Design Optimization Of Leaf Spring
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This paper discusses the replacement of multi-leaf steel spring with mono composite leaf spring for the same load carrying capacity and stiffness. The objective is to reduce the weight of the leaf spring without any reduction on load carrying capacity and stiffness. The design constraints were limiting stresses and displacement. ANSYS software was used for modeling and analysis. The subject is Mechanical Engineering and the course code is not mentioned. The college/university is Nova College Of Engineering & Technology, Jangareddy Gudem.
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Malaga. Anil Kumar, T.N.Charyulu, Ch.Ramesh / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
759 | P a g e
Design Optimization Of Leaf Spring
Malaga. Anil Kumar 1, T.N.Charyulu2, Ch.Ramesh 3
1. Student, 10a01d0407, M.Tech (Cad/Cam), Nova College Of Engineering & Technology, Jangareddy Gudem,
2. Associate Professor, Department Of Mechanical Engineering, Nova College Of Engineering & Technology,
Jangareddy Gudem,
3. Assistant Professor, Department Of Mechanical Engineering, Pace Institute Of Technology & Sciences,
Ongole,
Abstract
The automobile industry has shown
increased interest in the replacement of steel
spring with composite leaf spring due to high
strength to weight ratio. This work deals with the
replacement of multi-leaf steel spring with mono
composite leaf spring. Suspension system in an
automobile determines the riding comfort of
passengers and the amount of damage to the
vehicle. The main function of leaf spring
assembly as suspension element is not only to
support vertical load, but also to isolate road-
induced vibrations. The behavior of leaf spring is
complicated due to its clamping effects and inter-
leaf contact etc.
The objective of this paper is to replace
the multi-leaf steel spring by mono composite leaf
spring for the same load carrying capacity and
stiffness. Since the composite materials have
more elastic strain energy storage capacity and
high strength-to-weight ratio as compared to
those of steel. It is possible to reduce the weight
of the leaf spring without any reduction on load
carrying capacity and stiffness. The design
constraints were limiting stresses and
displacement. Modeling and analysis of both the
steel and composite leaf springs have been done
using ANSYS software.
1. Introduction
In order to conserve natural resources and
economize energy, weight reduction has been the
main focus of automobile manufacturer. Weight
reduction can be achieved primarily by the
introduction of better material, design optimization
and better manufacturing processes. The suspension
leaf spring is one of the potential items for weight
reduction in automobile as it accounts for ten to
twenty percent of the unsprung weight. Hence, the
strain energy of the material becomes a major factor
in designing the springs.
The introduction of composite materials was made it
possible to reduce the weight of the leaf spring
without any reduction on load carrying capacity and
stiffness. Since, the composite materials have more
elastic strain energy storage capacity and high
strength-to-weight ratio as compared to those of
steel. The introduction of fiber reinforced plastics
(FRP) made it possible to reduce the weight of a
machine element without any reduction of the load
carrying capacity.
Because of FRP materials high elastic strain energy
storage capacity and high strength-to-weight ratio
compared with those
Of steel, multi-leaf steel springs are being replaced
by mono leaf FRP springs.
2. Model Preparation And Formulation
Solid modeling is the first step for doing
any 3D analysis and testing and it gives 3D physical
picture for new products. FE models can easily be
created from solid models by the process of
meshing.
2.1 Solid Modeling
In the present work, multi-leaf steel spring
and mono-composite leaf spring are modeled. For
modeling the steel spring, the dimensions of a
conventional leaf spring of a light weight
commercial vehicle are chosen. Since the leaf spring
is symmetrical about the neutral axis only half of the
leaf spring is modeled by considering it as a
cantilever beam. Load is applied at the base of the
leaf spring in the middle in the upward direction.
2.2 Specifications for Steel Leaf Spring
Model : cdr 650md 2wd
Suspension : rear leaf
Span length : 1120 mm
Width : 50 mm
Thickness : 6 mm
Outer eye dia : 50 mm
Dia .of centre bolt : 8 mm
Camber : 180 mm
Ineffective length : 100 mm
Total no. Of leaves : 10
No. of full length leaves : 2
No. of graduated leaves : 8
Vehicle weight : 1910 kg
2.3 Geometric Properties of leaf spring
Camber = 180 mm
Span = 1120 mm
Thickness = 6 mm
Width = 50 mm
Number of full length leaves nF = 2
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
759 | P a g e
Design Optimization Of Leaf Spring
Malaga. Anil Kumar 1, T.N.Charyulu2, Ch.Ramesh 3
1. Student, 10a01d0407, M.Tech (Cad/Cam), Nova College Of Engineering & Technology, Jangareddy Gudem,
2. Associate Professor, Department Of Mechanical Engineering, Nova College Of Engineering & Technology,
Jangareddy Gudem,
3. Assistant Professor, Department Of Mechanical Engineering, Pace Institute Of Technology & Sciences,
Ongole,
Abstract
The automobile industry has shown
increased interest in the replacement of steel
spring with composite leaf spring due to high
strength to weight ratio. This work deals with the
replacement of multi-leaf steel spring with mono
composite leaf spring. Suspension system in an
automobile determines the riding comfort of
passengers and the amount of damage to the
vehicle. The main function of leaf spring
assembly as suspension element is not only to
support vertical load, but also to isolate road-
induced vibrations. The behavior of leaf spring is
complicated due to its clamping effects and inter-
leaf contact etc.
The objective of this paper is to replace
the multi-leaf steel spring by mono composite leaf
spring for the same load carrying capacity and
stiffness. Since the composite materials have
more elastic strain energy storage capacity and
high strength-to-weight ratio as compared to
those of steel. It is possible to reduce the weight
of the leaf spring without any reduction on load
carrying capacity and stiffness. The design
constraints were limiting stresses and
displacement. Modeling and analysis of both the
steel and composite leaf springs have been done
using ANSYS software.
1. Introduction
In order to conserve natural resources and
economize energy, weight reduction has been the
main focus of automobile manufacturer. Weight
reduction can be achieved primarily by the
introduction of better material, design optimization
and better manufacturing processes. The suspension
leaf spring is one of the potential items for weight
reduction in automobile as it accounts for ten to
twenty percent of the unsprung weight. Hence, the
strain energy of the material becomes a major factor
in designing the springs.
