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1. 1

To Assembly of the Clutch and Flywheel in Volkswagen Car


By

Student Name Enrollment No.

Dewal Hanuwantsingh R 140670102020
Patel Fenil S 140670102052
Patel Ronak D 140670102062
Prajapati Sunil R 140670102085


Guided By

Prof. Saras A Patel
(Automobile Engineering Department)


A Report is submitted to
Gujarat Technological University
In Partial Fulfillment of the Requirements for
The Degree of Bachelor of Engineering in
Automobile Engineering

2017-2018


Automobile Engineering Department
SAL Institute of Technology and Engineering Research
Ahmedabad, Gujarat.

2. September 2017 2

Acknowledgment:
Simply to acknowledge the help verbally is not the complete way of expressing the feelings.
Even though the words, if brought from bottom of the heart, can serve the purpose to a
considerable extent .this is also a small effort for the same.

First of all, I am humbly expressing thanks to my respected guide Prof Saras A Patel, Professor,
Automobile Engineering Department, SAL Institute of Technology and Engineering Research,
Ahmedabad, Gujarat, for his valuable time and constant help given to me. He encourages me to
express my ideas freely and gave valuable suggestion during the implementation of project work.
It was a great learning experience right from searching for the topic for my dissertation phase.

I would like to express my deeply thanks to Prof. Maulik B Patel, Prof. Ketan M Patel and the
Head of the Department Prof. Manish H Patel, Automobile Engineering Department,
SALITER- Ahmedabad, for their kind support in all the way.

I would like to thank Parth Patel and Vijay Patel, Owner of Car Décor Workshop, Science City
Road, Sola, Ahmedabad & Jagdish K Patel, Management Department of Car Décor Workshop,
Science City Road, Sola, Ahmedabad, to allow us to carry out our experimental work at their
Workshop.

I would also like to thank Vishal Patel, Owner of Shital Auto Care & Bhimsingh, manager of
Shital Auto Care to help and to allow us to carry out our experimental work at their Workshop.


Finally, I am indebted to my parents, who encouraged me and provided the moral support and all
my friends who have directly or indirectly helped me during this work.





Dewal Hanuwantsingh R. (140670102020)
Patel Fenil S. (140670102052)
Patel Ronak D. (140670102062)
Prajapati Sunil R. (140670102085)

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4. September 2017 4

5. September 2017 5

6. September 2017 6

7. September 2017 7

INDEX
1. Introduction
1.1. Introduction to Workshop
1.2. Introduction to Volkswagen
1.3. Introduction to Clutch
1.4. Introduction to Flywheel
1.5. Introduction to Polo Car
2. Literature Review
2.1. Research Papers (1-5)
2.2. Patents (1-5)
3. Problem Identification
4. Analysis of Work & Possible Solution
4.1. Clutch Parts Inspection
5. Conclusion
5.1 Future Scope
6. References

8. September 2017 8

List of Figures
Fig. 1 : CAR DECOR Workshop
Fig. 2 : Logo of Volkswagen
Fig. 3 : Clutch Plate and Pressure Plate
Fig. 4: Flywheel
Fig. 5 : Volkswagen Polo
Fig. 6 : Single Plate Clutch
Fig. 7 : Clutch Assembly
Fig. 8 : Dual Mass Flywheel
Fig. 9 : Analysis of Flywheel
Fig. 10 : Clutch and Pressure Plate
Fig. 11 : Clutch Adjustment
Fig. 12 : Full Clutch Assembly

9. September 2017 9

Abstract:
In this work, the problem of Clutch assembly in Volkswagen Polo
was found. In this vehicle after overhawing, assembly didn't fit properly.
By analysis, it is concluded that problem while assembly was Flywheel.
By changing dimension and material of flywheel, the problem was
sucessfully rectified.

