 Open Access
 Total Downloads : 38
 Authors : Jonnala Subba Reddy , M. Bhavani , J. Venkata Somi Reddy
 Paper ID : IJERTV7IS040120
 Volume & Issue : Volume 07, Issue 04 (April 2018)
 Published (First Online): 09042018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Simulation of Stress Distribution in Leaf Spring Under Variable Parametric and Loading Conditions
Jonnala Subba Reddy
Department of Mechanical Engineering Lakireddy Balireddy College of Engineering Mylavaram, India
M. Bhavani
Department of Mechanical Engineering Lakireddy Balireddy College of Engineering Mylavaram, India
J. Venkata Somi Reddy
Department of Mechanical Engineering Lakireddy Balireddy College of Engineering Mylavaram, India
Abstract Leaf springs are used in suspension systems. The past literature survey shows that leaf springs are designed as generalized force elements where the position, velocity and orientation of the axle mounting gives the reaction forces in the chassis attachment positions. The present work attempts to find the maximum pay load of the vehicle by performing static analysis using ANSYS software. The obtained results are compared analytically and found good agreement. The optimality conditions such as maximum bending stress and the corresponding pay load are designed with proper consideration of the factor of safety. To assess the behavior of the different parametric combinations of the leaf spring, the modal analysis using ANSYS software for the natural frequencies is carried out and the corresponding mode shapes are obtained. The natural frequencies are compared with the excitation frequencies at different speeds of the vehicle with the various widths of the road irregularity. These excitation frequencies are validated with analytical results.
Keywords Leaf Spring, ANSYS, pay load, natural frequency, camber

INTRODUCTION
A spring is an elastic body, whose function is to distort when loaded and to recovers its original shape when the load is removed. Semielliptic leaf springs are almost unanimously used for suspension in light and heavy industrial and commercial vehicles such as TATA 407, LPT1109, LPT 1613, utility vehicles like Tata Sumo, Tata safary, Scorpio, Quallise etc. The spring consists of a number of leaves called blades as shown in Fig 1.. The blades are varying in length. The blades are usually given an initial curvature or cambered so that they will tend to straighten under the load. The leaf spring is based upon the theory of a beam of uniform strength. The lengthiest blade has eyes on its ends. This blade is called main or master leaf, the remaining blades are called graduated leafs. All the blades are bound together by means of steel straps. The front eye of the leaf spring is constrained in all the directions, where as rear eye is not constrained in Xdirection. This rear eye is connected to the shackle. During loading the spring deflects and moves in the direction perpendicular to the load applied. The springs are initially cambered. More
cambered leaf springs are having high stiffness, so that provides hard suspension. Use of longer springs gives a soft suspension, because when length increases the softness increases. Generally rear springs are kept longer than the front springs. Sometimes the leaf springs are provided with metallic or fabric covers to exclude dirt. The covers also serve to contain the lubricant used in between the spring leaves. In case of metal covers, the design has to be of telescopic type to accommodate the length of cover after the change of spring length.
The suspension system consists of a spring and a damper. The energy of road shock causes the spring to oscillate. These oscillations are restricted to a reasonable level by the damper, which is more commonly called a shock absorber. When the rear wheel comes across a bump or pit on the road, it is subjected to vertical forces, tensile or compressive depending upon the nature of the road irregularity. These are absorbed by the elastic compression, shear, bending or twisting of the spring. The mode of spring resistance depends upon the type and material of the spring used.
Fig 1. Leaf Spring and its parts