The introduction of composite materials was made it
possible to reduce the weight of the leaf spring
without any reduction on load carrying capacity and
stiffness. Since, the composite materials have more
elastic strain energy storage capacity and high
strength-to-weight ratio as compared to those of
steel. The introduction of fiber reinforced plastics
(FRP) made it possible to reduce the weight of a
machine element without any reduction of the load
carrying capacity.
Because of FRP materials high elastic strain energy
storage capacity and high strength-to-weight ratio
compared with those
Of steel, multi-leaf steel springs are being replaced
by mono leaf FRP springs.
2. Model Preparation And Formulation
Solid modeling is the first step for doing
any 3D analysis and testing and it gives 3D physical
picture for new products. FE models can easily be
created from solid models by the process of
meshing.
2.1 Solid Modeling
In the present work, multi-leaf steel spring
and mono-composite leaf spring are modeled. For
modeling the steel spring, the dimensions of a
conventional leaf spring of a light weight
commercial vehicle are chosen. Since the leaf spring
is symmetrical about the neutral axis only half of the
leaf spring is modeled by considering it as a
cantilever beam. Load is applied at the base of the
leaf spring in the middle in the upward direction.
2.2 Specifications for Steel Leaf Spring
Model : cdr 650md 2wd
Suspension : rear leaf
Span length : 1120 mm
Width : 50 mm
Thickness : 6 mm
Outer eye dia : 50 mm
Dia .of centre bolt : 8 mm
Camber : 180 mm
Ineffective length : 100 mm
Total no. Of leaves : 10
No. of full length leaves : 2
No. of graduated leaves : 8
Vehicle weight : 1910 kg
2.3 Geometric Properties of leaf spring
Camber = 180 mm
Span = 1120 mm
Thickness = 6 mm
Width = 50 mm
Number of full length leaves nF = 2
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Malaga. Anil Kumar, T.N.Charyulu, Ch.Ramesh / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
760 | P a g e
Number of graduated leaves nG = 8
Total Number of leaves n = 10
Table: 1 Design Parameters of Steel leaf spring
2.4 Modeling Procedure for Leaf Spring
1. First create the key point100 at origin ,i.e. x ,y,
z=(0,0,0)
2. Create the another key point200 at some
arbitrary distance in Z-direction, say x, y, z = (0, 0,
200)
3. Join the above two key points 100 and 200 to get
the reference axis.
4. By using data from mathematical analysis create
the key point1 with a distance of radius of
curvature R1 in vertically down-ward direction, i.e
x, y, z = (0, -R1, 0).
5. Similarly key points 2 and 3 correspond to R2,
i.e. x, y, z = (0,-R2,0), key points 4 and 5
corresponds to R3, i.e. x, y, z = (0, -R3, 0), Key point
20 corresponds to R11. i.e x, y, z = (0, -R11, 0)
6. Join the pair of key points sequentially as
follows:
Key points 1 and 2, 2 and 3, 3 and 4...and 19
and 20.
7. Then line1 formed by the key points 1 and 2,
line2 formed by the key points 2 and 3 and line10
formed by the key points 19 and 20.
8. Extrude the above lines with respect to
reference axis stated in step3 as Follows:
Extrude line1 with an angle Ф1, will get area1
Extrude line2 with an angle Ф2, will get area2
…and
Extrude line10 with an angle Ф10, will get
area10.
9. After extruding all the lines, the semi area of
the spring without eye will form on XY- plane with
significant degeneracy.
10. To avoid degeneracy, extend the right side line
of smallest area i.e. area 10 to some extent such that
it cross the top most area i.e. area1.Now divide area
by line. For this, select the areas left to extended
line1 and divide with that line. Similarly, extend the
right side line of second smallest area i.e. area9 to
some extent such that it cross the top most area i.e.
area1. Again divide area by line. For this select the
areas left to extended line2 and divide with that line.
11. The above process is to be done up to
extension of line of area9 and divide area by
extension line9.
12. To get the full area of the leaf spring. Shift
the origin to the top left most area key point i.e. key
point1. Reflect the entire area with respect to YZ –
plane.
13. To get the solid model of the leaf spring
Extrude the area by Z -offset to a length equal to the
width of the leaf spring.
Fig.1 shows the model of the steel leaf spring.
Figures 2, 3, 4 represent the mono-composite leaf
springs modeled by using the above procedure.
Table.2. gives the geometric properties of mono
composite leaf spring where the thickness are
calculated basing on the same stiffness and are
shown in annexure-1
FIG.1 Solid Model of Steel Leaf Spring
FIG.2 Solid Model of E-Glass/Epoxy Mono
Composite Leaf Spring
Fig.3 Solid Model Of Graphite / Epoxy Mono
Composite Leaf Spring
FIG.4 Solid Model of Carbon/Epoxy Composite
Leaf Spring
Leaf
number
Full leaf
Length
(mm)
Half
leaf
Length
(mm)
Radius of
Curvature
(mm)
Half
rotational
Angle
(Deg)
1 1153.33 576.66 961.11 34.37
2 1153.33 576.66 967.11 34.37
3 1047.97 523.98 973.11 30.84
4 942.64 471.32 979.11 27.57
5 837.31 418.65 985.11 24.34
6 731.98 365.99 991.11 21.15
7 626.65 313.32 997.11 18.00
8 521.32 260.66 1003.11 14.88
9 415.99 207.99 1009.11 11.80
10 310.66 155.33 1015.11 8.76
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
760 | P a g e
Number of graduated leaves nG = 8
Total Number of leaves n = 10
Table: 1 Design Parameters of Steel leaf spring
2.4 Modeling Procedure for Leaf Spring
1. First create the key point100 at origin ,i.e. x ,y,
z=(0,0,0)
2. Create the another key point200 at some
arbitrary distance in Z-direction, say x, y, z = (0, 0,
200)
3. Join the above two key points 100 and 200 to get
the reference axis.
4. By using data from mathematical analysis create
the key point1 with a distance of radius of
curvature R1 in vertically down-ward direction, i.e
x, y, z = (0, -R1, 0).
5. Similarly key points 2 and 3 correspond to R2,
i.e. x, y, z = (0,-R2,0), key points 4 and 5
corresponds to R3, i.e. x, y, z = (0, -R3, 0), Key point
20 corresponds to R11. i.e x, y, z = (0, -R11, 0)
6. Join the pair of key points sequentially as
follows:
Key points 1 and 2, 2 and 3, 3 and 4...and 19
and 20.
7. Then line1 formed by the key points 1 and 2,
line2 formed by the key points 2 and 3 and line10
formed by the key points 19 and 20.
