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International Journal of Mechanical Engineering and Technology (IJMET)Volume 8, Issue 6, JuneAvailable online at ISSN Print: 0976 © IAEME
A THEORETICAL MODEL
ABSTRACTThis paper discusses the modelling of ball bearing for predicting the presence of
defects on outer and inner races. A computer program in Matlab is developed and DOF equations are solved. The output of the program is time domain signal of the bearing. The program takes into consideration the size of the defects, location of the defect and also the effect of changing the load on the bearing. The vibration signal obtained through modelling is analysed for frequencies. The peaks at the characteristic defect frequencies in the spectrum indicate the location of the fault on races. Key words:frequencies, spectrum indicator, fault on racesCite this ArticleDeep Groove Ball Bearing for Predicting the Effect of Localized Defects on Vibrations2017, pp. 760http://www.i
1. INTRODUCTIONVarious sources of vibration in any machine are unbalance, misalignment, faulty gear and faulty bearing etc. Among these the If a bearing fails, the entire production line is affected and ultimately, it will affect the productivity. Hence it is important that the rolling element bearings are monitored regularly for checkand theoretical. In theoretical methods, a model is developed and equations of motion are solved. Through this the vibration behaviour of bearings can be predicted.
As beardeveloped a model for studying vibrations produced by bearings carrying spalling etc.
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International Journal of Mechanical Engineering and Technology (IJMET)Volume 8, Issue 6, JuneAvailable online at http://www.iaeme.com/IJMEISSN Print: 0976-6340 and IS
© IAEME Publication
A THEORETICAL MODEL BALL BEARING FOR PREEFFECT OF LOCALIZED
M. Tech., BVDU
Professor, BVDU
ABSTRACT This paper discusses the modelling of ball bearing for predicting the presence of
defects on outer and inner races. A computer program in Matlab is developed and DOF equations are solved. The output of the program is time domain signal of the bearing. The program takes into consideration the size of the defects, location of the defect and also the effect of changing the load on the bearing. The vibration signal btained through modelling is analysed for frequencies. The peaks at the
characteristic defect frequencies in the spectrum indicate the location of the fault on races. Key words: ball bearing, size of defects, location of defects, vibration signals, defectfrequencies, spectrum indicator, fault on racesCite this ArticleDeep Groove Ball Bearing for Predicting the Effect of Localized Defects on Vibrations. International Journal of Mechanical E2017, pp. 760–76http://www.iaeme.com/IJME
INTRODUCTIONVarious sources of vibration in any machine are unbalance, misalignment, faulty gear and faulty bearing etc. Among these the If a bearing fails, the entire production line is affected and ultimately, it will affect the productivity. Hence it is important that the rolling element bearings are monitored regularly for checking their health. Mainly the methods of monitoring are categorised as experimental and theoretical. In theoretical methods, a model is developed and equations of motion are solved. Through this the vibration behaviour of bearings can be predicted.
As bearing rotates, the rolling elements change their positions. developed a model for studying vibrations produced by bearings carrying spalling etc.
http://www.iaeme.com/IJMET/index.
International Journal of Mechanical Engineering and Technology (IJMET)Volume 8, Issue 6, June 2017, pp.
http://www.iaeme.com/IJME6340 and ISSN Online: 0976
Publication
A THEORETICAL MODEL BALL BEARING FOR PREEFFECT OF LOCALIZED
M. Tech., BVDU -
Professor, BVDU -
This paper discusses the modelling of ball bearing for predicting the presence of defects on outer and inner races. A computer program in Matlab is developed and DOF equations are solved. The output of the program is time domain signal of the bearing. The program takes into consideration the size of the defects, location of the defect and also the effect of changing the load on the bearing. The vibration signal btained through modelling is analysed for frequencies. The peaks at the
characteristic defect frequencies in the spectrum indicate the location of the fault on
ball bearing, size of defects, location of defects, vibration signals, defectfrequencies, spectrum indicator, fault on racesCite this Article: Arundhati Garad and Prof. V. J. ShindeDeep Groove Ball Bearing for Predicting the Effect of Localized Defects on
International Journal of Mechanical E769.
aeme.com/IJME
INTRODUCTION Various sources of vibration in any machine are unbalance, misalignment, faulty gear and faulty bearing etc. Among these the If a bearing fails, the entire production line is affected and ultimately, it will affect the productivity. Hence it is important that the rolling element bearings are monitored regularly
ing their health. Mainly the methods of monitoring are categorised as experimental and theoretical. In theoretical methods, a model is developed and equations of motion are solved. Through this the vibration behaviour of bearings can be predicted.
ing rotates, the rolling elements change their positions. developed a model for studying vibrations produced by bearings carrying spalling etc.
IJMET/index.asp
International Journal of Mechanical Engineering and Technology (IJMET)2017, pp. 760–769, Article ID: IJM
http://www.iaeme.com/IJMESN Online: 0976
Scopus Indexed
A THEORETICAL MODEL BALL BEARING FOR PREEFFECT OF LOCALIZED
VIBRATIONSArundhati Garad
- Bharati Vidyapeeth Deemed University
Pro- Bharati Vidyapeeth Deemed University, Pune, India
This paper discusses the modelling of ball bearing for predicting the presence of defects on outer and inner races. A computer program in Matlab is developed and DOF equations are solved. The output of the program is time domain signal of the bearing. The program takes into consideration the size of the defects, location of the defect and also the effect of changing the load on the bearing. The vibration signal btained through modelling is analysed for frequencies. The peaks at the
characteristic defect frequencies in the spectrum indicate the location of the fault on
ball bearing, size of defects, location of defects, vibration signals, defectfrequencies, spectrum indicator, fault on races
Arundhati Garad and Prof. V. J. ShindeDeep Groove Ball Bearing for Predicting the Effect of Localized Defects on
International Journal of Mechanical E
aeme.com/IJMET/issues.asp?JType=IJMET&VType=8&IType=6
Various sources of vibration in any machine are unbalance, misalignment, faulty gear and faulty bearing etc. Among these the rolling element bearing is If a bearing fails, the entire production line is affected and ultimately, it will affect the productivity. Hence it is important that the rolling element bearings are monitored regularly
ing their health. Mainly the methods of monitoring are categorised as experimental and theoretical. In theoretical methods, a model is developed and equations of motion are solved. Through this the vibration behaviour of bearings can be predicted.
ing rotates, the rolling elements change their positions. developed a model for studying vibrations produced by bearings carrying spalling etc.
asp 760
International Journal of Mechanical Engineering and Technology (IJMET)Article ID: IJM
http://www.iaeme.com/IJMET/issues.asp?JType=IJMESN Online: 0976-6359
Indexed
A THEORETICAL MODEL BALL BEARING FOR PREEFFECT OF LOCALIZED
VIBRATIONSArundhati Garad
Bharati Vidyapeeth Deemed University
Prof. V. J. Shinde Bharati Vidyapeeth Deemed University, Pune, India
This paper discusses the modelling of ball bearing for predicting the presence of defects on outer and inner races. A computer program in Matlab is developed and DOF equations are solved. The output of the program is time domain signal of the bearing. The program takes into consideration the size of the defects, location of the defect and also the effect of changing the load on the bearing. The vibration signal btained through modelling is analysed for frequencies. The peaks at the
characteristic defect frequencies in the spectrum indicate the location of the fault on
ball bearing, size of defects, location of defects, vibration signals, defectfrequencies, spectrum indicator, fault on races.
