http://www.iaeme.com/IJMET/index.asp 9 editor@iaeme.com
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
Fatigue Analysis of Out-Put Shaft Subjected to Pure Torsion
http://www.iaeme.com/IJMET/index.asp 10 editor@iaeme.com
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
Percentage
Carbon
0.15-0.21
Silicon
0.17-.35
Nickel
1.40-1.70
Manganese
0.25-0.35
Phosphorus
0.035
Sulphur
0.015
Chromium
1.50-1.80
• 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
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
Kf = 𝑀aximum stress in notched specim𝑒𝑛
Stress concentration notch free specime𝑛. (2)
Kf =1+q (Kt −1) or Kfs=1+qshear (Kts−1) (3)
Where q = Notch sensitivity factor
q = 1
1+√𝑎
√𝑟
(4)
Where √𝑎= Neuber constant
r = Fillet radius
Neuber constant is given by the equation
Nagaraj S B, Chetan S, Shyamaprasad S, Venugopal Nair
http://www.iaeme.com/IJMET/index.asp 11 editor@iaeme.com
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
q = 1
1+√.0765
√1.414
=.9486
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
85 =.0235 𝐷
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
Fatigue Analysis of Out-Put Shaft Subjected to Pure Torsion
http://www.iaeme.com/IJMET/index.asp 12 editor@iaeme.com
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
Nagaraj S B, Chetan S, Shyamaprasad S, Venugopal Nair
http://www.iaeme.com/IJMET/index.asp 13 editor@iaeme.com
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