FE Analysis of Middle Axle suspension Spring of Electric Locomotive WAG-9 of Indian Railways

2nd International Conference on Simulation Modeling and Analysis - COSMA 2011, 14-16 December 2011,

Amrita School of Engineering, Coimbatore 641 112.

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FE Analysis of Middle Axle suspension Spring of Electric Locomotive WAG-9 of

Indian Railways

Manoj A. Kumbhalkar

1 and Prof. Y. L. Yenarkar

2

1M. Tech. Student

Department of Mechanical Engineering,

Rajiv Gandhi College of Engineering, Research &

Technology, Chandrapur

Chandrapur – 442 402, Maharashtra, India [email protected]

2Associate professor

Department of Mechanical Engineering,

Rajiv Gandhi College of Engineering, Research &

Technology, Chandrapur

Chandrapur – 442 402, Maharashtra, India [email protected]

Abstract

WAG-9 type electric locomotives, of Indian Railways'

fleet, used for Goods train hauling and maintained at

Ajani Electro loco shade, of central railway has the

history of frequent failure of the middle axle primary

inner suspension spring. Each of the six axles of Loco

has a set of springs to support the Loco bogie. The

different heights of springs makes the springs set to share

different loads

This paper discusses the observations on failures, load

analysis and FEA of middle axle composite spring. The

load analysis has been made to find the load on each of

the spring set and further middle axle composite spring

which has high frequency of failures has been analyzed

using FEA. The analysis has been carried out for the

critical loading conditions for the cases of loading on

straight and curved path.

Keywords: Helical compression spring, FE Analysis,

composite spring, gap element, axial & lateral load.

1. Introduction

The suspension of a locomotive is a complex system.

WAG-9 is an electric locomotive engine of Indian

railways used to haul specially goods train and is

maintained by Ajani Loco shed, Nagpur India. The Loco

is divided into two frames and each frame has three axles

in frontal and rear side. Two suspension springs are

mounted on each axle box attached near to each of the

wheels called primary springs. The figure 1 shows the

arrangement on end axles and figure 2 shows the

arrangement on middle axle. The end and middle axle

has primary outer spring with variable sizes but only the

middle axle has composite assembly of spring i.e.

primary inner and outer springs as shown in figure 3. The

inclined damper is provided on the end axle wheel

between axle and frame to reduce the load directly

coming on end axle spring. The vertical damper is

provided near middle axle wheel between frame and

bogie. This damper is not directly attached to the middle

axle because this axle is free to move laterally to

negotiate the curvature of the track.

Figure 1. Actual photo of End axle wheel Figure 2. Actual photo of Middle axle Figure 3. Actual photo of Middle axle

set with Primary spring wheel set with Composite spring composite spring (Primary Inner & outer spring)



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1.1. Observations

The problem identified in the arrangement of

suspension spring in WAG-9 railway engine is that the

middle axle primary spring are fails before its expected

life. The maintenance record at loco shade indicates that

there is very high rate of failure of primary inner spring.

For instance in 2009-10 the primary inner spring was

replaced on 51 instances as against 8 instances of middle

axle primary outer spring which is significantly high. It

has been observed that, the inner spring usually breaks

between first to third coils. The figure 4(a) shows the

failed piece of spring and figure 4(b) shows the scratches

on the damper that confirms the deformation of assembly

by about 25mm more than the stationary condition

indicating higher loads while running. It should be noted

that, the material report confirms the spring material is as

per requirements. Further every spring before assembly

tested for the required stiffness.

2. Load distribution on suspension springs

The overall load of about 123 tonne of engine is acted

over all primary suspension spring by the bogie (BG)

frame. At first the load is acted over each middle axle

primary outer spring as the height of this spring higher

than all the spring which is about 258 mm. Then the load

is acted on middle axle inner spring after 2 mm deflection

of outer spring as its height is 2 mm less than outer spring.

After 18 mm deflection the load is distributed over all the

springs as shown in figure 5.

2.1. Load analysis

Using the technical specifications of spring the forces

has been calculated analytically for the case of loco

moving at straight path and the loco moving at curved

path. The technical specifications of each spring are shown

in table 1.

