Optimization of suspension spring using Design of Experiments

1. 1
CHAPTER 1

2. 2
INTRODUCTION
1.1 SUSPENSION SYSTEM:
Suspension system is the term given to the system of springs, shock absorbers and
linkages that connects a vehicle to its wheels. Suspension systems serve a dual purpose
contributing to the vehicle's road holding/handling and braking for good active safety and driving
pleasure, and keeping vehicle occupants comfortable and reasonably well isolated from road
noise, bumps, and vibrations etc. These goals are generally at odds, so the tuning of suspensions
involves finding the right compromise. It is important for the suspension to keep the road wheel
in contact with the road surface as much as possible, because all the forces acting on the vehicle
do so through the contact patches of the tires. The suspension also protects the vehicle itself and
any cargo or luggage from damage and wear. The design of front and rear suspension of a car
may be different.
1.2 Types of suspension suspension :
Suspension systems can be broadly classified into two subgroups: dependent and
independent. These terms refer to the ability of opposite wheels to move independently of each
other.
Dependent Suspension system:
A dependent suspension normally has a beam, live axle that holds wheels parallel to each
other and perpendicular to the axle. When the camber of one wheel changes, the camber of the
opposite wheel changes in the same way (by convention on one side this is a positive change in
camber and on the other side this a negative change). De Dion suspensions are also in this
category as they rigidly connect the wheels together.
Example: Leaf springs
Longitudinal semi-elliptical springs used to be common and still are used in heavy-duty
trucks and aircraft. They have the advantage that the spring rate can easily be made progressive
(non-linear).

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In a front engine, rear-drive vehicle, dependent rear suspension is either "live axle"
or deDion axle, depending on whether or not the differential is carried on the axle. Live axle is
simpler but the unsprang weight contributes to wheel bounce.
Independent suspension system:
An independent suspension allows wheels to rise and fall on their own without affecting the
opposite wheel. Suspensions with other devices, such as sway bars that link the wheels in some
way are still classed as independent.
 Swing axle
 Sliding pillar
 MacPherson strut/Chapman strut
 Upper and lower A-arm (double wishbone)
 Semi-trailing arm suspension
Semi-dependent suspensions system:
A third type is a semi-dependent suspension. In this case, the motion of one wheel does
affect the position of the other but they are not rigidly attached to each other.
In these systems the wheels of an axle are able to move relative to one another as in an
independent suspension but the position of one wheel has an effect on the position and attitude of
the other wheel. This effect is achieved via the twisting or deflecting of suspension parts under
load.
The most common type of semi-independent suspension is the twist beam.
1.3 Macpherson suspension system:
MacPherson struts consist of a wishbone or a substantial compression link stabilized by a
secondary link which provides a bottom mounting point for the hub or axle of the wheel as
shown in Fig.1.1. This lower arm system provides both lateral and longitudinal location of the
wheel. The upper part of the hub is rigidly fixed to the inner part of the strut proper, the outer
part of which extends upwards directly to a mounting in the body shell of the vehicle

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Fig. 1.1 Macpherson system
The MacPherson strut required the introduction of unibody (or monocoque) construction,
because it needs a substantial vertical space and a strong top mount, which unibodies can
provide, while benefiting them by distributing stresses. The strut will usually carry both the
coil spring on which the body is suspended and the shock absorber, which is usually in the form
of a cartridge mounted within the strut. The strut also usually has a steering arm built into the
lower inner portion. The whole assembly is very simple and can be preassembled into a unit; also
by eliminating the upper control arm, it allows for more width in the engine bay, which is useful
for smaller cars, particularly with transverse-mounted engines such as most front wheel
drive vehicles have. It can be further simplified, if needed, by substituting an anti-roll

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bar (torsion bar) for the radius arm.[4]
For those reasons, it has become almost ubiquitous with
low cost manufacturers. Furthermore, it offers an easy method to set suspension geometry.
1.4 Why MacPherson suspension systems?
• Most of the economy cars have MacPherson strut suspension system.
• Much number of problems is produced in suspension.
• It is a basic independent type suspension system.
• It is easy to construct and working simple.
• The system can be easily optimized.

