scholarly journals Simple and Versatile Dynamic Model of Spherical Roller Bearing

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Behnam Ghalamchi ◽  
Jussi Sopanen ◽  
Aki Mikkola
Keyword(s):  
Roller Bearing ◽  
Model Verification ◽  
Hertzian Contact ◽  
Computationally Efficient ◽  
Essential Components ◽  
Rolling Element ◽  
Staggered Arrangement ◽  
Side Roller ◽  
Three Degree Of Freedom ◽  
Hertzian Contact Theory

Rolling element bearings are essential components of rotating machinery. The spherical roller bearing (SRB) is one variant witnessing increasing use because it is self-aligning and can support high loads. It is becoming increasingly important to understand how the SRB responds dynamically under a variety of conditions. This study introduces a computationally efficient, three-degree-of-freedom, SRB model that was developed to predict the transient dynamic behaviors of a rotor-SRB system. In the model, bearing forces and deflections were calculated as a function of contact deformation and bearing geometry parameters according to the nonlinear Hertzian contact theory. The results reveal how some of the more important parameters, such as diametral clearance, the number of rollers, and osculation number, influence ultimate bearing performance. One pair of calculations looked at bearing displacement with respect to time for two separate arrangements of the caged side-by-side roller arrays, when they are aligned and when they are staggered. As theory suggests, significantly lower displacement variations were predicted for the staggered arrangement. Following model verification, a numerical simulation was carried out successfully for a full rotor-bearing system to demonstrate the application of this newly developed SRB model in a typical real world analysis.

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.

scholarly journals Research on effect of damping variation on vibration response of defective bearings

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401982773 ◽  
Author(s):  
Fanzhao Kong ◽  
Wentao Huang ◽  
Yunchuan Jiang ◽  
Weijie Wang ◽  
Xuezeng Zhao
Keyword(s):  
Dynamic Model ◽  
Vibration Signal ◽  
Vibration Response ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Viscous Damping ◽  
Lubricating Grease ◽  
Rolling Element ◽  
Different Types ◽  
Hertzian Contact Theory

This article presents a dynamic model of ball bearings with a localised defect on the outer raceway to analyse the effect of damping variation on the vibration response of defective bearings. First, a dynamic model is built based on the Hertzian contact theory, the interaction between the bearing inner ring, outer ring, and rolling element; the effect of damping and stiffness is considered; and the vibration equation of the bearing system is solved by the fourth-order Runge–Kutta algorithm. Then, the damping ratios of the experimental bearings using different types of viscosity lubricating grease are measured and compared with the damping ratios of the dynamic model; in addition, the viscous damping coefficient of the experimental bearings are calculated. Finally, the numerical analysis and experimental results show that the grease with a different level of viscosity affects the vibration signal of the defective bearing.

Applications of vibro-acoustic measurement and analysis in conjunction with tribological parameters to assess surface fatigue wear developed in the roller-bearing system

2021 ◽  
pp. 135065012098246
Author(s):  
Shashikant Pandey ◽  
Muniyappa Amarnath
Keyword(s):  
Roller Bearing ◽  
Operating Conditions ◽  
Rolling Contact ◽  
Stribeck Curve ◽  
Fatigue Wear ◽  
Surface Fatigue ◽  
Rolling Element ◽  
Measurement And Analysis ◽  
Contact Surfaces ◽  
Bearing System

Rolling-element bearings are the most commonly used components in all rotating machinery. The variations in the operating conditions such as an increase in the number of operating cycles, load, speed, service temperature, and lubricant degradation result in the development of various defects such as pitting, spalling, scuffing, scoring, etc. The defects that appeared on rolling contact surfaces cause surface deterioration and change in the vibration and sound levels of the bearing system. The present experimental investigations are aimed at assessing the surface fatigue wear that appears on the contact surfaces of roller bearings. The studies considered the estimation of specific film thickness, analysis of surface fatigue wear developed on the rolling-element surfaces, surface roughness analysis, grease degradation analysis using Fourier transform infrared radiation, and vibration and sound signal measurement and analysis. The results obtained from the experimental investigation provide a good correlation between surface wear, vibration, and sound signals with a transition in the lubrication regimes in the Stribeck curve.

scholarly journals Analysis of Dynamic Response of a Two Degrees of Freedom (2-DOF) Ball Bearing Nonlinear Model

2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Hertzian Contact ◽  
Two Degrees Of Freedom ◽  
Wide Range ◽  
Shape Errors ◽  
Nonlinear Features ◽  
Fourier Transform Phase ◽  
Hertzian Contact Theory

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.

