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In order to accurately calculate high-speed nonlinear transient phenomena of a large order rotor system such as rotor collision and rubbing with stator repeatedly due to blade loss, a very small incremental time step is required in numerical integration. But a small time step is known to become a cause of divergence or flutter type numerical instability when a direct integration such as Newmark-β method is applied in terms of physical coordinates. Normal mode method, which uses eigen modes instead of physical freedoms, is effective on this numerical stability, but the modes in the calculation are usually complex-modes and also need recalculation in accordance with varying rotational speed. Therefore, this method is inconvenient for an analysis of a rotor, especially speed varying system. This paper presents a new method using constraint real mode synthesis in which rotor modes are derived by neglecting gyroscopic moment as at 0 rpm and by fixing bearing connection interface freedoms to zero. This method is proved to be highly stable and also to have good accuracy and efficiency in the calculation.

In the present paper, an analytical method is presented for predicting the nonlinear transient response of an aircraft engine due to the loss of a fan blade. The casing of an aircraft engine and rotors are modeled as Timoshenko beams and analyzed using the incremental transfer matrix method with the Newmark-β or Wilson-θ method. The local deflection effect of a casing cross section and the support stiffnesses are examined by FEM and are taken into account in the model. Nonliner elements are considered for contact and rubbing of the fan with casing and squeeze film dampers. Although some numerical problems still remain when very short time steps are chosen for the time integration, the present calculation method is fairly efficient and useful.

A new nonlinear steady-state calculation by substructure synthesis is presented for large-order rotordynamic systems with a few nonlinear elements, which is considered popular in actual rotating machines. In this paper, linear dynamic and static structural relations are reduced to small degrees of freedom on nonlinear elements such as nonlinear bearings. Using discreet Fourier transform (DFT, also using FFT), and the Newton-Raphson method, harmonic balance for this reduced nonlinear system can be obtained as efficiently as for a simple rotor system. As examples, the effect of a friction damper on a turbine blade model and nonlinear unbalance response of an actual turbine rotor supported by squeeze film dampers without centering springs are discussed.

This paper proposes a new method for rotor dynamics calculations, called the transfer coefficient method, which is more convenient than the conventional transfer matrix method. By treating only the displacement as the independent variable, where both the displacement and the force are considered as independent variables in the transfer matrix method, this method promises a substantial saving of computational time without loss of the accuracy of calculation. There are two types of transfer coefficient methods. In the first, the coefficients are treated as independent of the vibration frequencies, while in the other, the coefficients are considered dependent on the frequencies. Formulation of a fundamental rotor system and applications for either type are discussed in detail with a bearing box, a branched system, and a multi spool system as examples.

In this paper, two types of transfer coefficient methods, in which independent variables are only displacements, are applied to the calculation of the unbalance response of a rotating shaft. In one, the transfer coefficient is given in the form independent of rotating speed ω, and therefore this method is suitable for calculation at a large number of rotating speeds. In the other, formulation of transfer coefficient is easy and therefore this method can be applied to relatively complex totor systems, though the transfer coefficient is expressed in the form dependent on rotating speed ω. Even in the latter case, the computation can be done within 1/4 of the CPU time that is necessary for calculation by the conventional transfer matrix method.