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CHAPTER 2
SPRINGS

7. 7
2.1 SPRINGS:
A spring is an elastic object used to store mechanical energy. Springs are usually made
out of spring steel. Small springs can be wound from pre-hardened stock, while larger ones are
made from annealed steel and hardened after fabrication. Some non-ferrous metals are also used
including phosphor bronze and titanium for parts requiring corrosion resistance and beryllium
copper for springs carrying electrical current (because of its low electrical resistance).
When a spring is compressed or stretched, the force it exerts is proportional to its change in
length. The rate or spring constant of a spring is the change in the force it exerts, divided by the
change in deflection of the spring. An extension or compression spring has units of force divided
by distance, for example lbf/in or N/m
2.2 Types
Extension spring or Tension spring.
Compression spring
Torsion spring
Leaf spring
Conical spring
Disc or Belleville spring
2.2.1 EXTENSION SPRINGS:
Fig. 2.1 Extension spring

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Extension springs are attached at both ends to other components as shown in Fig.2.1.
When these components move apart, the spring tries to bring them together again. Extension
springs absorb and store energy as well as create a resistance to a pulling force. It is initial
tension that determines how tightly together an extension spring is coiled. This initial tension can
be manipulated to achieve the load requirements of a particular application. Extension Springs
are wound to oppose extension. They are often tightly wound in the no-load position and have
hooks, eyes, or other interface geometry at the ends to attach to the components they connect.
They are frequently used to provide return force to components that extend in the actuated
position.
2.2.2COMPRESSION SPRINGS:
Fig 2.2 Compression spring
Compression springs are open-coil helical springs wound or constructed to oppose
compression along the axis of wind as shown in Fig.2.2. Helical Compression Springs are the
most common metal spring configuration. Generally, these coil springs are either placed over a
rod or fitted inside a hole. When you put a load on a compression coil spring, making it shorter,
it pushes back against the load and tries to get back to its original length. Compression springs
offer resistance to linear compressing forces (push), and are in fact one of the most efficient
energy storage devices available.
2.2.3 TORSION SPRINGS:

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Fig 2.3 Torsion spring
Torsion springs are helical springs that exert a torque or rotary force. The ends of torsion
springs are attached to other components as shown in Fig.2.3, and when those components rotate
around the center of the spring, the spring tries to push them back to their original position.
Although the name implies otherwise, torsion springs are subjected to bending stress rather than
torsional stress. They can store and release angular energy or statically hold a mechanism in
place by deflecting the legs about the body centerline axis.
2.2.4 Leaf spring:
Fig 2.4 Leaf spring

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Laminated or carriage spring or a leaf spring is a simple form of spring, commonly used
for the suspension in wheeled vehicles. It is also one of the oldest forms of springing, dating
back to medieval times.
An advantage of a leaf spring over a helical spring is that the end of the leaf spring may
be guided along a definite path.
Sometimes referred to as a semi-elliptical spring or cart spring, it takes the form of a
slender arc-shaped length of spring steel of rectangular cross-section. The center of the arc
provides location for the axle, while tie holes are provided at either end for attaching to the
vehicle body. For very heavy vehicles, a leaf spring can be made from several leaves stacked on
top of each other in several layers, often with progressively shorter leaves. Leaf springs can serve
locating and to some extent damping as well as springing functions. While the interleaf friction
provides a damping action, it is not well controlled and results in stiction in the motion of the
suspension. For this reason manufacturers have experimented with mono-leaf springs.
A leaf spring can either be attached directly to the frame at both ends or attached directly
at one end, usually the front, with the other end attached through a shackle, a short swinging arm.
The shackle takes up the tendency of the leaf spring to elongate when compressed and thus
makes for softer springiness. Some springs terminated in a concave end, called a spoon
end (seldom used now), to carry a swiveling member.
2.2.5 Conical Compression Springs
Fig 2.5 Conical Compression Springs

