International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 04, April 2019, pp. 9-16, Article ID: IJMET_10_04_002
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=4
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication
Scopus Indexed
FATIGUE ANALYSIS OF OUT-PUT SHAFT
SUBJECTED TO PURE TORSION
Nagaraj S B
M Tech Student, Mechanical Engineering Dept, N.M.I.T, Bengaluru, India
Chetan S
Professor, Department of mechanical, Nitte Meenakshi Institute of Technology,
Bangalore, India
Shyamaprasad S
Sr.Manager, Off-highway R&D) AVTEC Ltd, Hosur, Tamilnadu, India
Venugopal Nair
AGM (Off-highway R&D) AVTEC Ltd, Hosur, Tamilnadu, India
ABSTRACT
In material engineering it is important to determine the cause of the failure &
prevention of the failure .In present day the failure of the machine component is about
90% of the failure is because of the fatigue. In present study the failure of the shaft in
the yaw gear box is analyzed .As we the shaft is rotating part of the engine it transmit
the power from the one part of the engine to another part. It holds the maximum stress.
In this case shaft of heat treated component with ultimate tensile strength Su= 2100Mpa
is analysis done with ANSYS (FEA) software & compared with the theoretical
calculation. There are different methods which are used to predict fatigue life include
stress life(S-N), strain Life (E-N) and Linear Elastic Fracture Mechanics (LEFM). In
this project study, S-N approach is used to predict fatigue life for out-put shaft.
Key words: Shaft, FEA-ANSYS (16.2), SN-curve, Fatigue –life, Fatigue factor of
safety, Fatigue damage
Cite this Article: Nagaraj S B, Chetan S, Shyamaprasad S, Venugopal Nair, Fatigue
Analysis of Out-Put Shaft Subjected to Pure Torsion, International Journal of
Mechanical Engineering and Technology 10(4), 2019, pp. 9-16.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=4
1. INTRODUCTION
A shaft has a circular cross section & it is a rotating component used in almost all the machine
.It is used to transfer the energy from the one part to another part .A shaft usually not a uniform
cross section because it is mounted by the bearing, fly wheels, clutches & other machine
http://www.iaeme.com/IJMET/index.asp
9
editor@iaeme.com
Fatigue Analysis of Out-Put Shaft Subjected to Pure Torsion
elements are mounted on the shaft .In the present shaft of heat treated material is mounted by
spur gear with pressure angle of 200 & supported by the two bearing (Roller bearing)
Stress Analysis
Stress in the Shaft In actual practice there are three kinds of stress are induced in it. a.) Shear
stress by the transmission of the torque. b.) Bending stress by the force acting upon machine
element, and weight of shaft itself. c.) Stress from both combined torsional and bending loads.
2. SHAFT MATERIAL COMPOSITION
Material is used in the shaft is 18CrNiM06
Table 1 Chemical composition of 18CrNiM06
Composition
Carbon
Silicon
Nickel
Manganese
Phosphorus
Sulphur
Chromium
•
Tensile yield strength Sy =1790Mpa
•
Ultimate tensile strength Su =2100Mpa
•
Young’s modulus of material E = 207Gpa
•
Passion’s ratio = 0.3
•
Density 𝛿=7800 Kg.m3
Percentage
0.15-0.21
0.17-.35
1.40-1.70
0.25-0.35
0.035
0.015
1.50-1.80
2.1. Fatigue stress concentration
When there is an existence of the existence of irregularities or discontinuities, such as holes,
grooves, or notches, in a part increases the theoretical stresses significantly in the immediate
vicinity of the discontinuity defined a stress concentration factor Kt or Kts
Effective maximum stress is fatigue is
𝜎max = Kf 𝜎nom 𝜏max =Kfs 𝜏nom
(1)
Where Kf is a reduced value of Kt and is the nominal stress 𝜎0 . The factor Kf is commonly
referred as fatigue stress-concentration factor and hence the subscript f. The resulting factor is
defined by the equation
𝑀aximum stress in notched specim𝑒𝑛
Kf = Stress concentration notch free specime𝑛.
