scholarly journals Modeling and Dynamic Analysis of Spherical Roller Bearing with Localized Defects: Analytical Formulation to Calculate Defect Depth and Stiffness

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Behnam Ghalamchi ◽  
Jussi Sopanen ◽  
Aki Mikkola
Keyword(s):  
Dynamic Model ◽  
Contact Stiffness ◽  
Roller Bearing ◽  
Measurement Data ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Outer Race ◽  
Rolling Elements ◽  
Localized Defects

Since spherical roller bearings can carry high load in both axial and radial direction, they are increasingly used in industrial machineries and it is becoming important to understand the dynamic behavior of SRBs, especially when they are affected by internal imperfections. This paper introduces a dynamic model for an SRB that includes an inner and outer race surface defect. The proposed model shows the behavior of the bearing as a function of defect location and size. The new dynamic model describes the contact forces between bearing rolling elements and race surfaces as nonlinear Hertzian contact deformations, taking radial clearance into account. Two defect cases were simulated: an elliptical surface on the inner and outer races. In elliptical surface concavity, it is assumed that roller-to-race-surface contact is continuous as each roller passes over the defect. Contact stiffness in the defect area varies as a function of the defect contact geometry. Compared to measurement data, the results obtained using the simulation are highly accurate.

scholarly journals A theoretical model for predicting the vibration response of outer race defective ball bearing

2018 ◽  
Vol 7 (2) ◽  
pp. 289
Author(s):  
Samir Shaikh ◽  
Sham Kulkarni
Keyword(s):  
Theoretical Model ◽  
Ball Bearing ◽  
Mathematical Formulation ◽  
Vibration Response ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Outer Race ◽  
Rolling Element ◽  
Rolling Elements ◽  
Extended Type

The theoretical model with 2 degree-of-freedom system is developed for predicting the vibration response and analyze frequency properties in an extended type defective ball bearing. In the mathematical formulation, the contact between the races and rolling element considered as non-linear springs. The contact forces produced during the collaboration of rolling elements are obtained by utilizing Hertzian contact deformation hypothesis. The second order nonlinear differential equation of motion is solved using a state space variable method with the help of MATLAB software and the vibration acceleration response of the defective ball bearing presented in the frequency spectrum. The effects of variation in speed and size of the defect on characteristic frequency of extended fault on the outer raceway of the ball bearing have been investigated. The theoretical results of the healthy (non defective) and defective bearing are compared with each other.

Dynamic Response of an Unbalanced Rotor Supported on Bearing With Outer Race Waviness

2013 ◽  
Author(s):  
P. K. Kankar ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
Dynamic Response ◽  
Chaotic Behavior ◽  
Mathematical Formulation ◽  
Rotational Frequency ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Outer Race ◽  
Unbalanced Rotor ◽  
Non Linear ◽  
Rolling Elements

The paper investigates the non-linear dynamic response of an unbalanced rotor supported on ball bearings with outer race waviness. The excitation is due to unbalanced force and waviness on outer race. The sources of non-linearities are both the radial clearance as well as the Hertzian contact between races and rolling elements. The nonlinear responses due to unbalanced rotor supported on bearings are investigated. The combined effects like non-linear stiffness and non-linear damping for unbalanced rotor with bearing waviness have been considered and analyzed in detail for a rotor bearing system. In the mathematical formulation, the contacts between the rolling elements and the races are considered as an oscillating spring-mass-damper system. The appearance of regions of periodic, sub-harmonic and chaotic behavior is seen to be strongly dependent on the number of waves in the outer race. The results show the appearance of instability and chaos in the dynamic response as the number of waves in the outer race is changed. The study indicates that the interaction of ball passage frequency (ωbp) due to outer race waviness and rotational frequency (X) due to the unbalanced rotor force. Poincaré maps and frequency responses are used to elucidate and to illustrate the diversity of the system behavior.

