Investigation of Static, Modal and Harmonic vibration analyses of Single Row SKF6205 Deep Groove Ball Bearing for thermal applications

Abstract

It is the necessary to predict the endurance capability of the mechanical element with its increased application and complexity. The present research work estimates the stress variation and displacement characteristics using finite element analyses of Single Row SKF6205 Deep Groove Ball Bearing under radial and axial loadings. The vibration analyses are evaluated in three aspects; static, modal, and harmonic analysis. The simulations show the variation of stress levels of the bearing in different loads. These results are used to predict the fatigue life, wear rate, and productivity of the ball bearing at various stochastic conditions.

Full text

* Corresponding author: thiagarajan.s@eec.srmrmp.edu.in
Investigation of Static, Modal and Harmonic vibration analyses
of Single Row SKF6205 Deep Groove Ball Bearing for thermal
applications
M. Raju1, S.Thiagarajan2*, D. Peter Pushpanathan3, S. Selvarasu4, S.Thirumavalavan5, R. Karthikeyan6
1,2,3Department of Mechanical Engineering, Easwari Engineering College, Ramapuram, Chennai, India
4,5Department of Mechanical Engineering, Arunai Engineering College, Thiruvannamalai, India,
6Department of Mechanical Engineering, Gokaraju Rangaraju Institute of Engineering and Technology, Hyderabad, India
Abstract. It is the necessary to predict the endurance capability of the mechanical element with its
increased application and complexity. The present research work estimates the stress variation and
displacement characteristics using finite element analyses of Single Row SKF6205 Deep Groove Ball
Bearing under radial and axial loadings. The vibration analyses are evaluated in three aspects; static, modal,
and harmonic analysis. The simulations show the variation of stress levels of the bearing in different loads.
These results are used to predict the fatigue life, wear rate, and productivity of the ball bearing at various
stochastic conditions.
1 Introduction
The ball bearing is one of the essential components for any
machine to rotate or to do its performance. So it is an essential
consideration to do structural analysis. This paper discusses
vibration analysis in all of its forms, including modal,
harmonic, and static. It describes how balanced fault-free ball
bearings vibrate. The restoring force of each ball in the load
zone is calculated by Hertzian contact theory as,
n
ii
FK

 (1)
Where K is known to be stiffness and n
i

is the radial
deformation. The expression for the radial deformation is
given by [2],
22
cos sin
n
iii
x
tyte
NN

 




(2)
It gives a detailed study on greases contaminated with
particles of different sizes and hardness that are tested to shed
new light [3]. There are two types of material used for the
manufacturing of the bearings such as polyetheretherketone
(PEEK) and polytetrafluoroethylene (PTFE). The inference
obtained is that the polyetheretherketone gives a low vibration.
The expression for calculating the coefficient of friction is
given by
*
*
FR
L
r




(3)
Where F is the force acting on the load cell, L is the axial load,
R is the distance between the centers of the load cell and the
bearing and r is the distance between the centers of the ball
and the bearing [4]. It gives the maximum contact forces on
the rolling element, which is done by the in-house developed
program and detailed finite element analysis of the contact
between the ball and the raceway. The force is given by,
1
n
tt
qF


 (4)
Illustrates the active magnetic bearing supported rotor as
misaligned cage-less backup bearings. The elasticity of the
rotor is modeled by the finite element method and the degree
of freedom is expressed using the component mode synthesis
[5]. The contact forces affecting the ball is obtained by,
3/2
()
tot tot
ici
FK

 (5)
The total stiffness coefficient,
3/2
2/3 2/3
11
tot
cin out
cc
KKK


 


 

 

(6)
, implies the updating of rotors supported on ball bearings by
inverse Eigen sensitivity method [6, 11]. It is used to identity
bearing stiffness, damping, and shaft material damping
parameters. The correlation is determined by the Modal
Assurance Criterion method, by the expression,
2
()
()()
iH j
FE X
iH j iH J
FE FE X X
MAC

 
 (7)
The modeling of angular contact ball bearings and axial
displacements for high-speed spindles equipped with angular
contact ball bearings [7-10] are predicted. The centrifugal
forces acting on bearing balls do not cause sleeve axial shifts.
The normal force,

https://doi.org/10.1051/e3sconf/202130
E3S Web of Conferences 309, 01096 (2021)
ICMED 2021
901096
© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative
Commons Attribution License 4.0
(http://creativecommons.org/licenses/by/4.0/).

