Rotor - Dual Control Model Of The Labyrinth Seal System Modeling And Solving

In rotating machinery, labyrinth seals are widely used to prevent fluid leakage. Due to deflection, misalignment or rotation of the whirl motion, it will produce a kind of force acting on the rotor-sealing force. With demanding of higher-speed, higher pressure and higher efficiency in rotating machinery, sealing force acting on the system becomes increasingly important. However, due to complicated sealing structures and the turbulent state in seal cavities, the research of rotor-seal system is still in its infancy.This paper introduces the Jeffcott rotor model and three common sealing force models:Thomas-Alford linear model and nonlinear Black-Childs model, Muszynska model. Then the three models are compared.Three governing equations are deduced with the two-control-volume model of sealing force. Quality equations and momentum equations in hydrodynamics are used during deducing. Then we get the dimensionless model to make the solving process simpler.In the third chapter, the perturbation method is used to solve the controlling equations. Then we put the solved pressure into Thomas-Alford model to get equivalent stiffness and damping of sealing force. Also factors which affect the stability of the system are discussed.Due to the limitation of linear method, a direct nonlinear method of solving the rotor-seal system is (?) proposed. We solve the controlling equations and rotor vibration equations simultaneously, using Galerking method with Runge-Kutta method and Newton-Raphson method. A non-eccentric rotor-seal system example shows the effectiveness of this method.At last, we calculate an eccentric rotor-seal system example and obtain the displacement of axis. Hopf bifurcation diagrams, trajectory diagrams and Poincare maps show the whole process of periodic motion until chaos state. Nonlinear characters are also obviously shown.