10. September 2017 10

Chapter 1
Introduction
1.1 Introduction of Workshop
CAR DECOR started its journey in 2002, having service centre. Car Decor has today
grown to be one of the leading service centre in the western Sola. This Automobile repair
workshops is independently owned and operated. This also include national franchise including
OEM car dealership. This is certified by Spare Parts manufacturer to perform warranty and recall
repairs by that manufacturer or distributor. In the India, a recent law allows motorists more
flexibility in selecting where they can get their car serviced. Due to this legislation, maintenance
and service work does not have to be done by the main dealer as long as the garage uses Original
Equipment 'Matching Quality' parts, and are recorded as such, and the garage follow the
manufacturer's service schedules. The Block Exemption Regulation covers service and
maintenance during the warranty period and prohibits vehicle manufacturers’ warranties from
including conditions that require normal maintenance to be provided within the vehicle
manufacturer’s network or that all parts used must be the manufacturer’s original spare parts.
This means that motorists benefit from open market competition in aftermarket parts, repairs and
services thus reducing the cost of servicing through better labor rates and competitively priced
parts. Also, this auto repair shop provides additional towing services. This repair shops offer
both mechanical and bodywork repair. This Automotive repair shop is specialize in bodywork
repair are known as body shops. They offer paintwork repairs to scratches, scuffs and dents, as
well as repairs to the bodies of vehicles damaged by collisions. This workshop now offer paint
less dent repair.


Fig. 1: CAR DECOR Workshop

11. September 2017 11


1.2 INTRODUCTION TO VOLKSWAGEN
Volkswagen AG known internationally as Volkswagen Group, is a
German multinational automotive manufacturing company headquartered in Wolfsburg, Lower
Saxony, Germany. It designs, manufactures and distributes passenger and commercial vehicles,
motorcycles, engines, and turbo machinery and offers related services including financing,
leasing and fleet management. In 2016, it was the world's largest automaker by sales,
overtaking Toyota. It has maintained the largest market share in Europe for over two decades.

It
ranked seventh in the 2016 Fortune Global 500 list of the world's largest companies.

Fig. 2: Logo of Volkswagen

Volkswagen India operates a manufacturing plant in Pune (Chakan) Maharashtra which
is capable of producing 200,000 vehicles per annum. Along with the manufacturing of
Volkswagen Polo and Volkswagen Vento and the newly launched Volkswagen Ameo, the plant
is also shared by Skoda Auto India Private Limited for manufacturing the Skoda Rapid.

12. September 2017 12

1.3 INTRODUCTION TO CLUTCH
A clutch is a mechanical device which engages and disengages power transmission
especially from driving shaft to driven shaft.
In the simplest application, clutches connect and disconnect two rotating shafts (drive
shafts or line shafts). In these devices, one shaft is typically attached to an engine or other power
unit (the driving member) while the other shaft (the driven member) provides output power for
work. While typically the motions involved are rotary, linear clutches are also possible.
In a torque-controlled drill, for instance, one shaft is driven by a motor and the other
drives a drill chuck. The clutch connects the two shafts so they may be locked together and spin
at the same speed (engaged), locked together but spinning at different speeds (slipping), or
unlocked and spinning at different speeds (disengaged)

1.3.1 Clutch works
In a modern car with a manual transmission the clutch is operated by the left-most pedal
using a hydraulic or cable connection from the pedal to the clutch mechanism. On older cars the
clutch might be operated by a mechanical linkage. Even though the clutch may physically be
located very close to the pedal, such remote means of actuation are necessary to eliminate the
effect of vibrations and slight engine movement, engine mountings being flexible by design.
With a rigid mechanical linkage, smooth engagement would be near-impossible because engine
movement inevitably occurs as the drive is "taken up."
The default state of the clutch is engaged - that is the connection between engine and
gearbox is always "on" unless the driver presses the pedal and disengages it. If the engine is
running with the clutch engaged and the transmission in neutral, the engine spins the input shaft
of the transmission but power is not transmitted to the wheels
The clutch is located between the engine and the gearbox, as disengaging it is usually
required to change gear. Although the gearbox does not stop rotating during a gear change, there
is no torque transmitted through it, thus less friction between gears and their engagement dogs.
The output shaft of the gearbox is permanently connected to the final drive, then the wheels, and
so both always rotate together, at a fixed speed ratio. With the clutch disengaged, the gearbox
input shaft is free to change its speed as the internal ratio is changed. Any resulting difference in
speed between the engine and gearbox is evened out as the clutch slips slightly during re-
engagement.
Clutches in typical cars are mounted directly to the face of the engine's flywheel, as this
already provides a convenient large diameter steel disk that can act as one driving plate of the
clutch. Some racing clutches use small multi-plate disk packs that are not part of the flywheel.
Both clutch and flywheel are enclosed in a conical bell housing, which (in a rear-wheel drive car)
usually forms the main mounting for the gearbox

