Nonlinear vibration analysis of angular contact ball bearings supporting a rigid rotor is presented herein considering the frictional moments (load dependent and load independent components of frictional moments) in the bearings. Six degrees of freedom (DOF) of rigid rotor is considered in the dynamic modeling of the rotor-bearings system. Moreover, waviness on surfaces of inner race, outer race, and ball are considered in the model by representing it as sinusoidal functions with waviness orders of 6, 15, and 25. Two amplitudes of waviness, 0.05 and 0.2 μm, are considered in the investigation looking for the practical aspects. The proposed model is validated with the experimental results by performing the experiments. Moreover, the present model has also been validated with published results of researchers by incorporating needful changes in the DOF in the proposed model. Based on the computed results, it is observed that load dependent frictional moment (LDFM) significantly enhances the amplitudes of vibrations in comparison to load independent frictional moment (LIFM) irrespective to values of waviness amplitude and waviness order. The influence of inner race waviness is relatively more on the vibrations in comparison to waviness of outer race and ball. Moreover, vibrations of system enhance considerably at high amplitude of waviness, increase in the order of waviness, and at elevated operating parameters.

Nonlinear vibration analysis of an elastically deformable shaft supported on two lubricated angular contact ball bearings is reported herein considering six-degrees of freedom (6-DOF) and waviness on races and balls. This is an extension work of the investigation published by the authors Babu, C. K., Tandon, N., and Pandey, R. K., 2012, “Vibration Modeling of a Rigid Rotor Supported on the Lubricated Angular Contact Ball Bearings Considering Six Degree of Freedom and Waviness on Balls and Races,” ASME J. Vib. Acoust., 134, p. 011006. Elastic deformation of shaft, frictional moment, and waviness on races and balls have been incorporated in the model for the vibration investigations of rotor's CG. Two noded 3D Timoshenko beam element having 6-DOF has been employed in the computation of the shaft's deformation. Governing equations with appropriate boundary conditions have been solved using 4th order Runge–Kutta method. It is observed that vibration amplitude enhances considerably after incorporating the elastic deformation in comparison to the amplitude achieved using rigid rotor model approach. Moreover, the influence of outer race's radial waviness is large on the amplitudes of vibrations in comparison to radial waviness of inner race. However, it is worth noting here that in case of rigid rotor model the presence of radial waviness on inner race yields high amplitudes of vibrations.

The standard techniques used to detect the misalignment in rotor systems are loopy orbits, multiple harmonics with predominant 2X component, and high axial vibration. This paper develops a new approach for the identification of misalignment in coupled rotor systems modelled using 2-node Timoshenko beam finite elements. The coupling connecting the turbine and generator rotor systems is modelled by a stiffness matrix, which has both static and additive components. While the magnitude of static stiffness component is fixed during operation, the time varying additive stiffness component displays a multi-harmonic behaviour and exists only in the presence of misalignment. To numerically simulate the multi-harmonic nature coupling force/moment as observed in experiments, a pulse wave is used as the steering function in the mathematical model of the additive coupling stiffness (ACS). The representative TG system has two-rotor systems, each having two discs and supported on two flexible bearings - connected by coupling. An active magnetic bearing (AMB) is used as an auxiliary bearing on each rotor for the purposes of vibration suppression and fault identification. The formulation of mathematical model is followed by the development of an identification algorithm based on the model developed, which is an inverse problem. Least-squares linear regression technique is used to identify the unbalances, bearing dynamic parameters, AMB constants and importantly the coupling static and additive stiffness coefficients. The sensitivity of the identification algorithm to signal noise and bias errors in modelling parameters have been tested. The novelty of paper is the representation and identification of misalignment using the ACS matrix coefficients, which are direct indicators of both type and severity of the misalignment.

This paper studies the rotor dynamic behavior of misaligned-coupled rotor systems integrated with active magnetic bearings. The simplest possible numerical model has been derived with a 4-degree of freedom two coupled Jeffcott rotor systems. The effect of flexible coupling on the interaction between the response due to unbalance and misalignment has been studied. To demonstrate the influence three cases have been considered a) pure misalignment b) pure unbalance c) presence of both unbalance and misalignment. This is an original attempt considering the standard practice of using beam element based finite element modeling techniques for such systems. To simplify the problem, the weight dominance of discs has been assumed. Also the coupling considered in the problem is of flexible type. Misalignment in coupled rotors has been reported in literature to produce all harmonics both odd and even (...−2, −1, 0, 1, 2...) on either side of full spectrum. A suitable coupling excitation function has been chosen so that the response yields all the harmonics in spectrum. The numerical simulation has been performed in MATLAB/SIMULINK™ to generate the responses in time domain. Though AMB is incorporated in the system for vibration attenuation, the emphasis of the present paper shall be to demonstrate the interplay between unbalance and misalignment in flexibly coupled rotor systems.

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