An Investigation of Rolling Element Vibrations Caused by Local Defects

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
H. Arslan ◽  
N. Aktürk
Keyword(s):  
Equations Of Motion ◽  
Angular Contact Ball Bearing ◽  
Frequency Spectra ◽  
Rolling Element ◽  
Rolling Elements ◽  
Computer Simulation Program ◽  
Localized Defects ◽  
Spring System ◽  
Mass Spring ◽  
Local Defects

In this paper, a shaft-bearing model is developed in order to investigate the rolling element vibrations for an angular contact ball bearing with and without defects. The shaft-bearing assembly is considered as a mass-spring system. The system shows a nonlinear characteristic under dynamic conditions. The equations of motion in radial and axial directions were obtained for shaft and rolling elements, and they were solved simultaneously with a computer simulation program. Additionally, the effect of localized defects on running surfaces (i.e., inner ring, outer ring, and ball) on the vibration of the balls is investigated. Vibration of rolling elements in the radial direction is analyzed in time and frequency domains. Characteristic defect frequencies and their components can be seen in the frequency spectra of rolling element vibrations. Comparison of the obtained results with similar studies available in literature showed reasonable qualitative agreement.

Rolling Element Bearing Non-Linearity Effects

2000 ◽  
Author(s):  
N. S. Feng ◽  
E. J. Hahn
Keyword(s):  
Equations Of Motion ◽  
Rolling Element Bearing ◽  
Radial Clearance ◽  
Rotor Systems ◽  
Bearing Life ◽  
Rolling Element ◽  
Bearing Load ◽  
Rolling Elements ◽  
Element Bearing ◽  
Negative Clearance

Non-linearity effects in rolling element bearings arise from two sources, viz. the Hertzian force deformation relationship and the presence of clearance between the rolling elements and the bearing races. Assuming that centrifugal effects may be neglected and that the presence of axial preload is appropriately reflected in a corresponding change in the radial clearance, this paper analyses a simple test rig to illustrate that non-linear phenomena such as synchronous multistable and nonsynchronous motions are possible in simple rigid and flexible rotor systems subjected to unbalance excitation. The equations of motion of the rotor bearing system were solved by transient analysis using fourth order Runge Kutta. Of particular interest is the effect of clearance, governed in practice by bearing specification and the amount of preload, on the vibration behaviour of rotors supported by ball bearings and on the bearing load. It is shown that in the presence of positive clearance, there exists an unbalance excitation range during which the bearing is momentarily not transmitting force owing to contact loss, resulting in rolling element raceway impact with potentially relatively high bearing forces; and indicating that for long bearing life, operation with positive clearance should be avoided in the presence of such unbalance loading. Once the unbalance excitation is high enough to avoid such contact loss, it is the bearings with zero or negative clearance which produce maximum bearing forces.

Parametric Vibrations in Discs: Point-Wise and Distributed Loads, Including Rotating Friction

1995 ◽  
Author(s):  
H. Ouyang ◽  
S. N. Chan ◽  
J. E. Mottershead ◽  
M. I. Friswell ◽  
M. P. Cartmell
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Transverse Load ◽  
Transverse Mass ◽  
Follower Load ◽  
Parametric Resonances ◽  
Spring System ◽  
Multiple Scales Analysis ◽  
Mass Spring ◽  
Rotating Load

Abstract This paper is concerned with the parametric resonances in a stationary annular disc when excited by a rotating load system. Two forms of the load system are considered. In the first, the load consists of a discrete transverse mass-spring-damper system and a frictional follower load. Secondly, a distributed mass-spring system (without friction) is studied. In both cases the transverse load is rotated at a uniform speed around the disc. Equations of motion are developed for the two cases, and the results of a multiple scales analysis are presented. The disc is found to exhibit many parametric resonances at subcritical speeds when friction is present.

Fault Diagnosis of High Speed Rolling Element Bearings Due to Localized Defects Using Response Surface Method

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
P. K. Kankar ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
Fault Diagnosis ◽  
Response Surface ◽  
Response Surface Method ◽  
High Speed ◽  
Mathematical Formulation ◽  
Rolling Element Bearings ◽  
Surface Method ◽  
Rolling Element ◽  
Rolling Elements ◽  
Localized Defects

In this paper, fault diagnosis of high speed rolling element bearings due to localized defects using response surface method has been done. The localized defects as spalls on outer race, on inner race, and on rolling elements are considered for this study. The mathematical formulation accounted for tangential motions of rolling elements and inner and outer races with the sources of nonlinearity such as Hertzian contact force and internal radial clearance. The nonlinear stiffness is obtained by the application of Hertzian elastic contact deformation theory. The mathematical formulation predicts discrete spectrum having peaks at the characteristic defect frequencies and their harmonics. Experimentation has also been performed to validate the results obtained from the mathematical model and it shows that the model can be successfully used to predict amplitude ratios among various spectral lines with localized surface defects. Combined parametric effects have been analyzed and their influence has been considered with design of experiments and surface response methodology is used to predict the dynamic response of a rotor bearing system.

A Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part I—Derivation of Governing Equations

1997 ◽  
Vol 119 (1) ◽  
pp. 126-131 ◽  
Author(s):  
J. Datta ◽  
K. Farhang
Keyword(s):  
Nonlinear Model ◽  
Contact Region ◽  
Equations Of Motion ◽  
Rolling Contact ◽  
Rolling Element Bearings ◽  
Structural Vibrations ◽  
Nonlinear Springs ◽  
Rolling Element ◽  
Rolling Elements ◽  
Constituent Elements

This paper, the first of two companion papers, presents a model for investigating structural vibrations in rolling element bearings. The analytical formulation accounts for tangential and radial motions of the rolling elements, as well as the cage, the inner and the outer races. The contacts between the rolling elements and races are treated as nonlinear springs whose stiffnesses are obtained by application of the equation for Hertzian elastic contact deformation. The derivation of the equations of motion is facilitated by assuming that only rolling contact exists between the races and rolling elements. Application of Lagrange’s equations leads to a system of nonlinear ordinary differential equations governing the motion of the bearing system. These equations are then solved using the Runge-Kutta integration technique. Using the formulation in the second part—“A Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part II—Simulation and Results,” a number of effects on bearing structural vibrations are studied. This work is unique from previous studies in that the model simulates vibration from intrinsic properties and constituent elements of the bearing, and takes into account every contact region within the bearing, representing it by a nonlinear spring.

A Research of Shaft Modal Simulation Method Based on the Preloaded Angular Contact Ball Bearing

2013 ◽  
Vol 389 ◽  
pp. 364-370
Author(s):  
Bei Li ◽  
Jian Bin Zhang ◽  
Lu Sha Jiang
Keyword(s):  
Simulation Analysis ◽  
Simulation Method ◽  
Numerical Control ◽  
Angular Contact Ball Bearing ◽  
Tightening Force ◽  
Shaft System ◽  
Element Simulation ◽  
Rolling Element ◽  
Bearing Stiffness ◽  
Main Spindle

In order to analysis modal characteristic of bearing with pre-tightening force on main spindle of numerical control lathe, this paper proposes a model of spindle modality analysis. This model is used to simulate the preloaded bearing shaft system modal, and the simulation results are verified by modal experiment. This paper takes 7005c as the research object to establish the equivalent-spring model based on the Hertz theory considering the pre-tightening force, whose focus is dealing with the contact between bearings rolling element and raceway. Then the model will be used to get the bearing stiffness for finite element simulation analysis. The shafting modal with preloaded bearing test platform is structured to get the shaft system modal parameters, which is compared with and verified the simulation analysis.

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.

Graphene-Based Resonant Sensors for Detection of Ultra-Fine Nanoparticles: Molecular Dynamics and Nonlocal Elasticity Investigations

NANO ◽  
2015 ◽  
Vol 10 (02) ◽  
pp. 1550024 ◽  
Author(s):  
S. Kamal Jalali ◽  
M. Hassan Naei ◽  
Nicola Maria Pugno
Keyword(s):  
Molecular Dynamics ◽  
Nonlocal Elasticity ◽  
Md Simulations ◽  
Small Scale ◽  
Frequency Shifts ◽  
Resonant Sensors ◽  
Embedded Atom ◽  
Metal Metal ◽  
Spring System ◽  
Mass Spring

Application of single layered graphene sheets (SLGSs) as resonant sensors in detection of ultra-fine nanoparticles (NPs) is investigated via molecular dynamics (MD) and nonlocal elasticity approaches. To take into consideration the effect of geometric nonlinearity, nonlocality and atomic interactions between SLGSs and NPs, a nonlinear nonlocal plate model carrying an attached mass-spring system is introduced and a combination of pseudo-spectral (PS) and integral quadrature (IQ) methods is proposed to numerically determine the frequency shifts caused by the attached metal NPs. In MD simulations, interactions between carbon–carbon, metal–metal and metal–carbon atoms are described by adaptive intermolecular reactive empirical bond order (AIREBO) potential, embedded atom method (EAM), and Lennard–Jones (L–J) potential, respectively. Nonlocal small-scale parameter is calibrated by matching frequency shifts obtained by nonlocal and MD simulation approaches with same vibration amplitude. The influence of nonlinearity, nonlocality and distribution of attached NPs on frequency shifts and sensitivity of the SLGS sensors are discussed in detail.

Size Effects in Dynamics of Dipolar Planar Nanosystems

2004 ◽  
Vol 99-100 ◽  
pp. 223-226
Author(s):  
H. Puszkarski ◽  
J.-C.S. Lévy ◽  
M. Krawczyk
Keyword(s):  
Size Effects ◽  
Equations Of Motion ◽  
Sample Surface ◽  
Dipolar Field ◽  
Dipolar Interactions ◽  
Planar System ◽  
Frequency Spectra ◽  
Magnetostatic Waves ◽  
Dynamic Components ◽  
Field Static

The equations of motion are derived for a magnetic planar system with dipolar interactions taken into account. Magnetostatic waves propagating perpendicularly to the sample surface and dipolar field static and dynamic components are calculated for the case when saturating field is applied perpendicularly to the sample surface. The corresponding frequency spectra and mode profiles are computed numerically with emphasis laid on size effects. It is established that two lowest-frequency modes are surface-localized modes. These modes preserve their surface-localized character with growing sample dimensions.

scholarly journals Reduced Mass-Weighted Proper Decomposition for Modal Analysis

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Venkata K. Yadalam ◽  
B. F. Feeny
Keyword(s):  
Modal Analysis ◽  
Mass Distribution ◽  
Mass Matrix ◽  
Linear Interpolation ◽  
Modal Identification ◽  
Distributed Parameter ◽  
Arbitrary Mass ◽  
Spring System ◽  
Mass Spring ◽  
Proper Orthogonal

A method of modal analysis by a mass-weighted proper orthogonal decomposition for multi-degree-of-freedom and distributed-parameter systems of arbitrary mass distribution is outlined. The method involves reduced-order modeling of the system mass distribution so that the discretized mass matrix dimension matches the number of sensed quantities, and hence the dimension of the response ensemble and correlation matrix. In this case, the linear interpolation of unsensed displacements is used to reduce the size of the mass matrix. The idea is applied to the modal identification of a mass-spring system and an exponential rod.

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