13. September 2017 13

1.3.2 Materials
Various materials have been used for the disc-friction facings, including asbestos in the
past. Modern clutches typically use a compound organic resin with copper wire facing or a
ceramic material. Ceramic materials are typically used in heavy applications such as racing or
heavy-duty hauling, though the harder ceramic materials increase flywheel and pressure plate
wear.
In the case of "wet" clutches, composite paper materials are very common. Since these
"wet" clutches typically use an oil bath or flow-through cooling method for keeping the disc
pack lubricated and cooled, very little wear is seen when using composite paper materials.

1.3.3 Wet vs. dry systems
A wet clutch is immersed in a cooling lubricating fluid that also keeps surfaces clean and
provides smoother performance and longer life. Wet clutches, however, tend to lose some energy
to the liquid. Since the surfaces of a wet clutch can be slippery (as with a motorcycle clutch
bathed in engine oil), stacking multiple clutch discs can compensate for the lower coefficient of
friction and so eliminate slippage under power when fully engaged. The Hele-Shaw clutch was a
wet clutch that relied entirely on viscous effects, rather than on friction.
A dry clutch, as the name implies, is not bathed in liquid and uses friction to engage.

1.3.4 Friction clutches

The vast majority of clutches ultimately rely on frictional forces for their operation. The
purpose of friction clutches is to connect a moving member to another that is moving at a
different speed or stationary, often to synchronize the speeds, and/or to transmit power. Usually,
as little slippage (difference in speeds) as possible between the two members is desired.

1.3.5 Common problem in Clutch
The most common problem with clutches is that the friction material on the disc wears
out. The friction material on a clutch disc is very similar to the friction material on the pads of a
disc brake or the shoes of a drum brake -- after a while, it wears away. When most or all of the
friction material is gone, the clutch will start to slip, and eventually it won't transmit any power
from the engine to the wheels.
The clutch only wears while the clutch disc and the flywheel are spinning at different
speeds. When they are locked together, the friction material is held tightly against the flywheel,
and they spin in sync. It's only when the clutch disc is slipping against the flywheel that wearing
occurs.

Sometimes the problem is not with slipping, but with sticking. If your clutch won't
release properly, it will continue to turn the input shaft. This can cause grinding, or completely
prevent your car from going into gear. Some common reasons a clutch may stick are:

14. September 2017 14

Broken or stretched clutch cable - The cable needs the right amount of tension to push
and pull effectively.
Leaky or defective slave and/or master clutch cylinders - Leaks keep the cylinders from
building the necessary amount of pressure.
Air in the hydraulic line - Air affects the hydraulics by taking up space the fluid needs to
build pressure.
Misadjusted linkage - When your foot hits the pedal, the linkage transmits the wrong
amount of force. Mismatched clutch components - Not all aftermarket parts work with your
clutch.
A "hard" clutch is also a common problem. All clutches require some amount of force to
depress fully. If you have to press hard on the pedal, there may be something wrong. Sticking or
binding in the pedal linkage, cable, cross shaft, or pivot ball are common causes. Sometimes a
blockage or worn seals in the hydraulic system can also cause a hard clutch.
Another problem associated with clutches is a worn throw-out bearing, sometimes called
a clutch release bearing. This bearing applies force to the fingers of the spinning pressure plate to
release the clutch. If you hear a rumbling sound when the clutch engages, you might have a
problem with the throw-out.