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Conical Compression Springs are conical coiled helical springs that resist a compressive
force applied axially as shown in Fig.2.5. Conical Compression Springs are conical, tapered,
concave or convex in shape. The spring is wound in a conical helix usually out of round wire.
The changing of spring ends, direction of the helix, material, and finish allows conical
compression springs to meet a wide variety of special industrial needs. Conical compression
springs can be manufactured to very tight tolerances; this allows the spring to precisely fit in a
hole or around a shaft. A digital load tester can be used to accurately measure the specific load
points in your spring. Conical Compression springs can be made from non-magnetic spring
material like Phosphor Bronze or Beryllium Copper as well as music wire (High Carbon Steel)
stainless steel and many other types of spring wire. The possibilities are almost endless for so
many applications.
2.2.6 Disc or Belleville spring:
Fig 2.6 Belleville spring
These springs consist of a number of conical discs held together against slipping by a
central bolt or tube as shown in the fig 2.6. these are used in application where high spring rates
and compact spring are required.

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3.3 Nomenclature:
3.3.1End configuration:
Fig. 2.7 Closed and Square
Closed and Square: The space between the coils is reduced at the ends to the point where the
wire at the tip make contact with the next coil, the end is said to be closed and square as shown
in Fig.2.7. This is done so that the spring can stand on its own. If there is no reduction in pitch at
the end coils, the end is referred to as "open" and the spring will not stand up vertically on its
own.
Fig 2.8 Closed and Ground Ends
Closed and Ground Ends: It means an additional grinding operation may be applied to the
closed end configuration. Grinding removes material from the spring's end coils to create a flat
surface perpendicular to the spring axis as shown in Fig.2.8. This may be done for a variety of
reasons including a more even distribution of the spring force.
Fig 2.9 Open Ends

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Open Ends: They are ends that there is no reduction in pitch at the end coils yet are ground
square as shown in Fig.2.9
2.3.2 Compression helical spring:
Fig 2.10 Compression helical spring
Nomenclature of Compression helical spring is shown in fig 2.10
Outside diameter (Do): The outer diameter of a spring.
Inner diameter (Di): The Inner diameter of a spring.
Mean diameter (D): the average of inner and outer diameter of spring
Wire diameter (d): The outer diameter of round wire.
Free Length (Lf): The overall length of a spring in the unloaded position.
Solid Height (S): The length of a compression spring when all the coils are fully compressed
and touching.
Spring Rate (K): (Stiffness) is the spring rate of force in pounds per inch of compression.
Examples: If the spring rate of a compression spring is 10 lbs. It will take you 10 lbs. of force
to move it 1inch of distance. If you move it 2 inches of distance it will take you 20 lbs. of force.
The rate is linear.
Pitch: It is defined as axial distance between adjacent coils in uncompressed state.
Spring index: it is defined as ratio of mean diameter of the coil to the diameter of the wire.

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2.3.3 Conical spring:
Fig 2.11 Conical spring
The definition for Stiffness, wire diameter, free length, pitch and solid height are same for
conical spring. The factor which differs are:
Small diameter (D1): this is the smaller diameter of the spring which is usually at the top.
Larger or outer diameter (d2) : this is the largest diameter present in the spring.
2.4 Materials used for production of springs
2.4.1 High carbon spring wires:
1) Music wire
Carbon: 0.7to 1.00 %
Manganese: 0.20 to 0.60 %
Modulus of rigidity G: 79.3 MPa
2) Hard drawn
Carbon: 0.45 to 0.85%

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Manganese:: 0.60 TO 1.3 %
Modulus of rigidity G: 79.3 MPa
3) Oil tempered:
Carbon: 0.55 to 0.85%
Manganese:: 0.60 TO 1.20%
Modulus of rigidity G: 79.3 MPa
2.4.2Alloy steel wire:
1) Chrome vanadium
Carbon: 0.48 to 0.53 %
Chromium: 0.80 to 1.10%
Vanadium: 0.15 % min
Modulus of rigidity: 79.3 MPa
2.4.3 Stainless steel wire
1) AISI 302/304:
Chromium: 17 to 19 %
Nickel: 8 to 10%
Modulus of rigidity: 69 MPa
2) AISI 316:
Chromium: 16 to 18 %
Nickel: 10 to 14%
Molybdenum: 2 to 3%