LITERATURE REVIEW
Zliahu Zahavi et all. [1] discussed the behavior of structures of leaf springs under practical conditions. Practically, a leaf spring is subjected to millions of load cycles leading to fatigue
failure. They performed free vibration analysis which determines the frequencies and mode shapes of leaf spring.
A.strzat and T.Paszek [2] performed a three dimensional contact analysis of the car leaf spring. They considered static three dimensional contact problem of the leaf car spring. The solution was obtained by finite element method performed in ADINA 7.5 professional system. Numerical results were verified with experimental investigations. The static characteristics of the car spring was obtained for different models and compared with experimental investigations.
FuCheng Wang [3] performed a detailed study on leaf springs. Classical network theory is applied to analyze the behavior of a leaf spring in active and passive suspensions. Typically, these situations involved in specifying a soft response from road disturbances.
Shahriar Tavakkoli, Farhang Aslani, and David S. Rohweder
[4] performed analytical prediction of leaf spring bushing loads using MSC/NASTRAN and MDI/ADAMS. Two models of leaf spring in MSC/NASTRAN and MDI/ADAMS were created to compare the bushing loads predicted by each model. Geometric nonlinear capability of MSC/NASTRAN (SOL106) was used to predict the bushing loads in MSC/NASTRAN model. The quasistatic simulation capability of MDI / ADAMS was used to predict the bushing loads in MDI/ADAMS model.

Rajendran and S.Vijayarangan [5] performed a finite element analysis on a typical leaf spring of a passenger car. Finite element analysis has been carried out to determine natural frequencies and mode shapes of the leaf spring. A simple road surface model was considered.
C.Madan Mohan Reddy, D.RavindraNaik, Dr M.Lakshmi Kantha Reddy [1] conducted study on analysis and testing of two wheeler suspension helical compression spring. The study on suspension system springs modelling, analysis and testing was carried out.
The present work discusses the behavior of the different parametric combinations of the leaf spring, the modal analysis is carried out using ANSYS software.

ANALYSIS OF LEAF SPRING
The material selected for analysis is Manganese Silicon Steel and variables such as thickness, camber, span and no. of leaves are considered as variables. Bending stress is computed under different loading conditions.

Material Properties of leaf spring
Material = Manganese Silicon Steel Youngs Modulus E = 2.1E5 N/mm2 Density = 7.86E6 kg/mm3 Poissons ratio = 0.3
Yield stress = 1680 N/mm2

Geometric Properties of leaf spring

Variation of thickness
The thickness of leaves changes from 7 mm to 10 mm with the interval of 1mm, the lengths, radius of curvatures, rotation angles are computed. The Sample readings for thickness 7 mm are shown in table 1.
Thickness of leaves = 7 mm to 10 mm Other parameters are taken as: Camber = 80 mm
Span = 1220 mm Number of leaves = 10
Number of full length leaves nF = 2 Number of graduated length leaves nG = 8 Width = 70mm
Ineffective length = 60 mm Eye diameter = 20 mm Bolt diameter = 10 mm
Table1. Length of leaves when thickness is 7 mm
Leaf number
Full leaf Length (mm)
Half leaf Length (mm)
Radius of Curvature (mm)
Half Rotation angle
(degrees)
1
1240
620
2372.625
p>14.972 2
1240
620
2379.625
14.928
3
1108
554
2386.625
13.299
4
978
489
2393.625
11.708
5
846
423
2400.625
10.096
6
716
358
2407.625
8.519
7
584
292
2414.625
6.929
8
454
227
2421.625
5.371
9
322
161
2428.625
3.798
10
190
95
2436.625
2.235

Variation of camber
The camber varies from 80mm to 110 mm with the interval of 10mm, the lengths, radius of curvatures, rotation angles are computed. The Sample readings for Camber 80 mm are shown in table 2.
Camber = 80 mm to 110 mm Span = 1220 mm
Thickness of leaves = 7 mm Number of leaves = 10
Number of full length leaves = 2 Number of graduated length leaves = 8 Width = 70mm
Ineffective length = 60 mm Eye diameter = 20 mm Bolt diameter = 10 mm
Table2. Length of leaves when camber 80 mm
Leaf number
Full leaf Length (mm)
Half leaf
Length (mm)
Radius of Curvature (mm)
Half Rotation angle (degrees)
1
1240
620
2372.625
14.972
2
1240
620
2379.625
14.928
3
1108
554
2386.625
13.299
4
978
489
2493.625
11.705
5
846
423
2400.625
10.096
6
716
358
2407.625
8.519
7
584
292
2414.625
6.929
8
454
227
2421.625
5.371
9
322
161
2428.625
3.798
10
190
95
2436.625
2.235