Arundhati Garad and Prof. V. J. ShindeDeep Groove Ball Bearing for Predicting the Effect of Localized Defects on
International Journal of Mechanical E
asp?JType=IJMET&VType=8&IType=6
Various sources of vibration in any machine are unbalance, misalignment, faulty gear and rolling element bearing is
If a bearing fails, the entire production line is affected and ultimately, it will affect the productivity. Hence it is important that the rolling element bearings are monitored regularly
ing their health. Mainly the methods of monitoring are categorised as experimental and theoretical. In theoretical methods, a model is developed and equations of motion are solved. Through this the vibration behaviour of bearings can be predicted.
ing rotates, the rolling elements change their positions. developed a model for studying vibrations produced by bearings carrying spalling etc.
International Journal of Mechanical Engineering and Technology (IJMET)Article ID: IJMET_08_06
asp?JType=IJME
A THEORETICAL MODEL OF DEEP GROOVE BALL BEARING FOR PREDICTING THE EFFECT OF LOCALIZED DEFECTS ON
VIBRATIONS Arundhati Garad
Bharati Vidyapeeth Deemed University
f. V. J. Shinde Bharati Vidyapeeth Deemed University, Pune, India
This paper discusses the modelling of ball bearing for predicting the presence of defects on outer and inner races. A computer program in Matlab is developed and DOF equations are solved. The output of the program is time domain signal of the bearing. The program takes into consideration the size of the defects, location of the defect and also the effect of changing the load on the bearing. The vibration signal btained through modelling is analysed for frequencies. The peaks at the
characteristic defect frequencies in the spectrum indicate the location of the fault on
ball bearing, size of defects, location of defects, vibration signals, defect
Arundhati Garad and Prof. V. J. ShindeDeep Groove Ball Bearing for Predicting the Effect of Localized Defects on
International Journal of Mechanical Engineering and Technology
asp?JType=IJMET&VType=8&IType=6
Various sources of vibration in any machine are unbalance, misalignment, faulty gear and rolling element bearing is the important machine element.
If a bearing fails, the entire production line is affected and ultimately, it will affect the productivity. Hence it is important that the rolling element bearings are monitored regularly
ing their health. Mainly the methods of monitoring are categorised as experimental and theoretical. In theoretical methods, a model is developed and equations of motion are solved. Through this the vibration behaviour of bearings can be predicted.
ing rotates, the rolling elements change their positions. developed a model for studying vibrations produced by bearings carrying spalling etc.
International Journal of Mechanical Engineering and Technology (IJMET) 06_080
asp?JType=IJMET&VType=8&IType=6
OF DEEP GROOVE DICTING THE DEFECTS ON
Bharati Vidyapeeth Deemed University, Pune
Bharati Vidyapeeth Deemed University, Pune, India
This paper discusses the modelling of ball bearing for predicting the presence of defects on outer and inner races. A computer program in Matlab is developed and DOF equations are solved. The output of the program is time domain signal of the bearing. The program takes into consideration the size of the defects, location of the defect and also the effect of changing the load on the bearing. The vibration signal btained through modelling is analysed for frequencies. The peaks at the
characteristic defect frequencies in the spectrum indicate the location of the fault on
ball bearing, size of defects, location of defects, vibration signals, defect
Arundhati Garad and Prof. V. J. Shinde. A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on
ngineering and Technology
asp?JType=IJMET&VType=8&IType=6
Various sources of vibration in any machine are unbalance, misalignment, faulty gear and the important machine element.
If a bearing fails, the entire production line is affected and ultimately, it will affect the productivity. Hence it is important that the rolling element bearings are monitored regularly
ing their health. Mainly the methods of monitoring are categorised as experimental and theoretical. In theoretical methods, a model is developed and equations of motion are solved. Through this the vibration behaviour of bearings can be predicted.
ing rotates, the rolling elements change their positions. In 1978 developed a model for studying vibrations produced by bearings carrying spalling etc.
T&VType=8&IType=6
OF DEEP GROOVE DICTING THE DEFECTS ON
Pune, India
Bharati Vidyapeeth Deemed University, Pune, India
This paper discusses the modelling of ball bearing for predicting the presence of defects on outer and inner races. A computer program in Matlab is developed and DOF equations are solved. The output of the program is time domain signal of the bearing. The program takes into consideration the size of the defects, location of the defect and also the effect of changing the load on the bearing. The vibration signal btained through modelling is analysed for frequencies. The peaks at the
characteristic defect frequencies in the spectrum indicate the location of the fault on
ball bearing, size of defects, location of defects, vibration signals, defect
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on
ngineering and Technology, 8(6),
asp?JType=IJMET&VType=8&IType=6
Various sources of vibration in any machine are unbalance, misalignment, faulty gear and the important machine element.
If a bearing fails, the entire production line is affected and ultimately, it will affect the productivity. Hence it is important that the rolling element bearings are monitored regularly
ing their health. Mainly the methods of monitoring are categorised as experimental and theoretical. In theoretical methods, a model is developed and equations of motion are
In 1978 Sunnersjo [1]
developed a model for studying vibrations produced by bearings carrying spalling etc.
T&VType=8&IType=6
OF DEEP GROOVE DICTING THE DEFECTS ON
This paper discusses the modelling of ball bearing for predicting the presence of defects on outer and inner races. A computer program in Matlab is developed and 2 DOF equations are solved. The output of the program is time domain signal of the bearing. The program takes into consideration the size of the defects, location of the defect and also the effect of changing the load on the bearing. The vibration signal btained through modelling is analysed for frequencies. The peaks at the
characteristic defect frequencies in the spectrum indicate the location of the fault on
ball bearing, size of defects, location of defects, vibration signals, defect
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on
, 8(6),
Various sources of vibration in any machine are unbalance, misalignment, faulty gear and the important machine element.
If a bearing fails, the entire production line is affected and ultimately, it will affect the productivity. Hence it is important that the rolling element bearings are monitored regularly
ing their health. Mainly the methods of monitoring are categorised as experimental and theoretical. In theoretical methods, a model is developed and equations of motion are
Sunnersjo [1] developed a model for studying vibrations produced by bearings carrying spalling etc. Tandon
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and Choudhury [2]bearings with defects those may occur on the surface of bearing. McFadden and Smith [4], [5] in their models have discussed the effect of single as well as multi point defects obearing. Tandon and Choudhury [6] have developed an analytical model considering the defects on races and ball. The load was simulated on bearing in axial and radial direction. The different shapes of pulses are considered for modelling the considered mass of the shaft along with mass of bearing to develop the vibration model. Patil et al. [8] have considered the bearing vibrations in the form of sine wave in the dynamic model. The theoretical models developed for monitoring health of bearings. Kulkarni and Sahasrabudhe [9] have simulated the defect pulse produced by the striking of defect by balls as cubic hermite spline.
2. MATHEMATICAL MODEL OWhile devmounted at the end of the shaft. The bearing is supported in bearing casing on which radial load is applied. The magnitude of the load is changed in the program to understand the of load on the vibrations of the bearing.
