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.

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.

Application of Cyclostationary Indicators for the Diagnostics of Distributed Faults in Ball Bearings

2013 ◽  
Author(s):  
Gianluca D’Elia ◽  
Simone Delvecchio ◽  
Marco Cocconcelli ◽  
Giorgio Dalpiaz
Keyword(s):  
Fault Diagnosis ◽  
Characteristic Frequency ◽  
Ball Bearings ◽  
Surface Wear ◽  
Radial Load ◽  
Test Rig ◽  
Statistical Parameters ◽  
Localized Defects ◽  
Distributed Faults ◽  
Fault Characteristic

This paper deals with the detection of distributed faults in ball bearings. In literature most of the authors focus their attention on the detection of incipient localized defects. In that case classical techniques (i.e. statistical parameters, envelope analysis) are robust in recognizing the presence of the fault and its characteristic frequency. In this paper the authors focalize their attention on bearings affected by distributed faults, due to the progressive growing of surface wear or to low-quality manufacturing process. These faults can not be detected by classical techniques; in fact, in this case the signal does not contain impulses at the fault characteristic frequency, but more complex components with strong non-stationary contents. Distributed faults are here detected by means of advanced tools directly derived from the theory of cyclostationarity. In particular three metrics — namely Integrated Cyclic Coherence (ICC), Integrated Cyclic Modulation Coherence (ICMC) and Indicator of Second-Order Cyclostationarity (ICS2x) — have been calculated in order to condense the information given by the cyclostationary analysis and to help the analyst in detecting the fault in a fast fault diagnosis procedure. These indicators are applied on actual signals captured on a test rig where a degreased bearing running under radial load developed accelerated wear. The results indicated that all the three cyclostationary indicators are able to detect both the appearance of a localized fault and its development in a distributed fault, whilst the usual approach fails as the fault grows.

Multiple Defects Detection in Outer Race of Gearbox Ball Bearing Using Time Domain Statistical Parameters

2016 ◽  
Vol 8 (3) ◽  
Author(s):  
A. Nabhan ◽  
A.M. Sami ◽  
M.O. Mousa ◽  
M. Nouby
Keyword(s):  
Ball Bearing ◽  
Three Dimensional ◽  
Simulated Data ◽  
Three Dimensional Model ◽  
Statistical Parameters ◽  
Outer Race ◽  
Multiple Defects ◽  
Single Defect ◽  
Deep Groove ◽  
Local Defects

Multiple defects are introduced on the outer race of vehicle gearboxes. The effect of the number of outer race defects in deep groove ball bearings are investigated using experimental and numerical methods. A three-dimensional model of the housing and outer race is developed using ABAQUS. Firstly, single defect located at 0˚and two defects located at 0˚ and 67.5˚ are analyzed. Then the number of defects was increased to three and the locations of the local defects are 0˚, 67.5˚ and 225˚. Finally the model with four defects located on the outer race at the angular positions 0˚, 67.5˚, 225˚ and 270˚, was investigated. The simulated data were also used to validate the experimental results.

A New Dynamic Model of Ball-Bearing Rotor Systems Based on Rigid Body Element

2016 ◽  
Vol 138 (7) ◽  
Author(s):  
Hongrui Cao ◽  
Yamin Li ◽  
Xuefeng Chen
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Ball Bearing ◽  
Rotor System ◽  
Radial Clearance ◽  
Fe Model ◽  
Ball Bearings ◽  
Rolling Ball ◽  
Rotor Systems ◽  
Body Element

Ball-bearing rotor systems are key components of rotating machinery. In this work, a new dynamic modeling method for ball-bearing rotor systems is proposed based on rigid body element (RBE). First, the concept of RBE is given, and then the rotor is divided into several discrete RBEs. Every two adjacent RBEs are connected by imaginary springs, whose stiffness is calculated according to properties of the RBEs. Second, all the parts of rolling ball bearings (i.e., outer ring, inner ring, ball, and cage) are considered as RBEs, and Gupta's model is employed to model bearings which include radial clearance, waviness, pedestal effect, etc. Finally, the rotor and all the rolling ball bearings are coupled to develop a dynamic model of the ball-bearing rotor system. The vibration responses of the ball-bearing rotor system can be calculated by solving dynamic equations of each RBE. The proposed method is verified with both simulation and experiment. The RBE model of the rotor is compared with its finite element (FE) model first, and numerical simulation shows the validity of the RBE model. Then, experiments are conducted on a rotor test rig which is supported with two rolling ball bearings as well. Good agreements between measurement and simulation show the ability of the model to predict the dynamic behavior of ball-bearing rotor systems.