(2)
Kf =1+q (Kt −1) or Kfs=1+qshear (Kts−1)
Where q = Notch sensitivity factor
(3)
q=
1
(4)
√𝑎
1+
√𝑟
Where √𝑎= Neuber constant
r = Fillet radius
Neuber constant is given by the equation
http://www.iaeme.com/IJMET/index.asp
10
editor@iaeme.com
Nagaraj S B, Chetan S, Shyamaprasad S, Venugopal Nair
a. Bending: √a =0.246−3.08 (10−3) Sut+1.51(10−5 ) (Sut)^2−2.67(10−8) (Sut )^3 (5)
b. Torsion: √a =0.190−2.51 (10−3) Sut +1.35(10−5 ) (Sut) ^2−2.67 (10−8) (Sut) ^3 (6)
Applying Sut = 304.57 Ksi (1Ksi = 6.895 Mpa)
For the torsion = -0.045
1
q=
1+
=.9486
√.0765
√1.414
Where Kt = Stress concentration torsion
Graph stress concentration factor for torsion
Where r = Fillet radius
d = Diameter of smaller shaft
D = Diameter of larger shaft
𝑟
𝑑
2
𝐷
= 85 =.0235
𝑑
100
= 85 =1.1764
From the graph & question (3) Kt =1.85
Kfs =1+.9486(1.85-1)
=1.80631
2.2. Generation of SN Curve
Fatigue strength (Endurance limit𝑆 ᾽ ) of the shaft material was calculated as Sn = 0.5* UTS =
0.5* 2100 = 1050 N/mm2.Considering the corrections factors for endurance limit we find the
new endurance
Table 2 Factor affecting the fatigue life of the shaft
Load factor (𝑪𝑳 ):
Temperature (𝑪𝑻 )
Surface factor 𝑪𝒔
Reliability
factor (𝑪𝑹 )
Gradient factor
(𝑪𝑮 )
.58
1
.5
.897
.9
᾽
𝑆 = .5*Sut*𝐶𝐿 ∗ 𝐶𝑇 ∗ 𝐶𝑠 *𝐶𝑅 *𝐶𝐺 (7)
= .5*2100*.58*1*.5*.897*.9
= 245.822 Mpa
http://www.iaeme.com/IJMET/index.asp
11
editor@iaeme.com
Fatigue Analysis of Out-Put Shaft Subjected to Pure Torsion
2.3. Meshing of shaft
Figure 1 Meshing of shaft
Basic idea of FEM is to perform calculations at limited number of points called nodes and
interpolate the results for entire domain using interpolation functions. Any continuous object
has infinite degrees of freedom and such problems cannot be solved using this method. So this
method reduces the degrees of freedom from infinite to finite by making assumptions and by
discretization/meshing in other terms creating nodes and elements. Hexa-dominant mesh is
used, relevance center is fine & elements size is 3mm created the nodes 1141216 and elements
315798
2.4. Loads acting on shaft
Stepped shaft is subjected to a torque of value 47960 Nm to the location of “B” & fixed location
of the spur gear “A”.
Figure 2 Load acting on the shaft
http://www.iaeme.com/IJMET/index.asp
12
editor@iaeme.com
Nagaraj S B, Chetan S, Shyamaprasad S, Venugopal Nair
3. RESULT AND DISCUSSION
3.1. Shaft Shear stresses
Figure 3 Shear stress in Mpa
The maximum shear stress is shown in which appears in the cross-section of the shaft
𝜏𝑚𝑎𝑥 With the fatigue stress concentration kfs = 1.8
𝜏𝑚𝑎𝑥 = 397.73 * 1.8
= 715.914 Mpa
3.2. Equivalent alternating stress or Equivalent von-mises stress
Figure 4 Equivalent alternating stress in Mpa
Equivalent von-mises stress or alternating stress 𝜎𝑣
𝜎𝑣 = √3 ∗ 𝜏𝑚𝑎𝑥
2
= √3 ∗ 715.9142
= 1239.99 Mpa
In a Stress Life fatigue analysis, one always needs to be query an SN curve to relate the
fatigue life to the stress state. Thus of the “equivalent alternating stress” is the stress used to
http://www.iaeme.com/IJMET/index.asp
13
editor@iaeme.com
Fatigue Analysis of Out-Put Shaft Subjected to Pure Torsion
query the fatigue SN curve after accounting for fatigue loading type, mean stress effects,
multiaxial effects and any other factors in the fatigue analysis. Thus in a fatigue analysis, the
equivalent alternating stress can be thought of as the fast calculated quantity before determining
the fatigue life. The maximum value of the equivalent stress is 1244.6 Mpa, which takes place
in the cross-section of the shaft where the Roller -bearing was located.
