A Simplified Model for Structural Vibrations in Ball Bearings

1994 ◽  
Author(s):  
Kambiz Farhang ◽  
Kapil Mehra ◽  
Jayanta Datta
Keyword(s):  
Linear Model ◽  
Equations Of Motion ◽  
Linear Representation ◽  
Accurate Estimate ◽  
Rolling Element Bearing ◽  
Hertzian Contact ◽  
Outer Ring ◽  
Rolling Bearings ◽  
Geometrical Properties ◽  
Rolling Element

Abstract More often than not, in studies involving dynamics and vibration of rotor systems, the bearings within a rotor system are treated as linear components. However, it is well understood that bearing systems are nonlinear due to both their geometrical properties and Hertzian contact between their components. This paper develops a linear formulation to approximate the vibration behavior of rolling bearings. A study of the approximation in the linear representation for rolling bearings is presented in which the effects of preload, lubricant viscosity and outer ring mass on the accuracy of the linear representation are determined. The equations of motion governing the vibrations of rolling element bearing are found to be a set of second-order, nonlinear ordinary differential equations with position periodic coefficients. These equations are linearized about nominal values of the position vectors of the rolling element and the outer ring center. The linearized equations of motion are solved to obtain the small perturbations (displacements) from the nominal positions. The results show that the linear model representation is applicable for bearings with preload. Existence of damping and/or greater outer ring mass enhance the approximation provided by the linear model. Most importantly, the linear representation provides a conservative estimate of the rolling element motion and very accurate estimate of the outer ring motion.

Rolling Bearing Parametric Excitation of a Jeffcott Rotor System

2020 ◽  
Author(s):  
Ghasem Ghannad Tehrani ◽  
Chiara Gastaldi ◽  
Teresa Maria Berruti
Keyword(s):  
Parametric Excitation ◽  
Rotational Speed ◽  
Input Parameter ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Mean Value ◽  
Hertzian Contact ◽  
Rolling Bearings ◽  
Jeffcott Rotor

Abstract Rolling bearings are still widely used in aeroengines. Whenever rotors are modeled, rolling bearing components are typically modeled using springs. In simpler models, this spring is considered to have a constant mean value. However, the rolling bearing stiffness changes with time due to the positions of the balls with respect to the load on the bearing, thus giving rise to an internal excitation known as Parametric Excitation. Due to this parametric excitation, the rotor-bearings system may become unstable for specific combinations of boundary conditions (e.g. rotational speed) and system characteristics (rotor flexibility etc.). Being able to identify these instability regions at a glance is an important tool for the designer, as it allows to discard since the early design stages those configurations which may lead to catastrophic failures. In this paper, a Jeffcott rotor supported and excited by such rolling bearings is used as a demonstrator. In the first step, the expression for the time–varying stiffness of the bearings is analytically derived by applying the Hertzian Contact Theory. Then, the equations of motion of the complete system are provided. In this study, the Harmonic Balance Method (HBM) is used to as an approximate procedure to draw a stability map, thus dividing the input parameter space, i.e. rotational speed and rotor physical characteristics, into stable and unstable regions.

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.

Transient Rotordynamic Modeling of Rolling Element Bearing Systems

2001 ◽  
Author(s):  
A. Liew ◽  
N. S. Feng ◽  
E. J. Hahn
Keyword(s):  
Rolling Element Bearing ◽  
Hertzian Contact ◽  
Centrifugal Load ◽  
Linear Behavior ◽  
Deep Groove ◽  
Rolling Element ◽  
Rolling Elements ◽  
Load Effects ◽  
Element Bearing ◽  
Bearing Preload

Non-linearity effects in rolling element bearings may arise from the Hertzian contact force deformation relationship, the presence of clearance between the rolling elements and the bearing races, and the bearing to housing clearance. Assuming zero bearing to housing clearance and ignoring rolling element centrifugal load effects, it has been shown in earlier work that Rotor Bearing Systems (RBSs) with deep groove ball bearings can give rise to non-linear behavior such as chaotic motion and jump. This paper extends the bearing model to include rolling element centrifugal load, angular contacts and axial dynamics. The effect of more sophisticated bearing models is illustrated in both a rigidly supported rigid RBS and a flexibly supported flexible RBS, the latter being a model of a test rig designed to simulate an aircraft mounted accessory drive unit. Results are presented on the effect of bearing preload on the unbalance response up to a speed of 18,000 rpm.