Variation of span
The span varies from 1120 mm to 1420 mm with the interval of 100 mm, the lengths, radius of curvatures, rotation angles are computed. The Sample readings for span of leaf spring 1120 mm are shown in table 3.
Span of leaf spring = 1120 mm to 1420 mm Span = 1220 mm
Thickness of leaves = 7 mm Number of leaves = 10
Number of full length leaves = 2 Number of graduated length leaves = 8 Width = 70mm
Ineffective length = 60 mm Eye diameter = 20 mm Bolt diameter = 10 mm
Table 3. Length of leaves when Span 1120 mm
Leaf number
Full leaf Length
(mm)
Half leaf Length (mm)
Radius of Curvature
(mm)
Half Rotation angle (degrees)
1
1140
570
2007
16.272
2
1140
570
2014
16.216
3
1020
510
2021
14.459
4
900
450
2028
12.714
5
780
390
2035
10.981
6
660
330
2042
9.259
7
540
270
2049
7.55
8
420
210
2056
5.852
9
300
150
2063
4.166
10
180
90
2070
2.489

Variation of no. of leaves
The number of leaves varies from 9 to 12 with the interval 1, the lengths, radius of curvatures, rotation angles are computed. The Sample readings for no. of leaves 9 are shown in table 4. number of leaves = 9 to 12
Span = 1220 mm
Thickness of leaves = 7 mm Number of leaves = 10
Number of full length leaves = 2 Number of graduated length leaves = 8 Width = 70mm
Ineffective length = 60 mm Eye diameter = 20 mm Bolt diameter = 10 mm
Table 4. Length of leaves when Number of leaves 9
Leaf number
Full leaf
Length (mm)
Half leaf Length (mm)
Radius of
Curvature (mm)
Half Rotation angle (degrees)
1
1240
620
1917.5
18.526
2
1240
620
1924.5
18.459
3
1092
546
1931.5
16.196
4
946
473
1938.5
13.980
5
798
399
1945.5
11.751
6
650
325
1952.5
9.537
7
502
251
1959.5
7.339
8
356
178
1966.5
5.186
9
208
104
1973.5
3.019


Bending Stress of leaf spring
The bending stress of a leaf spring may be obtained from the formula:
Static Bending stress = 6
2 (2+3)
Where W = Static Load in Newton L = Half span of leave spring in mm. b = width of the leaf spring in mm.
t = thickness of the leaf spring in mm. nG = number of graduated leaves.
nF = number of full length leaves.

Geometric Properties of leaf spring
The geometrical properties are mentioned below: Camber = 80 mm
Span = 1220 mm Thickness = 7 mm
Width = 70 mm
Number of full length leaves nF = 2 Number of graduated leaves nG = 8 Total Number of leaves n = 10

Material Properties of leaf spring
The material properties of the leaf spring material are presented:
Material = Manganese Silicon Steel Youngs Modulus E = 2.1E5 N/mm2 Density = 7.86E6 kg/mm3 Poissons ratio = 0.3
Yield stress = 1680 N/mm2
The bending stress for different loading conditions from 1000 N to 15000 N is given in the table 5.
Table 5 variation of Bending Stress with load
Load (N)
Bending Stress (N/mm2)
1000
48.502
2000
97.005
3000
145.075
4000
194.010
5000
242.512
6000
291.015
7000
339.517
8000
88.020
9000
436.52
10000
485.025
11000
533.527
12000
582.03
13000
630.532
14000
679.035
15000
727.537


