| Popis: |
This thesis examines the vibration behavior of rotor–stator systems coupled by intermediate viscous liquids. This problem is of particular importance in the design of pump-turbines, where the runner (rotor) is coupled to the head cover (stator) via the surrounding water. The elasticity of the rotor and the stator, their relative rotational motion and the various damping mechanisms contribute to the complexity of the vibration problem. We study this rotor–stator coupling on a simplified model, consisting of a circular stator disc (clamped at the outer circumference) and a ring-shaped rotor disc (clamped at the inner circumference) separated by an axial gap. In a first part, we present a concise theory of the dynamics of small perturbations (first order) which are superimposed on a stationary bias motion (zero order). The theory is systematically deduced from fundamental principles of continuum mechanics and presented in weak variational form, which is best suited for its implementation in the finite element framework. Special attention is paid to the correct linearization of the governing equations and the coupling condition between solid and liquid. The second part of the work is devoted to the experimental modal analysis of the rotor–stator system with the use of a specially engineered test bench. The test bench enables the measurement of eigenfrequencies, damping factors and mode shapes of rotor and stator. We have applied the laser interferometer technique to precisely measure the vibrations and therefore have developed a special mechanism for the vibration measurements on rotating parts. The measurements collected over a wide range of parameters form a substantial and unique experimental database for the verification of current and future simulation models. In the third part, we describe a new physically-based simulation technique for the prediction of modal parameters of fluid-coupled rotor–stator systems. We discretize the derived perturbation equations with the finite element method and solve the resulting eigenvalue problem numerically using the simulation software COMSOL Multiphysics. Both the stationary bias motion and the viscosity of the liquid are included in the model. As solutions we directly obtain the angular eigenfrequencies, the damping factors and the complex eigenforms of the respective vibration modes. The simulation model not only predicts the vibrational behavior of the system, but also provides valuable insights into the underlying mechanisms. The vibration modes can be characterized by an azimuthal wave number, a radial index as well as the relative motion between rotor and stator (varicose or sinuous). Modes with a non-zero azimuthal wave number appear in pairs of co- and counter-rotating modes (relative to the rotation of the rotor). In the inertial frame of reference, a higher frequency is observed for the co-rotating mode compared to the counter-rotating mode. The difference in frequency is approximately proportional to the rotor speed and the mode's azimuthal wave number. This frequency split effect, caused by the stationary bias motion, is excellently mapped by the simulation model. For the more challenging characterization of the damping, we have also found a good agreement between simulation and experiment over a wide range of parameters. |
