TY - GEN

T1 - Nonparametric stochastic modeling of uncertainty in rotordynamics

AU - Murthy, Raghavendra

AU - Mignolet, Marc

AU - El-Shafei, Aly

PY - 2009

Y1 - 2009

N2 - A systematic and rational approach is presented for the consideration of uncertainty in rotordynamics systems, i.e. in rotor mass and gyroscopic matrices, stiffness matrix, and bearing coefficients. The approach is based on the nonparametric stochastic modeling technique which permits the consideration of both data and modeling uncertainty. The former is induced by a lack of exact knowledge of properties such as density, Young's modulus, etc. The latter occurs in the generation of the computational model from the physical structure as some of its features are invariably ignored, e.g. small anisotropics, or approximately represented, e.g. detailed meshing of gears. The nonparametric stochastic modeling approach, which is briefly reviewed first, introduces uncertainty in reduced order models through the randomization of their system matrices (e.g. stiffness, mass, and damping matrices of nonrotating structural dynamic systems). Here, this methodology is first extended to permit the consideration of uncertainty in symmetric and asymmetric rotor dynamic systems. Its application is next demonstrated on a symmetric rotor on linear bearings and uncertainties on the rotor stiffness (stiffness matrix) and/or mass properties (mass and gyroscopic matrices) are introduced that maintain the symmetry of the rotor. The effects of these uncertainties on the Campbell diagram, damping ratios, mode shapes, forced unbalance response, and oil whip instability threshold are analyzed. The generalization of these concepts to uncertainty in the bearing coefficients is achieved next. Finally, the consideration of uncertainty in asymmetric rotors is addressed and exemplified.

AB - A systematic and rational approach is presented for the consideration of uncertainty in rotordynamics systems, i.e. in rotor mass and gyroscopic matrices, stiffness matrix, and bearing coefficients. The approach is based on the nonparametric stochastic modeling technique which permits the consideration of both data and modeling uncertainty. The former is induced by a lack of exact knowledge of properties such as density, Young's modulus, etc. The latter occurs in the generation of the computational model from the physical structure as some of its features are invariably ignored, e.g. small anisotropics, or approximately represented, e.g. detailed meshing of gears. The nonparametric stochastic modeling approach, which is briefly reviewed first, introduces uncertainty in reduced order models through the randomization of their system matrices (e.g. stiffness, mass, and damping matrices of nonrotating structural dynamic systems). Here, this methodology is first extended to permit the consideration of uncertainty in symmetric and asymmetric rotor dynamic systems. Its application is next demonstrated on a symmetric rotor on linear bearings and uncertainties on the rotor stiffness (stiffness matrix) and/or mass properties (mass and gyroscopic matrices) are introduced that maintain the symmetry of the rotor. The effects of these uncertainties on the Campbell diagram, damping ratios, mode shapes, forced unbalance response, and oil whip instability threshold are analyzed. The generalization of these concepts to uncertainty in the bearing coefficients is achieved next. Finally, the consideration of uncertainty in asymmetric rotors is addressed and exemplified.

KW - Nonparametric stochastic modeling

KW - Random matrices

KW - Rotordynamics

KW - Uncertain bearings

KW - Uncertain rotor

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=77953193349&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953193349&partnerID=8YFLogxK

U2 - 10.1115/GT2009-59700

DO - 10.1115/GT2009-59700

M3 - Conference contribution

AN - SCOPUS:77953193349

SN - 9780791848876

T3 - Proceedings of the ASME Turbo Expo

SP - 881

EP - 899

BT - Proceedings of the ASME Turbo Expo 2009

T2 - 2009 ASME Turbo Expo

Y2 - 8 June 2009 through 12 June 2009

ER -