Fig. 3: Clutch Plate and Pressure Plate

15. September 2017 15

1.4 INTRODUCTION OF FLYWHEEL
A flywheel is a mechanical device specifically designed to efficiently store rotational
energy. Flywheels resist changes in rotational speed by their moment of inertia. The amount of
energy stored in a flywheel is proportional to the square of its rotational speed. The way to
change a flywheel's stored energy is by increasing or decreasing its rotational speed applying a
torque aligned with its axis of symmetry,
Common uses of a flywheel include:
Smoothing the power output of an energy source. For example flywheels are used in
reciprocating engines because the active torque from the individual pistons is intermittent.
Delivering energy at rates beyond the ability of an energy source. This is achieved by
collecting energy in a flywheel over time and then releasing it quickly, at rates that exceed the
abilities of the energy source.
Controlling the orientation of a mechanical system, gyroscope and reaction wheel.
Flywheels are typically made of steel and rotate on conventional bearings; these are
generally limited to a maximum revolution rate of a few thousand RPM. High energy density
flywheels can be made of carbon fiber composites and employ magnetic bearings, enabling them
to revolve at speeds up to 60,000 RPM (1 kHz).

1.4.1 Modern automobile engine flywheel
A flywheel may also be used to supply intermittent pulses of energy at power levels that
exceed the abilities of its energy source. This is achieved by accumulating energy in the flywheel
over a period of time, at a rate that is compatible with the energy source, and then releasing
energy at a much higher rate over a relatively short time when it is needed. For example,
flywheels are used in power hammers and riveting machines.

Flywheels can be used to control direction and oppose unwanted motions,

1.4.2 Material Selection
Flywheels are made from many different materials, the application determines the choice
of material. Small flywheels made of lead are found in children’s toys. Cast iron flywheels are
used in old steam engines. Flywheels used in car engines are made of cast or nodular iron, steel
or aluminum. Flywheels made from high-strength steel or composites have been proposed for
use in vehicle energy storage and braking systems.
The efficiency of a flywheel is determined by the maximum amount of energy it can store
per unit weight. As the flywheel’s rotational speed or angular velocity is increased, the stored
energy increases; however, the stresses also increase. If the hoop stress surpass the tensile
strength of the material, the flywheel will break apart. Thus, the tensile strength limits the
amount of energy that a flywheel can store.
In this context, using lead for a flywheel in a child’s toy is not efficient; however, the
flywheel velocity never approaches its burst velocity because the limit in this case is the pulling-

16. September 2017 16

power of the child. In other applications, such as an automobile, the flywheel operates at a
specified angular velocity and is constrained by the space it must fit in, so the goal is to
maximize the stored energy per unit volume. The material selection therefore depends on the
application.

1.4.3 Applications
Flywheels are often used to provide continuous power output in systems where the
energy source is not continuous. For example, a flywheel is used to smooth fast angular velocity
fluctuations of the crankshaft in a reciprocating engine. In this case, a crankshaft flywheel stores
energy when torque is exerted on it by a firing piston, and returns it to the piston to compress a
fresh charge of air and fuel. Another example is the friction motor which powers devices such as
toy cars. In unstressed and inexpensive cases, to save on cost, the bulk of the mass of the
flywheel is toward the rim of the wheel. Pushing the mass away from the axis of rotation
heightens rotational inertia for a given total mass.



Fig. 4: Flywheel

17. September 2017 17

1.5 Introduction To Volkswagen Polo

The Polo 6R was face lifted in 2014 and is now known as the Polo 6C. With this came
subtle exterior styling such as redesigned bumpers. The interior was re-vamped which now
includes a touch screen as standard and a new steering wheel. The facelift Polo adds technology
such as Automatic Post-Collision Braking System as standard across all model lines. It also has
Car Play and Android Auto support since June 2015.
A new 1.4-litre three cylinder diesel engine replaced the 1.2-litre and 1.6-litre diesel
units, plus 1.4 TSI 132 kW of GTI was replaced by an Audi developed 1.8 TSI, produces
141 kW.




Fig. 5: Volkswagen POLO

18. September 2017 18

Chapter 2 Literature Review

2.1.1 Research Paper 1:
"Design and Structural Analysis of Single Plate Friction Clutch"

ABSTRACT :-

In design of the friction clutches of automobiles, knowledge on the thermo-elasticity a
priori is very informative in the initial design stage. Especially, the precise prediction technique
of maximum structural stress should be requested in design of mechanical clutches for their
durability and compactness. In this study, an efficient and reliable analysis technique for the
design of the mechanical clutches by using computer modeling and numerical method is
developed. This work contains stress analysis of single plate clutch of the automobile, in which
the stresses and forces developed in the clutch is tried to reduce with the help of software
approach. The detail study of clutch and modeling of clutch is done in pro-e software and the
analysis is to be done in Ansys software. Also in this work efficient and reliable design of
mechanical clutch is find out.