Modeling of Road Irregularity
An automobile assumed as a single degree of freedom system traveling on a sine wave road having wavelength of L as shown in Fig.2. The contour of the road acts as a support excitation on the suspension system of an automobile .The period is related to by t=2/ and L is the distance traveled as the sine wave goes through one period.
L = v.t = 2 v/.
so, Excitation frequency = 2 v/L
L = width of the road irregularity (WRI)
V = speed of the vehicle
The variation of road irregularities is highly random. However a range of values is assumed for the present analysis i.e. 1m to 5m for the width of the road irregularity (L).
Fig 2. An automobile traveling on a sine wave road

Variation of Exciting Frequency with Vehicle Speed The variation of exciting frequency with vehicle speed for assumed width of road irregularity. At low speeds the wheel of the vehicle passes over road irregularities and moves up and down to the same extent as the dimensions of the road irregularity. So, the frequency induced is less. If the speed
increases and the change in the profile of the road irregularity is sudden, then the movement of the body and the rise of the axles which are attached to the leaf spring are opposed by the value of their own inertia. Hence, the frequency induced also increases. The exciting frequency is very high for the lower value of road irregularity width, because of sudden width. The following table 6 shows the variation of exciting frequency with vehicle speed.
ten nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The element also has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities.
Fig 5. element Solid 92: 3D 10 Node Tetrahedral Structural solid with Rotations
Table 6. Variation of Exciting Frequency with Vehicle Speed
Speed
Frequency
Frequency
Frequency
Frequency
Frequency
(Kmph)
Hz
Hz
Hz
Hz
Hz
(at WRI
(at WRI =
(at WRI
(at WRI
(at WRI
=1m)
2m)
=3m)
=4m)
=5m)
20
5.5500
2.77
1.8518
1.3888
1.11111
40
11.1111
5.54
3.7037
2.7777
2.22222
60
16.6666
8.31
5.5555
4.1664
3.33333
80
22.2222
11.08
7.4074
5.5552
4.44444
100
27.7777
13.85
9.2593
6.9440
5.55555
120
33.3333
16.66
11.1111
8.3333
6.66666
140
38.8888
19.44
12.9630
9.7222
7.77777


Geometric Modeling of Leaf Spring
The solid model of the leaf spring is modeled in CATIA software under part design module are shown in figures 3 and 4.
Fig 3. Full model of Leaf Spring
Fig 4. Front eye of the leaf spring

Analysis of leaf spring by ANSYS
The stress, strain analysis is carried out using ANSYS software under static loading conditions for a given specifications. The natural frequencies and mode shapes are computed performing the modal analysis to assess the behavior of the leaf spring with various parametric combinations. The element Solid 92: 3D 10 Node Tetrahedral Structural solid with Rotations is considered for analysis. Solid92 has a quadratic displacement behavior and is well suited to model irregular meshes. The element is defined by

Static Analysis

Static analysis is to be performed to find the allowable stresses. The meshing and boundary conditions are given in ANSYS and are shown in Fig 6 and Fig7.
Fig. 6. Meshing, Boundary conditions and loading of leaf spring
Fig.7. Deformed and undeformed shape of leaf spring
The VonMises stresses with different loading conditions are tabulated and presented in Table 7.
Table 7 variation of VonMises stress with load
Load (N)
VonMises Stress (N/mm2)
1000
50.095
2000
101.856
3000
150.428
4000
200.712
5000
254.640
6000
305.150
7000
356.535
8000
407.469
9000
458.124
10000
509.928
11000
560.270
12000
611.204
13000
662.064
14000
713.071
15000
727.537