A Dynamic Modeling Approach for Spindle Bearing System Supported by Both Angular Contact Ball Bearing and Floating Displacement Bearing

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Songtao Xi ◽  
Hongrui Cao ◽  
Xuefeng Chen ◽  
Linkai Niu
Keyword(s):  
Dynamic Model ◽  
Dynamic Modeling ◽  
Ball Bearing ◽  
Radial Clearance ◽  
Fe Method ◽  
Angular Contact Ball Bearing ◽  
Modeling Approach ◽  
Spindle Shaft ◽  
Spindle Bearing ◽  
Bearing System

This paper presents a new dynamic modeling approach for spindle bearing system supported by both angular contact ball bearing (ACBB) and floating displacement bearing (FDB). First, a dynamic model of FDB is developed based on the discrete element method with each bearing component having six degrees-of-freedom (DOFs). Based on the developed FDB dynamic model and Gupta ACBB dynamic model, a fully coupled dynamic model of the spindle bearing system combined both ACBBs, and FDB is developed. In the proposed spindle bearing system model, the spindle shaft is modeled using finite element (FE) method based on the Timoshenko beam theory with the consideration of centrifugal force and gyroscopic moment. The coupling restriction between the dynamic bearing models and the FE spindle shaft model are the restoring forces and moments that are transmitted to the shaft by the bearings and the dynamic vibration response shared by both the bearing inner races and the corresponding nodes of the shaft where bearings are installed. A Fortran language-based program has been developed for the spindle bearing system with the dynamic bearing models solved using the Runge–Kutta–Fehlberg integration method and FE shaft model solved by Newmark-β method. Based on the developed model, the effect of the FDB radial clearance, system preload, and spindle rotating speed on the system dynamics, and the effect of the FDB radial clearance on the system unbalanced response have been investigated.

scholarly journals Optimal design of high efficiency double helical gear based on dynamics model

2021 ◽  
Vol 3 (8) ◽  
Author(s):  
Fengxia Lu ◽  
Xuechen Cao ◽  
Weiping Liu
Keyword(s):  
Dynamic Model ◽  
High Efficiency ◽  
Bending Strength ◽  
Sliding Friction ◽  
Elastohydrodynamic Lubrication ◽  
Optimization Method ◽  
Transmission Efficiency ◽  
Helical Gear ◽  
Transmission System ◽  
Vibration Displacement

AbstractA 16-degree-of-freedom dynamic model for the load contact analysis of a double helical gear considering sliding friction is established. The dynamic equation is solved by the Runge–Kutta method to obtain the vibration displacement. The method combines the friction coefficient model based on the elastohydrodynamic lubrication theory with the dynamic model, which provides a theoretical basis for the calculation of the power loss of the transmission system. Moreover, the sensitivity analysis of the parameters that affect the transmission efficiency is carried out, and an optimization method of meshing efficiency is proposed without reducing the bending strength of the gears. This method can directly guide the design of the double helical gear transmission system.

Recognition of Bearing Faults of the Same Kind

1991 ◽  
Author(s):  
Ming Bao ◽  
Chun-sheng Zhao
Keyword(s):  
Condition Monitoring ◽  
Characteristic Frequency ◽  
Correct Equation ◽  
Bearing Faults ◽  
Single Fault ◽  
Equipment Utilization ◽  
Bearing Part ◽  
Fault Characteristic

Abstract Condition monitoring has gained much acceptance because of the reduction of maintenance expenses and the increase of rate of equipment utilization. It is very important that the serious degrees of machinery faults is correctly predicted. Two faults in a bearing part is, of course, more serious than the single fault is. If the features of bearing faults of the same kind are not recognized, faults of the same kind are, then, mistaken for a single fault, the serious consequences may be caused. The features of bearing faults of the same kind are presented and the illustrations are given in the paper. Meanwhile, the correct equation of roller’ s fault characteristic frequency is expounded conveniently.

Mechanical Power Losses of Ball Bearings: Model and Experimental Validation

2021 ◽  
pp. 1-29
Author(s):  
Ahmet Dindar ◽  
Amit Chimanpure ◽  
Ahmet Kahraman
Keyword(s):  
Dynamic Model ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Mechanical Power ◽  
Ball Bearings ◽  
Power Losses ◽  
Euler Parameters ◽  
Surface Shear ◽  
Axial Forces ◽  
Set Up

Abstract A tribo-dynamic model of ball bearings is proposed to predict their load-dependent (mechanical) power losses. The model combines (i) a transient, point contact mixed elastohydrodynamic lubrication (EHL) formulation to simulate the mechanics of the load carrying lubricated ball-race interfaces, and (ii) a singularity-free dynamics model, and establishes the two-way coupling between them that dictates power losses. The dynamic model employs a vectoral formulation with Euler parameters. The EHL model is capable of capturing two-dimensional contact kinematics, velocity variations across the contact as well as asperity interactions of rough contact surfaces. Resultant contact surface shear distributions are processed to predict mechanical power losses of example ball bearings operating under combined radial and axial forces. An experimental set-up is introduced for measurement of the power losses of rolling-element bearings. Sets of measurements taken by using the same example ball bearings are compared to those predicted by the model to assess its accuracy in predicting mechanical power loss of a ball bearing within wide ranges of axial and radial forces.

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