scholarly journals A Simplified Mathematical Model for the Analysis of Varying Compliance Vibrations of a Rolling Bearing

2020 ◽  
Vol 10 (2) ◽  
pp. 670 ◽  
Author(s):  
Radoslav Tomović
Keyword(s):  
Mathematical Model ◽  
Parametric Analysis ◽  
Rolling Bearing ◽  
Influential Factors ◽  
Radial Clearance ◽  
Radial Load ◽  
Simplified Approach ◽  
Rolling Element ◽  
Rolling Elements ◽  
Varying Compliance

In this paper, a simplified approach in the analysis of the varying compliance vibrations of a rolling bearing is presented. This approach analyses the generation of vibrations in relation to two boundary positions of the inner ring support on an even and an odd number of the rolling element of a bearing. In this paper, a mathematical model for the calculation of amplitude and frequency of vibrations of a rigid rotor in a rolling bearing is presented. The model is characterized by a big simplicity which makes it very convenient for a practical application. Based on the presented mathematical model a parametric analysis of the influence of the internal radial clearance, external radial load and the total number of rolling elements on the varying compliance vibrations of rolling bearing was conducted. These parameters are the most influential factors for generating varying compliance vibrations. The results of the parametric analysis demonstrate that with the proper choice of the size of the internal radial clearance and external radial load, the level of the varying compliance vibrations in a rolling bearing can be theoretically reduced to zero. This result opposes the opinion that varying compliance vibrations of rolling bearing cannot be avoided, even for geometrically ideally produced bearing.

Investigation of the Effect of Rolling Bearing Construction on Internal Load Distribution and the Number of Active Rolling Elements

2013 ◽  
Vol 633 ◽  
pp. 103-116 ◽  
Author(s):  
Radoslav Tomovic
Keyword(s):  
Load Distribution ◽  
Load Transfer ◽  
Rolling Bearing ◽  
Radial Clearance ◽  
Radial Load ◽  
Rolling Bearings ◽  
Internal Load ◽  
Ring Support ◽  
Rolling Elements

One of the most important characteristics of a rolling bearing is the load distribution on rolling elements. This paper provides an analysis on the influence of the internal construction of rolling bearings on load distribution and the number of active rolling elements. The analysis was performed using a new mathematical model for the boundary level calculations of the bearing deflection and external radial load for the inner ring support onqrolling bearing elements. The model considers two boundary positions of inner ring support on an even and odd number of rolling elements. The developed model enables a very simple determination of the number of active rolling elements participating in an external load transfer, depending on the bearing type and internal radial clearance.

scholarly journals Load Calculation of the Most Loaded Rolling Element for a Rolling Bearing with Internal Radial Clearance

2020 ◽  
Vol 10 (19) ◽  
pp. 6934
Author(s):  
Radoslav Tomović
Keyword(s):  
Ball Bearing ◽  
Roller Bearing ◽  
Rolling Bearing ◽  
Radial Clearance ◽  
Load Factor ◽  
New Model ◽  
Load Factors ◽  
Rolling Element ◽  
Load Calculation ◽  
Rolling Elements

This paper presents a new model for calculation of load for the most loaded rolling element in a rolling bearing with internal radial clearance. The calculation is based on a so-called load factor. By multiplying this factor by the value of the external radial load, the load transferred by the most loaded rolling element of the bearing is obtained. The values of the load factor are shown in the tables and diagrams, which makes the model very suitable for practical use. The load factors are shown for a ball bearing as well as for a roller bearing. The model considers two support positions of the inner ring on an even and odd number of rolling elements. The new model was compared with the most commonly used models up to now. The results showed greater accuracy of the studied model.

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.