8. Extrude the above lines with respect to
reference axis stated in step3 as Follows:
Extrude line1 with an angle Ф1, will get area1
Extrude line2 with an angle Ф2, will get area2
…and
Extrude line10 with an angle Ф10, will get
area10.
9. After extruding all the lines, the semi area of
the spring without eye will form on XY- plane with
significant degeneracy.
10. To avoid degeneracy, extend the right side line
of smallest area i.e. area 10 to some extent such that
it cross the top most area i.e. area1.Now divide area
by line. For this, select the areas left to extended
line1 and divide with that line. Similarly, extend the
right side line of second smallest area i.e. area9 to
some extent such that it cross the top most area i.e.
area1. Again divide area by line. For this select the
areas left to extended line2 and divide with that line.
11. The above process is to be done up to
extension of line of area9 and divide area by
extension line9.
12. To get the full area of the leaf spring. Shift
the origin to the top left most area key point i.e. key
point1. Reflect the entire area with respect to YZ –
plane.
13. To get the solid model of the leaf spring
Extrude the area by Z -offset to a length equal to the
width of the leaf spring.
Fig.1 shows the model of the steel leaf spring.
Figures 2, 3, 4 represent the mono-composite leaf
springs modeled by using the above procedure.
Table.2. gives the geometric properties of mono
composite leaf spring where the thickness are
calculated basing on the same stiffness and are
shown in annexure-1
FIG.1 Solid Model of Steel Leaf Spring
FIG.2 Solid Model of E-Glass/Epoxy Mono
Composite Leaf Spring
Fig.3 Solid Model Of Graphite / Epoxy Mono
Composite Leaf Spring
FIG.4 Solid Model of Carbon/Epoxy Composite
Leaf Spring
Leaf
number
Full leaf
Length
(mm)
Half
leaf
Length
(mm)
Radius of
Curvature
(mm)
Half
rotational
Angle
(Deg)
1 1153.33 576.66 961.11 34.37
2 1153.33 576.66 967.11 34.37
3 1047.97 523.98 973.11 30.84
4 942.64 471.32 979.11 27.57
5 837.31 418.65 985.11 24.34
6 731.98 365.99 991.11 21.15
7 626.65 313.32 997.11 18.00
8 521.32 260.66 1003.11 14.88
9 415.99 207.99 1009.11 11.80
10 310.66 155.33 1015.11 8.76
Malaga. Anil Kumar, T.N.Charyulu, Ch.Ramesh / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
761 | P a g e
Table: 2. Geometric Properties of Mono Composite
leaf spring
3. Analysis of Steel Leaf Spring
3.1Material Properties:
Material selected is Manganese Silicon Steel (Steel
55Si2Mn90)
Young’s Modulus E = 2.1E5 N/mm2
Density = 7.86E-6 kg/mm3
Poisson’s ratio = 0.3
Tensile stress = 1962 N/mm2
Yield stress = 1470 N/mm2
3.2 Element type
• SOLID45- 3-D Structural Solid
• CONTA174 - 3-D 8-Node Surface-to-
Surface Contact
3.2.1 SOLID 45- 3-D Structural Solid
SOLID 45 is used for the 3-D modeling of solid
structures.
The element is defined by eight nodes having three
degrees of freedom at each node: translations in the
nodal x, y, and z directions
3.2.2 CONTA174/170 - 3-D 8-Node Surface-to-
Surface Contact
CONTA174 is an 8-node element that is intended
for general rigid-flexible and flexible-flexible
contact analysis.
CONTA174 is surface-to-surface contact element .
CONTA174 is applicable to 3-D geometries. It may
be applied for contact between solid bodies or
shells.
3.3 Static Analysis
The fig.5 shows the contact pressure in the leaf
spring and it varies from 0 to 19.989MPa
FIG.5 Plot of Contact Pressure in Steel Leaf Spring
The following fig. 6 shows the contact total stress
whose value is 19.991MPa
FIG.6 Plot of Contact Total Stress in Steel Leaf
Spring
The fig. 7 shows the contact gap distance along the
length of the leaf and it is -0.888E-15
FIG.7 Plot of Contact Gap Distance in Steel Leaf
Spring
FIG.8 Plot of Contact Penetration in Steel Leaf
Spring
3.4 Modal Analysis
Modal analysis is carried out to determine
the natural frequencies and mode shapes of the leaf
spring. Modal analysis need only boundary
conditions, it is not associated with the loads
applied, because natural frequencies are resulted
from the free vibrations. The boundary conditions
are same as in the case of static analysis.
From the modal analysis results, the natural
frequencies of the steel leaf spring are found to be
Material
HHaallff
LLeennggtthh
((mmmm))
WWii
ddtthh
((mm
mm))
TThhiicckk
nneessss
((mmmm))
RRaaddiiuu
ss ooff
ccuurrvvaatt
uurree
((mmmm))
HHaallff
rroottaattiioo
nnaall
AAnnggllee
((DDeegg))
Carbon/
epoxy
576.66 50 13.68 961.1
1
34.37
Graphite/
epoxy
576.66 50 11.55 961.1
1
34.37
E-
Glass/epo
xy
576.66 50 21.50 961.1
1
34.37
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
761 | P a g e
Table: 2. Geometric Properties of Mono Composite
leaf spring
3. Analysis of Steel Leaf Spring
3.1Material Properties:
Material selected is Manganese Silicon Steel (Steel
55Si2Mn90)
Young’s Modulus E = 2.1E5 N/mm2
Density = 7.86E-6 kg/mm3
Poisson’s ratio = 0.3
Tensile stress = 1962 N/mm2
Yield stress = 1470 N/mm2
3.2 Element type
• SOLID45- 3-D Structural Solid
• CONTA174 - 3-D 8-Node Surface-to-
Surface Contact
3.2.1 SOLID 45- 3-D Structural Solid
SOLID 45 is used for the 3-D modeling of solid
structures.
The element is defined by eight nodes having three
degrees of freedom at each node: translations in the
nodal x, y, and z directions
3.2.2 CONTA174/170 - 3-D 8-Node Surface-to-
Surface Contact
CONTA174 is an 8-node element that is intended
for general rigid-flexible and flexible-flexible
contact analysis.
CONTA174 is surface-to-surface contact element .
CONTA174 is applicable to 3-D geometries. It may
be applied for contact between solid bodies or
shells.