Following assumptions were made for simplification of

cases applied for the analysis of the spring.

i) The rails are smooth and there are no geometrical

irregularities.

ii) The loading is static.

iii) Impact load during operation are neglected.

iv) All other kind of load than mentioned in calculations is

neglected.

v) Wheels are perfectly round and of equal in sizes.

vi) Longitudinal deflection (along the direction of track) of

all the spring is neglected.

vii) Maximum speed of train 80 km/hr in all cases.

viii) Axial deflection of all the springs is same.

ix) Springs are assumed to be linear.

(a) (b)

Figure 4: (a) Failed middle axle inner spring (b) Rubbing

marks over inclined damper on end axle

Table 1: Technical specification of spring set

Particulars Unit

Middle

axle

Outer

Spring

Middle

axle

Inner

Spring

End

Axle

spring

Free length (Lf) mm 258.6 252.4 238.8

Outer diameter (DO) mm 212 104 221

Mean diameter (Dm) mm 180.5 87.5 185

Coil diameter (d) mm 31.5 16.5 36

No. of active coil (n) - 3.5 7.5 3

Total No. of coil - 5.0 9.0 4.5

Pitch mm 51.72 28.04 53.06

Modulus of Rigidity

(G)

N/mm2

78500 78500 78500

stiffness (k) N/mm 470 144 868

Tensile Strength (σu) N/mm2 1550 – 1720

Ultimate shear stress

(τ) N/mm2 860 860 860

Figure 5. Load distribution on all spring



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2.1.1. CASE I: For loco moving at straight path

The various load acted upon the axle assembly when

loco is moving on straight path are as given below.

1) Total weight of loco = 123 T

2) Unsprung mass per wheel set = 3.984 T

3) Total unsprung mass = 23.904

4) Net load on all axles = 99.096 T

5) This net load is distributed over each of frontal and rear

wheel sets through front and rear wheel frames.

Thus net load distributed on each frame = 49.548 T

6) This load of 49.548 tonne is acted over all the spring as

per figure 5. After 20 mm deflection of middle axle spring

(inner & outer); the load ‘Wd’ is distributed over end axle

springs.

7) The total load and deflection of end axle and middle

axle springs has obtained by load Wd,

Each end axle and middle axle spring set = 4

Total no. of spring set on end axle = 4 ×2 = 8

Wd = (We × 8) + (Wo × 4) + (Wi × 4)

Wd = [(4×ko) + (4×ki) + (8×ke)] δd

Using technical specification of spring the load and

other design parameters were calculated for the case of

loading on straight path and are shown in table 2.

2.1.2. CASE I: For loco moving at curved path

To negotiate curves on the railway track, only the

middle axles are given the free play of about 16 mm in a

lateral direction perpendicular to the direction of motion. It

should be noted that the axle do not turn about the loco but

there is a sliding of the middle axle which helps in

negotiating the curve. While moving on the curved path

the loco is subjected to additional lateral load because of

centrifugal force with its bending moment maximum at the

top end. The figure 6 shows the load acting when the loco

is moving on curved path. Following are the details for

calculation of the load.

1) The loco speed is 80 km/hr.

2) The radius of curvature is 292 m, which is the minimum

recommended radius.

3) The banking angle is 60.

4) Distance between track, x = 1.676m

5) Height of CG from surface, h = 1/3 H = 1.45066m

6) Mass of bogie, m = 99096 kg

7) Diameter of wheel is 1016 mm

8) Angular velocity of wheel is 43.74 rad/s

9) Angular velocity of precession is 0.076 rad/s

10) Moment of Inertia of wheel is 514.06 kg-m2

11) Gyroscopic couple is 1720.46 N-m

12) Reaction at gyroscopic couple (calculated)

RGB = 1026.53 N , RGA = 1026.53 N ↓

13) Reaction at outer rail and inner rail

RB = 564.47 KN , RA = 449.85 KN

14) Lateral load on all springs by considering equally

acting over all springs is 6981.52 KN.

The table 3 shows the load acting on middle axle and

end axle wheel set when the loco at curved path.