The bearing is subjected to a rotating force which causes the system to undergo vibrations in the dynamic state. In the mathematical model, the ball bearings are considered as a nonlinear spring
The model presented here considers the fixed outer race, loaded radially with a rotating force and the imbalanced force acting as a combination. The imbalanced force considered is the result of residual imba
As per ISO 1940Permissible unbalance in gm
quality grade in mm/sec=0.4 for spindles and drives of highin kg = 4 kg
While developing the model, the assumptions considered are mentioned bel The ball bearing model has equi
There is no Slipping of the balls
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and Choudhury [2]bearings with defects. A book by Harris [3] discusses a detailed study on different types of defects those may occur on the surface of bearing. McFadden and Smith [4], [5] in their models have discussed the effect of single as well as multi point defects obearing. Tandon and Choudhury [6] have developed an analytical model considering the defects on races and ball. The load was simulated on bearing in axial and radial direction. The different shapes of pulses are considered for modelling the considered mass of the shaft along with mass of bearing to develop the vibration model. Patil et al. [8] have considered the bearing vibrations in the form of sine wave in the dynamic model. The theoretical models developed for monitoring health of bearings. Kulkarni and Sahasrabudhe [9] have simulated the defect pulse produced by the striking of defect by balls as cubic hermite spline.
MATHEMATICAL MODEL OWhile developing the mathematical model of bearing, it is assumed that the bearing is mounted at the end of the shaft. The bearing is supported in bearing casing on which radial load is applied. The magnitude of the load is changed in the program to understand the of load on the vibrations of the bearing.
The bearing is subjected to a rotating force which causes the system to undergo vibrations in the dynamic state. In the mathematical model, the ball bearings are considered as a nonlinear spring-mass syste
The model presented here considers the fixed outer race, loaded radially with a rotating force and the imbalanced force acting as a combination. The imbalanced force considered is the result of residual imba
As per ISO 1940-1:2003(E)Permissible unbalance in gm
quality grade in mm/sec=0.4 for spindles and drives of highin kg = 4 kg
While developing the model, the assumptions considered are mentioned belThe ball bearing model has equi
There is no Slipping of the balls
http://www.iaeme.com/IJMET/index.
and Choudhury [2] discussed various measurement methods for diagnosis of health of defects. A book by Harris [3] discusses a detailed study on different types of
defects those may occur on the surface of bearing. McFadden and Smith [4], [5] in their models have discussed the effect of single as well as multi point defects obearing. Tandon and Choudhury [6] have developed an analytical model considering the defects on races and ball. The load was simulated on bearing in axial and radial direction. The different shapes of pulses are considered for modelling the considered mass of the shaft along with mass of bearing to develop the vibration model. Patil et al. [8] have considered the bearing vibrations in the form of sine wave in the dynamic model. The theoretical models developed for monitoring health of bearings. Kulkarni and Sahasrabudhe [9] have simulated the defect pulse produced by the striking of defect by balls as cubic hermite spline.
MATHEMATICAL MODEL Oeloping the mathematical model of bearing, it is assumed that the bearing is
mounted at the end of the shaft. The bearing is supported in bearing casing on which radial load is applied. The magnitude of the load is changed in the program to understand the of load on the vibrations of the bearing.
The bearing is subjected to a rotating force which causes the system to undergo vibrations in the dynamic state. In the mathematical model, the ball bearings are considered as a non
mass system. Fig. 1 shows a bearing subjected to loading. The model presented here considers the fixed outer race, loaded radially with a rotating
force and the imbalanced force acting as a combination. The imbalanced force considered is the result of residual imbalance left in the system.
Figure
1:2003(E) Permissible unbalance in gm
quality grade in mm/sec=0.4 for spindles and drives of high
While developing the model, the assumptions considered are mentioned belThe ball bearing model has equi
There is no Slipping of the balls
Arundhati Garad and Prof. V. J. Shinde
IJMET/index.asp
discussed various measurement methods for diagnosis of health of defects. A book by Harris [3] discusses a detailed study on different types of
defects those may occur on the surface of bearing. McFadden and Smith [4], [5] in their models have discussed the effect of single as well as multi point defects obearing. Tandon and Choudhury [6] have developed an analytical model considering the defects on races and ball. The load was simulated on bearing in axial and radial direction. The different shapes of pulses are considered for modelling the considered mass of the shaft along with mass of bearing to develop the vibration model. Patil et al. [8] have considered the bearing vibrations in the form of sine wave in the dynamic model. The theoretical models developed for monitoring health of bearings. Kulkarni and Sahasrabudhe [9] have simulated the defect pulse produced by the striking of defect by balls as cubic hermite spline.
MATHEMATICAL MODEL Oeloping the mathematical model of bearing, it is assumed that the bearing is
mounted at the end of the shaft. The bearing is supported in bearing casing on which radial load is applied. The magnitude of the load is changed in the program to understand the of load on the vibrations of the bearing.
The bearing is subjected to a rotating force which causes the system to undergo vibrations in the dynamic state. In the mathematical model, the ball bearings are considered as a non
m. Fig. 1 shows a bearing subjected to loading. The model presented here considers the fixed outer race, loaded radially with a rotating
force and the imbalanced force acting as a combination. The imbalanced force considered is lance left in the system.
Figure 1 Bearing subjected to radial load
Permissible unbalance in gm-mm Uper= 1000 (eper.Ω) M/Ωquality grade in mm/sec=0.4 for spindles and drives of high
While developing the model, the assumptions considered are mentioned belThe ball bearing model has equi-spaced
There is no Slipping of the balls
Arundhati Garad and Prof. V. J. Shinde
asp 761
discussed various measurement methods for diagnosis of health of defects. A book by Harris [3] discusses a detailed study on different types of
defects those may occur on the surface of bearing. McFadden and Smith [4], [5] in their models have discussed the effect of single as well as multi point defects obearing. Tandon and Choudhury [6] have developed an analytical model considering the defects on races and ball. The load was simulated on bearing in axial and radial direction. The different shapes of pulses are considered for modelling the considered mass of the shaft along with mass of bearing to develop the vibration model. Patil et al. [8] have considered the bearing vibrations in the form of sine wave in the dynamic model. The theoretical models developed for bearing defect modelling gives accurate results for monitoring health of bearings. Kulkarni and Sahasrabudhe [9] have simulated the defect pulse produced by the striking of defect by balls as cubic hermite spline.
MATHEMATICAL MODEL OF SYSTEMeloping the mathematical model of bearing, it is assumed that the bearing is
mounted at the end of the shaft. The bearing is supported in bearing casing on which radial load is applied. The magnitude of the load is changed in the program to understand the
The bearing is subjected to a rotating force which causes the system to undergo vibrations
in the dynamic state. In the mathematical model, the ball bearings are considered as a nonm. Fig. 1 shows a bearing subjected to loading.
The model presented here considers the fixed outer race, loaded radially with a rotating force and the imbalanced force acting as a combination. The imbalanced force considered is
lance left in the system.
Bearing subjected to radial load
mm Uper= 1000 (eper.Ω) M/Ωquality grade in mm/sec=0.4 for spindles and drives of high
While developing the model, the assumptions considered are mentioned belspaced
Arundhati Garad and Prof. V. J. Shinde
discussed various measurement methods for diagnosis of health of defects. A book by Harris [3] discusses a detailed study on different types of
defects those may occur on the surface of bearing. McFadden and Smith [4], [5] in their models have discussed the effect of single as well as multi point defects obearing. Tandon and Choudhury [6] have developed an analytical model considering the defects on races and ball. The load was simulated on bearing in axial and radial direction. The different shapes of pulses are considered for modelling the defects. Patel et al. [7] have considered mass of the shaft along with mass of bearing to develop the vibration model. Patil et al. [8] have considered the bearing vibrations in the form of sine wave in the dynamic
for bearing defect modelling gives accurate results for monitoring health of bearings. Kulkarni and Sahasrabudhe [9] have simulated the defect pulse produced by the striking of defect by balls as cubic hermite spline.