Analysis of radial roller bearing rating life in complex loading conditions

2021 ◽  
pp. 1-27
Author(s):  
Vladimir Ivannikov ◽  
Mikhail Leontiev ◽  
Sergey Degtyarev ◽  
Valeriy Popov
Keyword(s):  
High Performance ◽  
Roller Bearing ◽  
Complex Loading ◽  
Contact Forces ◽  
Loading Conditions ◽  
Jet Engines ◽  
Inertia Effects ◽  
Internal Contact ◽  
Rolling Elements ◽  
Life Analysis

Abstract An approach for accurate life analysis of radial roller bearings in complex loading conditions is presented. It employs ISO~16281 and accounts not only for external radial loads applied to the inner ring, but also for (i) internal bearing clearance, (ii) flexibility of the bearing rings, (iii) rings out-of-roundness, (iv) inertia effects, (v) rolling elements profile and (vi) rings misalignment. In the last decades these factors have been becoming more and more important for modern high-performance jet engines, whose shafts are commonly hollow and the housing and the rings thicknesses may be of comparable magnitudes. To obtain the distribution of internal contact forces, an advanced static model of a bearing with deformable, potentially misaligned, rings is developed. The bending deformations of the rings are reproduced superimposing deformed shapes from each of the arising internal contact force applied individually. Bearing rollers are allowed to have non-cylindrical profile, its geometry is approximated by means of slices each having constant diameter. A robust numerical scheme for solving the resultant set of equations with the aid of the barrier functions method is constructed. To increase even further the accuracy of rating life analysis, distributions of the contact stresses between the roller and the ring surfaces, obtained by solving numerically the problem of non-Hertzian interaction, are added to computations. A numerical benchmark test is presented to demonstrate the applicability of the developed approach. It shows how the aforementioned factors influence the bearing contact forces and its rating life.

A 4-DOF dynamic model for ball bearing with multiple defects on raceways

2020 ◽  
pp. 146441932097287
Author(s):  
Xianghong Gao ◽  
Changfeng Yan ◽  
Yaofeng Liu ◽  
Pengfei Yan ◽  
Junbao Yang ◽  
...  
Keyword(s):  
Dynamic Model ◽  
Characteristic Frequency ◽  
Ball Bearing ◽  
Elastohydrodynamic Lubrication ◽  
Radial Clearance ◽  
Multiple Defects ◽  
Single Defect ◽  
Localized Defects ◽  
Fourier Function ◽  
Fault Characteristic

Localized defects in ball bearing components would cause additional vibration and it is imperative to reveal the vibration mechanism. The relationship between fault characteristic frequency (fBPFI and fBPFO) and multiple defect parameters of ball bearing were given in this paper. Considering elastohydrodynamic lubrication (EHL), radial clearance, time-varying displacement and excitation force generated from multiple defects, a 4 degree-of-freedom (DOF) dynamic model for ball bearing with multiple defects on inner or outer raceway was established, and the model has been verified by experiments. Vibration signals of ball bearing with different defects parameters were simulated, the effects of the angle between two defects ( θIAD and θOAD), the number of defects ( NDI and NDO) and the location of defects on outer raceway on dynamic response were studied. Comparing simulated signals with experimental results, it is shown that more impulses of acceleration signals are generated by multiple defects than that by single defect, meanwhile time delay due to two defects on raceways could also be found, fault characteristic frequency and their harmonics frequencies appeared in the envelope spectrums. Harmonics frequencies of fBPFI are modulated mainly by 2 fs instead of fs in frequency domain for multiple defects on inner raceway. The amplitudes of fBPFO and fBPFI change as Fourier curve when θOAD and θIAD varied within a certain range, and a series of Fourier function are given to describe the mathematic relationship.

