Coupled Analysis of the Rotor-Dynamic Fluid Forces in the Annular Plain Seal and the Shaft Vibration

Abstract

In recent years, along with demands for higher rotational speed and higher efficiency in the rotating machinery, shaft vibration has been a serious problem. One of the causes of this shaft vibration problem is the rotor-dynamic fluid force (RD fluid force) generated by working fluid at turbo machinery parts. It is important in the design stage of rotating machines to estimate the RD fluid force and predict the stability of the rotor system accurately. Therefore, many researches have been conducted to clarify the characteristics of RD fluid force. One of the traditional methods for analyzing the RD fluid force is the bulk flow theory. However, in conventional bulk flow analysis, it is assumed that the amplitude of the shaft displacement is sufficiently smaller than the clearance. Therefore, influence of nonlinearity in the large amplitude whirl may not be included in this analysis. Accordingly, this paper focuses on constructing a coupled analysis of the fluid force and the shaft vibration that describes each behavior of fluid and shaft at the same time. By using this coupled analysis, the interaction between fluid and shaft systems can be taken into consideration more accurately. Regarding the fluid region, finite difference method is used for bulk flow continuity and momentum transport equations. Incompressible fluid is assumed, and the pressure field is calculated by solving the Poisson equation of pressure. In solving the Poisson equation of pressure, a specific problem for this coupled analysis relating unknown shaft acceleration arises. In this paper, this problem is solved by obtaining the approximated acceleration based on Newmark-beta technique. This coupled analysis is conducted for a simple flexible rotor system with annular plain seal, and the frequency response is obtained. First, the case with isotropic support stiffness and with no gravitational force is considered. Then, the case with the constant load and the case with anisotropic support stiffness are analyzed. These analytical results show that both the constant load and structural anisotropy may affect the stability of the rotor system. As a result, the usefulness of the proposed coupled analysis procedure of the fluid force and the shaft vibration is validated.