Table 2: Analytical Results of all springs for the Loco at

Straight path

Particulars Unit

Middle

Axle

Outer

Spring

Middle

Axle

Inner

Spring

End

Axle

Spring

Spring Index (C) - 5.73 5.3 5.14

Wahl’s Factor (K) - 1.27 1.29 1.30

Deflection (δ) mm 66.6 64.6 46.6

Load (W) N 31268.7 9351.46 40451.38

Table 3: Analytical Results of All Springs for Loco at Curved Path

Particulars Unit

Middle

Axle

Outer

Spring

Middle

Axle

Inner

Spring

End

Axle

Spring

Load (W) N 35250 10512 47740

Deflection (δ) mm 75 73 55

Figure 6: Loco at radius of curvature



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4. Modeling of spring

Pro-Engineer 5.0, a 3D modeling software is used to

model the middle axle primary inner spring and

composite spring. Pro/E 5.0 included the part modeling

environment in which the helical sweep command is used

for the modeling of helical spring and it is squared at the

end by using swept blend command. The file generated

has saved in PRT file format which is converted in IGES

to import the geometry in ANSYS, FE modeler

environment. The parameters required for the modeling of

spring are free height, mean diameter, pitch and coil

diameter.

ANSYS 12.0 is the finite element analysis software which

is used for the analysis of middle axle primary inner

spring and composite spring. In design simulation 10-

node tetrahedral SOLID187 element is used for meshing

of spring. SOLID187 element is a higher order 3-D, 10-

node element having three degrees of freedom at each

node: translations in the nodal x, y, and z directions. It has

a quadratic displacement behavior and is well suited to

modeling irregular meshes (such as those produced from

various CAD/CAM systems). The material properties like

modulus of elasticity of 206×103 N/mm

2 and poisons ratio

of 0.3 for the chrome vanadium material are input to the

ANSYS engineering data. For the analysis purpose the

plate with higher rigidity was mounted on the top and

below the spring of modulus of elasticity 250×103 N/mm

2

and poisons ratio of 0.3 for axial loading and fixing up the

displacement. Figure 7 shows the mesh model of middle

axle primary inner spring with 10823 elements and 23386

nodes and composite spring with 20630 elements and

42330 nodes.

5. FE analysis of middle axle primary spring

The FE analysis of middle axle composite spring has been

carried out for both the above mentioned loading cases as

the load is shared by both spring causes the failure of

inner spring. The deflection and maximum shear stresses

are obtained indicating the failure region of spring. The

figure 9 depicts the loading and boundary condition for

each of the cases. For the FE analysis of middle axle

primary composite spring, the load as calculated has been

applied at the top plate and fixed at bottom plate for the

cases discussed. The ANSYS finite element analysis

program offers contact elements designed to treat cases of

changing mechanical contact between the parts of an

assembly or between different faces of a single part. The

gap element, ‘pinball region’ in ANSYS workbench of

radius has been introduced for the deflection of both

springs as there is a gap of 2 mm between outer and inner

spring. The results obtained in the form of deflection and

maximum shear stress for composite spring when the loco

moving at straight path are shown in figure 9 and for

composite spring when the loco moving at curved path

are shown in figure 10.

(a) (b)

Figure 7: Mesh model of middle axle primary (a) inner spring & (b) composite spring

(a) (b)

Figure 8: Loading and Boundary condition for Middle axle composite spring (a) at straight path and (b) at curved path.



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Spring under consideration is highly loaded. This is

purely the case of limiting design as the maximum shear

stress of 748.89 N/mm2

for composite spring at straight

path is nearer to the ultimate shear stress of 860 N/mm2

which increases to 870.06 N/mm2 when the loco at curved

path is enough to initialize a shearing process. FE analysis

of composite spring for all the cases is shown in table 3.

The FE analysis is also shows the region of high

stresses at about one and half coil at which the failure is

known to happen frequently. Hence analysis proves that

the spring is heavily loaded and on some instances like

loco moving on curvature, it crosses the ultimate shear

stress. Further the actual loading condition would have the

additional load as gap in track, alignment errors, jumping

of wheel, breaking loads etc. All these factor shall

contribute to increase in the load (Which can be observed

from the fact that, the damper has scratch) marks, and

hence the stress.

Therefore it can be concluded that, there is an urgent

need to reduce this stresses to the safer limits. One way to

do this would be reduction in pre-stresses by increasing

the length of end axle spring. This shall reduce the pre-

stressing of middle axle spring assembly increasing the

overall stiffness of composite assembly of suspension. The

gap between the middle axle outer spring and end axle

spring is 20 mm because of this there is much pre-stressing

of middle axle springs both outer and inner due to more

(a) Max deflection = 68.58 mm (b) Max shear stress =748.89 N/mm2

Figure 9: FE analysis of middle axle primary composite spring for loco moving at straight path

a) Max deflection = 80.742 mm (b) Max shear stress = 870.06 N/mm2

Figure 10: FE analysis of middle axle primary composite spring for loco moving at curved path