Dynamic Interactions Between the Rolling Element and the Cage in Rolling Bearing Under Rotational Speed Fluctuation Conditions

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Wenbing Tu ◽  
Ya Luo ◽  
Wennian Yu
Keyword(s):  
Dynamic Model ◽  
Rotational Speed ◽  
Rolling Bearing ◽  
Nonlinear Dynamic Model ◽  
Dynamic Interactions ◽  
Interaction Forces ◽  
Rolling Element ◽  
Speed Fluctuation ◽  
Rolling Elements ◽  
Fluctuation Frequency

Abstract A nonlinear dynamic model is proposed to investigate the dynamic interactions between the rolling element and cage under rotational speed fluctuation conditions. Discontinuous Hertz contact between the rolling element and the cage and lubrication and interactions between rolling elements and raceways are considered. The dynamic model is verified by comparing simulation result with the published experimental data. Based on this model, the interaction forces and the contact positions between the rolling element and the cage with and without the rotational speed fluctuation are analyzed. The effects of fluctuation amplitude, fluctuation frequency, and cage pocket clearance on the interaction forces between the rolling element and the cage are also investigated. The results show that the fluctuation of the rotational speed and the cage pocket clearance significantly affects the interaction forces between the rolling element and the cage.

Stabilizing Effects of Speed Fluctuations on the Dynamic Response of Rolling Element Bearings With Radial Clearances

2005 ◽  
Author(s):  
A. N. Lioulios ◽  
I. A. Antoniadis
Keyword(s):  
Theory Of Elasticity ◽  
Contact Forces ◽  
Radial Clearance ◽  
Rolling Element Bearings ◽  
Governing Parameter ◽  
Frequency Distributions ◽  
Rolling Element ◽  
Stabilization Effect ◽  
Speed Fluctuations ◽  
Varying Compliance

A horizontal balanced rotor supported on ball bearings with radial internal clearance, subjected to rotational speed fluctuations is modeled. The dynamic model takes under consideration contact forces derived by the hertzian theory of elasticity between the balls and the races, the effect of varying compliance, the internal radial clearance and the rotor’s speed fluctuations. The effect of variation in speed fluctuations is examined for periodic, unstable periodic and chaotic responses with the use of frequency distributions, higher order Poincare maps, and Lyapunov exponents. All results presented show a dominant stabilization effect of the speed fluctuations to the system behavior. From the analysis performed, it is concluded that even a minimum fluctuation of the rotor speed may result to major changes of the system dynamics, indicating that speed fluctuations of the rotor are a governing parameter to the dynamic behavior of the system.

Rolling bearing damping for dynamic analysis of multi-body systems—experimental and theoretical results

2000 ◽  
Vol 214 (1) ◽  
pp. 33-43 ◽  
Author(s):  
P Dietl ◽  
J Wensing ◽  
G C van Nijen
Keyword(s):  
Hydrodynamic Lubrication ◽  
Rolling Bearing ◽  
Classical Approach ◽  
Lubricated Contacts ◽  
Rolling Element ◽  
Rolling Elements ◽  
Experimental Approaches ◽  
Multi Body ◽  
Damping Model ◽  
Damping Capability

The present paper deals with the measurement and calculation of the damping capability of rolling element bearings. Rolling bearing damping is strongly influenced by the lubricated contacts between rolling elements and raceways. A theoretical model for calculating lubricant film (elasto-hydrodynamic lubrication) damping is briefly described in the first part of this paper. Furthermore, a relationship for estimating damping due to other dissipative mechanisms in the bearing is suggested. In the second part, two experimental approaches for measuring rolling bearing damping are discussed. The first (more ‘classical’) approach is based on conventional frequency response measurements and was used to verify the developed damping model regarding the influence of bearing lubrication, speed and preload. Finally, a new experimental approach for identifying rolling bearing damping is presented, eliminating some of the drawbacks of the ‘classical’ approach.

scholarly journals Analisa Getaran Akibat Kerusakan Deep Grove Ball Bearing Seri 6003RS

2019 ◽  
Vol 9 (02) ◽  
pp. 39-43
Author(s):  
Muhamad Riva’i ◽  
Nanda Pranandita
Keyword(s):  
Ball Bearing ◽  
Rolling Bearing ◽  
Internal Diameter ◽  
Outer Diameter ◽  
Outer Race ◽  
Deep Groove ◽  
Deep Groove Ball Bearing ◽  
Rolling Element ◽  
Rolling Elements ◽  
Vibration Measuring

