The successful operation of a spiral groove liquid film seal is critically dependent on the dynamic tracking property of the flexibly mounted stationary ring to the rotating ring. In this paper, a mathematical model of the spiral groove liquid film seal is formulated on the basis of the mass-conserving Jakobsson–Floberg–Olsson cavitation boundary condition. Using a combination of the finite element method and a perturbation method, the dynamic characteristic coefficients are calculated. The equations of motion of the stationary ring are solved using a complex number method. The dynamic tracking property is characterized in terms of the amplitude ratios and the phase differences between the response of the stationary ring and the excitation of the rotating ring. The influence of the operating parameters and structural parameters on the tracking property of the stationary ring is then analyzed. The results indicate that higher rotational speed, viscosity of the medium, and mass of the stationary ring all contribute to improving the stationary ring’s tracking property, whereas a larger film thickness has the opposite effect. A zero-phase-difference tracking state can be achieved by appropriate selection of spring stiffness and O-ring damping.
Yang et al. (Wed,) studied this question.