Design Optimization Of Leaf Spring
Added on 2023-06-04
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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
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
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