Keywords :- Clutch, Structural Analysis, Ansys

CONCLUSION :-

After completion of the analysis in CAE software i.e. ANSYS 9.0 based on the values of
Equivalent stresses for material loading conditions it is clearly seen that these are less than the
allowable stresses for that particular material under applied conditions the part not going to yield
and hence the design is safe. The result occurred are quiet favorable which was expected. The
stresses as well as deformation clear the idea about what parameter should have been taken into
account while defining the single plate friction clutch.


Fig. 6: Single Plate Clutch

19. September 2017 19

2.1.2 Research Paper 2:
“A Literature Review on Failure in Single Plate Clutch System”

ABSTRACT :-

Clutch system is among the main systems inside a vehicle. Clutch is a mechanical device
located between a vehicle engine and its transmission and provides mechanical coupling between
the engine and transmission input shaft. Clutch system comprise of flywheel, clutch disc plate
and friction material, pressure plate, clutch cover, diaphragm spring and the linkage necessary to
operate the clutch. The clutch engages the transmission gradually by allowing a certain amount
of slippage between the flywheel and the transmission input shaft. However, the slipping
mechanism of the clutch generates heat energy due to friction between the clutch disc and the
flywheel. At high sliding velocity, excessive frictional heat is generated which lead to high
temperature rise at the clutch disc surface, and this causes thermo-mechanical problems such as
thermal deformations and thermo-elastic instability which can lead to thermal cracking, wear and
other mode of failure of the clutch disc component.

Key words:- Clutch system comprise of flywheel, clutch disc plate and friction material,
pressure plate, clutch cover.


CONCLUTION :-

Clutch failure and damaged due to excessive frictional heat and heat fluctuations to the
clutch counter mate disc often happens to any type of automotive clutches. These situations
contribute to thermal fatigue to the component which causes the clutch counter mate disc to
crack and deform. This later will create problems such as clutch slip, clutch drag or failure of
clutch to disengage properly and clutch rattling as well as shortening the lifecycle of the
component.

Fig. 7: Clutch Assembly

20. September 2017 20

2.1.3Research Paper 3:
“A Review paper on Dual Mass Flywheel system”

ABSTRACT:-

During the power stroke vibrations are occurred due to the slight twist in the crankshaft.
The combustion cycles of a 4-stroke engine produce torque fluctuations which excite torsional
vibration to be passed down the drive train. Hence it is necessary that the vibrations generated by
engine be reduced or isolate, so that the operator / driver was feel lesser fatigue. Dual mass
flywheel is a multi-clutch device which is used to dampen. The torsional frequency is defined as
the rate at which the torsional vibration occurs. When the torsional frequency of the crankshaft is
equal to the transaxles torsional frequency an effect known as the torsional resonance occurs.
When the operating speed of the engine is low, vibration occurs due to the torsional resonance
and this can be avoided using dual mass flywheel. The resulting noise and vibration, such as gear
rattle, body boom and load change vibration, result in poor noise behavior and driving comfort.
The objective while developing this concept was to isolate the drive train from the torsional
vibrations. This paper includes the development of inertia augmentation mechanism and
development of optimized flywheel using this mechanism. The dual mass flywheel comprises
primary flywheel and secondary flywheel and two springs.

Keywords:- Dual Mass Flywheel, Arc Spring, Torsional Resonance and Torsional Frequency.

CONCLUSION:-

It is observed that there is approximately 7 to 8 % increase in power output by using the
Dual mass flywheel and also observed that the Dual mass flywheel is 5 to 6% efficient than the
conventional flywheel which will also result in increasing fuel economy of the engine.

