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Modelling, Static and Dynamic Analysis Of
Locomotive Wheel Axle
Chittiboyina Kiran Kumar
Asst.Professor,
Visakha Institute of Engineering and Technology, Visakhapatnam
S. Ananth
Asst.Professor,
Baba Institute of Technology and Sciences, Visakhapatnam
Abstract- A rolling element is often pressed onto an shaft and mounted directly on a locomotive or indirectly on a
bogie. A railroad wheel generally consists of 2 main parts: the wheel itself, axle. A rail wheel and shaft are typically made
of steel, and typically heated and pressed onto the wheel, wherever it remains firmly because it shrinks and cools. Over
160 years past failures of iron railway axles led to analysis into what we currently understand as metal fatigue. Today’s
railways consider a wide kind of materials from all the foremost classes of materials. in this project so as to get the
dynamic forces on the locomotive shaft, it had been recognized that axles suffer many dynamic load cycles as they rotate
and in the past several fanciful theories were projected to elucidate why failures occurred after periods of productive
service. The dynamic characteristics analysis of wheel shaft of the locomotive is especially concerned in the calculation
concerning natural frequency and operational frequency. the objective is to calculate the natural frequency and operational
frequency of wheel axle of the locomotive is modulating those frequencies and avoiding resonance by the use of the
harmonic response, so the vibrations of wheel axle of the locomotive might scale back. Resonance is vibration
development that happens at bound rotor speeds once the wheel axle of the locomotive is on the work. The influence of
wheel shaft of the locomotive design resonance development is investigated by ANSYS software system. In this project,
the 3D model of wheel shaft of the locomotive is modelled in NX-CAD and imported into ANSYS software system to
perform static and dynamic analysis to investigate strength and dynamic characteristics of wheel shaft of the locomotive
and optimize if required.
Keywords: locomotive wheel shaft, natural frequency, operational frequency, resonance. NX-CAD, ANSYS.
INTRODUCTION
A train wheel or rail wheel is kind of wheel specially designed to be used on rail tracks. A rolling
element is often pressed onto shaft and mounted directly on a rail or locomotive or indirectly on a bogie,
known as a truck. Wheels are forged or cast (wrought) and are heat-treated to possess a particular hardness.
New wheels are trued, employing a lathe, to a particular profile before being pressed onto axle. All wheel
profiles got to be sporadically monitored to insure correct wheel-rail interface. Improperly trued wheels
increase rolling resistance, scale back energy potency and will create unsafe operation. A railroad wheel
generally consists of 2 main parts: the wheel itself, and therefore the tire (or tyre) round the outside. A rail tire
is sometimes made of steel, and is typically heated and pressed onto the wheel, wherever it remains firmly
because it shrinks and cools. Mono block wheels don't have peripheral tires, whereas resilient rail wheels
have a resilient material, like rubber, between the wheel and tire. Most train wheels have a conical geometry,
that is the primary means of keeping the train's motion aligned with the track. Train wheels have a projection
on one facet to stay the wheels, and therefore the train, running on the rails, once the bounds of the pure
mathematics based mostly alignment area unit reached, e.g. because of some emergency or defect. See
hunting oscillation. Some wheels have a cylindrical pure mathematics, wherever flanges area unit essential to
stay the train on the rail track.
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3635
Table 1.1 shows Locomotive wheel data table
All dimensions in mm Wheel type W61, W63, W64
New wheel diameter (mm) 1016
Condemn wheel diameter (mm) 930
Thickness of Rim at Condemn on Back Flange (mm) 38
Thickness of Tread at Condemn on Back Flange (mm) 6
Minimum flange width (mm) 19
Maximum flange height (mm) 35
Maximum tread hollowing (mm) 3
Wheel width (mm) 130
Wheel drawing W61 – 206-328/1 W63 – 206-
328/3 W64 – 206-328/4
Clearance to structure gauge (mm) 40
OBJECTIVE
In this paper, main objective is to get the dynamic forces on the locomotive shaft. It was
recognized that axles suffer a good several dynamic load cycles as they rotate and in the past several fanciful
theories were projected to elucidate why failures occurred after periods of prosperous service.
