In this thesis, a novel approach is presented for blade loss simulation of an aircraft gas turbine rotor mounted on rolling element bearings with squeeze film dampers, seal rub and enclosed in a flexible housing. The modal truncation augmentation (MTA) method provides an efficient tool for modeling this large order system with localized nonlinearities in the ball bearings. The gas turbine engine, which is composed of the power turbine and gas generator rotors, is modeled with 38 lumped masses. A nonlinear angular contact bearing model is employed, which has ball and race degrees of freedom and uses a modified Hertzian contact force between the races and balls and for the seal rub. This combines a dry contact force and viscous damping force. A flexible housing with seal rub is also included whose modal description is imported from ANSYS. Prediction of the maximum contact load and the corresponding stress on an elliptical contact area between the races and balls is made during the blade loss simulations. A finite-element based squeeze film damper (SFD), which determines the pressure profile of the oil film and calculates damper forces for any type of whirl orbit is utilized in the simulation. The new approach is shown to provide efficient and accurate predictions of whirl amplitudes, maximum contact load and stress in the bearings, transmissibility, thermal growths, maximum and minimum damper pressures and the amount of unbalanced force for incipient oil film cavitation. It requires about 4 times less computational time than the traditional approaches and has an error of less than 5 %.

In this thesis, a novel approach is presented for blade loss simulation of an aircraft gas turbine rotor mounted on rolling element bearings with squeeze film dampers, seal rub and enclosed in a flexible housing. The modal truncation augmentation (MTA) method provides an efficient tool for modeling this large order system with localized nonlinearities in the ball bearings. The gas turbine engine, which is composed of the power turbine and gas generator rotors, is modeled with 38 lumped masses. A nonlinear angular contact bearing model is employed, which has ball and race degrees of freedom and uses a modified Hertzian contact force between the races and balls and for the seal rub. This combines a dry contact force and viscous damping force. A flexible housing with seal rub is also included whose modal description is imported from ANSYS. Prediction of the maximum contact load and the corresponding stress on an elliptical contact area between the races and balls is made during the blade loss simulations. A finite-element based squeeze film damper (SFD), which determines the pressure profile of the oil film and calculates damper forces for any type of whirl orbit is utilized in the simulation. The new approach is shown to provide efficient and accurate predictions of whirl amplitudes, maximum contact load and stress in the bearings, transmissibility, thermal growths, maximum and minimum damper pressures and the amount of unbalanced force for incipient oil film cavitation. It requires about 4 times less computational time than the traditional approaches and has an error of less than 5 %.

While moment matching can effectively reduce the dimension of a linear, time-invariant system, it can simultaneously fail to improve the stable time-step for the forward Euler scheme. In the context of a semi-discrete heat equation with spatially smooth forcing, the high frequency modes are virtually insignificant. Eliminating such modes dramatically improves the stable time-step without sacrificing output accuracy. This is accomplished by modal filtration, whose computational cost is relatively palatable when applied following an initial reduction stage by moment matching. A bound on the norm of the difference between the transfer functions of the moment-matched system and its modally-filtered counterpart yields an intelligent choice for the mode of truncation. The dual-stage algorithm disappoints in the context of highly nonnormal semi-discrete convection-diffusion equations. There, moment matching can be ineffective in dimension reduction, precluding a cost-effective modal filtering step.