Explore the vast range of titles available.

This article classifies the dynamic response of rolling bearings in terms of radial internal clearance values. The value of the radial internal clearance in rolling-element bearings cannot be described in a deterministic manner, which shows the challenge of its detection through the analysis of the bearing’s dynamics. In this article, we show the original approach to its intelligent detection through the analysis of short-time intervals and the calculation of chosen indicators, which can be assigned to the specific clearance class. The tests were carried out on a set of 10 brand new bearings of the same type (double row self-aligning ball bearing NTN 2309SK) with different radial internal clearances corresponding to individual classes of the ISO-1132 standard. The classification was carried out based on the time series of vibrations recorded by the accelerometer and then digitally processed. Window statistical indicators widely used in the diagnosis of rolling bearings, which served as features for the machine learning models, were calculated. The accuracy of the classification turned out to be unsatisfactory; therefore, it was decided to use a more advanced method of time series processing, which allows for the extraction of subsequent dominant frequencies into experimental modes (Variational Mode Decomposition (VMD)). Applying the same statistical indicators to the modes allowed for an increase in classification accuracy to over 90%.

The performance of rolling element bearings is one of the machine quality measures in industry. The fatigue life and performance of rolling element bearings depends mainly on the dynamic characteristics of those bearings. This paper studied the effect of the internal radial clearance on the damping characteristics, natural modes of vibration, and fatigue life of rolling element bearings. Vibration modal analysis was performed on rolling bearings of the same size and type to measure their dynamic characteristics. These dynamic characteristics include the natural frequency of the first mode of vibration, damping, and amplitude of frequency response function at resonance. The internal radial clearances of these bearings were measured. A statistical analysis was performed to study the correlation between the internal radial clearance and the dynamic characteristics of rolling bearings. It was found that the damping ratio of the bearing assembly increased by reducing the internal radial clearance of the bearing. Similarly, rolling bearings that have large internal clearances showed short predicted fatigue life. It is concluded that the dynamic characteristics, and consequently the dynamic performance, of rolling bearings are significantly affected by the internal radial clearance.

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.

In this paper, a simplified approach in the analysis of the varying compliance vibrations of a rolling bearing is presented. This approach analyses the generation of vibrations in relation to two boundary positions of the inner ring support on an even and an odd number of the rolling element of a bearing. In this paper, a mathematical model for the calculation of amplitude and frequency of vibrations of a rigid rotor in a rolling bearing is presented. The model is characterized by a big simplicity which makes it very convenient for a practical application. Based on the presented mathematical model a parametric analysis of the influence of the internal radial clearance, external radial load and the total number of rolling elements on the varying compliance vibrations of rolling bearing was conducted. These parameters are the most influential factors for generating varying compliance vibrations. The results of the parametric analysis demonstrate that with the proper choice of the size of the internal radial clearance and external radial load, the level of the varying compliance vibrations in a rolling bearing can be theoretically reduced to zero. This result opposes the opinion that varying compliance vibrations of rolling bearing cannot be avoided, even for geometrically ideally produced bearing.

One of the most important factors influencing ball bearings service life is its internal radial clearance. However, this parameter is also very complex because it depends on applied radial load and ball bearings dimensions, surface finish and manufacturing materials. Thermal condition of ball bearings also significantly affects internal radial clearance. Despite many researches performed in order to find out relevant facts about different aspects of ball bearings thermal behaviour, only few of them are dealing with the real working conditions, where high concentration of solid contaminant particles is present. That?s why the main goal of research presented in this paper was to establish statistically significant correlation between ball bearings temperatures, their working time and concentration of contaminant particles in their grease. Because of especially difficult working conditions, the typical conveyor idlers bearings were selected as representative test samples and appropriate solid particles from open pit coal mines were used as artificial contaminants. Applied experimental methodology included thermographic inspection, as well as usage of custom designed test rig for ball bearings service life testing. Finally, by obtained experimental data processing in advanced software, statistically significant mathematical correlation between mentioned bearings characteristics was determined and applied in commonly used internal radial clearance equation. That is the most important contribution of performed research - the new equation and methodology for ball bearings internal clearance determination which could be used for eventual improvement of existing bearings service life equations.

