Evaluation of Factors Affecting the Simulation of Structural Vibrations in Rolling Bearings

1994 ◽  
Author(s):  
Kapil Mehra ◽  
Jayanta Datta ◽  
Kambiz Farhang
Keyword(s):  
High Speed ◽  
Contact Deformation ◽  
Structural Vibrations ◽  
Appreciable Change ◽  
Factors Affecting ◽  
Outer Race ◽  
Nonlinear Springs ◽  
Lumped Parameter ◽  
Rolling Element ◽  
Centers Of Mass

Abstract An analytical model is developed for studying in-plane structural vibrations in rolling element bearings. A lumped parameter approach is employed in developing the model. The mass and moment of inertia of the components comprising the bearing are lumped at their respective centers of mass. The localized stiffnesses due to contact deformation phenomenon are treated as nonlinear springs. The variable spring rates are obtained by application of Hertz equation for elastic contact deformation. Effects of preload, ball rotational speed, and damping are studied using the formulation. An interesting observation is made as to the influence of preload. It is found that in the presence of preload, irrespective of the load magnitude, contact is maintained with both the inner and the outer races. Hence, responses obtained with and without the check for ball/inner race and ball/outer race interferences are identical. In addition, no appreciable change is observed in the responses when the preload value is varied from 10 N to 1N. At high speed of operation, the balls are found to maintain contact with the outer ring, whereas intermittent contact with the inner ring occurs for brief periods of time. Introduction of lubricant is found to dampen the oscillations considerably.

scholarly journals Investigation of Factors Influencing the Structural Vibration in Ball Bearings

2000 ◽  
Vol 6 (5) ◽  
pp. 321-331 ◽  
Author(s):  
Kapil Mehra ◽  
Kambiz Farhang ◽  
Jayanta Datta
Keyword(s):  
High Speed ◽  
Structural Vibration ◽  
Ball Bearings ◽  
Appreciable Change ◽  
Outer Race ◽  
Nonlinear Springs ◽  
Lumped Parameter ◽  
Intermittent Contact ◽  
Parameter Approach ◽  
Inner Race

Hertzian equation for elastic contact is utilized along with lumped parameter approach to obtain the equations that govern the structural vibration of ball bearings. The lumped parameter formulation is obtained by treating various elements with mass lumped at their centers of gravity and the contact as nonlinear springs with nonlinear spring rates.Effects of preload, ball rotational speed, and damping are studied using the formulation. It is found that in the presence of preload, irrespective of the load magnitude, contact is maintained with both the inner and the outer races. Hence, responses obtained with and without the check for ball/inner race and ball/outer race interferences are identical. In addition, no appreciable change is observed in the responses when the preload value is varied from 1 to 10 N. At high speed of operation, the balls are found to maintain contact with the outer ring, whereas intermittent contact with the inner ring occurs for brief periods of time. Introduction of lubricant is found to dampen the oscillations considerably.

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 Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part II—Simulation and Results

1997 ◽  
Vol 119 (2) ◽  
pp. 323-331 ◽  
Author(s):  
J. Datta ◽  
K. Farhang
Keyword(s):  
Nonlinear Model ◽  
Relative Size ◽  
Operating Conditions ◽  
Rolling Element Bearings ◽  
Governing Equations ◽  
Structural Vibrations ◽  
Outer Race ◽  
Vibrational Response ◽  
Rolling Element

This is the second of two companions papers. In the first paper, “A Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part I—Derivation of Governing Equations,” equations governing the vibrational response of rolling element bearings were developed. The mathematical formulations are utilized in this paper to study a number of effects on bearing structural vibrations. These include the effects of relative size of roller and inner and outer races, and inertias of inner and outer race assemblies, i.e., inertia of the races plus the components of an external system to which the inner and outer races are attached; the load acting on the bearing, its magnitude and nature (i.e., whether linear, rotational etc.). The studies are made under constant operating conditions (speed, lubrication) and the results obtained are discussed.

