Nonstationary motion and instability of a shaft/casing system with rubs

The partial differential equations governing the shaft/casing system with rubs during passage through the first several critical speeds are solved by an explicit stable finite difference scheme. The rotational speed of the shaft is increased at a constant angular acceleration. The contact force theory is used to calculate the impacting forces and friction forces. First, the effect of the rotating angular acceleration of the shaft on the instability of the nonstationary motion with rubs is investigated. Then, the irregular changes of the deflection of the shaft, in which are found many modes of bending, and diagrams of the bending moment in rub events are depicted. The results suggest that the instability of motion in rub events could lead to structural shaft failure ultimately due to the unlimited increases of the bending moment and bending stress of the shaft accordingly.