Table 3: FE analysis of composite spring for loco moving at

straight path and curved path

Spring Condition Load (N)

FE Analysis

(ANSYS)

Deflecti

on (mm)

Max shear

stress

(N/mm2)

Composite

spring

At straight

path 40620.16 68.58 748.89

Composite

spring

a. Axial &

b. Lateral

load at

curved path

a. 45762

&

b.6981.52

80.742 870.06



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difference. To reduce the pre-stressing of middle axle

springs it is necessary to increase the height of end axle

spring by adding shim into it. By FE analysis it is observed

that the stresses over middle axle composite spring are

reduced by adding shim at end axle spring as shown in

table 4. Since this shall lead to decrease in pre-stressing of

middle axle springs, the life of spring shall definitely

improve. Further this would also mean utilizing the end

axle springs to their capacity as the stress on them will

increase as currently they are stressed much lesser than the

middle axle springs. This “equal stress in all springs

approach” shall yield better life for each of the spring.

However, this shall lead to increase in overall stiffness

and hence reduction of bogie deflection on assembly. This

further shall lead to increase in height of loco which result

of difficulty in join loco with other bogies and increasing

the C.G. of loco. The railway has stringent rules regarding

these aspects and hence the addition of shim has to be

done with care and confirming the railway standards.

Conclusion

From the FE analysis it is clear that the spring under

consideration has shear stresses sufficient to bear while the

loco is moving on the straight path. However while

traveling on the curved path the shear stress are higher

making the design critical. Further the loco has to travel on

the rails which have the joints and local irregularities

which bring the impact loads. It should be noted that the

middle axle does not have lateral damping and it has a free

play of 16 mm to slide to negotiate curvatures. While

negotiating with this curvature, the middle axle springs are

subjected to lateral loading causing the highest moment

and shear stresses at the top end of springs. The FE

analysis suggests the maximum shear stress of about

870.74 N/mm2

while moving on the critical curvatures at

the prescribed speed of 80 km/hr. This is almost same as

that of allowable maximum shear stress of 860 N/mm2.

Further actual working conditions also have additional

loads due to jerks and impact in all three directions making

the loading further complex. Hence the actual stresses are

much more than calculated. Therefore the bending stress

due to lateral loading may initiate a failure which is further

enhance and aggregated because of stress concentration at

the failure region and nature of loading and once there is

significant development of this crack the shearing occurs

almost instantaneously. An observation on the failed

spring confirms this failure by crack initiating followed by

shear failure. Hence it is suggested that (i) the spring

should have some damping for lateral loads that the spring

is subjected to while negotiating the curvatures. (ii) The

initial stresses in the middle axle spring can be reduced by

increasing the length of end axle springs but limiting by

shift in C.G. of loco.

References

[1] Indian railways suspension spring drawing, Drawing number

1209-01-115-008,009, Ajni, Nagur.

[2] Joseph E. Shigley & Charles R. Mischke, “A textbook of

Mechanical Engineering Design”, Tata McGraw Hill, sixth

edition, pg. 588-595.

[3] V. B. Sood & Professor Bridges, (2009), “Notes on curves for

railways”, Indian Railways Institute of Civil Engineering, Pune.

[4] Y. Prawoto, M. Ikeda and S. K. Manville, A. Nishikawa,

(2008), “Failure Analysis of Automotive Suspension Coil

Spring”, 35-48.

[5] Harris Yong, (1998), “The Helical Spring: Theory and

Calculation in the Context of the Automobile Suspension

system”, CIV 205 Term Project.

[6] M. Ruzicka & K. Doubrava, “Loading Regimes and

Designing Helical Coiled Spring”, RES. AGR. ENG., 51, 2005

(2): 50–55

[7] Koutaro Watanabe, Hideo Yamamoto, Yuichi Ito, Hisao

Isobe, “Simplified Stress Calculation Method for Helical

Spring”.

Figure 11: Distribution of load on all spring by adding shim at

end axle spring

Table 4: FE analysis for addition of 5mm shim at end axle spring.

Spring Load (N)

FE Analysis (ANSYS)

Deflection

(mm)

Max shear

stress

(N/mm2)

Composite

spring 38193.465 64.215 702.34

FE Analysis of Middle Axle suspension Spring of Electric Locomotive WAG-9 of Indian Railways

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