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Modulus of rigidity: 69 MPa
3)17-7PH:
Chromium: 16to 18 %
Nickel: 10 to 14%
Aluminum: 0.75 to 1.5 %
Modulus of rigidity: 78.5 MPa
2.4.4 Nonferrous alloy wire:
1) Beryllium copper
2) Monel
3) Phosphor bronze
2.5 Manufacturing process:
Springs are manufactured by performing following process:
Heating the wire
Coiling
Hardening
Grinding
2.5.1 Heating the wire:
The wire of required diameter made up of required materials is bought according to
standard wire gauge range.
When a spring having a wire diameter above 8 mm is to be produced, the wire is
preheated so that is can easily machined.
When this is done, on the other hand a mandrel made of steel has to be produced.

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The mandrel diameter should be 1mm less the mean diameter of the spring to be
produced. This is done to recover losses which will happen in bending.
The equipment for the production of spring is a lathe machine in which the machined
mandrel is fitted in the four jaw chuck
2.5.2 Coiling:
The next process is winding the coil for the spring.
The preheated wire is clamped at one end of the mandrel as shown in figure 2.12 with
clamps
Fig 2.12 Loading of spring wire
Then the lathe spindled is rotated at low rpm says 6 to 10 which is idle for making
springs
Fig 2.13 Coiling of spring

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When the spindle rotates, the wire gets the shape of mandrel where it is being placed.
The pitch is maintained by feeding the wire to the lathe, length is also maintained in same
manner as shown in Fig.2.13.
When the spring reaches its final position, the supply is stopped and rotation of spindled
is stopped slowly making the coil larger which would return to decreased state due to
bending.
Then the spring is taken out of the mandrel and cooled in room temperature.
2.5.3 Hardening:
Whether the steel has been coiled hot or cold, the process has created stress within the
material. To relieve this stress and allow the steel to maintain its characteristic resilience, the
spring must be tempered by heat treating it. The spring is heated in an oven, held at the
appropriate temperature for a predetermined time, and then allowed to cool slowly. For example,
a spring made of music wire is heated to 500°F (260°C) for one hour.
2.5.4 Grinding:
If the design calls for flat ends on the spring, the ends are ground at this stage of the
manufacturing process. The spring is mounted in a jig to ensure the correct orientation during
grinding, and it is held against a rotating abrasive wheel until the desired degree of flatness is
obtained. When highly automated equipment is used, the spring is held in a sleeve while both
ends are ground simultaneously, first by coarse wheels and then by finer wheels. An appropriate
fluid (water or an oil-based substance) may be used to cool the spring, lubricate the grinding
wheel, and carry away particles during the grinding.

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2.6 Formulae:
2.6.1 For helical spring:
Stiffness:
N/mm
Deflection:
mm
Shear stress:
T= N/mm2
3.6.2 For conical spring:
Stiffness:
K = N/mm
Deflection:
mm

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Shear stress:
T= N/mm2
K → Stiffness of spring in N/mm
d → wire diameter in mm
D → mean diameter in mm
)
→ Greater diameter in conical spring in mm
→ Greater diameter in conical spring in mm
N → number of turns
→ Spring Deflection in mm
W → load applied in N
T → Shear stress acting in spring in N/mm2
k → Wahl stress factor
k = +
C → Spring index
C =

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2.7 Applications:
Springs are used in:
In two-wheeler and four-wheeler compression spring are used as shock absorbers in
suspension system.
In spring balance tension springs are used to measure the load by deflection produced.
In car engine valve springs are used to operate the engine valves.
In staplers, exam pads torsion spring are used to provide required tension.
In bike stand spring are used to keep the stand in required position.
In pen, spring provide the working mechanism.
Leaf spring serves as suspension system in weight lifting heavy duty vehicles.
In railway wagon heavy-duty compression spring provide suspension system.
In home, the sofa has spring that provides cushioning effect.
In governors (hartung and hartnell) the speed is controlled using the springs.
It is widely used in printing, textile and automobile industries
Smaller springs are used in watches and toys.