F SYSTEM eloping the mathematical model of bearing, it is assumed that the bearing is
mounted at the end of the shaft. The bearing is supported in bearing casing on which radial load is applied. The magnitude of the load is changed in the program to understand the
The bearing is subjected to a rotating force which causes the system to undergo vibrations in the dynamic state. In the mathematical model, the ball bearings are considered as a non
m. Fig. 1 shows a bearing subjected to loading. The model presented here considers the fixed outer race, loaded radially with a rotating
force and the imbalanced force acting as a combination. The imbalanced force considered is
Bearing subjected to radial load
mm Uper= 1000 (eper.Ω) M/Ωquality grade in mm/sec=0.4 for spindles and drives of high-precision systems
While developing the model, the assumptions considered are mentioned bel
Arundhati Garad and Prof. V. J. Shinde
discussed various measurement methods for diagnosis of health of defects. A book by Harris [3] discusses a detailed study on different types of
defects those may occur on the surface of bearing. McFadden and Smith [4], [5] in their models have discussed the effect of single as well as multi point defects obearing. Tandon and Choudhury [6] have developed an analytical model considering the defects on races and ball. The load was simulated on bearing in axial and radial direction. The
defects. Patel et al. [7] have considered mass of the shaft along with mass of bearing to develop the vibration model. Patil et al. [8] have considered the bearing vibrations in the form of sine wave in the dynamic
for bearing defect modelling gives accurate results for monitoring health of bearings. Kulkarni and Sahasrabudhe [9] have simulated the defect pulse produced by the striking of defect by balls as cubic hermite spline.
eloping the mathematical model of bearing, it is assumed that the bearing is mounted at the end of the shaft. The bearing is supported in bearing casing on which radial load is applied. The magnitude of the load is changed in the program to understand the
The bearing is subjected to a rotating force which causes the system to undergo vibrations in the dynamic state. In the mathematical model, the ball bearings are considered as a non
m. Fig. 1 shows a bearing subjected to loading. The model presented here considers the fixed outer race, loaded radially with a rotating
force and the imbalanced force acting as a combination. The imbalanced force considered is
Bearing subjected to radial load
mm Uper= 1000 (eper.Ω) M/Ω eper.Ω= selected balance precision systems
While developing the model, the assumptions considered are mentioned bel
discussed various measurement methods for diagnosis of health of defects. A book by Harris [3] discusses a detailed study on different types of
defects those may occur on the surface of bearing. McFadden and Smith [4], [5] in their models have discussed the effect of single as well as multi point defects on the races of bearing. Tandon and Choudhury [6] have developed an analytical model considering the defects on races and ball. The load was simulated on bearing in axial and radial direction. The
defects. Patel et al. [7] have considered mass of the shaft along with mass of bearing to develop the vibration model. Patil et al. [8] have considered the bearing vibrations in the form of sine wave in the dynamic
for bearing defect modelling gives accurate results for monitoring health of bearings. Kulkarni and Sahasrabudhe [9] have simulated the defect
eloping the mathematical model of bearing, it is assumed that the bearing is mounted at the end of the shaft. The bearing is supported in bearing casing on which radial load is applied. The magnitude of the load is changed in the program to understand the
The bearing is subjected to a rotating force which causes the system to undergo vibrations in the dynamic state. In the mathematical model, the ball bearings are considered as a non
The model presented here considers the fixed outer race, loaded radially with a rotating force and the imbalanced force acting as a combination. The imbalanced force considered is
eper.Ω= selected balance precision systems M=Rotor mass
While developing the model, the assumptions considered are mentioned below:
discussed various measurement methods for diagnosis of health of defects. A book by Harris [3] discusses a detailed study on different types of
defects those may occur on the surface of bearing. McFadden and Smith [4], [5] in their n the races of
bearing. Tandon and Choudhury [6] have developed an analytical model considering the defects on races and ball. The load was simulated on bearing in axial and radial direction. The
defects. Patel et al. [7] have considered mass of the shaft along with mass of bearing to develop the vibration model. Patil et al. [8] have considered the bearing vibrations in the form of sine wave in the dynamic
for bearing defect modelling gives accurate results for monitoring health of bearings. Kulkarni and Sahasrabudhe [9] have simulated the defect
eloping the mathematical model of bearing, it is assumed that the bearing is mounted at the end of the shaft. The bearing is supported in bearing casing on which radial load is applied. The magnitude of the load is changed in the program to understand the effect
The bearing is subjected to a rotating force which causes the system to undergo vibrations in the dynamic state. In the mathematical model, the ball bearings are considered as a non-
The model presented here considers the fixed outer race, loaded radially with a rotating force and the imbalanced force acting as a combination. The imbalanced force considered is
eper.Ω= selected balance M=Rotor mass
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
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The motions of race and balls occur in the plane of the bearing only.
The outer race is fixed in a rigid support.
There is no change in temperature of bearing
2.1. Motions and Load Different expressions for developing the bearing model are derived in book by Harris. A sketch of bearing with rotating inner race is shown in Fig. 2
Bearing load distribution with equation [3]:
=
where
=
In general the deflection ball located at any angular position given by:δ =where
x is deflection along X axis y is deflection along Y axi C is clearance
The elastic modulus for the contact of a ball with the inner race is
=The elastic modulus for the contact of a ball with the inner race is
=The effective elastic modulus K for the bearing system is written as
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
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The motions of race and balls occur in the plane of the bearing only.
The outer race is fixed in a rigid support.
There is no change in temperature of bearing
otions and Load Different expressions for developing the bearing model are derived in book by Harris. A sketch of bearing with rotating inner race is shown in Fig. 2
Bearing load distribution with equation [3]:
= 1 −
where
=
1 −
In general the deflection ball located at any angular position given by:= xcosθ + ysin
where θ is location of the ball.x is deflection along X axisy is deflection along Y axiC is clearance
The elastic modulus for the contact of a ball with the inner race is
= 3.12 × 10The elastic modulus for the contact of a ball with the inner race is
= 3.12 × 10The effective elastic modulus K for the bearing system is written as
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
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The motions of race and balls occur in the plane of the bearing only.
The outer race is fixed in a rigid support.
There is no change in temperature of bearing
otions and Load Distribution in a Ball BDifferent expressions for developing the bearing model are derived in book by Harris. A sketch of bearing with rotating inner race is shown in Fig. 2
Figure
Bearing load distribution with
− (1 −
In general the deflection ball located at any angular position given by:ysinθ − C
is location of the ball.x is deflection along X axisy is deflection along Y axiC is clearance
The elastic modulus for the contact of a ball with the inner race is
10 ∑ (The elastic modulus for the contact of a ball with the inner race is
10 ∑The effective elastic modulus K for the bearing system is written as
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
IJMET/index.asp
The motions of race and balls occur in the plane of the bearing only.
The outer race is fixed in a rigid support.
There is no change in temperature of bearing
Distribution in a Ball BDifferent expressions for developing the bearing model are derived in book by Harris. A sketch of bearing with rotating inner race is shown in Fig. 2
Figure 2 Bearing with rotating inner race
Bearing load distribution with respect to angular position of ball is calculated by the
Ψ)
In general the deflection ball located at any angular position given by:
is location of the ball. x is deflection along X axis y is deflection along Y axis
The elastic modulus for the contact of a ball with the inner race is ( ∗)
The elastic modulus for the contact of a ball with the inner race is ( ∗)
The effective elastic modulus K for the bearing system is written as
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on Vibrations
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The motions of race and balls occur in the plane of the bearing only.
