Varying compliance vibrations of rolling bearings
The most fundamental cause of noise and unsteady running of rolling bearings is the so-called varying compliance vibrations. These are parametrically excited vibrations that occur irrespective of the quality and accuracy of the bearing. Varying compliance of the bearing assembly can give rise to both radial and axial displacements of a shaft supported by rolling bearings. In this study, however, attention is focused on radial vibrations of radially loaded bearings having a positive radial clearance. Previous studies of this phenomena are quasi-static in approach—the inclusion of inertia forces reveals characteristics not previously recognized. Examples of theoretical solutions obtained through digital simulation are presented and comparisons with experimentally obtained results are made.
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Cited by (173)
Dynamic characteristics investigation of a dual rotor-casing system considering the comprehensive stiffness of the intermediate bearing
2024, Journal of Sound and VibrationThis paper focuses on the vibrational properties of a dual rotor-casing coupled system with nonlinear clearance in the intermediate bearing, considering both the oil film stiffness and Hertzian contact stiffness between rolling elements and raceways. A comprehensive stiffness model for the intermediate bearing has been developed based on elastohydrodynamic lubrication (EHL) and Hertz contact theory. Subsequently, a dynamical model of the dual rotor-bearing-casing system is established using the finite element method, thereby verifying the feasibility of simulating the casing with beam elements. The dimensionality of the system equation is reduced using the fixed-interface component mode synthesis (CMS) method, and the resulting reduced-dimensionality equation is solved using the improved Newmark-β method. The effects of casing support, rotational speed, and radial clearance on the vibration characteristics of the system are investigated. Then, the comprehensive stiffness and coupled vibration characteristics of the system are analyzed to elucidate its intrinsic mechanism. Finally, the contact characteristics within the intermediate bearing under dynamic load are also studied. The results indicate that the support stiffness of the casing has a more significant impact on the second resonance caused by both the inner and outer rotors. The system is prone to experiencing varying compliance (VC) resonance at low rotational speeds. The excessive bearing clearance leads to complex vibrational characteristics of the system, making it challenging to predict its motion. The impact of minor changes in stiffness on system vibration is small when the comprehensive stiffness is large. At this time, the limited effect of oil film stiffness allows it to be disregarded in terms of comprehensive stiffness. Furthermore, the speed significantly influences the contact characteristics within the intermediate bearing under the unbalanced force of the rotor and gravity.
Analysis of contact behaviours and vibrations in a defective deep groove ball bearing
2024, Journal of Sound and VibrationRolling element bearings are vital parts for rotating machinery. When a defect occurs on the surface of the bearing raceway or rolling element, giving rise to the abnormal vibration of the bearing and even the rotating machine. Thus, it is of great significance to understand the vibration characteristics of the bearing for fault diagnosis and machine condition monitoring. In recent decades, researches on defect-induced bearing vibration in machine condition monitoring have attracted increasing attention. Model-based investigation is a highly useful method for enhancing our understanding of defect-induced vibration and fault excitation mechanism of the bearing. It also serves as a basis for establishing the theory of bearing failure. With this in mind, a novel dynamic model of deep groove ball bearing (DGBB) with a localized outer race defect is proposed in this paper. In this model, the additional displacement excitation which is modelled as a piecewise function based on kinematics is considered, and the angle-based contact force is developed and modelled as a piecewise function taking into account the angular position, collision velocity, and impact force. In addition, an analytical formulation of the angle-varying effective stiffness matrix of the DGBB with a localized raceway defect of varying size is established. The proposed dynamic model is used to study the influences of different defect scenarios (i.e. angular positions and widths) on the time-varying contact stiffness, contact force, spectral characteristics, and bearing vibrations. The comparisons between the simulations and the experiments show that the proposed model is effective.