3.3 Static Analysis
The fig.5 shows the contact pressure in the leaf
spring and it varies from 0 to 19.989MPa
FIG.5 Plot of Contact Pressure in Steel Leaf Spring
The following fig. 6 shows the contact total stress
whose value is 19.991MPa
FIG.6 Plot of Contact Total Stress in Steel Leaf
Spring
The fig. 7 shows the contact gap distance along the
length of the leaf and it is -0.888E-15
FIG.7 Plot of Contact Gap Distance in Steel Leaf
Spring
FIG.8 Plot of Contact Penetration in Steel Leaf
Spring
3.4 Modal Analysis
Modal analysis is carried out to determine
the natural frequencies and mode shapes of the leaf
spring. Modal analysis need only boundary
conditions, it is not associated with the loads
applied, because natural frequencies are resulted
from the free vibrations. The boundary conditions
are same as in the case of static analysis.
From the modal analysis results, the natural
frequencies of the steel leaf spring are found to be
Material
HHaallff
LLeennggtthh
((mmmm))
WWii
ddtthh
((mm
mm))
TThhiicckk
nneessss
((mmmm))
RRaaddiiuu
ss ooff
ccuurrvvaatt
uurree
((mmmm))
HHaallff
rroottaattiioo
nnaall
AAnnggllee
((DDeegg))
Carbon/
epoxy
576.66 50 13.68 961.1
1
34.37
Graphite/
epoxy
576.66 50 11.55 961.1
1
34.37
E-
Glass/epo
xy
576.66 50 21.50 961.1
1
34.37
Malaga. Anil Kumar, T.N.Charyulu, Ch.Ramesh / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
762 | P a g e
2.847Hz, 19.443Hz, 21.523Hz, 55.91Hz, and
56.627Hz
4. Analysis of Mono Composite leaf spring
The aim of the analysis is to study the
mono composite leaf spring and verification of the
results to be within the desirable limits. Three
different composite materials have been selected
.They are E-Glass / Epoxy, Graphite / Epoxy and
Carbon/ epoxy composite materials. Analysis is
done using ANSYS.
4.1. Analysis of E-Glass /Epoxy Composite Leaf
Spring
4.1.1 FEM Model details
Mechanical properties:
Extensional Elastic Modulus E1 =
43E+3 MPa
Transverse Elastic Modulus E2 = 9E+3
MPa
In-plane Shear Modulus G12 =
4.5E+3 MPa
Major Poisson’s Ratio 12 = 0.27
Minor Poisson’s Ratio 21 = 0.06
Density =
2000kg/m3
Yield strength Sy =
2000MPa
4.1.2 Element type
The element used in descretization of the
solid model is 8 noded brick element (SOLID 45)
which has 3 translational degrees of freedom in x, y
and z direction.
4.1.3 Stress Analysis
FE analysis for stress and deformation are
carried out. For this load of 3330N is applied at the
base of leaf spring in the middle. The constraints
are, the front eye is constrained as UY, UZ and the
nodes at the middle are constrained as UX, UZ.
The fig: 9 shows the von-mises stress at different
positions of the leaf spring and it varies from
0.1147MPa to 475.606Mpa
FIG.9 Von-Mises Stress Plot of E-Glass/Epoxy
Composite Leaf Spring
4.1.4 Modal Analysis
Modal analysis is performed to determine
the natural frequencies and mode shapes of the leaf
spring.
After the post processing, from solution options,
new analysis is selected as modal. The analysis can
be performed by Block Lancos method or Subspace
method. The subspace method is selected. In the
next step select the no. of modes to extract and
expand are taken as 5. From the modal analysis
results, it is found that the first five natural
frequencies of E-Glass / epoxy mono composite leaf
spring are 1.244Hz, 10.244 Hz, 15.231 Hz, 27.902
Hz, and 46.612 Hz
The fig.10 shows the mode shape at a natural
frequency of 1.209Hz and the displacement is
1.244mm
FIG.10 Total Deformation Plot for 1st Natural
Frequency
4.2 Analysis of Graphite / Epoxy Composite Leaf
Spring
4.2.1 FEM Model details
Mechanical Properties:
Extensional Elastic ModulusE1 =294E+3MPa
Transverse Elastic Modulus E2 =6.4E+3 MPa
In-plane Shear Modulus G12 =4.9E+3 MPa
Major Poisson’s Ratio 12 = 0.23
Minor Poisson’s Ratio 21 = 0.01
Density = 1590kg/m3
Yield Strength Sy = 2067Mpa
4.2.2 Element Type
The element used in descretization of the
solid model is 8 noded brick element (SOLID 45)
which has 3 translational degrees of freedom in x, y
and z direction.
4.2.3 Stress Analysis
FE analysis for stress and deformation are
carried out. For this load of 3330N is applied at the
base of leaf spring in the middle. The constraints
are, the front eye is constrained as UY, UZ and the
nodes at the middle are constrained as UX, UZ.
From the results it is found that displacement is
80.369mm and maximum stress is 1573 Mpa.
The fig: 11 shows the deformed shape of
the leaf spring with respect to undeformed shape for
the load of 3300N
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
762 | P a g e
2.847Hz, 19.443Hz, 21.523Hz, 55.91Hz, and
56.627Hz
4. Analysis of Mono Composite leaf spring
The aim of the analysis is to study the
mono composite leaf spring and verification of the
results to be within the desirable limits. Three
different composite materials have been selected
.They are E-Glass / Epoxy, Graphite / Epoxy and
Carbon/ epoxy composite materials. Analysis is
done using ANSYS.
4.1. Analysis of E-Glass /Epoxy Composite Leaf
Spring
4.1.1 FEM Model details
Mechanical properties:
Extensional Elastic Modulus E1 =
43E+3 MPa
Transverse Elastic Modulus E2 = 9E+3
MPa
In-plane Shear Modulus G12 =
4.5E+3 MPa
Major Poisson’s Ratio 12 = 0.27
Minor Poisson’s Ratio 21 = 0.06
Density =
2000kg/m3
Yield strength Sy =
2000MPa
4.1.2 Element type
The element used in descretization of the
solid model is 8 noded brick element (SOLID 45)
which has 3 translational degrees of freedom in x, y
and z direction.
4.1.3 Stress Analysis
FE analysis for stress and deformation are
carried out. For this load of 3330N is applied at the
base of leaf spring in the middle. The constraints
are, the front eye is constrained as UY, UZ and the
nodes at the middle are constrained as UX, UZ.
