Transient Response Analysis of a High Speed Rotor Using Constraint Real Mode Synthesis

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.