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.

Fault Diagnosis of Bearings Based on Time-Delayed Correlation Demodulation and Fuzzy Clustering

2011 ◽  
Vol 211-212 ◽  
pp. 510-514 ◽  
Author(s):  
Pan Fu ◽  
Wei Lin Li ◽  
Wei Qing Cao
Keyword(s):  
Fault Diagnosis ◽  
Vibration Signal ◽  
Failure Diagnosis ◽  
Rolling Element Bearing ◽  
Rolling Bearings ◽  
Bearing Fault Diagnosis ◽  
Rolling Element ◽  
Fuzzy C Means Clustering ◽  
Important Means ◽  
Set Up

As one of the most common parts of various rolling mechanical equipments, rolling element bearing is vulnerable. Therefore, great attentions have been attributed to the theories, failure diagnosis methods and their applications for rolling bearings. Vibration analysis is also a very important means for bearing fault diagnosis. This paper aims at the research on the methods of signal processing and pattern recognition. An experimental platform was set up for the failure diagnosis of rolling bearings, on which we have done a lot of experiments. Then the vibration signals of normal rolling bearings, rolling bearings with failure on the outer and inner race were collected. Time-delayed correlation demodulation was applied and the features of vibration signal were effectively extracted. Fuzzy C-means clustering system was established to carry out the recognition of the fault of bearings. Experimental results have proved the developed fault diagnostic architecture is reliable and effective.

Simulations of Gear-Rolling Element Bearing Interactions in Geared Transmissions

2003 ◽  
Author(s):  
F. Lahmar ◽  
P. Velex
Keyword(s):  
Equations Of Motion ◽  
Rolling Element Bearing ◽  
Integration Scheme ◽  
Time Step ◽  
Normal Contact ◽  
Contact Algorithm ◽  
Rolling Element ◽  
Non Linear ◽  
External Forces ◽  
Gear Rolling

The modular model of geared systems presented in this paper makes it possible to simultaneously account for the contact conditions in gears and rolling element bearings. Gears are modeled as two rigid cylinders connected by distributed mesh stiffnesses while ball and roller bearings contribute to the equations of motion as time-varying, non-linear external forces. Solutions are obtained by combining a Newmark time-step integration scheme, a Newton-Raphson method for ball bearing non-linearity and a normal contact algorithm that deals with the contact problem between the teeth. It is found that the static gear-bearing couplings are generally more important than the dynamic couplings with a significant influence of the gear on the bearing response. Finally, it is shown that, in certain conditions, bearings can generate non-linear parametric excitations of the same orders of magnitude as those associated with the meshing of helical gears.

scholarly journals Experimental Rig for Measuring Lubricant Film Thickness in Rolling Bearings

2014 ◽  
Vol 658 ◽  
pp. 381-386
Author(s):  
Xing Nan Zhang ◽  
Karolina Jablonka ◽  
Romeo Glovnea
Keyword(s):  
Film Thickness ◽  
Lubricant Film ◽  
Hertzian Contact ◽  
Lubricant Film Thickness ◽  
Rolling Bearings ◽  
The Past ◽  
Rolling Element ◽  
Rolling Elements ◽  
Experimental Rig ◽  
Made In

Electrical capacitance has been applied in the past for measuring the lubricant film thickness in rolling element bearings. The main difficulty arises from the fact that the measured capacitance is a combination of the capacitances of many rolling elements, which come in contact with both the inner and outer rings. Besides, the capacitance of the Hertzian contact itself and the surrounding area must also be separated. It results in a complex system which, in order to be solved for the film thickness at a particular location on the bearing many approximations have to be made. In the present study the authors use an experimental rig in which the capacitance of a single ball can be isolated. Moreover the capacitance of the ball – inner ring and ball – outer ring contacts can be measured separately.