The outer race is fixed in a rigid support.
There is no change in temperature of bearing
Distribution in a Ball BDifferent expressions for developing the bearing model are derived in book by Harris. A sketch of bearing with rotating inner race is shown in Fig. 2
Bearing with rotating inner race
respect to angular position of ball is calculated by the
In general the deflection ball located at any angular position given by:
The elastic modulus for the contact of a ball with the inner race is
N/mm The elastic modulus for the contact of a ball with the inner race is
N/mm The effective elastic modulus K for the bearing system is written as
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on Vibrations
The motions of race and balls occur in the plane of the bearing only.
Distribution in a Ball Bearing Different expressions for developing the bearing model are derived in book by Harris. A sketch of bearing with rotating inner race is shown in Fig. 2
Bearing with rotating inner race
respect to angular position of ball is calculated by the
In general the deflection ball located at any angular position given by:
The elastic modulus for the contact of a ball with the inner race is
The elastic modulus for the contact of a ball with the inner race is
The effective elastic modulus K for the bearing system is written as
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
The motions of race and balls occur in the plane of the bearing only.
Different expressions for developing the bearing model are derived in book by Harris. A
Bearing with rotating inner race
respect to angular position of ball is calculated by the
In general the deflection ball located at any angular position given by:
The elastic modulus for the contact of a ball with the inner race is
The elastic modulus for the contact of a ball with the inner race is
The effective elastic modulus K for the bearing system is written as
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
Different expressions for developing the bearing model are derived in book by Harris. A
respect to angular position of ball is calculated by the
(1)
(2)
(3)
(4)
(5)
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
Different expressions for developing the bearing model are derived in book by Harris. A
respect to angular position of ball is calculated by the
Arundhati Garad and Prof. V. J. Shinde
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= (6)
To compute effective elastic modulus (K) for bearing system, ( ) and ( ) are referred from Table 2 and ∗ and ∗ are based on Table 1.
Table 1 Dimensionless Contact Parameters
( ) ∗ 0 1
0.1075 0.9974 0.3204 0.9761 0.4795 0.9429 0.5916 0.9077 0.6716 0.8733 0.7332 0.8394 0.7948 0.7961 0.83495 0.7602 0.87366 0.7169 0.90999 0.6636 0.93657 0.6112 0.95738 0.5551 0.97290 0.4960 0.983797 0.4352 0.990902 0.3745 0.995112 0.3176 0.997300 0.2705 0.9981847 0.2427 0.9989156 0.2106 0.9994785 0.17167 0.9998527 0.11995
1 0
Table 2 Input Data for the model
Inner race diameter 52 mm Outer race diameter 25 mm Pitch diameter 39 mm Ball diameter 7.94 mm Normal Clearance 20 µm Radial load 212 N Mass of rotor 4 kg No of balls 9 Speed of rotor 2400 rpm Damping factor 200 Ns/m Contact angle 00
Knowing above parameters, the contact force (F) is
= {3.12 × 10 (∑ ) ( ∗) } (N) (7)
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
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2.2. Simulation of Defective BMathematical model is developed or defective bearing defect on inner and outer race. Fig. 3 shows a ball striking the defect on the race
While deriving the mathematical model, the presence of defect on the races is accounted for by modelling the defect as a sinusoidal wave.
respectively and describes the angular extent of the fault measured about the outer race centre. The cage angle at which the ball enters the fault
Similarly the cage angle at the exit edge is expressed as:
Δ =
Thus the additional deflection outer race can be determined as:
where h is depth of the defect. The defect on the outer race doesand is defined as:
=
The defect on inner race rotates with the speed of the shaft
2.3. Equation of MTaking x and y as the displacements along X and Y directions, the governing equations for a two degree of freedom system are formed.
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
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. Simulation of Defective BMathematical model is developed or defective bearing defect on inner and outer race. Fig. 3 shows a ball striking the defect on the race
While deriving the mathematical model, the presence of defect on the races is accounted for by modelling the defect as a sinusoidal wave.
and are the location of entry edge and exirespectively and describes the angular extent of the fault measured about the outer race centre. The cage angle at which the ball enters the fault
=
Similarly the cage angle at the exit edge is expressed as:
= ℎ
Thus the additional deflection outer race can be determined as:
Δ = ℎ
where h is depth of the defect. The defect on the outer race doesis defined as:= +
The defect on inner race rotates with the speed of the shaft= ( −
. Equation of MTaking x and y as the displacements along X and Y directions, the governing equations for a two degree of freedom system are formed.
+ + ∑
+ +
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
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. Simulation of Defective BMathematical model is developed or defective bearing defect on inner and outer race. Fig. 3 shows a ball striking the defect on the race
Figure
While deriving the mathematical model, the presence of defect on the races is accounted for by modelling the defect as a sinusoidal wave.
are the location of entry edge and exirespectively and describes the angular extent of the fault measured about the outer race centre. The cage angle at which the ball enters the fault
Similarly the cage angle at the exit edge is expressed as:
(
Thus the additional deflection outer race can be determined as:
−where h is depth of the defect. The defect on the outer race does
is defined as: ( − )
The defect on inner race rotates with the speed of the shaft) + (
. Equation of Motion Taking x and y as the displacements along X and Y directions, the governing equations for a two degree of freedom system are formed.
[(
[(
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
IJMET/index.asp
. Simulation of Defective BearingMathematical model is developed or defective bearing defect on inner and outer race. Fig. 3 shows a ball striking the defect on the race
Figure 3 Ball in the defective region of race [9]
While deriving the mathematical model, the presence of defect on the races is accounted for by modelling the defect as a sinusoidal wave.
are the location of entry edge and exirespectively and describes the angular extent of the fault measured about the outer race centre. The cage angle at which the ball enters the fault
Similarly the cage angle at the exit edge is expressed as:
( − )
Thus the additional deflection Δ for the travel of the ball in the defectiveouter race can be determined as:
( −
where h is depth of the defect. The defect on the outer race does
The defect on inner race rotates with the speed of the shaft( − )
otion Taking x and y as the displacements along X and Y directions, the governing equations for a two degree of freedom system are formed.
+
+
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on Vibrations
asp 764
earing Mathematical model is developed or defective bearing defect on inner and outer race. Fig. 3 shows a ball striking the defect on the race.
Ball in the defective region of race [9]
While deriving the mathematical model, the presence of defect on the races is accounted for by modelling the defect as a sinusoidal wave.
are the location of entry edge and exirespectively and describes the angular extent of the fault measured about the outer race centre. The cage angle at which the ball enters the fault
Similarly the cage angle at the exit edge is expressed as:
for the travel of the ball in the defective
)
where h is depth of the defect. The defect on the outer race does
The defect on inner race rotates with the speed of the shaft
Taking x and y as the displacements along X and Y directions, the governing equations for a two degree of freedom system are formed.