RESULTS AND DISCUSSIONS

Static Analysis
Static analysis is performed to find the VonMises stress by using ANSYS software and these results are compared with bending stresses calculated in mathematical analysis at various loads and are tabulated in Table 8.
Load (N)
VonMises stress N/mm2
Theoretical
ANSYS
1000
48.502
50.095
2000
97.005
101.856
3000
145.075
150.428
4000
194.010
200.712
5000
242.512
254.640
6000
291.015
305.585
7000
339.517
356.565
8000
388.020
407.469
9000
436.520
458.124
10000
485.025
509.928
11000
533.527
560.270
12000
582.030
611.204
13000
630.532
662.264
14000
679.035
703.071
15000
727.537
764.005
Table 8 variation of VonMises stress with load comparison between theoretical and ANSYS
1
NODAL SOLUTION
STEP=1 SUB =1 TIME=1
SEQV (AVG) DMX =1.786
SMN =.165967
SMX =458.124
MX
ANSYS 10.0
FZEB 25 2010
Y 13:24:56
X
.165967 101.934
51.05 152.819
203.703
254.587
305.471
356.356
407.24
458.124
Fig. 9 Vnmises Stress contour plot of Front eye of leaf spring
1
NODAL SOLUTION
STEP=1 SUB =1 TIME=1
SEQV (AVG) DMX =1.786
SMN =.165967
SMX =458.124
MX
FEB 25 2010
13:31:04
.165967
51.05
101.934
152.819
203.703
254.587
305.471
356.356
407.24
458.124
From Theoretical and ANSYS the allowable design stress is found between the corresponding loads 8000 to 10000 N, the near corresponding safe loads are given in Table 9.
Table 9. VonMises stress under different loading conditions Comparison between Theoretical and ANSYS
Load (N)
VonMises stress N/mm2
Theoretical
ANSYS
9500
460.770
481.916
9700
470.470
494.565
9900
480.174
504.243
Fig 8 Variation of Vonmises stress with load
Fig. 10. Vonmises Stress contour plot of Rear eye of leaf spring

Modal Analysis
From the leaf spring specification width is fixed and other parameters namely thickness, camber, span and number of leaves are taken for parametric variation. First ten modes are considered for analysis. Variations of natural frequencies with spring parameters are studied.

Variation of natural frequency with span
The variation of natural frequency is computed with different span and tabulated in Table 10 and variations of arc radius are shown in Table 11.
Table 10. Variation of natural frequency with Span
Span in mm
Frequency Hz at
1120
1220
1320
1420
Mode 1
2.464
2.362
2.038
1.741
Mode 2
3.700
3.624
3.053
2.603
Mode 3
7.168
6.874
5.916
5.042
Mode 4
14.409
14.240
12.192
10.416
Mode 5
15.553
15.412
14.862
12.995
Mode 6
18.224
17.652
15.246
13.413
Mode 7
26.208
25.596
23.181
20.292
Mode 8
31.377
31.126
26.798
22.968
Mode 9
31.690
31.149
27.889
24.651
Mode 10
46.567
45.532
39.470
33.549
Table 11. Variation of Arc radius with Span
Span in mm
Arc radius in mm
1120
2000.000
1220
2365.600
1320
2762.500
1420
3190.625
Fig. 11. Frequency vs span for different modes
It is observed from the Fig 11. that, when span increases the spring becomes soft and hence the natural frequency decreases. Every three modes are in one set of range. There is a considerable gap between mode3 to mode4, mode6 to mode 7 and mode 9 to mode10. It is observed from the Fig. 8.4 that the decrease of frequency value with the increase of span is very high for mode10 compared to remaining modes.

Variation of natural frequency with camber
The variation of natural frequency is computed with different span and tabulated in Table 12 and variations of arc radius are shown in Table 13.
Table 12. Variation of natural frequency with Camber
Camber in mm
Frequency Hz at
80
90
100
110
Mode 1
2.362
2.344
2.344
2.414
Mode 2
3.624
3.527
3.446
3.571
Mode 3
6.874
6.791
6.760
7.063
Mode 4
14.240
14.107
13.988
14.361
Mode 5
15.412
16.006
16.642
15.395
Mode 6
17.652
17.506
17.458
18.122
Mode 7
25.596
25.625
25.741
27.007
Mode 8
31.126
30.895
30.702
30.557
Mode 9
31.149
31.215
31.391
31.667
Mode 10
45.532
45.241
45.109
45.915
Table 13. Variation of Arc radius with Camber
Camber in mm
Arc radius in mm
80
2165.60
90
2112.20
100
1910.50
110
1746.36
Fig. 12. Frequency vs Camber for different modes
It is noticed from the Fig 12 that it shows the variation of natural frequency with camber. When camber increases the spring becomes stiff and hence the natural frequency increases. Every three modes are almost in one set of range. There is a considerable gap between mode 3 to mode4, mode6 to mode 7 and mode 9 to mode 10. It is observed from the Fig.12 that the increase of frequency value with the increase of camber is very high for mode 10 compared to remaining modes.