An Analytical Dynamic Model of a Hollow Cylindrical Roller Bearing

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Jing Liu ◽  
Yimin Shao
Keyword(s):  
Fatigue Life ◽  
Dynamic Model ◽  
Contact Stiffness ◽  
Roller Bearing ◽  
Great Influence ◽  
Radial Load ◽  
Shaft Speed ◽  
Roller Bearings ◽  
Cylindrical Roller ◽  
Analytical Dynamic

Hollow cylindrical roller bearings (HCRBs) have obtained much attention from design engineers in bearing industries since they can perform better than solid cylindrical roller bearings (SCRBs) in centrifugal forces, contact stiffness, cooling ability, fatigue life, etc. In this study, an analytical dynamic model of a lubricated HCRB is presented to analyze the influences of the radial load, the shaft speed, and the hollowness percentage of the roller on the bearing vibrations, which cannot be formulated by the methods in the reported literature. Both the support stiffness of the shaft and the roller mass are formulated in the presented dynamic model. The hollow hole in the roller is modeled as a uniform one. Numerical results show that the hollowness percentage of the roller has a great influence on the vibrations of the roller and the inner race of the HCRB. Moreover, the vibrations of the components of the HCRB are not only determined by the hollowness percentage of the roller, but also depended on the external radial load and shaft speed. Therefore, during the design process for the hollowness percentage of the roller, the influences of the radial load and the shaft speed on the vibrations of the bearing components should be considered, except for the fatigue life. The results show that this work can give a new dynamic method for analyzing the vibrations of the HCRBs. Moreover, it can give some guidance for the design method for the HCRBs.

Analysis of a Rolling-Element Idler Gear Bearing Having a Deformable Outer-Race Structure

1963 ◽  
Vol 85 (2) ◽  
pp. 273-278 ◽  
Author(s):  
A. B. Jones ◽  
T. A. Harris
Keyword(s):  
Fatigue Life ◽  
High Speed ◽  
Roller Bearing ◽  
Rolling Element Bearing ◽  
Outer Ring ◽  
Outer Race ◽  
Rolling Element ◽  
Rolling Elements ◽  
Planet Gear ◽  
Bearing Rings

Conventional calculations of ball and roller bearing carrying capacity and fatigue life assume that the raceway bodies are rigid structures and that all elastic deformation occurs at the rolling elements’ contact with the raceways. In many instances, and particularly with aircraft applications, the bearing rings and their supports cannot be considered rigid. One such application is the planet gear in a transmission. This report develops a theory whereby the effects of the elastic distortions of the outer race of a rolling-element bearing on the internal load distribution and fatigue life of the bearing can be considered. The theory has been programmed for a high-speed, digital computer. An example of calculation for a planet gear roller bearing whose outer race is integral with the gear and of relatively thin section is given. The distortions of the flexible outer ring cause a significantly lower bearing fatigue life (L10) than would occur if the outer ring were rigid and considering a practical range of bearing diametral clearances. Mr. Jones developed the theoretical analysis for this paper and Mr. Harris provided the programming and the experimental data.

A Multiphase Computational Study of Oil-Air Flow Within the Bearing Sector of Aeroengines

2015 ◽  
Author(s):  
Akinola A. Adeniyi ◽  
Hervé P. Morvan ◽  
Kathy A. Simmons
Keyword(s):  
Boundary Conditions ◽  
Computational Study ◽  
Roller Bearing ◽  
Operating Conditions ◽  
Rolling Contact ◽  
Contact Friction ◽  
Outer Race ◽  
Roller Bearings ◽  
Rolling Elements ◽  
Inner Race

The bearing chamber of an aeroengine houses roller bearings and other structural parts. The spatial limitation, high operational speeds of the HP shaft and the proximity to the combustion chamber can make the operating conditions of the bearing chamber challenging. A roller bearing consists of an inner race, an outer race and a cage constraining a number of rolling elements. In the aeroengine application, oil is introduced into the bearing chamber via the inner race regions of the bearing into the rolling elements interstices. This provides lubrication for the roller bearings. The source of heat in the bearing chamber is mainly from rolling contact friction and the high temperature of combustion. Cooling results from the oil transport within the bearing chamber and thus an efficient transport of oil is critical to maintaining the integrity of the entire structure. The bearing chamber contains the oil which is eventually scavenged and recycled for recirculation. Experiments have been conducted over the years on bearing chamber flows but often simplified to create the best emulation of the real aeroengine. The complexity of the bearing chamber structure is also challenging for experimental measurements of the oil characteristic in the roller bearing elements and the bearing chamber compartment. Previous experiments have shown that the oil continuum breaks up in the bearing chamber compartment but it is not quantitatively clear how and what parameters affect these. Previous simulation attempt of bearing chamber, also, have been limited by the boundary conditions for the oil. This work presents a computational fluid dynamics (CFD) transient simulation of flow in the bearing sector in an attempt create boundary conditions for such models. The current results show that the oil emerges in the form of droplets into the bearing chamber compartment with speed of the order of 10% of the shaft rotation.