) − ( + ∆
) − ( + ∆
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on Vibrations
Mathematical model is developed or defective bearing defect on inner and outer race. Fig. 3
Ball in the defective region of race [9]
While deriving the mathematical model, the presence of defect on the races is accounted
are the location of entry edge and exit edge of the fault on the outer race respectively and describes the angular extent of the fault measured about the outer race centre.
is expressed as:
Similarly the cage angle at the exit edge is expressed as:
for the travel of the ball in the defective
where h is depth of the defect. The defect on the outer race does
The defect on inner race rotates with the speed of the shaft(
Taking x and y as the displacements along X and Y directions, the governing equations for a
∆)]
∆)]
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
Mathematical model is developed or defective bearing defect on inner and outer race. Fig. 3
Ball in the defective region of race [9]
While deriving the mathematical model, the presence of defect on the races is accounted
t edge of the fault on the outer race respectively and describes the angular extent of the fault measured about the outer race centre.
is expressed as:
for the travel of the ball in the defective
where h is depth of the defect. The defect on the outer race does not change its position
( ). Thus ϕ
Taking x and y as the displacements along X and Y directions, the governing equations for a
= +
=
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
Mathematical model is developed or defective bearing defect on inner and outer race. Fig. 3
While deriving the mathematical model, the presence of defect on the races is accounted
t edge of the fault on the outer race respectively and describes the angular extent of the fault measured about the outer race centre.
(8)
(9)
for the travel of the ball in the defective region of the
(10)
not change its position
(11)
ϕt is defined as: (12)
Taking x and y as the displacements along X and Y directions, the governing equations for a
(1
(1
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
Mathematical model is developed or defective bearing defect on inner and outer race. Fig. 3
While deriving the mathematical model, the presence of defect on the races is accounted
t edge of the fault on the outer race respectively and describes the angular extent of the fault measured about the outer race centre.
region of the
not change its position
)
is defined as: )
Taking x and y as the displacements along X and Y directions, the governing equations for a
(13)
14)
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In above equations, over the defect. The unbalance force The damping in this system is represented by an equivalent viscous damping
3. COMPUTATIONAL PROCEDUsing Euler’s method Eqs. (13) andand their time derivatives are obtained. Initial conditions of x and y are 10later modified according to acceleration values to account for steady state condition. The time step of MATLAB is developed for solving the equations.
4. RESULTS AND DISCUSSI
4.1. Variation of Defect Size on Outer Race Defect with Constant L
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In above equations, over the defect. The unbalance force The damping in this system is represented by an equivalent viscous damping
COMPUTATIONAL PROCEDUsing Euler’s method Eqs. (13) andand their time derivatives are obtained. Initial conditions of x and y are 10later modified according to acceleration values to account for steady state condition. The time step of 6.95x10-6 MATLAB is developed for solving the equations.
RESULTS AND DISCUSSI
. Variation of Defect Size on Outer Race Defect with Constant L
http://www.iaeme.com/IJMET/index.
In above equations, ∆ term corresponds to additional deflection for the coover the defect. The unbalance force The damping in this system is represented by an equivalent viscous damping
COMPUTATIONAL PROCEDUsing Euler’s method Eqs. (13) andand their time derivatives are obtained. Initial conditions of x and y are 10later modified according to acceleration values to account for steady state condition. The time
sec has been considered in the computation. A computer program in MATLAB is developed for solving the equations.
RESULTS AND DISCUSSI
. Variation of Defect Size on Outer Race Defect with Constant L
Arundhati Garad and Prof. V. J. Shinde
IJMET/index.asp
term corresponds to additional deflection for the coover the defect. The unbalance force accounts for the residual imbalance left in the system. The damping in this system is represented by an equivalent viscous damping
COMPUTATIONAL PROCEDUsing Euler’s method Eqs. (13) and (14) are solved and displacements in X and Y directions and their time derivatives are obtained. Initial conditions of x and y are 10later modified according to acceleration values to account for steady state condition. The time
sec has been considered in the computation. A computer program in MATLAB is developed for solving the equations.
RESULTS AND DISCUSSION
. Variation of Defect Size on Outer Race Defect with Constant L
0.1
0.4
Arundhati Garad and Prof. V. J. Shinde
asp 765
term corresponds to additional deflection for the coaccounts for the residual imbalance left in the system.
The damping in this system is represented by an equivalent viscous damping
COMPUTATIONAL PROCEDURE (14) are solved and displacements in X and Y directions
and their time derivatives are obtained. Initial conditions of x and y are 10later modified according to acceleration values to account for steady state condition. The time
sec has been considered in the computation. A computer program in MATLAB is developed for solving the equations.
ON
. Variation of Defect Size on Outer Race Defect with Constant L
0.1 mm defect
0.4 mm defect
1 mm defect
Arundhati Garad and Prof. V. J. Shinde
term corresponds to additional deflection for the coaccounts for the residual imbalance left in the system.
The damping in this system is represented by an equivalent viscous damping
(14) are solved and displacements in X and Y directions and their time derivatives are obtained. Initial conditions of x and y are 10later modified according to acceleration values to account for steady state condition. The time
sec has been considered in the computation. A computer program in
. Variation of Defect Size on Outer Race Defect with Constant L
mm defect
mm defect
1 mm defect
Arundhati Garad and Prof. V. J. Shinde
term corresponds to additional deflection for the coaccounts for the residual imbalance left in the system.
The damping in this system is represented by an equivalent viscous damping
(14) are solved and displacements in X and Y directions and their time derivatives are obtained. Initial conditions of x and y are 10later modified according to acceleration values to account for steady state condition. The time
sec has been considered in the computation. A computer program in
. Variation of Defect Size on Outer Race Defect with Constant L
term corresponds to additional deflection for the contact of each ball accounts for the residual imbalance left in the system.
The damping in this system is represented by an equivalent viscous damping c.
(14) are solved and displacements in X and Y directions and their time derivatives are obtained. Initial conditions of x and y are 10-6 are chosen and later modified according to acceleration values to account for steady state condition. The time
sec has been considered in the computation. A computer program in
. Variation of Defect Size on Outer Race Defect with Constant Load
ntact of each ball accounts for the residual imbalance left in the system.
(14) are solved and displacements in X and Y directions are chosen and
later modified according to acceleration values to account for steady state condition. The time sec has been considered in the computation. A computer program in
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It is clear based on different cases shown in Fig. 4 that as defect size increases the peak at the outer race defect frequency increases. This correspobearings.
4.2. Variation of
Fig. 5 shows the time domain signal obtained through matlab program.
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
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It is clear based on different cases shown in Fig. 4 that as defect size increases the peak at the outer race defect frequency increases. This correspobearings.
Variation of
Fig
Fig. 5 shows the time domain signal obtained through matlab program.
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
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Figure 4
It is clear based on different cases shown in Fig. 4 that as defect size increases the peak at the outer race defect frequency increases. This correspo
Variation of Load for
Figure 5 Simulated vibration signal with defect on inner race.
Fig. 5 shows the time domain signal obtained through matlab program.
Figure
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1.5
4 Effect of defect size on vibrations of bearing.
It is clear based on different cases shown in Fig. 4 that as defect size increases the peak at the outer race defect frequency increases. This correspo
oad for Inner Race
Simulated vibration signal with defect on inner race.
Fig. 5 shows the time domain signal obtained through matlab program.
6 Spectrum of
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on Vibrations
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1.5 mm defect
Effect of defect size on vibrations of bearing.
It is clear based on different cases shown in Fig. 4 that as defect size increases the peak at the outer race defect frequency increases. This correspo
ace Defect
Simulated vibration signal with defect on inner race.
Fig. 5 shows the time domain signal obtained through matlab program.
Spectrum of bearing with inner race defect.
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on Vibrations
mm defect
Effect of defect size on vibrations of bearing.
It is clear based on different cases shown in Fig. 4 that as defect size increases the peak at the outer race defect frequency increases. This corresponds to the progressive degradation in
Simulated vibration signal with defect on inner race.