Optimization of rolling bearing dynamic model based on improved golden jackal optimization algorithm and sensitive feature fusion
2023, Mechanical Systems and Signal ProcessingSome simplified modeling parameters in the traditional rolling bearing dynamics model led to poor consistency between the simulated and measured vibration signals. In addition, the simulated signal has low accuracy, which in turn reduces the accuracy of bearing fault diagnosis based on the simulated signal. Thus, to resolve the above-mentioned issues, this study presents a method for optimizing rolling bearing dynamics models based on an improved golden jackal optimization (IGJO) algorithm and sensitive feature fusion. Firstly, this study proposes an IGJO algorithm using a dimension-by-dimension reverse learning strategy and adaptive weights to address the interplay of dimensions in the multidimensional optimization process and the imbalance between the global and local search abilities of the GJO. Secondly, a fusion strategy for bearing fault-sensitive features is proposed based on the binary's improved golden jackal optimization (B-IGJO) algorithm and principal component analysis (PCA). In this strategy, the Sigmoid function discretization method is used to obtain the B-IGJO algorithm, which is then applied to the measured signal to select the bearing fault sensitivity features. These features are analyzed using PCA to obtain the fused sensitivity feature expression. Finally, the fusion-feature expressions are used to calculate the fusion-sensitive features of the measured and simulated vibration signals, and then the residuals of the two are used as the objective function for model optimization. The parameters of the rolling bearing dynamics model are updated using the IGJO. The proposed method is experimentally verified through a single pitting fault dynamics model of the outer ring of the rolling bearing. In conclusion, our results confirm the effectiveness and feasibility of the proposed method.
Comprehensive study on the nonlinear parameter vibrations of the rotor system due to the varying compliance of ball bearing
2023, Communications in Nonlinear Science and Numerical SimulationIn this paper, based on the restoring force coupling method, a novel mathematical model is established to study the VC parameter vibration responses of the ball bearing-rotor system, and both the rotor radial and tilting motions have been considered. Firstly, the steady state analysis on the stiffness fluctuation is conducted to determine the equivalent linear resonant frequencies of the nonlinear ball bearing-rotor system. Secondly, both the two-way sweep-frequency and fixed frequency-analysis are adopted to study the different transient response mechanisms of the rotor VC parameter vibrations, Finally, the results show that not only the multiple resonant responses including the super-harmonic, sub-harmonic, Hopf bifurcation and chaos are generated for the rotor parametric vibration, but also the complex internal resonance phenomenon occurs when the rotor natural frequency ratio in different radial directions is close to 1:2.
Electrotribodynamics of ball bearings in electrical machines
2023, Tribology InternationalThe trend towards electrification presents new challenges in bearing design. One such consideration is the occurrence of electrical discharge contact pathways, which can lead to surface damage. The current study presents a novel comprehensive multiphysics model, incorporating bearing dynamics, mechanics of lubricated rolling element-to-races contacts and electrical contact model for both DC and AC voltages. The model also includes both electrical resistance and capacitance effects in the bearing contacts. Key bearing vibration frequencies such as cage frequency and the bearing base natural frequency along with the voltage supply frequency are observed as influential in the electric current discharge. The developed model enables the prediction of rhythmic fluting patterns commonly observed in the failed bearing applications subject to electrical discharge.
Investigation on stability and slip characteristic of the cage in cylindrical roller bearing with localized failure on raceways
2023, Mechanical Systems and Signal ProcessingThe vibration characteristics of the cylindrical roller bearings (CRBs) with localized failures have been extensively discussed. However, there remains a lack of precise understanding regarding how failures affect the dynamical behavior of the bearing cage. Therefore, for investigating the operating mechanism of the cage in bearing with failures, a modeling approach for calculating the contact force between components is developed, and a simulation model of CRBs with localized failure on raceways is proposed. Moreover, the model established is confirmed experimentally using the vibration response. The result shows that when the rotating speed and radial load are increased, the behavior change of the cage can be divided into three processes, and the increased radial load may cause the cage operation to transition into a vortex state at an accelerated rate. The running stability and slip rate of cage are also critically affected by the bearing internal size. Then, the generation mechanism of cage vortex and slip characteristics is analyzed, the excellent performance of cage is closely related to the collision force and collision frequency between guide ring and cage, excessive contact between cage and roller will directly threaten the dynamic behavior of cage. When there are localized failures on raceway, the shock will be generated when the rollers pass through the failure zone, the collision force and collision frequency between rollers and cage will be considerably increased, while the collision frequency between guide ring and cage is reduced, which makes the cage operation stability decreased and skid rate increased.
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Now at Stal Laval Research Laboratories, 612 00, Fingspong, Sweden.