The Error Caused by Order Analysis for Rolling Bearing Fault Signal

2013 ◽  
Vol 819 ◽  
pp. 254-258 ◽  
Author(s):  
Wei Dong Cheng ◽  
Robert X. Gao ◽  
Jin Jiang Wang ◽  
Tian Yang Wang ◽  
Wei Gang Wen ◽  
...  
Keyword(s):  
High Speed ◽  
Vibration Signal ◽  
Rolling Bearing ◽  
Rate Of Change ◽  
Rolling Element Bearings ◽  
Factors Affecting ◽  
Order Analysis ◽  
Rolling Element ◽  
Angular Interval ◽  
The Time Domain

Defect diagnosis of rolling element bearings operating under time-varying rotational speeds entails order tracking and analysis techniques that convert a vibration signal from the time domain to the angle domain to eliminate the effect of speed variations. When a signal is resampled at a constant angular increment, the amount of data padded into each data segment will vary, depending on the rate of change in the rotational speeds. This leads to changes in the distance between the adjacent impulse peaks, and consequently, the result of order analysis. This paper presents a quantitative analysis of key factors affecting the accuracy of order analysis on rolling element bearings under variable speeds. An analytical model is established and simulated. The effects of speed variation, instantaneous speed, angular interval between impulses, and the rising time of impulse are specified. It is concluded that the results of order analysis will be smaller as the rotational speed increases, and becomes larger when the speed decreases. Furthermore, the error is larger under low speeds than high speed.

Simplified Analysis Strategies for Fluid-Structure Interaction in High Speed Turbomachinery

2009 ◽  
Author(s):  
Brittany Consuegra ◽  
George T. Flowers
Keyword(s):  
High Pressure ◽  
High Speed ◽  
Fluid Structure Interaction ◽  
Parameter Analysis ◽  
Structural Vibrations ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Machine Failure ◽  
Lumped Parameter ◽  
Wide Range

High pressure seals are usually mounted between the rotating and stationary components in high-pressure turbomachinery and often experience intense vibration. These vibrations can interact with the fluid to produce unsteady flows, which can in turn induce structural vibrations that result in machine failure. The reduction of the adverse effects of these vibrations is considered one of the most challenging problems for turbopump design. However, detailed analyses of such fluid-structure interaction problems can be extremely time-consuming and inefficient. The purpose of the present study is to evaluate the effectiveness of simplified, lumped-parameter techniques in analyzing and predicting such behavior, as compared to more sophisticated techniques, with the goal of defining the range of validity for such techniques. A fluid-structure driven vibration is evaluated using a lumped parameter analysis for a wide range of parametric configurations and the results are validated and compared using a bench-top laboratory test rig.

Rolling Element Bearing Monitoring Using High Gain Eddy Current Transducers

1985 ◽  
Vol 107 (1) ◽  
pp. 160-164 ◽  
Author(s):  
R. G. Harker ◽  
J. S. Hansen
Keyword(s):  
Eddy Current ◽  
High Speed ◽  
High Gain ◽  
Activity Monitor ◽  
Rolling Element Bearing ◽  
Bearing Failure ◽  
Outer Race ◽  
Rolling Element ◽  
Element Bearing ◽  
Bearing Monitoring

A technique is described which provides early detection of rolling element bearing failure through direct observation of the bearing outer race with a high-gain eddy current probe. Data is presented that compares REBAM™—Rolling Element Bearing Activity Monitor—to traditional monitoring approaches that employ case mounted velocity and acceleration transducers. Generally, the REBAM approach simplifies the analysis of bearing condition because of its proximity to the bearing and its insensitivity to extraneous vibration sources due to the relative mounting approach employed. A summary of field results is presented and its suitability to high speed gas turbine monitoring is discussed.