Fig. 5 shows the time domain signal obtained through matlab program.
bearing with inner race defect.
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
Effect of defect size on vibrations of bearing.
It is clear based on different cases shown in Fig. 4 that as defect size increases the peak at nds to the progressive degradation in
Simulated vibration signal with defect on inner race.
Fig. 5 shows the time domain signal obtained through matlab program.
bearing with inner race defect.
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
It is clear based on different cases shown in Fig. 4 that as defect size increases the peak at nds to the progressive degradation in
Simulated vibration signal with defect on inner race.
Fig. 5 shows the time domain signal obtained through matlab program.
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
It is clear based on different cases shown in Fig. 4 that as defect size increases the peak at nds to the progressive degradation in
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The spectrum of the bearing with faulty inner race is shown in Fig. 6. The peak at 220 Hz indicate that the defect is present on the inner race.
Various cases discussed in Fig. 7 are with respect to what happens when the load on bearing is changed.
The simulated study changes the intensity of load on the bearing. It is observed that as load is decreased, the peaks at inner race dehigh peak and at lower loads the peaks are low at the characteristic defect frequency.
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The spectrum of the bearing with faulty inner race is shown in Fig. 6. The peak at 220 Hz indicate that the defect is present on the inner race.
Various cases discussed in Fig. 7 are with respect to what happens when the load on bearing is changed.
The simulated study changes the intensity of load on the bearing. It is observed that as load is decreased, the peaks at inner race dehigh peak and at lower loads the peaks are low at the characteristic defect frequency.
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The spectrum of the bearing with faulty inner race is shown in Fig. 6. The peak at 220 Hz indicate that the defect is present on the inner race.
Figure
Various cases discussed in Fig. 7 are with respect to what happens when the load on bearing is changed.
The simulated study changes the intensity of load on the bearing. It is observed that as load is decreased, the peaks at inner race dehigh peak and at lower loads the peaks are low at the characteristic defect frequency.
Arundhati Garad and Prof. V. J. Shinde
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The spectrum of the bearing with faulty inner race is shown in Fig. 6. The peak at 220 Hz indicate that the defect is present on the inner race.
ure 7 Effect of load on vibratio
Various cases discussed in Fig. 7 are with respect to what happens when the load on
The simulated study changes the intensity of load on the bearing. It is observed that as load is decreased, the peaks at inner race dehigh peak and at lower loads the peaks are low at the characteristic defect frequency.
Arundhati Garad and Prof. V. J. Shinde
asp 767
The spectrum of the bearing with faulty inner race is shown in Fig. 6. The peak at 220 Hz indicate that the defect is present on the inner race.
600 N load
400 N load
200 N load
Effect of load on vibratio
Various cases discussed in Fig. 7 are with respect to what happens when the load on
The simulated study changes the intensity of load on the bearing. It is observed that as load is decreased, the peaks at inner race defect frequency reduces. . At higher loads, there is high peak and at lower loads the peaks are low at the characteristic defect frequency.
Arundhati Garad and Prof. V. J. Shinde
The spectrum of the bearing with faulty inner race is shown in Fig. 6. The peak at 220 Hz
600 N load
Effect of load on vibrations of bearing
Various cases discussed in Fig. 7 are with respect to what happens when the load on
The simulated study changes the intensity of load on the bearing. It is observed that as fect frequency reduces. . At higher loads, there is
high peak and at lower loads the peaks are low at the characteristic defect frequency.
Arundhati Garad and Prof. V. J. Shinde
The spectrum of the bearing with faulty inner race is shown in Fig. 6. The peak at 220 Hz
ns of bearing
Various cases discussed in Fig. 7 are with respect to what happens when the load on
The simulated study changes the intensity of load on the bearing. It is observed that as fect frequency reduces. . At higher loads, there is
high peak and at lower loads the peaks are low at the characteristic defect frequency.
The spectrum of the bearing with faulty inner race is shown in Fig. 6. The peak at 220 Hz
Various cases discussed in Fig. 7 are with respect to what happens when the load on
The simulated study changes the intensity of load on the bearing. It is observed that as fect frequency reduces. . At higher loads, there is
high peak and at lower loads the peaks are low at the characteristic defect frequency.
The spectrum of the bearing with faulty inner race is shown in Fig. 6. The peak at 220 Hz
Various cases discussed in Fig. 7 are with respect to what happens when the load on
The simulated study changes the intensity of load on the bearing. It is observed that as fect frequency reduces. . At higher loads, there is
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4.3. Effect of
The effect of unbalance present in the rotor is studied by unbalance of 100 gm at 2400 rpm. Fig. 9 shows significant peak at the rotational frequency which 40 Hz. This high peak at 1X corresponds to the unbalance
5. CONCLUSIONBased on the results presented in above section, it is concluded that the model based studies for assessing health of bearing provides reasonably good results. The model developed in the paper focuses on the effect of chanvibration behaviour o bearing. Additionally results are presented for effect of unbalanced rotor on vibrations of bearing.
REFERENCES[1]
[2]
[3]
[4]
[5]
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
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Effect of Unbalanced
Fig
The effect of unbalance present in the rotor is studied by unbalance of 100 gm at 2400 rpm. Fig. 9 shows significant peak at the rotational frequency which 40 Hz. This high peak at 1X corresponds to the unbalance
CONCLUSIONBased on the results presented in above section, it is concluded that the model based studies for assessing health of bearing provides reasonably good results. The model developed in the paper focuses on the effect of chanvibration behaviour o bearing. Additionally results are presented for effect of unbalanced rotor on vibrations of bearing.
REFERENCES C. S. Sunnersjo, “Varying compliance vibrations of rolling bear
and Vibration”, 58(3) (1978) 363
N. Tandon, A. Choudhury, “A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings”, Tribology International, 32 (1999) 469-480.
T. A. Harris, “Rolling Bearing Analysis”, Third Ed. John Wiley and Son’s, New York, USA (2001).
P. D. McFadden and J. D. Smith, defect in a rolling element bearing”, Journal of Sound and Vibration,
P. D. McFadden and J. D. Smith, defects in a rolling element bearing”, Journal of Sound and Vibration,73.
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
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nbalanced F
Figure 8 Time domain signal for unbalanced mass in the rotor
Figure
The effect of unbalance present in the rotor is studied by unbalance of 100 gm at 2400 rpm. Fig. 9 shows significant peak at the rotational frequency which 40 Hz. This high peak at 1X corresponds to the unbalance
CONCLUSIONS Based on the results presented in above section, it is concluded that the model based studies for assessing health of bearing provides reasonably good results. The model developed in the paper focuses on the effect of chanvibration behaviour o bearing. Additionally results are presented for effect of unbalanced rotor on vibrations of bearing.
REFERENCES C. S. Sunnersjo, “Varying compliance vibrations of rolling bearand Vibration”, 58(3) (1978) 363
N. Tandon, A. Choudhury, “A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings”, Tribology International, 32 (1999)
480.
A. Harris, “Rolling Bearing Analysis”, Third Ed. John Wiley and Son’s, New York, USA (2001).
P. D. McFadden and J. D. Smith, defect in a rolling element bearing”, Journal of Sound and Vibration,
P. D. McFadden and J. D. Smith, defects in a rolling element bearing”, Journal of Sound and Vibration,
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
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Force in the
Time domain signal for unbalanced mass in the rotor
ure 9 Spectrum for unbalance in the rotor
The effect of unbalance present in the rotor is studied by unbalance of 100 gm at 2400 rpm. Fig. 9 shows significant peak at the rotational frequency which 40 Hz. This high peak at 1X corresponds to the unbalance present in the rotor.