A Series of New Nonlinear Dynamic Equations of Rolling Element Bearing Systems

2010 ◽  
Vol 118-120 ◽  
pp. 896-901
Author(s):  
Dong Xu ◽  
Yong Cheng Xu ◽  
Xun Chen ◽  
Yong Min Yang ◽  
Xing Lin Li
Keyword(s):  
Rolling Bearing ◽  
Rolling Element Bearing ◽  
Evolution Process ◽  
Radial Clearance ◽  
Rolling Bearings ◽  
Nonlinear Dynamic Equations ◽  
Rolling Element ◽  
Element Bearing ◽  
Fault Evolution ◽  
Additional Equation

As one of the key parts of rotating machinery, rolling bearing is the primary fault source, therefore it is urgent to research failure mechanism and its evolution process. First, the number of laden rollers of rolling bearings in different states without radial clearance and preload is summed up, and then nonlinear analytical equations and an additional equation are proposed. To some extent it will be helpful for researching the fault evolution process of rolling element bearings combined with fatigue theories. Further they will conduce to analyze and predict the remaining life of ball bearings.

Hydrodynamic support and dynamic response for an inner-piloted bearing cage

2003 ◽  
Vol 217 (1) ◽  
pp. 19-28 ◽  
Author(s):  
D R Ashmore ◽  
E J Williams ◽  
S McWilliam
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Rolling Element Bearing ◽  
Computationally Efficient ◽  
Support Mechanism ◽  
Rolling Element ◽  
Element Bearing ◽  
Analytical Expressions ◽  
Inner Race ◽  
Generalized Reynolds Equation

Although many attempts have been made to model rolling-element bearings with inner-piloted cages, they all simplify the hydrodynamic cage-support mechanism. This can mean that some cage behaviour is inadequately explained, such as cage lap. This paper presents the development of a new three-dimensional analysis of the hydrodynamic support for an inner-piloted cage for a rolling-element bearing incorporating starved-film conditions. The solution of the generalized Reynolds equation along with a continuity equation leads to analytical expressions for the hydrodynamic forces. The equations of motion for the cage are then integrated numerically using the Newmark beta method to predict the cage response. The availability of analytical hydrodynamic force expressions means that the numerical integration process is computationally efficient. The influence of key parameters such as the level of lubrication and the angular velocity of the inner race are investigated.

scholarly journals Dynamic Analysis of a Rotor-Bearing-SFD System with the Bearing Inner Race Defect

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Junhong Zhang ◽  
Xin Lu ◽  
Jiewei Lin ◽  
Liang Ma ◽  
Jun Wang
Keyword(s):  
Dynamic Behavior ◽  
Equations Of Motion ◽  
Elastohydrodynamic Lubrication ◽  
Hertzian Contact ◽  
System Stability ◽  
Time Frequency ◽  
Runge Kutta Method ◽  
Rolling Element ◽  
Rotor Bearing ◽  
Inner Race

In this paper, the dynamic behavior of a rotor-bearing-SFD system with the inner race defect of bearing is investigated. The contact force between the rolling element and the race is calculated in Hertzian contact and elastohydrodynamic lubrication condition. The supporting force of the SFD is simulated by integrating the pressure distribution derived from Reynolds’s equation. The equations of motion of the rotor-bearing-SFD system are derived and solved using the fourth-order Runge-Kutta method. The dynamic behavior and the fault characteristics are analyzed with two configurations of the SFD: (1) mounted on the unfaulted bearing and (2) mounted on the faulty bearing. According to the analysis of time-frequency diagram, waterfall plot, and spectral diagram, the results show that the characteristics of inner race defects on bearing frequencies are related to the characteristic multiple frequency of the inner race defect and the fundamental frequency. The speed and defect width have different influence on the distribution and amplitude of frequency. The SFD can enhance the system stability under the bearing fault but the enhancement decreases with the increasing speed. Meanwhile, the beneficial effect of the SFD varies according to the mounted position in the rotor system.

Sign in / Sign up

Export Citation Format

Share Document