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CHAPTER 3
ANALYSIS OF OLD SPRING

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3.1 Material test:
Fig 3.1 Material test
The materials test is done and to above composition it corresponds to music wire type of spring
steel as shown in Fig.3.1.

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3.2 Result from SiTrac:
• Spring material : Spring steel
• Coil Diameter d0 : 12 mm
• Number of turns n = 6
• Inner diameter Di : 108 mm
• Outer diameter Do : 133 mm
• Mean diameter D : 120.85 mm
• Stiffness K : 19.19 N/mm
• Modulus of rigidity G: 78400N/mm2
or 78.4Gpa
• Maximum load then can be carried : 500 kg
• Weight to be carried = 380 kg
• (i.e. total weight =weight of car= 915 kg + maximum passenger load = 600 kg =1515
kg divided by four =380 kg)

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Fig 3.2 Reading from SiTarc lab
The reading taken from the lab is shown in fig 3.2

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Fig 3.3 Graph for load Vs Deflection
The fig 3.3 shows the load vs deflection fraph for old spring.

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3.3 Analysis using ansys :
3.3.1 Catia diagram:
Fig 3.4 CATIA Part diagram of the old spring
The diagram for the value taken from the spring is drawn in CATIA V5R16 is in fig 3.4.

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The CATIA model is imported and meshing is done using ANSYS 13.0

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3.3.2 Application of load :
Load which is found from the SiTrac is applied using ANSYS 13.0

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3.3.3 Deflection:
As the load been applied the solution is solved and its deflection is shown in ANSYS 13.0

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3.3.4 Shear stress:
The shear stress for the applied load generated using ANSYS 13.0 is shown

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Equivalent stress:
The equivalent stress for load applied is generated using ANSYS 13.0.

33. 33
3.4 Calculated values:
Table 3.1 Calculation of stiffness from reading for old springError! Not a valid link.
Stiffness calculation:
K= 19.11 N/mm
Shear stress calculation:
T=
k = +
C=
C=10.08
k = + = 1.14
T=
Shear stress = 1103.84 N/mm2

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CHAPTER 4

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OPTIMIZATION
Optimization
An act, process, or methodology of making something (as a design, system, or decision)
as fully perfect, functional, or effective as possible; specifically: the mathematical procedures (as
finding the maximum of a function) involved in this.
4.1 Optimization technique:
4.1.1 Numerical Methods of Optimization
Linear programming: studies the case in which the objective function f is linear and the set A is
specified using only linear equalities and inequalities. (A is the design variable space)
Integer programming: studies linear programs in which some or all variables are constrained to
take on integer values.
Quadratic programming: allows the objective function to have quadratic terms, while the set A
must be specified with linear equalities and inequalities
Nonlinear programming: studies the general case in which the objective function or the
constraints or both contain nonlinear parts.
•Stochastic programming: studies the case in which some of the constraints depend on random
variables.
•Dynamic programming: studies the case in which the optimization strategy is based on
splitting the problem into smaller sub-problems.
•Combinatorial optimization: is concerned with problems where the set of feasible solutions is
discrete or can be reduced to a discrete one.
•Infinite-dimensional optimization: studies the case when the set of feasible solutions is a
subset of an infinite-dimensional space, such as a space of functions.
•Constraint satisfaction: studies the case in which the objective function fis constant (this is
used in artificial intelligence, particularly in automated reasoning).
4.1.2 Advanced Optimization Techniques