0
0
cos(( ) / 2)
cos(( ) / 2)
i
NC
i
FF




 (8)
The tangential force,
0
0
sin
cos(( ) / 2)
PC
i
FF


 (9)
The above equations are useful in predicting the moving
sleeve positions, which has an influential impact on the
location of the rear spindle support and as a result on the
location of its tips.
2 Vibration analysis
In general, the vibration analysis is normally done in three
aspects such as static, modal, and harmonic analysis. The Pro-
e modal of ball bearing is converted into IGS format to import
it into the multi-physics software for undergoing finite
element analysis, namely ANSYS. The material used is M19
steel has a density of 7600 Kg/m3, Young’s modulus as 2e11
N/m2, and Poisson’s ratio as 0.3. The ball bearing specification
is listed in Table 1. The deformation in the X and Y direction
is shown in Fig 1 and Fig 2.
Table 1: Ball Bearing Specifications
S.no Parameters Dimensions
1 Inner bore diameter 25 mm
2 Outer ring diameter 52 mm
3 Pitch diameter 39 mm
4 Ball diameter 7.94 mm
5 Width 15 mm
6 Mass 0.13 Kg
2.1 Static Analysis
First, the IGES modal file is imported into the FEA
packages. The material assigned to the modal is plane 42 since
it is executed in 2D analysis. The static analysis is used to
show the displacement of the bearing due to its gravity and its
self-weight. Table 2 detailed the displacement due to static
conditions in X, Y direction, and vector sum.
Table 2: Displacement due to static loading
S.
No
Amplitude
(m)
X-Direction
displacement
Y-Direction
Displacement
Displacement
Vector Sum
1 Minimum - 0.207e-5 0 0
2 Maximum 0.026e5 0.414e-5 0.416e-5
Fig 1: Displacement in X-axis due to gravity
Fig 2: Displacement in Y-axis due to gravity
2.2 Modal Analysis
The modal analysis is used to calculate the natural
frequency of the bearings. In this analysis, the first five modes'
natural frequency is estimated. If in the case during rotation
the acoustic noises will be produced, if the vibrating and
natural frequency coincides with each other.
Fig 3: Mode 1 at 70.544 Hz

https://doi.org/10.1051/e3sconf/202130
E3S Web of Conferences 309, 01096 (2021)
ICMED 2021
901096
2

Fig 4: Mode 2 at 285.603 Hz
Fig 5: Mode 3 at 286.178 Hz
Fig 6: Mode 4 at 419.413 Hz.
Fig 7: Mode 5 at 420.612 Hz
Table 3: modal frequencies and displacement
Mode Frequency
(Hz)
Maximum
Displacement (m)
1 70.544 5.842e-3
2 285.603 6.960 e-3
3 286.178 6.998 e-3
4 419.413 7.600 e-3
5 420.612 7.720 e-3
Fig 3 to Fig 7 demonstrates the modal frequencies with their
corresponding frequencies. From these figures, it is evident
that the maximum displacement of the balls increases with
applied frequency. The maximum displacements of the balls
are resisted to the modular vibrations applied on the balls
under different frequency levels. The contours of the various
frequency levels and their displacements show the reaction
forces that act radially outward direction. Table 3 implies the
natural frequency and the corresponding displacement.
2.3 Harmonic Analysis
The harmonic analysis is used to estimate the amplitude of
vibration by the modal frequencies. The applied force is 100N.
Fig 8: Node 5109 of X-axis at inner race

https://doi.org/10.1051/e3sconf/202130
E3S Web of Conferences 309, 01096 (2021)
ICMED 2021
901096
3