3.3. Number of cycles
Figure 5 Showing the fatigue life
This represents the number of cycles until the part will fail due to fatigue
2500
2000
1500
4408,
1000
500
0
1
10
100
1000
10000
100000
1000000
Graph of theoretical calculation
http://www.iaeme.com/IJMET/index.asp
14
editor@iaeme.com
Nagaraj S B, Chetan S, Shyamaprasad S, Venugopal Nair
3.4. Factor of safety of fatigue life
Figure 6 Factor of safety
Endurance stress
Factor of safety of fatigue life =𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑎𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑠𝑠
Endurance stress = 245.82 Mpa
FOS =
245.82
1240
= .19824
3.5. Fatigue damage
Figure 7 Fatigue damage
Fatigue Damage is a contour plot of the fatigue damage at a given design life. Fatigue
damage is defined as the design life divided by the available life
Design life
Fatigue damage = Availble life
=
106
4408
= 226.86
http://www.iaeme.com/IJMET/index.asp
15
editor@iaeme.com
Fatigue Analysis of Out-Put Shaft Subjected to Pure Torsion
Table 2 Result of Comparison
Parameters
a. Shear stress in Mpa
b. Equivalent alternating in Mpa
c. Fatigue life cycles
d. Factor of safety
e. Fatigue damage
Analytical results
715.91
1239.99
4408
.1984
226.82
FEM results
718.58
1244.6
4330
.1975
232.52
4. CONCLUSIONS
Failure analysis of the shaft is investigated in detail. Force acting on the bearing due to the
torque is determined .Endurance limit & fatigue factor of safety is calculated. Fatigue life of
the shaft is estimated & fatigue damage is calculated. Forces and stresses are calculated by
using an analytical approach and ANSYS software. Both methods show that the stresses and
fatigue life are nearly same and in the admissible range.
1. From the static analysis it was observed that maximum stress is located at the change in the
cross-section area of the shaft it is found 1313 Mpa.
2. Fatigue life is found to be 4330 cycles.
3. Factor of safety is .1975<1 which means the design is not safety.
4. Fatigue damage at the given life is 232.52
5. Stress concentration is more where there is a change in the cross-section of the shaft.
ACKNOWLEDGMENT
The author would like to thank Prof. Chetan S (Guide, Associate Professor), NMIT, Bangalore,
Shyamaprasad S (Sr Manager) & Venugopal Nair (AGM) AVTEC Ltd, Hosur, India.
REFERENCES
[1]
Failure Analysis and Fatigue Life Estimation of a Shaft of a Rotary Draw Bending Machine
B. Engel, Sara Salman Hassan Al-Maeeni Vol:11, No:11, 2017
[2]
M. G. Deepan Marudachalam, K. Kanthavel, and R. Krishnaraj, “Optimization of shaft
design under fatigue loading using Goodman method,” International Journal of Scientific
& Engineering Research, Vol. 2, Issue. 8, ISSN 2229-5518, 2011.
[3]
S. Gujaran, and S. Gholap, “Fatigue analysis of drive shaft,” International Journal of
Research in Aeronautical and Mechanical Engineering, Vol. 2, Issue. 10, P. 22-28, 2014.
[4]
Prediction of Fatigue Life of Crank Shaft using S-N Approach Mahesh L. Raotole Prof. D.
B. Sadaphale , Prof. J. R.Chaudhari (ISSN 2250-2459, ISO 9001:2008 )
[5]
“Finite Element Structural and Fatigue Analysis of Single Cylinder Engine Crank Shaft”
Bhumesh J. Bagde Laukik P. Raut ISSN: 2278-0181 Vol. 2 Issue 7, July – 2013
[6]
“Mechanical Engineering Design” Shigley-Ninth Edition
[7]
“Fundamentals of Machine Component Design” ROBERT C. JUVINALL Professor of
Mechanical Engineer
http://www.iaeme.com/IJMET/index.asp
16
editor@iaeme.com