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Hill climbing: it is a graph search algorithm where the current path is extended with a
successor node which is closer to the solution than the end of the current path.
In simple hill climbing, the first closer node is chosen whereas in steepest ascent hill
climbing all successors are compared and the closest to the solution is chosen. Both forms fail if
there is no closer node. This may happen if there are local maxima in the search space which are
not solutions.
Hill climbing is used widely in artificial intelligence fields, for reaching a goal state from
a starting node. Choice of next node/ starting node can be varied to give a number of related
algorithms.
Genetic algorithms:
Genetic algorithms are typically implemented as a computer simulation, in which a
population of abstract representations (called chromosomes) of candidate solutions (called
individuals) to an optimization problem evolves toward better solutions.
The evolution starts from a population of completely random individuals and occurs in
generations.
In each generation, the fitness of the whole population is evaluated, multiple individuals
are stochastically selected from the current population (based on their fitness), and modified
(mutated or recombined) to form a new population.
Ant colony optimization
In the real world, ants (initially) wander randomly, and upon finding food return to their
colony while laying down pheromone trails. If other ants find such a path, they are likely not to
keep traveling at random, but instead follow the trail laid by earlier ants, returning and
reinforcing it if they eventually find food
Over time, however, the pheromone trail starts to evaporate, thus reducing its attractive
strength. The more time it takes for an ant to travel down the path and back again, the more time
the pheromones have to evaporate.
A short path, by comparison, gets marched over faster, and thus the pheromone density
remains high

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Pheromone evaporation has also the advantage of avoiding the convergence to a locally
optimal solution. If there were no evaporation at all, the paths chosen by the first ants would tend
to be excessively attractive to the following ones. In that case, the exploration of the solution
space would be constrained.
Design of Experiments:
DOE is used to find the variables and their interaction that causes maximum change in the
response variable. Here we use DOE to find the perfect levels of different variables that gives us
the best output in terms of stiffness of spring.
4.2 Parameter to be changed:
The aim of our project is to
Increase the stiffness of the spring and Load carrying capacity of the spring with
some modification to the old spring.
The shear stress of the spring has also to be considered, because springs are tested
for shear stress only.
If the change made in the old spring lead to increase in the stress the new spring has the
tendency to break or fail.
The changes that can be made in the springs are:
The type of spring can be changed (i.e. conical, disc, etc.).
The material in which it had to be made can be changed.
We know that stiffness is directly proportional to the coil diameter and inversely
proportional to the mean diameter and number of turns.
From the formula

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And from this formula,
T=
Shear stress is directly proportional to maximum diameter of the coil and inversely
proportional to coil diameter.
I.e. when we increase the parameter which would increase the stiffness only would bring
an increase in shear stress value which leads to failure.
To increase the stiffness, the coil diameter is increased from 12 mm to 12.7 mm
Since the stiffness is directly proportional to fourth power of coil diameter, the stiffness
will increase.
The number of turns is also reduced from 7 to 6, which will also increase the stiffness.
Then the type of spring is changed from helical to conical due to its following
advantages:
Variable Rate: These springs offer a constant, or uniform pitch, and have an increasing
force rate instead of a constant force rate (regular compression springs). The larger coils
gradually begin to bottom as a force is applied. A variable pitch can be designed to give a
uniform rate if necessary.
Stability: Conical compression offers more lateral stability and fewer tendencies to
buckle than regular compression springs.
Vibration: Resonance and vibration is reduced because Conical Compression springs
have a uniform pitch and an increasing natural period of vibration (instead of a constant)
as each coil bottoms.
It compensate for the increase in shear stress the spring shear stress i.e.

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The smaller diameter is made as 130 mm and larger diameter as 160 mm. which make a
taper angle of 86o
to the horizontal surface.
The above calculation are calculated for value check on the stiffness and shear stress and
proved to be adequate.
Then analysis is made using ANSYS 13.0 to be accurate about the calculated results.
The results from ANSYS also proved that the design is possible.
With that above two facts the spring with above said type and dimension is
manufactured.
The manufactured spring is tested in SiTrac testing facility and it indicates an increase in
stiffness and load carrying capacity.
Design of Experiments:
Factors selected:
Shape of spring
Number of turns
Coil diamter
Factors High Low
Shape of Spring Helical Conical
Number of turns 7 6

