CHAPTER 1

1

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).

2

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

3

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

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

4

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

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.

5

6

CHAPTER 2

SPRINGS

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:

7

Fig. 2.1 Extension spring

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

8

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:

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:

9

Fig 2.4 Leaf spring

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

10

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

  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:

11

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.

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.

12

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

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. 

13

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.

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:

14

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%

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

15

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%

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:

16

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.

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

17

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

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:

18

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.

2.6 Formulae:

2.6.1 For helical spring:

Stiffness:

N/mm

Deflection:

mm

Shear stress:

T= N/mm2

19

3.6.2 For conical spring:

Stiffness:

K = N/mm

Deflection:

mm

Shear stress:

T= N/mm2

K → Stiffness of spring in N/mm

d → wire diameter in mm

D → mean diameter in mm

)

20

→ 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 =

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.

21

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.

22

CHAPTER 3

ANALYSIS OF OLD SPRING

3.1 Material test:

23

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.

3.2 Result from SiTrac:

24

• 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)

25

Fig 3.2 Reading from SiTarc lab

The reading taken from the lab is shown in fig 3.2

26

Fig 3.3 Graph for load Vs Deflection

The fig 3.3 shows the load vs deflection fraph for old spring.

27

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.

28

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

29

3.3.2 Application of load :

Load which is found from the SiTrac is applied using ANSYS 13.0

30

3.3.3 Deflection:

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

31

3.3.4 Shear stress:

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

32

Equivalent stress:

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

33

3.4 Calculated values:

Table 3.1 Calculation of stiffness from reading for old spring

S.No Load, N Deflection , mm Spring rate, N/mm Modulus of Ridigity , N/mm2 Modulus of Ridigity, N/mm2

1 0 0 0

2 130 10.01 12.99 53059.78578 53071.98953

3 302 20.02 15.08 61630.98194 61610.90085

4 486 30.01 16.19 66164.72187 66145.92074

5 687 40.09 17.14 70012.7116 70027.24407

6 887 50.09 17.71 72348.37909 72356.03807

7 1087 60.07 18.1 73931.26369 73949.42344

8 1287 70.03 18.38 75084.55963 75093.39242

9 1487 80.05 18.58 75893.72157 75910.51312

10 1684 90.03 18.7 76420.70757 76400.78554

11 1925 100.06 19.24 78600.70705 78607.01143

12 2152 110.18 19.53 79798.68164 79791.83645

13 2375 120.06 19.78 80820.49246 80813.23733

14 2600 130 20 81712.0701 81712.0701

15 2833 140 20.24 82675.10521 82692.61494

16 3075 150 20.5 83754.87185 83754.87185

17 3323 160.05 20.76 84826.36955 84817.12876

18 3569 170.04 20.99 85753.46336 85756.81757

19 3817 180.01 21.2 86632.67917 86614.7943

20 3958 190.03 20.83 85096.13573 85103.12101

21 4206 200 21.02 85920.24171 85879.38567

22 4456 210.01 21.22 86688.4873 86696.50637

23 4721 220.05 21.45 87653.4158 87636.19518

24 5001 230.5 21.74 88642.52984 88821.0202

34

Stiffness

average value 19.19 N/mm 78396.61233 N/mm2 78402.73126 N/mm2

Stiffness calculation:

K= 19.11 N/mm

Shear stress calculation:

T=

k = +

C=

C=10.08

k = + = 1.14

35

T=

Shear stress = 1103.84 N/mm2

36

CHAPTER 4

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.

37

•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

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

38

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

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:

39

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

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

40

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.

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

41

Factors High Low

Shape of Spring Helical Conical

Number of turns 7 6

Coil Diameter(mm) 12.7 12

Minitab input:

StdOrder RunOrder CenterPt Blocks ShapeNo of turns Coil dia Stiffness

7 1 1 1 Helical 7 12.7 19.811 2 1 1 Helical 6 12 19.433 3 1 1 Helical 7 12 19.114 4 1 1 Conical 7 12 20.018 5 1 1 Conical 7 12.7 21.82 6 1 1 Conical 6 12 21.66 7 1 1 Conical 6 12.7 22.125 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

42

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

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

43

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

No of turns*Coil dia 0.207143

Shape*No of turns*Coil dia 1.60714

Effects Pareto for Stiffness

Alias Structure

I

Shape

44

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.

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

45

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%

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

46

CHAPTER 5

ANALYSIS OF NEW SPRING

47

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.

• 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

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5.2 ANSYS results:

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.

49

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

50

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

51

5.2.1 Deflection:

The deflection for the load applied is generated in ANSYS.

52

5.2.2 Equivalent stress:

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

53

5.2.3 Shear stress:

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

54

Fig 5.2 Reading from SiTrac lab for new spring

The fig 3.3 shows the load vs deflection fraph for old spring.

55

Fig 5.3 Graph for load Vs Deflection

The fig 3.3 shows the load vs deflection fraph for old spring.

56

5.3 Calculted values:

Table 5.1 for calculation of Stiffness from Reading for new spring

S.No Load, N

Deflection , mm

Spring rate, N/mm

1 0 0 0

2 374 20.01 18.69

3 786 40.09 19.61

4 1200 60.1 19.97

5 1615 80.07 20.17

6 2047 100.01 20.47

7 2474 120.04 20.61

8 2921 140.09 20.85

9 3400 160.09 21.24

10 3827 180.06 21.25

11 4359 200.01 21.79

12 4889 220.04 22.22

13 5244 230.01 22.8

14 5842 236.08 24.75

Stiffness

average 21.10923077 N/mm

57

Stiffness calculation:

K =

)

)

= 1239500 mm3

K =

K= 22.12 N/mm

Deflection:

=243.09 mm

58

Shear stress calculation:

T=

Where,

k = +

Where,

C =

C=

→C=12.59

k = +

59

→k= 1.11

T=

→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

60

Stiffness and load carrying capacity of the spring has increased and the shear stress of the spring

has decreased.

61

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.

62

63

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

64

3) www. wikipedia .org/

4) www.acewirespring.com/conical-compression-springs.html

5) http://www.tribology-abc.com/calculators/t14_3.htm

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

65