Dynamic modeling and simulation of inter-shaft bearings with localized defects excited by time-varying displacement

2019 ◽  
Vol 25 (8) ◽  
pp. 1436-1446 ◽  
Author(s):  
Jing Tian ◽  
Yan-Ting Ai ◽  
Cheng-Wei Fei ◽  
Feng-Ling Zhang ◽  
Yat-Sze Choy
Keyword(s):  
Dynamic Model ◽  
Defect Size ◽  
Time Varying ◽  
Radial Load ◽  
Dynamic Features ◽  
Outer Race ◽  
Counter Rotation ◽  
Localized Defects ◽  
Bearing Vibration ◽  
Inner Race

To accurately describe the dynamic features of inter-shaft bearings with localized defect under operation, the dynamic model of inter-shaft bearing with localized defects was established with respect to time-varying displacement excitation. Based on fault simulations on a birotor experimental rig, the developed dynamic model of inter-shaft bearing is validated to have high accuracy (over 99%) when localized defects happen on inner and outer race with co- and counter-rotation, which indicates that the model can be adopted to simulate the faults of inter-shaft bearing instead of experiment. Through investigation of the square-root (SR) amplitudes of bearing vibration with different defect sizes, radial loads, and rotational directions, we find that the SR amplitudes of bearing vibration increase with increasing defect size and radial load for both co- and counter-rotation. The amplitudes of counter-rotation are larger than those of co-rotation for inner race and outer race, and the amplitude of inner race defect are larger than that of outer race defect for the same defect size or same radial load. This work reveals the SR variation of bearing vibration with localized surface defects under different defect sizes and radial loads, and accurately describes the dynamic characteristics of inter-shaft bearing with localized defects. The efforts of this study open a door to adopt a dynamic model in the future to evaluate and monitor the health condition of inter-shaft bearings in an aeroengine or other rotating machinery.

An improved analytical model for a lubricated roller bearing including a localized defect with different edge shapes

2017 ◽  
Vol 24 (17) ◽  
pp. 3894-3907 ◽  
Author(s):  
Jing Liu ◽  
Yimin Shao
Keyword(s):  
Analytical Model ◽  
Contact Stiffness ◽  
Roller Bearing ◽  
Numerical Results ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Time Varying ◽  
Sharp Edges ◽  
Detection And Diagnosis ◽  
Hertzian Contact Theory

Vibrations of a roller bearing (RB) with a localized defect (LOD) are determined by LOD edge shapes, which can be used to detect and diagnose the LODs. Therefore, it is very helpful to analyze the relationships between impulses and LOD edge shapes for detection and diagnosis of the early LODs. In this study, an improved analytical model for a lubricated RB with a LOD considering different edge shapes is proposed. The LOD edge propagation is determined by the size of small cylindrical surface at its edge. A time-varying impact force (TVIF) model for the LOD with different edge shapes is also presented depended on Hertzian contact theory. The time-varying displacement excitation (TVDE) and time-varying contact stiffness coefficient (TVSC) between the roller and LOD edges can be formulated by the presented model, which cannot be formulated by the previous models considering sharp edges in the literatures. Influences of LOD edge shapes on vibrations of the unlubricated and lubricated RB are investigated. The numerical results show that the amplitude and impulse waveform of the accelerations of the RB will be affected by the LOD edge shape and lubricated oil; however, the peak frequencies in the spectrum are slightly influenced by the LOD edge shape and lubricated oil. It seems that the presented numerical results can give some guidance for the incipient LOD detection and diagnosis for RBs.

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