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Coil Diameter(mm) 12.7 12
Minitab input:
StdOrder RunOrder CenterPt Blocks Shape
No of
turns Coil dia Stiffness
7 1 1 1 Helical 7 12.7 19.81
1 2 1 1 Helical 6 12 19.43
3 3 1 1 Helical 7 12 19.11
4 4 1 1 Conical 7 12 20.01
8 5 1 1 Conical 7 12.7 21.8
2 6 1 1 Conical 6 12 21.6
6 7 1 1 Conical 6 12.7 22.12
5 8 1 1 Helical 6 12.7 21.11
Minitab Project Report
Factorial Fit: Stiffness versus Shape, No of turns, Coil dia
Estimated Effects and Coefficients for Stiffness (coded units)
Term Effect Coef
Constant 20.6238
Shape 1.5175 0.7588
No of turns -0.8825 -0.4412
Coil dia 1.1725 0.5862
Shape*No of turns -0.0725 -0.0362
Shape*Coil dia -0.0175 -0.0087
No of turns*Coil dia 0.0725 0.0362
Shape*No of turns*Coil dia 0.5625 0.2812

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S = * PRESS = *
Analysis of Variance for Stiffness (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 3 8.91274 8.91274 2.97091 * *
Shape 1 4.60561 4.60561 4.60561 * *
No of turns 1 1.55761 1.55761 1.55761 * *
Coil dia 1 2.74951 2.74951 2.74951 * *
2-Way Interactions 3 0.02164 0.02164 0.00721 * *
Shape*No of turns 1 0.01051 0.01051 0.01051 * *
Shape*Coil dia 1 0.00061 0.00061 0.00061 * *
No of turns*Coil dia 1 0.01051 0.01051 0.01051 * *
3-Way Interactions 1 0.63281 0.63281 0.63281 * *
Shape*No of turns*Coil dia 1 0.63281 0.63281 0.63281 * *
Residual Error 0 * * *
Total 7 9.56719
Estimated Coefficients for Stiffness using data in uncoded units
Term Coef
Constant 22.3021
Shape 130.552
No of turns -3.44071
Coil dia 0.328571
Shape*No of turns -19.9207
Shape*Coil dia -10.4714

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No of turns*Coil dia 0.207143
Shape*No of turns*Coil dia 1.60714
210-1-2
99
95
90
80
70
60
50
40
30
20
10
5
1
Effect
Percent
A Shape
B No of turns
C Coil dia
Factor Name
Not Significant
Significant
Effect Type
A
Normal Plot of the Effects
(response is Stiffness, Alpha = 0.20)
Lenth's PSE = 0.84375
Effects Pareto for Stiffness
Alias Structure
I
Shape
No of turns
Coil dia
Shape*No of turns
Shape*Coil dia
No of turns*Coil dia
Shape*No of turns*Coil dia
degrees of freedom for error = 0.

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AC
BC
AB
ABC
B
C
A
1.61.41.21.00.80.60.40.20.0
Term
Effect
1.496
A Shape
B No of turns
C Coil dia
Factor Name
Pareto Chart of the Effects
(response is Stiffness, Alpha = 0.20)
Lenth's PSE = 0.84375
Regression Analysis: Stiffness versus No of turns, Coil dia, Shape_1
The regression equation is
Stiffness = 3.40 - 0.883 No of turns + 1.67 Coil dia + 1.52 Shape_1
Predictor Coef SE Coef T P
Constant 3.398 5.397 0.63 0.563
No of turns -0.8825 0.2860 -3.09 0.037
Coil dia 1.6750 0.4086 4.10 0.015
Shape_1 1.5175 0.2860 5.31 0.006
S = 0.404490 R-Sq = 93.2% R-Sq(adj) = 88.0%

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Analysis of Variance
Source DF SS MS F P
Regression 3 8.9127 2.9709 18.16 0.009
Residual Error 4 0.6545 0.1636
Total 7 9.5672
Source DF Seq SS
No of turns 1 1.5576
Coil dia 1 2.7495
Shape_1 1 4.6056
Selected combination for new spring:
Shape of spring: Conical
Number of turns: 6
Coil diameter: 12.7 mm

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CHAPTER 5
ANALYSIS OF NEW SPRING
Analysis of new spring:
5.1 Dimension of the new spring:
• Spring material : Spring steel
• Coil Diameter d0 : 12.7 mm
• Types of spring: conical spring.