Measurement of the damage of elements in bearing can be by measuring the vibration generated in the form of a frequency signal when the pad is rotating. Measurement of vibration on the bearing by using vibration measuring instrument. Damage to the rolling bearing includes damage to the cage, outer ring, inner ring and balls. The rolling bearings used in this study are deep groove ball bearing type 6003 RS with internal diameter (d) = 17 mm, outer diameter (D) = 35 mm, bearing thickness (B) = 10, number of rolling elements (Nb) = 10 pieces, and the diameter of the rolling element (Bd) = 4.75 mm. In the rotation of the bearing (Fr) = 2003 rpm (33.38 Hz) we found the experimental results of bearings that have been damaged in the outer race at 138 Hz frequency, inner race damage at 196 Hz frequency, (ball) at a frequency of 88.8 Hz and cage damage at a frequency of 13.8 Hz.

Hysteretic Resonances and Intermittency Chaos in Ball Bearings

2018 ◽  
Author(s):  
Zhiyong Zhang ◽  
Xiaoting Rui ◽  
Yushu Chen ◽  
Wenkai Dong ◽  
Lei Li
Keyword(s):  
Ball Bearing ◽  
Harmonic Balance Method ◽  
Rolling Bearing ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Rolling Bearings ◽  
Rotor Systems ◽  
Revolute Joints ◽  
Rolling Elements ◽  
Varying Compliance

Ball bearings are essential parts of mechanical systems to support the rotors or constitute the revolute joints. The time-varying compliance (VC), bearing clearance and the Hertzian contact between the rolling elements and raceways are three fundamental nonlinear factors in a ball bearing, hence the ball bearing can be considered as a nonlinear system. The hysteresis and jumps induced by the nonlinearities of rolling bearings are typical phenomena of nonlinear vibrations in the rolling bearing-rotor systems. And the corresponding hysteretic impacts have direct effects on the cleavage derivative and fatigue life of the system components. Therefore, the behaviors of hysteresis and jumps are given full attentions and continued studies in the theoretical and engineering fields. Besides, many researchers have done a lot of calculations to depict the various characteristics of bifurcations and chaos in the rolling bearings and their rotor systems, but few researches have been addressed on the inherent mechanism of the typical intermittency vibrations in rolling bearings. With the aid of the HB-AFT (the harmonic balance method and the alternating frequency/time domain technique) method and Floquet theory, this paper will investigate deeply the resonant hysteresis and intermittency chaos in ball bearings.

Detection of the Process Equipment Components Flaws with the Aid of Thermography

2008 ◽  
Vol 59 (3) ◽  
pp. 325-330
Author(s):  
Atef Mazioud ◽  
Jean Felix Durastanti ◽  
Laurent Ibos ◽  
Nicoleta Teodorescu
Keyword(s):  
Mechanical Vibration ◽  
Flaw Detection ◽  
Infrared Camera ◽  
Rolling Bearing ◽  
Process Equipment ◽  
Rolling Element ◽  
Rolling Elements ◽  
Detection And Diagnosis ◽  
Bearing Cap ◽  
Spalling Defect

The paper presents the problem of the process equipment parts flaw detection with the aid of thermography instead of vibratory analysis. It is presented as an example, a new method (proposed by the authors) of the spalling in rolling-element bearings detection and diagnosis. The idea is to show the existing correlation between the outside temperature of the bearing cap and the vibratory level generated by increasing occurrence of the defect. An experimental study was performed on the test ring which allows the generation, in a progressive manner, of a spalling defect on the external ring of the rolling bearing. On this test rig, simultaneously were measured the mechanical vibration in the radial direction (by means of a piezoelectric accelerometer) and the bearing cap external surface temperature (by means of an infrared camera). The results exhibit a significant correlation between both measures. A detailed study of the heat transfer between the rolling elements and the spalling outside border permits evaluation of the temperature rise due to the heat generated from the defect.

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