An Improved Catcher Bearing Model and an Explanation of the Forward Whirl/Whip Phenomenon Observed in Active Magnetic Bearing Transient Drop Experiments

Abstract

Though many approaches have been proposed in the literature to model the reaction forces in a catcher bearing (CB), there are still phenomena observed in experimental tests that cannot be explained by existing models. The following paper presents a novel approach to model a CB system. Some of the elements in the model have been previously introduced in the literature; however, there are other elements in the proposed model that are new, providing an explanation for the forward whirling phenomena that has been observed repeatedly in the literature. The proposed CB model is implemented in a finite element rotordynamic package, and nonlinear time-transient simulations are performed to predict published experimental results of a high speed vertical sub-scale compressor; with no other forces present in the model, the agreement between simulations and experimental data is favorable. The results presented herein show that friction between the journal and axial face of the catcher bearing results in a forward cross-coupled force that pushes the rotor in the direction of rotation. This force is proportional to the coefficient of friction between the axial face of the rotor and catcher bearing and the axial thrust on the rotor. This force results in synchronous whirl when the running speed is below a combined natural frequency of the rotor-stator system, and constant frequency whip when the speed is above a whip frequency.

Touchdown bearing models for rotor-AMB systems

“…Vertically dropped rotors were studied in references [3,4,5,6,7]. The gravity does not lead to stable motion and the rotor is more able to develop 15 a forward whirl motion, as explained by Wilkes et al [8]. The forward whirl motion is frequency-limited and this is consistent with many of the previous studies concerning the rotor-stator interaction, see references [9, 10,11,12,13].…”

“…Sometimes a cross-coupled stiffness term opposed to the outer race whirling 210 motion is applied to counteract rotor whirl, see references [7,8].…”

“…Most studies done on rotor drop dynamics consider the ribbon as a classical Kelvin-Voigt model. Wilkes et al [8] used a cross-coupled stiffness coefficient that counteracts whirl motion depending 70 on the sign of the outer race whirl speed. However, dynamic characterization tests of the ribbon, presented in this work, have shown the damping would be related to dry friction rather than viscous damping.…”

Development and Experimental Validation of Auxiliary Rolling Bearing Models for Active Magnetic Bearings (AMBs) Applications

“…where x i contains the coordinates of the inner race center of gravity, M i is the inner race mass matrix, C i is the inner race damping matrix, P is the weight force of the inner race, and the vector F is the sum of the radial forces acting on the bearing inner race (see also Figure 7): F io is the interaction force on the inner race exerted by the rolling elements, F ir is the contact force exchanged between the inner race and the rotor during the contact (including a normal F rN component and a tangential one F fr ; see (15)), and F rub is the resultant force generated during the axial rub between the thrust surface of the bearing inner race and the lateral surface of the rotor sleeve (see (19)). Equation (8) describes the rotational dynamics of the bearing inner race:Ω…”

“…Other researchers like J. Wilkes et al [19] observed strong circular forward whirl following an AMB failure and developed specific models to reproduce such phenomenon. They developed an innovative model of auxiliary bearing system that represents a great step forward in the reproduction of rotor-dynamic system behavior; in fact the model allows reproducing the forward whirl rotor orbit observed during International Journal of Rotating Machinery the landing tests.…”