The target is to calculate the natural frequency and operating frequency of wheel shaft of the
locomotive is modulating those frequencies and avoiding resonance by making use of the harmonic response,
so the vibrations of wheel axle of the locomotive could scale back. Resonance is vibration development that
happens at bound rotor speeds once the wheel shaft of the locomotive is on the work.
During this project, the 3D model of wheel shaft of the locomotive is modelled in NX-CAD and
imported into ANSYS software system to perform static and dynamic analysis to investigate strength and
dynamic characteristics of wheel axle of the locomotive and optimize if needed.
METHODOLOGY:
3d Modeling Of Rail Wheel Axle:
The 3D model of the Rail wheel axle is made through UNIGRAPHICS NX software system from
the 2 D drawings. UNIGRAPHICS NX is world’s leading 3D development resolution. This software system
allows designers and engineers to bring good product to the market quicker. It takes care of the entire product
definition to utility. NX delivers measurable worth to manufacturing firms of all sizes and all told industries.
NX is employed in a very large range of industries from producing of rockets to pc peripherals.
With over 1 100000 seats put in in worldwide several cad users are exposed to NX and revel in using NX for
its power and capability.
Fig. 3.1 The 3D model of Rail wheel shaft (Right facet view)
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3636
Fig. 3.2 The 3D model of Rail wheel axle (top view)
Isometric View of Rail Wheel Axle
Fig. 3.3 The 3D model of Rail wheel axle (isometric view)
MATERIAL PROPERTIES:
30 NiCrMoV12 steel properties are used to Rail wheel axle:
Young’s Modulus (E) =180GPa
Poisson’s Ratio = 0.3
Density = 8900Kg/mm3
Yield Strength = 490MPa
In the follwing, chemical composition and main mechanical charecteristics of 30NiCrMoV12
steel ae shown.
Table:4.1 Chemical compostion and mechanical properties:
C S
i
M
n
P
a
S C
r
C
u
M
o
N
i
V
30Ni
CrMo
v12
0
2
6
0
.
3
2
-
0
.
4
0
0
.
4
0
0
.
7
0
-
0
.
0
2
0
-
0
.
0
1
5
0
.
6
0
1
.
0
0
-
0
.
2
0
0
.
4
0
0
.
6
0
2
.
7
0
3
.
3
0
0
.
0
8
0
.
1
3
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3637
Ra(N/m
m²)
Rm(N/m
m²)
As
%
KU
longitudinal
(J)
KU
transverse
(J)
30NiCrMov
12
≥834 932-1079 ≥1
5
≥47 ≥22
Mechanical Properties:
s in the Tensile strength, [MPa]
s T The limit of proportionality (Yield strain) [MPa]
5 d Specific elongation at fracture, [%]
y Reduction of area, [%]
KCU Impact strength, [kJ/m2]
HB Brinell hardness, [MPa]
Physical property:
T The temperature at which the properties of the obtained data, [Grade]
E Modulus [MPa]
a Coefficient (linear) expansion (range 20oT), [Grade]
l Thermal conductivity (heat), [W / (m · Grade)]
r Density[kg/m3]
C Specific heat (range 20o T), [J / (kg · Grade)]
R Electrical resistance, [Ohmm]
Weld ability:
Without limitations – welding is done without heating and subsequent heat treatment.
Limited weld ability- welding is feasible below heating up to 100120 degrees. And
subsequent heat treatment
Element Type Used:
Element type: Solid92
No. of nodes: Ten
Degrees of freedom: Six
Structural Analysis
Finite part Modelling (FEM) and Finite part Analysis (FEA) are 2 preferred technology
applications offered by existing CAE systems. this is often attributed to the very fact that the FEM is probably
the most popular numerical technique for resolution engineering issues. The method is general enough to
handle any complicated form of pure mathematics (problem domain), any material properties, any boundary
conditions and any loading conditions. The generality of the FEM fits the analysis necessities of today’s
complicated engineering systems and styles wherever closed type solutions area unit governing equilibrium
equations are not offered. In addition it's AN economical design tool by that designers will perform constant
quantity design finding out numerous cases (different shapes, material hundreds etc.) analyzing them and
choosing the optimum style.