Fig. 8: Dual Mass Flywheel

21. September 2017 21

2.1.4 Research Paper 4:
“Analysis of Flywheel Used in Petrol Engine Car”

ABSTRACT :-

A flywheel used in machines serves as a reservoir which stores energy during the period
when the supply of energy is more than the requirement and releases it during the period when
the requirement of energy is more than supply. For example, in I.C. engines, the energy is
developed only in the power stroke which is much more than engine load, and no energy is being
developed during the suction, compression and exhaust strokes in case of four stroke engines.
The excess energy is developed during power stroke is absorbed by the flywheel and releases its
to the crank shaft during the other strokes in which no energy is developed, thus rotating the
crankshaft at a uniform speed. The flywheel is located on one end of the crankshaft and serves
two purposes. First, through its inertia, it reduces vibration by smoothing out the power stroke as
each cylinder fires. Second, it is the mounting surface used to bolt the engine up to its load. The
aim of the project is to design a flywheel for a multi cylinder petrol engine flywheel using the
empirical formulas.

CONCLUSION:-

In this paper we have designed a four wheeler flywheel used in a petrol engine using
theoretical calculations. 2d drawing is created and modeling of flywheel is done using
Pro/Engineer. We have done structural and modal analysis on flywheel using two materials
Aluminum Alloy A360 and Cast Iron to validate our design. By observing the results, for all the
materials the stress values are less than their respective permissible yield stress values. So our
design is safe. We have also done modal analysis for number of modes to see the displacement of
flywheel for number of frequencies. By comparing the results for two materials, the stress value
for Aluminum Alloy A360 is less than that of Cast Iron. So we conclude that for our design,
Aluminum A360 is better material for flywheel. By using Aluminum A360 we can reduce
Weight. Also it is rust free.

Fig. 9: Analysis of Flywheel

22. September 2017 22

2.1.5Research Paper 5:
"REVIEW ON FRICTION CLUTCH PLATE OF AN ATV "

ABSTRACT:-

Clutch is a mechanical device located between a vehicle engine and its transmission and
provides mechanical coupling between the engine and transmission input shaft. Multi plate
clutch is one of the important part in the power transmission systems. Good design of clutch
provides better engine performance. Multi plate clutch is most widely used in ATV's, racing cars
and heavy duty vehicle where high torque transmission required and limited space is available.
The multi plate clutch has modeled in NX 9 software and imported in ANSYS Workbench 15.
The structural analysis has been carried out for friction material clutch plate. The result of
friction materials is based on the static and dynamic analysis, stress and total deformation and
temperature variation and heat flux of the friction plate. Uniform wear theory were used for the
analysis. The Grey Cast Iron and Kevlar 49 friction material are compared based on the total
deformation of the clutch plate to find the better lining material. The Von Mises stress has been
determined by varying the friction surfaces material-Grey Cast Iron and Kevlar 49. After that the
FEM analysis is done for Kevlar friction material. The stresses & deformation obtained for this
friction material is then compared to analysis software result. The analysis is done for worn out
friction disc. By extracting the result we found that Kevlar49 as friction material solve this
difficulty.

Key words: ANSYS, Clutch, friction plate, Grey Cast Iron, Kevlar49, Stress, Strain, Von Mises
stress, Deformation.

CONCLUSION:-

In this thesis, a Multi friction plate clutch is modeled in 3D modeling software Uni-
graphics . Present used material for clutch is Gray cast iron. In this thesis static and thermal
analysis is done to find the temperature variation and heat flux of the friction plate. Theoretical
calculations are done to determine stress intensity factor, crack extension force, crack opening
displacement. By observing the analysis results, the stress values are more for composite
materials and when the crack is started the composite materials, stress values increases more than
the condition of no crack so the composite materials fails faster once the crack propagates. And it
is found that the temperature developed during the engagement and disengagement process is
beyond the maximum temperature of the gray cast iron material, i.e. why there is crack and
erosion of the friction material of the friction plate that the values of temperature increase
linearly with disc radius and the maximum temperature. By changing the friction lining material
of 125cc ATV life of the cultch plate can be increased.

23. September 2017 23

2.2.1Patent 1:
“DRY DISC-TYPE CLUTCH”

ABSTRACT:-
A clutch of the single-plate dry-disc type is structured to include annular friction facings
secured to opposite surfaces of a supporting plate of a clutch plate and a plurality of recesses or
shallow grooves are defined in the surface of one of the annular friction facings. The shallow
grooves extend from the inner periphery of the one annular friction facing and
terminate short of the outer periphery thereof.