Based on the results presented in above section, it is concluded that the model based studies for assessing health of bearing provides reasonably good results. The model developed in the paper focuses on the effect of change in defect size and effect of change if the load on vibration behaviour o bearing. Additionally results are presented for effect of unbalanced rotor on vibrations of bearing.
C. S. Sunnersjo, “Varying compliance vibrations of rolling bearand Vibration”, 58(3) (1978) 363
N. Tandon, A. Choudhury, “A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings”, Tribology International, 32 (1999)
A. Harris, “Rolling Bearing Analysis”, Third Ed. John Wiley and Son’s, New York,
P. D. McFadden and J. D. Smith, defect in a rolling element bearing”, Journal of Sound and Vibration,
P. D. McFadden and J. D. Smith, defects in a rolling element bearing”, Journal of Sound and Vibration,
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on Vibrations
asp 768
orce in the Rotor
Time domain signal for unbalanced mass in the rotor
Spectrum for unbalance in the rotor
The effect of unbalance present in the rotor is studied by unbalance of 100 gm at 2400 rpm. Fig. 9 shows significant peak at the rotational frequency which 40 Hz. This high peak at
present in the rotor.
Based on the results presented in above section, it is concluded that the model based studies for assessing health of bearing provides reasonably good results. The model developed in the
ge in defect size and effect of change if the load on vibration behaviour o bearing. Additionally results are presented for effect of unbalanced
C. S. Sunnersjo, “Varying compliance vibrations of rolling bearand Vibration”, 58(3) (1978) 363-373.
N. Tandon, A. Choudhury, “A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings”, Tribology International, 32 (1999)
A. Harris, “Rolling Bearing Analysis”, Third Ed. John Wiley and Son’s, New York,
P. D. McFadden and J. D. Smith, “Model for the vibration produced by a single point defect in a rolling element bearing”, Journal of Sound and Vibration,
P. D. McFadden and J. D. Smith, “Model for the vibration produced by multiple point defects in a rolling element bearing”, Journal of Sound and Vibration,
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects on Vibrations
Time domain signal for unbalanced mass in the rotor
Spectrum for unbalance in the rotor
The effect of unbalance present in the rotor is studied by unbalance of 100 gm at 2400 rpm. Fig. 9 shows significant peak at the rotational frequency which 40 Hz. This high peak at
present in the rotor.
Based on the results presented in above section, it is concluded that the model based studies for assessing health of bearing provides reasonably good results. The model developed in the
ge in defect size and effect of change if the load on vibration behaviour o bearing. Additionally results are presented for effect of unbalanced
C. S. Sunnersjo, “Varying compliance vibrations of rolling bear
N. Tandon, A. Choudhury, “A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings”, Tribology International, 32 (1999)
A. Harris, “Rolling Bearing Analysis”, Third Ed. John Wiley and Son’s, New York,
Model for the vibration produced by a single point defect in a rolling element bearing”, Journal of Sound and Vibration,
Model for the vibration produced by multiple point defects in a rolling element bearing”, Journal of Sound and Vibration,
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
Time domain signal for unbalanced mass in the rotor
Spectrum for unbalance in the rotor
The effect of unbalance present in the rotor is studied by unbalance of 100 gm at 2400 rpm. Fig. 9 shows significant peak at the rotational frequency which 40 Hz. This high peak at
Based on the results presented in above section, it is concluded that the model based studies for assessing health of bearing provides reasonably good results. The model developed in the
ge in defect size and effect of change if the load on vibration behaviour o bearing. Additionally results are presented for effect of unbalanced
C. S. Sunnersjo, “Varying compliance vibrations of rolling bearings”, Journal of Sound
N. Tandon, A. Choudhury, “A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings”, Tribology International, 32 (1999)
A. Harris, “Rolling Bearing Analysis”, Third Ed. John Wiley and Son’s, New York,
Model for the vibration produced by a single point defect in a rolling element bearing”, Journal of Sound and Vibration,
Model for the vibration produced by multiple point defects in a rolling element bearing”, Journal of Sound and Vibration,
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
Time domain signal for unbalanced mass in the rotor
The effect of unbalance present in the rotor is studied by unbalance of 100 gm at 2400 rpm. Fig. 9 shows significant peak at the rotational frequency which 40 Hz. This high peak at
Based on the results presented in above section, it is concluded that the model based studies for assessing health of bearing provides reasonably good results. The model developed in the
ge in defect size and effect of change if the load on vibration behaviour o bearing. Additionally results are presented for effect of unbalanced
ings”, Journal of Sound
N. Tandon, A. Choudhury, “A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings”, Tribology International, 32 (1999)
A. Harris, “Rolling Bearing Analysis”, Third Ed. John Wiley and Son’s, New York,
Model for the vibration produced by a single point defect in a rolling element bearing”, Journal of Sound and Vibration, 96(1)(1984) 69
Model for the vibration produced by multiple point defects in a rolling element bearing”, Journal of Sound and Vibration, 98(2) (1985) 263
A Theoretical Model of Deep Groove Ball Bearing for Predicting the Effect of Localized Defects
The effect of unbalance present in the rotor is studied by unbalance of 100 gm at 2400 rpm. Fig. 9 shows significant peak at the rotational frequency which 40 Hz. This high peak at
Based on the results presented in above section, it is concluded that the model based studies for assessing health of bearing provides reasonably good results. The model developed in the
ge in defect size and effect of change if the load on vibration behaviour o bearing. Additionally results are presented for effect of unbalanced
ings”, Journal of Sound
N. Tandon, A. Choudhury, “A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings”, Tribology International, 32 (1999)
A. Harris, “Rolling Bearing Analysis”, Third Ed. John Wiley and Son’s, New York,
Model for the vibration produced by a single point 96(1)(1984) 69-82.
Model for the vibration produced by multiple point 98(2) (1985) 263–
Arundhati Garad and Prof. V. J. Shinde
http://www.iaeme.com/IJMET/index.asp 769 [email protected]
[6] N. Tandon, A. Choudhury, “An analytical model for the prediction of the vibration response of rolling element bearings due to a localized defect”, Journal of Sound and Vibration, 205(3) (1997)275–92.
[7] V. N. Patel, N. Tandon, R. K. Pandey, “A dynamic model for vibration studies of deep groove ball bearings considering single and multiple defects in races”, Journal of Tribology, 132 (2010) 041101-1-10.
[8] M.S.Patil, Jose Mathew, P.K.Rajendrakumar, Sandeep Desai, “A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing,” International Journal of Mechanical Sciences, 52 (2010) 1193–1201.
[9] P. G. Kulkarni, A. D. Sahasrabudhe, “A dynamic model of ball bearing for simulating localized defects on outer race using cubic hermite spline”, Journal of Mechanical Science and Technology, 28 (9) (2014) 3433-3442.
[10] Prof. Dr. Zena K. Kadhim and Hadi O. Mery. Free Convection From Optimum Sinusoidal Surface Exposed to Vertical Vibrations, International Journal of Mechanical Engineering and Technology, 7 (1), 2016, pp. 214-224.
[11] Prince Kumar and Sandeep Nasier, An Analytic and Constructive Approach to Control Seismic Vibrations in Buildings. International Journal of Civil Engineering and Technology, 7(5), 2016, pp.103–110.