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• Number of turns n = 5.5
• Inner diameter Di : 130 mm
• Outer diameter Do : 160 mm
• Stiffness K : 21.10 N/mm
• Modulus of rigidity G: 78400N/mm2
or 78.4Gpa
• Maximum load then can be carried : 584 kg
• Weight to be carried = 380 kg
• (i.e. total weight =weight of car= 915 kg + maximum passenger load = 600 kg =1515
kg divided by four =380 kg)
• Maximum Shear stress :1040 N/mm2
• Equivalent stress : 1730 N/mm2
• Maximum load is calculated by putting factor of safety as 1.5 i.e. 380*1.5= 570 Kg
5.2 ANSYS results:

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Fig 5.1 CATIA part diagram of new spring
The new dimension are drawn using CATIA VR5R16 is shown in Fig 5.1and is used in ANSYS.

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The model drawn in the CATIA is imported in the ANSYS13.0

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The imported model is given properties and is being meshed in ANSYS.

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5.2.1 Deflection:
The deflection for the load applied is generated in ANSYS.

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5.2.2 Equivalent stress:
The Equivalent stress for the load applied is generated by ANSYS.

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5.2.3 Shear stress:
The Shear stress for the load is generated is generated in ANSYS.

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Fig 5.2 Reading from SiTrac lab for new spring
The fig 3.3 shows the load vs deflection fraph for old spring.

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Fig 5.3 Graph for load Vs Deflection
The fig 3.3 shows the load vs deflection fraph for old spring.

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5.3 Calculted values:
Table 5.1 for calculation of Stiffness from Reading for new springError! Not a valid link.
Stiffness calculation:
K =
)
)
= 1239500 mm3
K =
K= 22.12 N/mm
Deflection:

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=243.09 mm
Shear stress calculation:
T=
Where,
k = +
Where,
C =
C=
→C=12.59
k = +
→k= 1.11
T=

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→T= 1103.93N/mm2
5.4 COMPARISON OF RESULTS:
The old spring has following data:
Stiffness: 19.19 N/mm
Maximum load: 5000 N
Shear stress maximum: 1104 N/mm2
Maximum deflection: 230 mm
The new spring has:
Stiffness: 21.10 N/mm
Maximum load: 5824 N
Shear stress at 5000 N = 1103 N/mm2
Maximum deflection: 236 mm
From these
Stiffness and load carrying capacity of the spring has increased and the shear stress of the spring
has decreased.

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CHAPTER 6
CONCLUSION
6.1 Conclusion:
Thus, the old suspension system of indica is studied by conducting analysis using
ANSYS.
The optimized design is produced by doing modifications of the old spring model which
is studied.
The optimized model is manufactured as per the dimension stated.
The manufactured model is studied and the result is compared with model.
An increase in stiffness and load carrying denote that our model is optimized.

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CHAPTER 7
REFERENCES
REFERENCES:
Books:
1) Kirpal Singh (2011), ‘Automobile Engineering- Volume I’, Standard Publishers and
distributors, New Delhi
2) R S Khurmi, (2010) ‘Theory of machines’, S.Chand Publications.
3) PSG College of technology (2010) ‘Design data book’, Kalaikathir Achchagam,
Coimbatore
4) R.S. Khurmi and J.K.Gupta (2010) ‘A textbook of Machine Design’ , S.Chand
Publications
Websites:
1) www.madehow.com/Volume-6/Springs.html#
2) www.roymech.co.uk/Useful_Tables/Springs/Springs_helical.html
3) www.wikipedia.org/
4) www.acewirespring.com/conical-compression-springs.html
5) http://www.tribology-abc.com/calculators/t14_3.htm

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6) http://www.planetspring.com/spring-knowledge/1002/conical-springs