One of the most important characteristics of a rolling bearing is the load distribution on rolling elements. This paper provides an analysis on the influence of the internal construction of rolling bearings on load distribution and the number of active rolling elements. The analysis was performed using a new mathematical model for the boundary level calculations of the bearing deflection and external radial load for the inner ring support on q rolling bearing elements. The model considers two boundary positions of inner ring support on an even and odd number of rolling elements. The developed model enables a very simple determination of the number of active rolling elements participating in an external load transfer, depending on the bearing type and internal radial clearance.

The clearance flow passage of a pump-turbine is a multi-stage thin-layer cavity composed of the impeller and the head cover or bottom ring. Since the clearance flow passage is extremely small in size and complex in shape, current research on the impeller hydraulic thrust often ignores its influence, making it difficult to fully reveal the unbalanced force on the impeller and the vibration mechanism of the unit. Therefore, it is essential to study the clearance flow of ultra-high-head pump-turbine impellers. In this study, numerical simulations of the impeller clearance flow in a pump-turbine at 3 different operating cases were conducted using CFX, based on the Navier-Stokes equations and the SST k-ω turbulence model. The internal flow state within the sealing clearance was analyzed through pressure distribution maps and velocity vector diagrams, thereby revealing the formation and distribution mechanism of vortices within the clearance. In addition, by using the preset clearance model and through the pressure contour maps, velocity vectors, and streamlines obtained from the simulation, the influence of the clearance flow on the axial hydraulic thrust under the pump condition was evaluated.

This study investigates the effect of radial clearance between the impeller and diffuser on the aerodynamic performance and internal flow in a centrifugal compressor with a large flow coefficient. Three different types of radial clearances were examined: D 3  = 1.05 D 2 , 1.10 D 2 , and 1.15 D 2 . Qualitative and quantitative analysis of the effect of radial clearance on the internal flow field of the centrifugal compressor impeller and vaned diffuser, utilizing a combination of time-averaged flow field and modal decomposition method. The results indicate that compared to a smaller impeller-diffuser radial clearance, a larger radial clearance reduces the operating range of the centrifugal compressor under low flow conditions. As a result, the stall (or surge) margin is reduced by at least 6.68%. The appropriate radial clearance in the centrifugal compressor stage can improve its flow adaptability at low mass flow rate conditions. The Proper Orthogonal Decomposition method and the flow field reconstruction technique are used to identify the spatial and temporal distribution of large-scale coherent flow structures in the impeller and diffuser near the shroud side, as well as the key factors contributing to unstable flow. The findings of this research enhance the understanding of flow loss and the mechanisms behind the unstable flow associated with radial clearance in centrifugal compressors.

One of the most important factors influencing the study of the tribological behaviour of a rolling bearing is the calculation of the loads transmitted by individual rolling elements of the bearing. However, the calculation of the internal load distribution of rolling bearings is quite complicated. It is a nonlinear, statically indeterminate problem, which can only be solved numerically, through a number of iterations. This is often a problem in analysis because it complicates the mathematical model. This paper is presenting a case study with the goal to show the benefits of the application of a new approach for the calculation of the load of the most-loaded rolling element in the rolling bearing with the internal radial clearance. The calculation is based on the so-called load factors. By multiplying the load factors with the value of the external radial load, the load that is transferred by the most-loaded rolling element of the bearing is obtained. The accuracy of the results largely depends on the correct choice of the load factor. The case study aims to define guidelines for the correct choice of load factors. The case study is made for two types of bearings: the ball bearing and the roller bearing. Obtained results were compared with the results obtained based on the calculation using some of the most commonly used methods so far. The analysis showed greater precision of the considered model with the same or much simpler use. For this reason, the proposed model is considered very suitable for practical application.

This paper presents a new model for calculation of load for the most loaded rolling element in a rolling bearing with internal radial clearance. The calculation is based on a so-called load factor. By multiplying this factor by the value of the external radial load, the load transferred by the most loaded rolling element of the bearing is obtained. The values of the load factor are shown in the tables and diagrams, which makes the model very suitable for practical use. The load factors are shown for a ball bearing as well as for a roller bearing. The model considers two support positions of the inner ring on an even and odd number of rolling elements. The new model was compared with the most commonly used models up to now. The results showed greater accuracy of the studied model.