Investigation on the drag effect of a rolling element confined in the cavity of a cylindrical roller bearing

2021 ◽  
pp. 135065012110260
Author(s):  
Wenjun Gao ◽  
Shuo Zhang ◽  
Xiaohang Li ◽  
Zhenxia Liu
Keyword(s):  
Open Space ◽  
Roller Bearing ◽  
Flow Characteristics ◽  
Experimental Tests ◽  
Windward Side ◽  
Leeward Side ◽  
Drag Effect ◽  
Rolling Element ◽  
Cylindrical Roller Bearing ◽  
Cylindrical Roller

In cylindrical roller bearings, the drag effect may be induced by the rolling element translating in a fluid environment of the bearing cavity. In this article, the computational fluid dynamics method and experimental tests are employed to analyse its flow characteristics and pressure distribution. The results indicate that the pressure difference between the windward side and the leeward side of the cylinder is raised in view of it blocking the flow field. Four whirl vortexes are formed in four outlets of two wedge-shaped areas between the front part of the cylindrical surface and adjacent walls for the cylinder of L/ D = 1.5 at Re = 4.5 × 103. Vortex shedding is found in the direction of cylinder axis at Re = 4.5 × 104. The relationship between drag coefficient and Reynolds number is illustrated, obviously higher than that of the two-dimensional cylinder in open space.

Dynamics of Rolling-Element Bearings—Part I: Cylindrical Roller Bearing Analysis

1979 ◽  
Vol 101 (3) ◽  
pp. 293-302 ◽  
Author(s):  
P. K. Gupta
Keyword(s):  
Differential Equations ◽  
Normal Force ◽  
Equations Of Motion ◽  
Roller Bearing ◽  
Rolling Element Bearings ◽  
Analytical Formulation ◽  
Rolling Element ◽  
Cylindrical Roller Bearing ◽  
Cylindrical Roller ◽  
Bearing Analysis

An analytical formulation for the roller motion in a cylindrical roller bearing is presented in terms of the classical differential equations of motion. Roller-race interaction is analyzed in detail and the resulting normal force and moment vectors are determined. Elastohydrodynamic traction models are considered in determining the roller-race tractive forces and moments. Formulation for the roller end and race flange interaction during skewing of the roller is also considered. Roller-cage interactions are assumed to be either hydrodynamic or fully metallic. Simple relationships are used to determine the churning and drag losses.

Approximate Analytical Model for Hertzian Elliptical Wheel/Rail or Wheel/Crossing Contact Problems

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
F. D. Fischer ◽  
M. Wiest
Keyword(s):  
Contact Pressure ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Technical Accuracy ◽  
Elliptical Contact ◽  
Current Approximation ◽  
Analytical Expressions ◽  
Maximum Contact ◽  
Hertzian Contact Theory

The Hertzian contact theory is approximated according to a concept by Tanaka (2001, “A New Calculation Method of Hertz Elliptical Contact Pressure,” ASME J. Tribol., 123, pp. 887–889) yielding simple analytical expressions for the elliptical semi-axes, the maximum contact pressure, the mutual approach and the contact spring constant. Several configurations are compared using the exact Hertz theory and the current approximation. The results agree within technical accuracy.

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.

A New Quasi-Static Cylindrical Roller Bearing Model to Accurately Consider Non-Hertzian Contact Pressure in Time Domain Simulations

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Simon Kabus ◽  
Michael R. Hansen ◽  
Ole Ø. Mouritsen
Keyword(s):  
Fatigue Life ◽  
Time Domain ◽  
Roller Bearing ◽  
Rolling Bearing ◽  
Elastic Half Space ◽  
Hertzian Contact ◽  
Fatigue Life Analysis ◽  
Cylindrical Roller Bearing ◽  
Six Degree Of Freedom ◽  
Cylindrical Roller

The accuracy of the fatigue life calculations in rolling bearing simulations is highly dependent on the precision of the roller-raceway contact simulations. Several different methods exist to simulate these pressure distributions and in time domain bearing simulations, where many contacts need evaluation, the simple and time efficient methods are more popular, yielding erroneous life estimates. This paper presents a new six degree of freedom frictionless quasi-static time domain cylindrical roller bearing model that uses high precision elastic half-space theory to simulate the contact pressures. The potentially higher computational demand using the advanced contact calculations is addressed by preprocessing a series of contacts at different centerline approaches and roller tilt angles, which are used for interpolating contact results during time domain simulations. It is demonstrated that this new model allows for simulation of bearing misalignments, roller centrifugal forces, and flange contact induced roller tilt moments, and that the effect of these conditions is directly evaluated in a detailed fatigue life analysis. Finally, the stiffness of the bearing model is validated against existing experimental data with good correlation.

Simulation of Traction Drive Ratio Changes

2000 ◽  
Author(s):  
Z. Zou ◽  
Y. Zhang ◽  
X. Zhang ◽  
W. Tobler
Keyword(s):  
Hertzian Contact ◽  
Contact Theory ◽  
Hydrodynamic Theory ◽  
Traction Drive ◽  
Input And Output ◽  
Piston Displacement ◽  
Simulation Results ◽  
Traction Drives ◽  
Stability And Accuracy ◽  
Hertzian Contact Theory

Abstract In the simulation model presented in this paper, the kinematic characteristics of traction drives are formulated using classical Hertzian contact theory and elasto-hydrodynamic theory. The roller swing motion is governed by an equation derived based on Newton’s Second Law and is coupled to the side slip, torque input and output, as well as ratio variations. A control strategy with feedbacks for both the roller swing and the piston displacement is applied for ratio control based on stability and responsiveness considerations. The model has been implemented systematically in Matlab/Simulink environment. The effectiveness of the ratio control system in terms of stability and accuracy is illustrated by the simulation results included in this paper.

Sign in / Sign up

Export Citation Format

Share Document