The fig: 9 shows the von-mises stress at different
positions of the leaf spring and it varies from
0.1147MPa to 475.606Mpa
FIG.9 Von-Mises Stress Plot of E-Glass/Epoxy
Composite Leaf Spring
4.1.4 Modal Analysis
Modal analysis is performed to determine
the natural frequencies and mode shapes of the leaf
spring.
After the post processing, from solution options,
new analysis is selected as modal. The analysis can
be performed by Block Lancos method or Subspace
method. The subspace method is selected. In the
next step select the no. of modes to extract and
expand are taken as 5. From the modal analysis
results, it is found that the first five natural
frequencies of E-Glass / epoxy mono composite leaf
spring are 1.244Hz, 10.244 Hz, 15.231 Hz, 27.902
Hz, and 46.612 Hz
The fig.10 shows the mode shape at a natural
frequency of 1.209Hz and the displacement is
1.244mm
FIG.10 Total Deformation Plot for 1st Natural
Frequency
4.2 Analysis of Graphite / Epoxy Composite Leaf
Spring
4.2.1 FEM Model details
Mechanical Properties:
Extensional Elastic ModulusE1 =294E+3MPa
Transverse Elastic Modulus E2 =6.4E+3 MPa
In-plane Shear Modulus G12 =4.9E+3 MPa
Major Poisson’s Ratio 12 = 0.23
Minor Poisson’s Ratio 21 = 0.01
Density = 1590kg/m3
Yield Strength Sy = 2067Mpa
4.2.2 Element Type
The element used in descretization of the
solid model is 8 noded brick element (SOLID 45)
which has 3 translational degrees of freedom in x, y
and z direction.
4.2.3 Stress Analysis
FE analysis for stress and deformation are
carried out. For this load of 3330N is applied at the
base of leaf spring in the middle. The constraints
are, the front eye is constrained as UY, UZ and the
nodes at the middle are constrained as UX, UZ.
From the results it is found that displacement is
80.369mm and maximum stress is 1573 Mpa.
The fig: 11 shows the deformed shape of
the leaf spring with respect to undeformed shape for
the load of 3300N
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Malaga. Anil Kumar, T.N.Charyulu, Ch.Ramesh / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
763 | P a g e
FIG.11 Deformed & Undeformed Plot of Mono
Composite Leaf Spring
The fig: 12 shows the von-mises stress at different
positions of the leaf spring and it varies from
2.36MPa to 1573MPa
FIG.12 Von-Mises Stress Plot of Graphite /Epoxy
Composite Leaf Spring
4.2.4 Modal Analysis
Modal analysis is performed to determine
the natural frequencies and mode shapes of the leaf
spring.
After the model is created, select the
analysis as modal analysis. The analysis can be
performed by Block Lancos method or Subspace
method. The subspace method is selected. In the
next step select the no. of modes to extract and
expand as 5. Then the problem is solved. From the
modal analysis results, it is found that the first five
natural frequencies are 1.924Hz, 16.868 Hz, 42.56
Hz, 46.337 Hz, and 90.172 Hz
The fig.13 shows the mode shape at a natural
frequency of 1.985Hz and the displacement is
1.924mm
FIG.13 Total Deformation Plot for 1st Natural
Frequency
4.3 Analysis of Carbon / Epoxy Composite Leaf
Spring
4.3.1 FEM Model details
Mechanical Properties:
Extensional Elastic ModulusE1 = 177E+3 MPa
Transverse Elastic ModulusE2 = 10.6E+3 MPa
In-plane Shear Modulus G12 = 7.6E+3 MPa
Major Poisson’s Ratio 12 = 0.27
Minor Poisson’s Ratio 21 = 0.02
Density = 1600kg/m3
Yield strength Sy= 1900MPa
4.3.2 Element type
The element used in descretization of the
solid model is 8 noded brick element (SOLID 45)
which has 3 translational degrees of freedom in x, y
and z direction.
4.3.4 Stress Analysis
FE analysis for stress and deformation are
carried out. For this load of 3330N is applied at the
base of leaf spring in the middle. The constraints
are, the front eye is constrained as UY, UZ and the
nodes at the middle are constrained as UX, UZ. We
can obtain the stresses and displacement by
performing this analysis. From the results it is found
that the maximum stress is 1061Mpa and
displacement is 82.662mm
The fig: 14 shows the deformed shape of the leaf
spring with respect to undeformed shape for the load
of 3300N
FIG.14 Deformed & Undeformed Plot of Mono
Composite Leaf Spring
The fig: 15 shows the von-mises stress at different
positions of the leaf spring and it varies from
1.006MPa to 1061MPa
FIG.15 Von-Mises Stress Plot of Carbon/Epoxy
Composite Leaf Spring
4.3.5 Modal Analysis
Modal analysis is performed to determine
the natural frequencies and mode shapes of the leaf
spring.
After the model is created, select the analysis as
modal analysis. The analysis can be performed by
Block Lancos method or Subspace method. The
subspace method is selected. In the next step select
the no. of modes to extract and expand as 5. Then
the problem is solved. From the modal analysis
results, it is found that the first five natural
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
763 | P a g e
FIG.11 Deformed & Undeformed Plot of Mono
Composite Leaf Spring
The fig: 12 shows the von-mises stress at different
positions of the leaf spring and it varies from
2.36MPa to 1573MPa
FIG.12 Von-Mises Stress Plot of Graphite /Epoxy
Composite Leaf Spring
4.2.4 Modal Analysis
Modal analysis is performed to determine
the natural frequencies and mode shapes of the leaf
spring.
After the model is created, select the
analysis as modal analysis. The analysis can be
performed by Block Lancos method or Subspace
method. The subspace method is selected. In the
next step select the no. of modes to extract and
expand as 5. Then the problem is solved. From the
modal analysis results, it is found that the first five
natural frequencies are 1.924Hz, 16.868 Hz, 42.56
Hz, 46.337 Hz, and 90.172 Hz
The fig.13 shows the mode shape at a natural
frequency of 1.985Hz and the displacement is
1.924mm
FIG.13 Total Deformation Plot for 1st Natural
Frequency
4.3 Analysis of Carbon / Epoxy Composite Leaf
Spring
4.3.1 FEM Model details
Mechanical Properties:
Extensional Elastic ModulusE1 = 177E+3 MPa
Transverse Elastic ModulusE2 = 10.6E+3 MPa
In-plane Shear Modulus G12 = 7.6E+3 MPa
Major Poisson’s Ratio 12 = 0.27
Minor Poisson’s Ratio 21 = 0.02
Density = 1600kg/m3
Yield strength Sy= 1900MPa
4.3.2 Element type
The element used in descretization of the
solid model is 8 noded brick element (SOLID 45)
which has 3 translational degrees of freedom in x, y
and z direction.