BOUNDARY CONDITIONS
shaft was in remission all told Dof at the first ending of the shaft mounted with wheel.
Allowable axial load of 587N has been applied at the second ending of the shaft mounted with
wheel.
Allowable Axle Load calculation
Analytical calculation of Rail wheel shaft to style the Rail wheel shaft first we opt the diameter of
the shaft which might bear the applied stress at a secure vary.
we all know that shaft load formula
*2 ------------------------------------------>Eq. 4.1
Where,
P= Allowable Axle load
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3638
n = number of fixed points
E= Young’s modulus of material
l = length between the fixed points
I= moment of inertia
------------------------------------>Eq. 4.2
d =Diameter of the axle= 180mm
n = number of fixed points = 2
E= Young’s modulus of material = 180000 N/mm2
l = length between the fixed points = 1684mm
I= moment of inertia
I = 51503880 mm2
*2
P=32232004 N
We know,
Area of load acting location A= 2πrL
Where,
A = Surface area (mm2)
r = radius of axle loading area (mm)
L = length of axle loading area (mm)
A= 2*3.14*110*194
We know,
Axle Force (F) = P/A
F = 587.9N/mm2
DEFLECTION
5.1.1 The Maximum deformation determined 1.5mm on Rail wheel shaft in X-dir:
Fig. 5.1 the deformation of Rail wheel shaft in X-dir
5.1.2 The Max. Deformation determined 0.049mm on Rail wheel shaft in Y-dir:
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3639
Fig. 5.2 the deformation of Rail wheel shaft in Y-dir
5.1.3 The Max. Deformation determined 0.8mm on Rail wheel shaft in Z-dir:
Fig. 5.3 shows the deformation of Rail wheel shaft in Z-dir
5.1.4 The Max.Displacement resultant observed 1.6mm on Rail wheel shaft:
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3640
Fig. 5.4 shows the Max. Deformation of Rail wheel axle
STRESS
5.2.1 1st principle Stress observed 97MPa on Rail wheel axle in X- Dir:
Fig. 5.5 shows the 1st principle Stress of Rail wheel axle
5.2.2 2nd
principle Stress observed 4.3MPa on knuckle joint in Y- Dir:
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3641
Fig. 5.6 the 2nd principle Stress of Rail wheel axle
5.2.3 3rd
principle Stress observed 0.01MPa on Rail wheel axle in Z- Dir:
Fig. 5.7 shows the 3rd principle Stress of Rail wheel axle
5.2.4 The Max. Von Mises Stress observed 163MPa on Rail wheel axle:
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3642
Fig. 5.8 the Von Mises stress of Rail wheel axle
Table.5.1 The Max. Deflection and Max. Stress:
S.
N
O.
DEFLECTION (mm) STRESS(MPa)
U
X
U
Y
U
Z
U
S
U
M ơX ơY ơZ
Von
mises
1
1.
5
0.
04
0.
8
1.
6 97
4.
3
0.
01 163
From the above analysis:
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3643
The Max Deflection and the Max Avg. VonMises Stress observed on the Rail wheel axle
for axial loads is 1.6mm and 163MPa with respectively. And the Yield strength of the material stainless steel
is 490 MPa.
Therefore in step with the Maximum Yield Stress Theory, the VonMises stress is a smaller
amount than the yield strength of the material. the look of Rail wheel shaft is safe for the on top of in
operation loads. But the factor of safety is (490/163=3).