Fig 9: Node 5109 of Y-axis at inner race
The displacements of bearing for 100 N applied force at 2500
Hz in the X-axis and Y-axis is shown in Fig. 8 and Fig.9
respectively at the inner race for node 5109.
Fig 10: Node 966 of X-axis at outer race
Fig 11: Node 966 of Y-axis at outer race
Fig 10 and Fig 11 are used to understand the amplitude
displacement for the outer race (Node 966). It is obvious that
for the 700 Hz frequency loading, the X axis inner race shows
higher displacement amplitude than the Y axis of bearing 5109
node. But for the 900 Hz frequency loading, the Y axis outer
race shows higher displacement amplitude than the X axis of
bearing 966 node. This is because of the unbalanced of
rotating elements (cage balls or rollers).
Table 4 shows the X-axis and Y-axis displacement variation
for various frequencies of node 5109 and 966 nodes
respectively.
Table 4: Harmonic analysis displacement and frequency
S.
No Node Axis Displacement
(m)
Frequency
(Hz)
1 5109
(Inner Race) X 3.60e-7 700
2 5109
(Inner Race) Y 0.23e-7 700
3 966
(Outer Race) X 0.60e-7 900
4 966
(Outer Race) Y 1.90e-7 900
3 Conclusion
As a method for assisting predictive and preventive
maintenance, vibration analysis is becoming incredibly
influential. Both time domain and frequency domain vibration
analyses may provide valuable information when tracking
rolling element bearings. The vibration analysis in the time
domain will reveal whether a bearing is operating abnormally
and display the amplitude increase trend. Vibration analysis in
the frequency domain may determine if the enhanced
vibrations are caused by a specific bearing defect or by
external causes. The increase in vibration energy on the
bearing's characteristic frequencies may also signify the
progress of that particular fault.
In this present research, the vibration analyses of Single
Row SKF6205 Deep Groove Ball Bearing are investigated. To
obtain the noiseless motion in its applications, various
analyses are performed. The static analysis in Table 2 shows
the displacement vector sum of the bearing due to its gravity
and its self-weight. The simulation results from Fig 1 and Fig
11, show the X-axis and Y-axis deformations in different
modes. The modal analysis is performed for five modes the
natural frequency of the bearings. Acoustic noises are
generated by the bearings during rotation when the vibrating
and natural frequencies correspond to each other. By the
harmonic analysis, with the applied force of 100 N, the
amplitude of the vibration of the nodes showed that the outer
race has less displacement than the inner race.
4 References
1. S.H. Ghafari, E.M. Abdel-Rahman, F. Golnaraghi, F.
Ismail, Journal of Sound and Vibration, 329(9), 1332
(2010)
2. D. Koulocheris, A. Stathis, T. Costopoulos, D. Tsantiotis,
Engineering Failure Analysis, 39, 164 (2014)
3. R.K. Sreenilayam-Raveendran, M.H. Azarian, C. Morillo,
M.G. Pecht, K. Kida, E.C. Santos, T. Honda, H. Koike,
Wear, 302(1-2), 1499 (2013)

https://doi.org/10.1051/e3sconf/202130
E3S Web of Conferences 309, 01096 (2021)
ICMED 2021
901096
4

4. P. Göncz, J. Flašker, and S. Glodež, Procedia
Engineering, 2(1), 1877 (2010)
5. O. Halminen, A. Kärkkäinen, J. Sopanen, A. Mikkola,
Mechanical Systems and Signal Processing, 50, 692
(2015)
6. T. Karacay, N. Akturk, Tribology International, 42(6),
836-(2009)
7. J. Jedrzejewski, W. Kwasny, CIRP annals, 59(1), 377
(2010)
8. G.K. Nikas, Proceedings of the Institution of Mechanical
Engineers, Part J: Journal of Engineering
Tribology, 224(5), 453 (2010)
9. M.M. Maru, R.S. Castillo, L.R. Padovese, Tribology
International, 40(3), 433 (2007)
10. S. Padmanabhan, S.Thiagarajan, A.D.R. Kumar, D.
Prabhakaran, M. Raju, Materials Today: Proceedings, 44,
3550 (2021)
11. R.S. Dwyer-Joyce, Wear, 233, 692 (1999)

https://doi.org/10.1051/e3sconf/202130
E3S Web of Conferences 309, 01096 (2021)
ICMED 2021
901096
5