4.3.4 Stress Analysis
FE analysis for stress and deformation are
carried out. For this load of 3330N is applied at the
base of leaf spring in the middle. The constraints
are, the front eye is constrained as UY, UZ and the
nodes at the middle are constrained as UX, UZ. We
can obtain the stresses and displacement by
performing this analysis. From the results it is found
that the maximum stress is 1061Mpa and
displacement is 82.662mm
The fig: 14 shows the deformed shape of the leaf
spring with respect to undeformed shape for the load
of 3300N
FIG.14 Deformed & Undeformed Plot of Mono
Composite Leaf Spring
The fig: 15 shows the von-mises stress at different
positions of the leaf spring and it varies from
1.006MPa to 1061MPa
FIG.15 Von-Mises Stress Plot of Carbon/Epoxy
Composite Leaf Spring
4.3.5 Modal Analysis
Modal analysis is performed to determine
the natural frequencies and mode shapes of the leaf
spring.
After the model is created, select the analysis as
modal analysis. The analysis can be performed by
Block Lancos method or Subspace method. The
subspace method is selected. In the next step select
the no. of modes to extract and expand as 5. Then
the problem is solved. From the modal analysis
results, it is found that the first five natural
Malaga. Anil Kumar, T.N.Charyulu, Ch.Ramesh / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
764 | P a g e
frequencies are 1.784Hz, 15.155 Hz, 33.443 Hz,
41.586 Hz, and 80.744 Hz
The fig.166 shows the mode shape at a natural
frequency of 1.784Hz and the displacement is
1.761mm
FIG16. Total Deformation Plot for 1st Natural
Frequency
5. Results And Discussions
From the results of static analysis of steel leaf
spring, it is seen the displacement of leaf spring is
92.591mm which is well below the camber length of
leaf spring (i.e. 180mm). Therefore from the static
analysis, the stiffness of the leaf spring is found to
be 35.60mm. It is seen that the maximum Von-
Mises stress is about 596.047Mpa, which is less
than the yield strength of the material. The FEA
results are compared with the theoretical results.
From the modal analysis, the first five natural
frequencies are found to be are found to be 2.847Hz,
19.443Hz, 21.523Hz, 55.91Hz, and 56.627Hz.
Static analysis has been done for three different
mono composite leaf springs of different materials.
They are E-glass/epoxy, carbon/epoxy,
graphite/epoxy. From the results of static analysis of
mono composite leaf spring, the displacements of
the E- glass /epoxy, carbon/epoxy, graphite/epoxy
are 89.858mm, 82.662mm and 80.369mm. And the
corresponding stiffness is 36.72N/mm, 39.92N/mm
and 41.06N/mm.
TABLE: 3 Displacement and Stiffness Results
Material Displace
ment
(Theoreti
cal)
Displacem
ent
(Ansys)
Stiffness
(Theoretic
al)
Stiffness
(Ansys)
Steel 102.20 92.591 32.28 35.60
E-Glass/epoxy 108.48 89.858 30.42 36.72
Carbon/epoxy 102.20 82.662 32.28 39.92
Graphite/epoxy 102.20 80.369 32.28 41.06
From the table, when compared with the stiffness of
steel leaf spring, the stiffness of all the mono
composite leaf springs is higher.
TABLE: 4 Theoretical and Ansys Results
Material Theoretical Stress
(MPa)
Von-Mises Stress
(MPa)
Steel 621.60 596.05
E-glass/epoxy 479.74 475.60
Carbon /epoxy 1184.00 1061.00
Graphite/epoxy 1662.00 1573.00
The following table shows the first five natural
frequencies of the three mono-composite leaf
springs which are obtained by modal analysis:
TABLE: 5 Modal Analysis Results
SET E-Glass/Epoxy Carbon/Epoxy Graphite/Epoxy
1 1.209 1.784 `1.985
2 10.244 15.155 16.868
3 15.231 33.443 42.560
4 27.902 41.586 46.337
5 46.612 80.744 90.172
The following table shows the weight reduction due
to replacement of steel leaf spring with mono-
composite leaf spring.
TABLE: 6 Results Showing the % Weight
Reduction
Material Weight(N) % weight
reduction
Steel 88.290 -
E-glass / epoxy 12.528 85.00
Carbon / epoxy 5.133 92.94
Graphite /
epoxy
6.233 94.18
Composite mono leaf spring reduces the weight by
85 % for E-Glass/Epoxy, 94.18% for
Graphite/Epoxy, and 92.94 % for Carbon/Epoxy
over conventional leaf spring.
6. CONCLUSIONS
In the present work, a steel leaf spring was
replaced by a mono composite leaf spring due to
high strength to weight ratio for the same load
carrying capacity and stiffness. The dimensions of a
leaf spring of a light weight vehicle are chosen and
modeled using ANSYS 9.0. As the leaf spring is
symmetrical about the axis, only half part of the
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
764 | P a g e
frequencies are 1.784Hz, 15.155 Hz, 33.443 Hz,
41.586 Hz, and 80.744 Hz
The fig.166 shows the mode shape at a natural
frequency of 1.784Hz and the displacement is
1.761mm
FIG16. Total Deformation Plot for 1st Natural
Frequency
5. Results And Discussions
From the results of static analysis of steel leaf
spring, it is seen the displacement of leaf spring is
92.591mm which is well below the camber length of
leaf spring (i.e. 180mm). Therefore from the static
analysis, the stiffness of the leaf spring is found to
be 35.60mm. It is seen that the maximum Von-
Mises stress is about 596.047Mpa, which is less
than the yield strength of the material. The FEA
results are compared with the theoretical results.
From the modal analysis, the first five natural
frequencies are found to be are found to be 2.847Hz,
19.443Hz, 21.523Hz, 55.91Hz, and 56.627Hz.
Static analysis has been done for three different
mono composite leaf springs of different materials.
