Effect of shaft eccentricity on dynamic characteristics for different geometries of stationary labyrinth seals

The present paper introduces a theoretical study carried out to investigate the effect of shaft lateral misalignment on the dynamic characteristics of labyrinth seals under stationary conditions. The flow inside the seal is considered to be laminar, incompressible and three-dimensional. It is required to obtain the direct and cross-coupled stiffness and damping coefficients of the seal. Determination of the dynamic coefficients of the seal is obtained using the method of small disturbances. The governing equations of motion are derived for small motion of the shaft center in two orthogonal coordinates and the equations governing the variations of the flow variables are obtained for different shaft eccentricity ratios. By integration in axial and circumferential directions, the aerodynamic forces, direct and cross-coupled stiffness and damping coefficients are determined. In the absence of shaft rotation, the effects of aspect ratio and eccentricity ratio on the dynamic characteristics are examined for different seal geometries. The results show that when the leakage rate or the aspect ratio increases the dynamic coefficients increase. These effects become more pronounced as the misalignment of the shaft is increased.