Estimation of the Dynamic Parameters of the Bearings in a Flexible Rotor System Utilizing Electromagnetic Excitation by a Built-In Motor

Estimation of the dynamic parameters of bearings is essential in order to be able to interpret the performance of rotating machinery. In this paper, we propose a method to estimate the dynamic parameters of the bearings in a flexible rotor system. By utilizing the electromagnetic excitation generated by a built-in PM motor and finite element (FE) modeling of the rotor, safe, low-cost, and real-time monitoring of the bearing dynamics can be achieved. The radial excitation force is generated by injecting an alternating d-axis current into the motor windings. The FE model of the rotor and the measured frequency responses at the motor and bearing locations are used to estimate the dynamic parameters of the bearings. To evaluate the feasibility of the proposed method, numerical simulation and experiments were carried out on a flexible rotor system combined with a bearingless motor (BELM) having both motor windings and suspension windings. The numerical simulation results show that the proposed algorithm can accurately estimate the dynamic parameters of the bearings. In the experiment, the estimates made when utilizing the excitation force generated by the motor windings are compared with the estimates made when utilizing the excitation force generated by the suspension windings. The results show that most of the stiffness and damping coefficients for the two experiments are in good agreement, within a maximum error of 8.92%. The errors for some coefficients are large because the base values of these coefficients are small in our test rig, so these coefficients are sensitive to deviations. The natural frequencies calculated from the dynamic parameters estimated from the two experiments are also in good agreement, within a maximum relative error of 3.04%. The proposed method is effective and feasible for turbomachines directly connected to motors, which is highly significant for field tests.

A Method for Predicting the Influences of Bearing Support Stiffness and Position on the Vibrations of a Flexible Rotor System

The bearing support stiffness and position can greatly affect the vibrations of flexible rotor systems (FRSs). However, most previous works only focused on the effect of the bearing support stiffness on the critical speeds or modal characteristics including the natural frequencies and mode shapes of rigid rotor systems (RRSs). The previous studies missed the combined effects of the bearing support stiffness and position. To overcome this issue, an analytical method of a FRS based on the finite element (FE) method is proposed. Our model considers the bearing support stiffness and rotational inertia of FRS. The frequency equation of FRS is established for solving the critical speeds. The critical speeds and modal deformations of FRS from our model and the numerical model based on a commercial software are compared to verify the effectiveness of the presented method. The effects of the bearing support stiffness and position on the critical speeds of FRS are analyzed. The results show that the critical speeds are positively correlated with the bearing support stiffness. The critical speeds of FRS are also greatly affected by the bearing position. This study can provide some guidance for the optimization design method of bearing support stiffness and position in FRSs.

Investigation of the Dynamic Characteristics of an Eccentric Annular Seal on the Basis of a Transient CFD Method with Three Whirl Models

Many annular seals suffer eccentricity because of rotor–stator misalignment or the deflection of a flexible rotor, which has a strong influence on the vibration characteristics and stability of rotating machines. In this article, a transient CFD method based on three whirl models is employed to research the dynamic characteristics of annular seals at various static eccentricities. The influence of the whirl amplitude on the dynamic characteristics of eccentric annular seals are also explored. The results of the transient CFD method are compared with the bulk flow model results and the experimental results. It is shown that the transient CFD method possesses high prediction precision for direct damping, with a maximum error of 25%. Negative kyx increases by 166% when the static eccentricity ratio is increased from 0 to 0.5. The dynamic characteristics of the annular seal operating at high static eccentric ratio are sensitive to whirl amplitude, and the model with an amplitude of 1% Cr has great advantages for the prediction of direct virtual-mass, while the model with an amplitude of 10% Cr has great advantages for the prediction of cross-coupled damping.