They are E-glass/epoxy, carbon/epoxy,
graphite/epoxy. From the results of static analysis of
mono composite leaf spring, the displacements of
the E- glass /epoxy, carbon/epoxy, graphite/epoxy
are 89.858mm, 82.662mm and 80.369mm. And the
corresponding stiffness is 36.72N/mm, 39.92N/mm
and 41.06N/mm.
TABLE: 3 Displacement and Stiffness Results
Material Displace
ment
(Theoreti
cal)
Displacem
ent
(Ansys)
Stiffness
(Theoretic
al)
Stiffness
(Ansys)
Steel 102.20 92.591 32.28 35.60
E-Glass/epoxy 108.48 89.858 30.42 36.72
Carbon/epoxy 102.20 82.662 32.28 39.92
Graphite/epoxy 102.20 80.369 32.28 41.06
From the table, when compared with the stiffness of
steel leaf spring, the stiffness of all the mono
composite leaf springs is higher.
TABLE: 4 Theoretical and Ansys Results
Material Theoretical Stress
(MPa)
Von-Mises Stress
(MPa)
Steel 621.60 596.05
E-glass/epoxy 479.74 475.60
Carbon /epoxy 1184.00 1061.00
Graphite/epoxy 1662.00 1573.00
The following table shows the first five natural
frequencies of the three mono-composite leaf
springs which are obtained by modal analysis:
TABLE: 5 Modal Analysis Results
SET E-Glass/Epoxy Carbon/Epoxy Graphite/Epoxy
1 1.209 1.784 `1.985
2 10.244 15.155 16.868
3 15.231 33.443 42.560
4 27.902 41.586 46.337
5 46.612 80.744 90.172
The following table shows the weight reduction due
to replacement of steel leaf spring with mono-
composite leaf spring.
TABLE: 6 Results Showing the % Weight
Reduction
Material Weight(N) % weight
reduction
Steel 88.290 -
E-glass / epoxy 12.528 85.00
Carbon / epoxy 5.133 92.94
Graphite /
epoxy
6.233 94.18
Composite mono leaf spring reduces the weight by
85 % for E-Glass/Epoxy, 94.18% for
Graphite/Epoxy, and 92.94 % for Carbon/Epoxy
over conventional leaf spring.
6. CONCLUSIONS
In the present work, a steel leaf spring was
replaced by a mono composite leaf spring due to
high strength to weight ratio for the same load
carrying capacity and stiffness. The dimensions of a
leaf spring of a light weight vehicle are chosen and
modeled using ANSYS 9.0. As the leaf spring is
symmetrical about the axis, only half part of the
Malaga. Anil Kumar, T.N.Charyulu, Ch.Ramesh / International Journal of Engineering
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
765 | P a g e
spring is modeled by considering it as a cantilever
beam. Analysis has been performed by using
ANSYS by applying the boundary conditions and
the load. The boundary conditions are UY, UZ at the
front eye end and UX, UZ in the middle. A load of
3300N was applied at the base in the middle of the
leaf spring in the Y-direction. Later a mono
composite leaf spring of uniform thickness and
width was modeled so as to obtain the same
displacement and hence same stiffness as that of
steel leaf spring. Three different composite materials
have been used for analysis of mono-composite leaf
spring. They are E-glass/epoxy, Graphite/epoxy and
carbon/epoxy. Static and model analysis has been
performed.
1. From the static analysis results it is found that
there is a maximum displacement of 92.591mm
in the steel leaf spring and the corresponding
displacements in E-glass / epoxy,
graphite/epoxy, and carbon/epoxy are
89.858mm, 80.369mm and 82.662mm. And all
the values are nearly equal and are below the
camber length for a given load of 3300N.
2. From the static analysis results, we see that the
von-mises stress in the steel is 596.047MPa. And
the von-mises stress in E-glass/epoxy, Graphite
/epoxy and Carbon/epoxy is 475.606MPa,
1556MPa and 1061MPa. Among the three
composite leaf springs, only E-glass/epoxy
composite leaf spring has lower stresses than the
steel leaf spring.
3. All the FEA results are compared with the
theoretical results and it is found that they are
within the allowable limits and nearly equal to
the theoretical results.
4. The composite leaf spring is modeled for the
same stiffness as that of the steel leaf spring. It is
found that the stiffness of all the composite leaf
springs is more when compared with that of the
steel leaf spring. The stiffness of steel leaf spring
is 35.60N/mm and similarly stiffness of E-
glass/epoxy, graphite/epoxy and carbon/epoxy
composite leaf springs are 36.72N/mm,
39.92N/mm and 41.06N/mm respectively.
5. E-glass/epoxy composite leaf spring can be
suggested for replacing the steel leaf spring both
from stiffness and stress point of view.
6. A comparative study has been made between
steel and composite leaf spring with respect to
strength and weight. Composite mono leaf spring
reduces the weight by 85% for E-Glass/Epoxy,
94.18% for Graphite/Epoxy, and 92.94 % for
Carbon/Epoxy over conventional leaf spring.
7. For the modal analysis, same boundary
conditions are applied and the load need not be
applied. The natural frequencies and the mode
shapes are important parameters in the design of
a structure for dynamic loading conditions.
8. From the modal analysis results, the natural
frequencies of the steel leaf spring are found to
be 2.847Hz, 19.443Hz, 21.523Hz, 55.91Hz, and
56.627Hz.
9. The first five natural frequencies of E-Glass /
epoxy mono composite leaf spring are 1.244Hz,
10.244 Hz, 15.231 Hz, 27.902 Hz, and 46.612
Hz.
10. The first five natural frequencies of Graphite /
epoxy composite leaf spring are 1.924Hz, 16.868
Hz, 42.56 Hz, 46.337 Hz, and 90.172 Hz.
11. It is found that the first five natural frequencies
of carbon/epoxy are 1.784Hz, 15.155 Hz, 33.443
Hz, 41.586 Hz, and 80.744 Hz
REFERNCES
[1] Gary Leevy and Khoa Cao, 2004
“Evaluation of a Multi-Leaf Hybrid
Springs for Automotive Suspensions” SAE
paper series, 2004-01-0782
[2] Mouleeswaran SENTHIL KUMAR,
Sabapathy VIJAYARANGAN, “
Analytical and Experimental studies on
Fatigue Life Prediction of steel and
composite Multi-leaf spring for Light
Passenger Vehicles using Life Data
Analysis” Materials science .
vol.13.No.2.2007
[3] Erdogan KILIC “Analysis of composite
leaf springs” 2006, http://
www.elsevier.com
[4] C.K. Clarke and G.E. Borowski “
Evaluation of a leaf spring failure” ASM
International 1547-7029
[5] Thimmegowda RANGASWAMY.,
Sabapathy VIJAYARANGAN, Optimal
Sizing and Stacking Sequence of
Composite Drive Shafts MATERIALS
SCIENCE Vol. 11, No. 2. 2005
[6] Tirupathi R. Chandrupatla & Ashok
D.Belegundu, “Introduction to Finite
Elements in Engineering”. Third Edition-
Pearson Education Pvt. Ltd- 2002.