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.

scholarly journals Evaluation of Electron-Beam Welded Hollow Balls for High-Speed Ball Bearings

1971 ◽  
Vol 93 (1) ◽  
pp. 47-55 ◽  
Author(s):  
Harold H. Coe ◽  
Richard J. Parker ◽  
Herbert W. Scibbe
Keyword(s):  
Fatigue Life ◽  
High Speed ◽  
Ball Bearing ◽  
Similar Data ◽  
Ball Bearings ◽  
Outer Race ◽  
Rolling Element ◽  
Solid Ball ◽  
Steel Balls ◽  
Weld Area

An experimental investigation was performed with two series (115 and 215) of 75 mm bore ball bearings using hollow balls as the rolling elements. The bearings were tested at 500 and 1000 pounds thrust loads at shaft speeds up to 24000 rpm. The 115 series bearings with 1/2-in. SAE 52100 steel balls showed very little difference in torque, outer-race temperature, or rolling-element fatigue life when compared to similar data for a solid ball bearing. The 215 series bearings with 11/16-in. AISI M-50 steel balls showed only slight differences in torque and outer-race temperature but a very significant decrease in rolling-element fatigue life compared to a solid ball bearing. The balls failed in flexure fatigue, due to a stress concentration in the weld area.

Experimental investigation on time-domain features in the diagnosis of rolling element bearings by acoustic emission

2021 ◽  
pp. 107754632110161
Author(s):  
Aref Aasi ◽  
Ramtin Tabatabaei ◽  
Erfan Aasi ◽  
Seyed Mohammad Jafari
Keyword(s):  
Acoustic Emission ◽  
Condition Monitoring ◽  
Time Domain ◽  
Central Moment ◽  
Rolling Element Bearings ◽  
Test Rig ◽  
Acoustic Emission Sensor ◽  
Outer Race ◽  
Common Time ◽  
Rolling Element

Inspired by previous achievements, different time-domain features for diagnosis of rolling element bearings are investigated in this study. An experimental test rig is prepared for condition monitoring of angular contact bearing by using an acoustic emission sensor for this purpose. The acoustic emission signals are acquired from defective bearing, and the sensor takes signals from defects on the inner or outer race of the bearing. By studying the literature works, different domains of features are classified, and the most common time-domain features are selected for condition monitoring. The considered features are calculated for obtained signals with different loadings, speeds, and sizes of defects on the inner and outer race of the bearing. Our results indicate that the clearance, sixth central moment, impulse, kurtosis, and crest factors are appropriate features for diagnosis purposes. Moreover, our results show that the clearance factor for small defects and sixth central moment for large defects are promising for defect diagnosis on rolling element bearings.

Reynolds-averaged Navier–Stokes simulation of hydrofoil effects on hydrodynamic coefficients of a catamaran in forced oscillation

2016 ◽  
Vol 231 (2) ◽  
pp. 364-383
Author(s):  
Amin Najafi ◽  
Mohammad Saeed Seif
Keyword(s):  
High Speed ◽  
Experimental Approach ◽  
Navier Stokes ◽  
Hydrodynamic Coefficients ◽  
Laboratory Equipment ◽  
Factors Affecting ◽  
High Frequencies ◽  
Frequency Independent ◽  
Reynolds Averaged Navier Stokes

Determination of high-speed crafts’ hydrodynamic coefficients will help to analyze the dynamics of these kinds of vessels and the factors affecting their dynamic stabilities. Also, it can be useful and effective in controlling the vessel instabilities. The main purpose of this study is to determine the coefficients of longitudinal motions of a planing catamaran with and without a hydrofoil using Reynolds-averaged Navier–Stokes method to evaluate the foil effects on them. Determination of hydrodynamic coefficients by experimental approach is costly and requires meticulous laboratory equipment; therefore, utilizing the numerical methods and developing a virtual laboratory seem highly efficient. In this study, the numerical results for hydrodynamic coefficients of a high-speed craft are verified against Troesch’s experimental results. In the following, after determination of hydrodynamic coefficients of a planing catamaran with and without foil, the foil effects on its hydrodynamic coefficients are evaluated. The results indicate that most of the coefficients are frequency-independent especially at high frequencies.

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