Variation of natural frequency with thickness
The variation of natural frequency is computed with different span and tabulated in Table 14.
Table 14. Variation of natural frequency with thickness
Thickness in mm
Frequency Hz at
7
8
9
10
Mode 1
2.362
2.744
2.945
3.270
Mode 2
3.624
3.697
3.650
3.702
Mode 3
6.874
7.950
8.502
9.403
Mode 4
14.240
14.293
14.092
14.116
Mode 5
15.412
15.710
15.656
15.736
Mode 6
17.652
20.244
21.716
23.691
Mode 7
25.596
26.669
26.678
27.275
Mode 8
31.126
31.233
30.955
31.004
Mode 9
31.149
34.630
37.249
40.714
Mode 10
45.532
51.608
51.091
51.025
Fig. 13. Frequency vs Camber for different modes
<>It is observed from the Fig 13. that it shows the variation of natural frequency with thickness of the spring. When thickness increases the natural frequency also increases. Its natural frequency increases like variation of natural frequency with camber, but with thickness the natural frequency increasing rate is lesser than that of variation of natural frequency with camber. Every three modes are almost in one set of range. There is a considerable gap between mode3 to mode4, mode6 to mode 7 and mode 9 to mode 10.It is observed from Fig. 13 that the increase of frequency value with the increase of thickness is very high for mode9 and mode10 compared to remaining modes.

Variation of natural frequency with number of leaves The variation of natural frequency is computed with different span and tabulated in Table 15.