[7] S.S.Rao, “The Finite Element Method in
Engineering”. Third Edition- Butterworth
Heinemann Publications-2001.
[8] T.V.S.Sundarajamoorthy, N.Shanmugam “
Machine Design”- Eighth Edition-
Published by M.Sethuraaman, Anuradha
Agencies- 2000
[9] O.P.Khanna, “Material science and
metallurgy”-First edition –Dhanapati Rai
Publications-1999.
[10] Autar. K.Kaw, “ Mechanics of Composite
materials” CRC Press-1999
[11] Gummadi Sanjay, Akula Jagadeesh Kumar
“Optimum design and analysis of a
composite drive shaft for an automobile”
Masters Degree Thesis.
Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue 6, November- December 2012, pp.759-765
765 | P a g e
spring is modeled by considering it as a cantilever
beam. Analysis has been performed by using
ANSYS by applying the boundary conditions and
the load. The boundary conditions are UY, UZ at the
front eye end and UX, UZ in the middle. A load of
3300N was applied at the base in the middle of the
leaf spring in the Y-direction. Later a mono
composite leaf spring of uniform thickness and
width was modeled so as to obtain the same
displacement and hence same stiffness as that of
steel leaf spring. Three different composite materials
have been used for analysis of mono-composite leaf
spring. They are E-glass/epoxy, Graphite/epoxy and
carbon/epoxy. Static and model analysis has been
performed.
1. From the static analysis results it is found that
there is a maximum displacement of 92.591mm
in the steel leaf spring and the corresponding
displacements in E-glass / epoxy,
graphite/epoxy, and carbon/epoxy are
89.858mm, 80.369mm and 82.662mm. And all
the values are nearly equal and are below the
camber length for a given load of 3300N.
2. From the static analysis results, we see that the
von-mises stress in the steel is 596.047MPa. And
the von-mises stress in E-glass/epoxy, Graphite
/epoxy and Carbon/epoxy is 475.606MPa,
1556MPa and 1061MPa. Among the three
composite leaf springs, only E-glass/epoxy
composite leaf spring has lower stresses than the
steel leaf spring.
3. All the FEA results are compared with the
theoretical results and it is found that they are
within the allowable limits and nearly equal to
the theoretical results.
4. The composite leaf spring is modeled for the
same stiffness as that of the steel leaf spring. It is
found that the stiffness of all the composite leaf
springs is more when compared with that of the
steel leaf spring. The stiffness of steel leaf spring
is 35.60N/mm and similarly stiffness of E-
glass/epoxy, graphite/epoxy and carbon/epoxy
composite leaf springs are 36.72N/mm,
39.92N/mm and 41.06N/mm respectively.
5. E-glass/epoxy composite leaf spring can be
suggested for replacing the steel leaf spring both
from stiffness and stress point of view.
6. A comparative study has been made between
steel and composite leaf spring with respect to
strength and weight. Composite mono leaf spring
reduces the weight by 85% for E-Glass/Epoxy,
94.18% for Graphite/Epoxy, and 92.94 % for
Carbon/Epoxy over conventional leaf spring.
7. For the modal analysis, same boundary
conditions are applied and the load need not be
applied. The natural frequencies and the mode
shapes are important parameters in the design of
a structure for dynamic loading conditions.
8. From the modal analysis results, the natural
frequencies of the steel leaf spring are found to
be 2.847Hz, 19.443Hz, 21.523Hz, 55.91Hz, and
56.627Hz.
9. The first five natural frequencies of E-Glass /
epoxy mono composite leaf spring are 1.244Hz,
10.244 Hz, 15.231 Hz, 27.902 Hz, and 46.612
Hz.
10. The first five natural frequencies of Graphite /
epoxy composite leaf spring are 1.924Hz, 16.868
Hz, 42.56 Hz, 46.337 Hz, and 90.172 Hz.
11. It is found that the first five natural frequencies
of carbon/epoxy are 1.784Hz, 15.155 Hz, 33.443
Hz, 41.586 Hz, and 80.744 Hz
REFERNCES
[1] Gary Leevy and Khoa Cao, 2004
“Evaluation of a Multi-Leaf Hybrid
Springs for Automotive Suspensions” SAE
paper series, 2004-01-0782
[2] Mouleeswaran SENTHIL KUMAR,
Sabapathy VIJAYARANGAN, “
Analytical and Experimental studies on
Fatigue Life Prediction of steel and
composite Multi-leaf spring for Light
Passenger Vehicles using Life Data
Analysis” Materials science .
vol.13.No.2.2007
[3] Erdogan KILIC “Analysis of composite
leaf springs” 2006, http://
www.elsevier.com
[4] C.K. Clarke and G.E. Borowski “
Evaluation of a leaf spring failure” ASM
International 1547-7029
[5] Thimmegowda RANGASWAMY.,
Sabapathy VIJAYARANGAN, Optimal
Sizing and Stacking Sequence of
Composite Drive Shafts MATERIALS
SCIENCE Vol. 11, No. 2. 2005
[6] Tirupathi R. Chandrupatla & Ashok
D.Belegundu, “Introduction to Finite
Elements in Engineering”. Third Edition-
Pearson Education Pvt. Ltd- 2002.
[7] S.S.Rao, “The Finite Element Method in
Engineering”. Third Edition- Butterworth
Heinemann Publications-2001.
[8] T.V.S.Sundarajamoorthy, N.Shanmugam “
Machine Design”- Eighth Edition-
Published by M.Sethuraaman, Anuradha
Agencies- 2000
[9] O.P.Khanna, “Material science and
metallurgy”-First edition –Dhanapati Rai
Publications-1999.
[10] Autar. K.Kaw, “ Mechanics of Composite
materials” CRC Press-1999
[11] Gummadi Sanjay, Akula Jagadeesh Kumar
“Optimum design and analysis of a
composite drive shaft for an automobile”
Masters Degree Thesis.
1 out of 7
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