Table.5.2 Frequencies in the range of 0-1000Hz
MO
DE
FREQUEN
CY
PARTIC.FACTOR EFFECTIVE MASS
X Y Z X Y Z
1 468
-
0.1
E-
01
0.8
E-
05
0.4
5
0.3
E-3
0.7
E-
10
0.2
07
2 469 0.4
-
0.3
E-
04
0.1
E-
01
0.2
07
0.1
E-
08
0.3
E-
03
The mode shapes for the above frequencies are plotted below:
A) Results –Mode1 @ 468 Hz
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3644
Fig. 5.3 Shows Mode shape 1@468 Hz for Rail wheel axle
B) Results –Mode2 @ 469 Hz
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3645
Fig.5.4 Shows Mode shape 2@ 469 Hz for Rail wheel axle
GRAPHS: Amplitude v/S Forcing Frequency:
1. Harmonic response at face
Fig. 6.1 harmonic response at 1st fixed end of Rail wheel axle liner scale
Fig.6.2 harmonic response at 2nd fixed end of Rail wheel axle liner scale
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3646
Fig.6.3 harmonic response at mid location of Rail wheel axle liner scale
From the above graphs, the subsequent amplitude were observed:
Amplitude of 0.0002mm is observed on the 1st fixed end of Rail wheel axle at a frequency
of 465Hz.
Amplitude of 0.079mm is observed on the 2nd
fixed end of Rail wheel axle at a frequency of
465Hz.
Amplitude of 0.42 mm is observed on the mid location of Rail wheel axle at a frequency of
465Hz.
6.1 MAX. DEFLECTION AND STRESS OF FREQUENCY @ 468HZ
Max. Deflection:
Fig. 6.4 shows the max. Deflection of Rail wheel axle
Von-Mises stress:
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3647
Fig.6.5 shows the Von-Mises stress of Rail wheel axle.
6.2 Max. Deflection And Stress Of Frequency @ 469hz
Max. Deflection:
Fig.6.6 shows the max. Deflection of Rail wheel axle
Von-Mises stress:
Fig.6.7 shows the Von-Mises stress of Rail wheel axle.
Table 6.3 Deflections and von-mises stress for critical frequencies
S
.no
FREQUENCY(
Hz)
DEFLEC
TIONS (mm)
VON MISES STRESS
(MPa)
1 468 1.8 336
2 469 1.7 333
International Journal of Management, Technology And Engineering
Volume 8, Issue XII, DECEMBER/2018
ISSN NO : 2249-7455
Page No:3648
From the above results it's determined that the crucial frequencies 468Hz and 469Hz are having
stress 336MPa and 333MPa. The yield strength of the material (stainless steel) used for gear is 490MPa.
In step with the Von-Mises Stress Theory, the Von-Mises stress of drugs at frequencies 468Hz
and 469Hz having stresses less than the yield strength of the fabric. Hence the design of Rail wheel shaft is
safe for the above in operation loading conditions.
CONCLUSION
NX-CAD model of the wheel axle is generated in solid works and this model is imported to
ANSYS for processing work. An axial load of 587N is applied on the circumference of the wheel shaft and
track is mounted.
Following are the conclusions from the results obtained:
Maximum stress by ANSYS is lower than the yield stress of material.
Von-Mises stresses are less than ultimate strength.
Since the Von-Mises stresses are less than the ultimate strength, taking deflections under
consideration, 30 NiCrMoV12 steel is preferred as best material for designed Rail wheel axle.
So as to get the forces working on the shaft, a dynamic model with six Dof is made. Then, a
discussion on dynamic forces working on the shaft is given very well.
From the above results it's determined that the crucial frequencies 468Hz and 469Hz are
having stress 336MPa and 333MPa. The yield strength of the material (stainless steel) used for gear is
490MPa.
The Von-Mises stress at frequencies 468Hz and 469Hz having stresses less than the yield
strength of the material. Hence the design of Rail wheel axle is safe for the above operating loading
conditions.
SCOPE FOR FUTURE WORK
In the above projected work solely force acting circumferentially on the wheel shaft is just
thought of, this may be extended to different forces that act on the wheel rim and structural analysis is
administered, this can be extended to Transient Analysis.
If it's potential, damping ought to be other to the system. Because, it's clear that within the
damping case, abrupt force rise may be avoided and additionally, dynamic forces for different speeds may be
decreased.
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International Journal of Management, Technology And Engineering
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ISSN NO : 2249-7455
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