.e., the one without uncertainty.…”

“…[2,3] is quite extensive, including the formulation and application of uncertainty on either the rotor stiffness or mass properties as well as bearing properties. [2,3] is quite extensive, including the formulation and application of uncertainty on either the rotor stiffness or mass properties as well as bearing properties.…”