Table 15 variation of natural frequency with number of leaves
ANSYS 10.0
1
FEB 25 2010
17:53:51
NODAL SOLUTION STEP=1
SUB =1 FREQ=2.362 USUM (AVG) RSYS=0
PowerGraphics EFACET=1 AVRES=Mat
Z
XMX Y
MN
DMX =.210091
SMX =.210091
XV =.803253
YV =.246554
ZV =.542214
*DIST=700.36
*XF =.144703
*YF =14.731
*ZF =38.884 AZS=97.519 ZBUFFER
0
.023343
.046687
.07003
.163404
.186748
.210091
No. of leaves
Frequency Hz at
9
10
11
12
Mode 1
2.240
2.362
2.527
2.559
Mode 2
3.571
3.624
3.440
3.285
Mode 3
6.506
6.874
7.262
7.301
Mode 4
14.202
14.240
14.006
13.720
Mode 5
16.473
15.412
16.410
15.887
Mode 6
17.044
17.652
18.873
19.360
Mode 7
25.060
25.596
26.346
26.188
Mode 8
30.567
31.126
30.789
30.446
Mode 9
30.906
31.149
33.002
33.751
Mode 10
42.669
45.532
48.544
50.096
Fig.15 Mode 1 (Camber 80 mm, Span 1220 mm)
1
ANSYS 10.0
FEB 25 2010
17:55:21
NODAL SOLUTION STEP=1
SUB =3 FREQ=6.874 USUM (AVG) RSYS=0
PowerGraphics EFACET=1 AVRES=Mat
Z
X
DMX =.284142
Y
SMX =.284142
MN
MX
XV =.944828
YV =.285095
ZV =.161307
*DIST=700.36
*XF =.144703
*YF =14.731
*ZF =38.884 AZS=87.384 ZBUFFER
0
.031571
.063143
.094714
.220999
.252571
.284142
Fig. 16 Mode 3 (Camber 80 mm, Span 1220 mm)
Fig. 14. Frequency vs No. of leaves for different modes
Figure 14 shows the variation of natural frequency with number of leaves of the spring. Even though the number of leaves increases there is no considerable increase in natural frequency, it is almost constant. It is observed from the Fig.14 every three modes are in gradual increment, there is considerable increase in natural frequency from mode3 to mode4, there is much increase in natural frequency from mode6 to mode7 and there is very much in increase in natural frequency from mode 9 to mode 10.
The mode shapes for modes 1, 3 & 10 and for different parameters like Camber, Span, Thickness of leaves and number of leaves are presented in the following Figures 15 to 23.
ANSYS 10.0
1
MN
Z
X Y
MX
FEB 25 2010
17:57:38
NODAL SOLUTION STEP=1
SUB =10 FREQ=45.532 USUM (AVG) RSYS=0
PowerGraphics EFACET=1 AVRES=Mat
DMX =.459032
SMX =.459032
XV =.942515
YV =.32687
ZV =.069442
*DIST=700.36
*XF =.144703
*YF =14.731
*ZF =38.884 AZS=102.976 ZBUFFER
0
.051004
.102007
.153011
.357025
.408029
.459032
Fig. 17. Mode 10 (Camber 80 mm, Span 1220 mm)
1
MN
Z XY
MX
Fig. 18. Mode 1 ( Thickness 8 mm )
1
MN
Z XY
MX
Fig. 19. Mode 3 ( Thickness 8 mm )
1
MN
Z XY
MX
Fig. 20. Mode 7 (Thickness 8 mm)
FEB 25 2010
19:10:02
NODAL SOLUTION STEP=1
SUB =1 FREQ=2.744 USUM (AVG) RSYS=0
PowerGraphics EFACET=1 AVRES=Mat
DMX =.196781
SMX =.196781
XV =.79749
YV =.582004
ZV =.159
*DIST=701.825
*XF =.086462
*YF =15.074
*ZF =43.349 AZS=106.601 ZBUFFER
0
.021865
.043729
.065594
.131187
.153052
.174916
.196781
FEB 25 2010
19:10:53
NODAL SOLUTION STEP=1
SUB =3 FREQ=7.951 USUM (AVG) RSYS=0
PowerGraphics EFACET=1 AVRES=Mat
DMX =.265981
SMX =.265981
XV =.79749
YV =.582004
ZV =.159
*DIST=701.825
*XF =.086462
*YF =15.074
*ZF =43.349 AZS=106.601 ZBUFFER
0
.029553
.059107
.08866
.177321
.206874
.236427
.265981
FEB 25 2010
19:11:24
NODAL SOLUTION STEP=1
SUB =7 FREQ=26.669 USUM (AVG) RSYS=0
PowerGraphics EFACET=1 AVRES=Mat
DMX =.242804
SMX =.242804
XV =.79749
YV =.582004
ZV =.159
*DIST=701.825
*XF =.086462
*YF =15.074
*ZF =43.349 AZS=106.601 ZBUFFER
0
.026978
.053956
.080935
.161869
.188847
.215825
.242804
1
MN Z
XMX Y
Fig. 21. Mode 1 ( umber of leaves 10)
1
MN
Z
X
Y
MX
Fig. 22. Mode 3 (Number of leaves 10)
1
MN
Z
X Y
MX
Fig. 23. Mode 10 (Number of leaves 10)
ANSYS 10.0
FEB 25 2010
17:53:51
NODAL SOLUTION STEP=1
SUB =1 FREQ=2.362 USUM (AVG) RSYS=0
PowerGraphics EFACET=1 AVRES=Mat
DMX =.210091
SMX =.210091
XV =.803253
YV =.246554
ZV =.542214
*DIST=700.36
*XF =.144703
*YF =14.731
*ZF =38.884 AZS=97.519 ZBUFFER
0
.023343
.046687
.07003
.163404
.186748
.210091
ANSYS 10.0
FEB 25 2010
17:55:21
NODAL SOLUTION STEP=1
SUB =3 FREQ=6.874 USUM (AVG) RSYS=0
PowerGraphics EFACET=1 AVRES=Mat
DMX =.284142
SMX =.284142
XV =.944828
YV =.285095
ZV =.161307
*DIST=700.36
*XF =.144703
*YF =14.731
*ZF =38.884 AZS=87.384 ZBUFFER
0
.031571
.063143
.094714
.220999
.252571
.284142
ANSYS 10.0
FEB 25 2010
17:57:38
NODAL SOLUTION STEP=1
SUB =10 FREQ=45.532 USUM (AVG) RSYS=0
PowerGraphics EFACET=1 AVRES=Mat
DMX =.459032
SMX =.459032
XV =.942515
YV =.32687
ZV =.069442
*DIST=700.36
*XF =.144703
*YF =14.731
*ZF =38.884 AZS=102.976 ZBUFFER
0
.051004
.102007
.153011
.357025
.408029
.459032
The following table shows the variation of exciting frequency with vehicle speed.
Table 16 variation of natural frequency with vehicle speed
Spe ed in Km ph
Freque ncy at WRI =
1 m
Freque ncy at WRI =
2 m
Freque ncy at WRI =
3 m
Freque ncy at WRI =
4 m
Freque ncy at WRI =
5 m
20
5.5500
2.77
1.8518
1.3888
1.11111
40
11.1111
5.54
3.7037
2.7777
2.22222
60
16.6666
8.31
5.5555
4.1664
3.33333
80
22.2222
11.08
7.4074
5.5552
4.44444
100
27.7777
13.85
9.2593
6.9440
5.55555
120
33.3333
16.66
11.1111
8.3333
6.66666
140
38.8890
19.44
12.9630
9.7222
7.77777
Fig 24. Variation of Excitation frequency with vehicle speed (wri = width of road irregularity in meters)
The variation of exciting frequency is computed with vehicle speed as parameter under dynamic conditions, for assumed width of road Irregularity. At low speeds the wheel of the vehicle passes over road irregularities and moves up and down to the same extent as the dimensions of the road irregularity.
So, the frequency induced is less. If the speed increases and the change in the profile of the road irregularity are sudden, then the movement of the body and the rise of the axles which are attached to the leaf spring are opposed by the value of their own inertia. Hence, the frequency induced also increases. The exciting frequency is very high for the lower value of road irregularity width, because of sudden width.
It is noted that the some of the excitation frequencies are very close to natural frequencies of the leaf spring, but they are not exactly matched, hence no resonance will take place.


CONCLUSIONS AND FUTURE SCOPE OF WORK

The leaf spring is considered for analysis under static and dynamic loading conditions. The spring is modeled using CATIA software and analysis is carried out in ANSYS for different loading conditions. The following conclusions are made.

The Leaf spring has been modeled using solid tetrahedron 10 node element.

By performing static analysis it is concluded that the maximum safe load is 9900 N for the given specification of the leaf spring from the analysis.

In model analysis, the leaf spring width is kept as constant and variation of natural frequency with leaf thickness, span, camber and numbers of leafs are studied.

It is observed from the present work that the natural frequency increases with the increase of thickness of leaves as well as camber, and decreases with decrease of thickness of leaves as well as camber.

The natural frequency decreases with increase of span, and increases with decrease of span.

The natural frequency almost constant with number of leaves.

The natural frequencies of various parametric combinations are compared with the excitation frequency for different road irregularities.

This study concludes that it is advisable to operate the vehicle such that its excitation frequency does not match the above determined natural frequencies i.e. the excitation frequency should fall between any two natural frequencies of the leaf spring.

An extended study of this nature can be used along with appropriate sensors and microprocessors to enable achievement of optimum speed at which one can drive the vehicle with maximum comfort.

In this work no contact elements are considered only nodal coupling has taken, instead of nodal coupling contact elements can be considered.

Also, instead of steel leaf springs the composite material can be considered to optimize the cost and weight of the vehicle through experimental setup.
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