SUMMARY :-
According to the present invention, there is provided a dry-disc type clutch including a
fly wheel having an annular engaging surface and secured on a drive shaft or a crank shaft of an
engine; a clutch plate which is axially slid ably supported on a driven shaft or an input shaft of a
transmission, which is coaxial with the drive shaft; annular friction facings secured to the
opposite surfaces of a supporting plate of the clutch plate; an annular pressure plate adapted to
urge one of the friction facings of the clutch plate against the engaging surface of they wheel,
said clutch being characterized in that air inlets are needed in the body of the fly wheel to extend
there through in communication with shallow grooves needed in a surface of one of the friction
facings which faces the engaging surface of the fly wheel.



Fig. 10: Clutch and Pressure Plate

24. September 2017 24

2.2.2Patent 2
“SINGLE MIXTURE METALLIC CLUTCH PLATE ”

ABSTRACT:-
A disc-like brake or clutch component suitable for being carried in non-rotatable fashion
by one of two relatively rotatable members of a brake or clutch and having relatively porous
axially protruding spaced sectors for receiving abrasion carried between and integral with spaced
spokes of a wheel-like relatively nonporous carrying member of much higher density than said
sectors is prepared from a single powdered metal mixture, by placing two different thicknesses
of metal powder in portions of a mold for powdered compressing powdered metal portions of
greater thickness being joined by portions of lesser thickness and compressing the portions of
lesser thickness with a pressure about 40 to 50 or more Tsi and compressing the portions of
greater thickness with a lesser pressure of about 5 to 15 or 20 Tsi to produce a reform and then
sintering said preform in a reducing or inert atmosphere under a moderate pressure of the order
of 200 to 500 Psi and at a temperature of about 1,500° to 1,900° F. in the case the powder
mixture contains substantial copper and at a temperature of 1,900 to
2,200° F. when the metal powder is substantially entirely iron.

Fig. 11: Clutch Adjustment

25. September 2017 25

2.2.3Patent 3:
“SEGMENTED CLUTCH PLATES ”

ABSTRACT:-
A segmented annular clutch plate for use in any conventional clutch plate mechanism.
The segments are of equal aureate dimension so that they are interchangeable- Each segment
possesses the same annular uniformly serrated surface. Each segment may be provided with a
key-slot mating connection to restrict the radial movement of the clutch plate while in operation.
The clutch plates are designed and oriented so that in the clutch assembly the plates in one set of
plates have different numbers of segments than the plates in the other set of plates, whereby
adjoining plates can have only two segment joints in axial alignment at any one instant.

SUMMARY :-
This invention relates to segmented annular clutch plates which are usable in any
conventional vehicle clutch plate system that employs one series of annular clutch plates having
serrated outer annular edges and which are slid ably mounted to the casing of the clutch
mechanism by means of splint surfaces and another series of annular clutch plates having
serrated inner annular edges and slid ably mounted by means of spline surfaces to input shaft and
which are alternately sand wiched between the casing clutch plates. A Fluid activated piston
means is arranged in the casing walls to press the clutch plates together for the transmission of
power from the input shaft to the casing. This invention pertains to a clutch plate which is
stamped in segments and assembled for use in the above described conventional clutch plate
mechanisms. An object of this invention is to minimize scrap losses in the manufacturing process
by eliminating the unused central plate area within the annulus of the clutch plate. Another object
of my invention is to increase the total production per grinding cycle because there is less unused
work area as the segments can be placed close together during the surface grinding operation.
An other object of my invention is to reduce the scrap material occasioned by grinding bows out
of the clutch plates. Another object of my invention is to allow for quick disassembly of the
plates from the clutch mechanism because the housing need only be partially disassembled.‘
Another object of my invention is to reduce the space necessary for storage of the clutch plates,
as they may be more compactly stacked as compared to annular plates.

26. September 2017 26

2.2.4Patent 4:
“FLYWHEEL AUTOMOTIVE VEHICLE ”

ABSTRACT:-
An automotive system employing a high velocity, moderate mass flywheel capable of
storing and rapidly dissipating large supplies of kinetic energy coupled with a transmission
adapted to permit the smooth release of stored kinetic energy from the flywheel to the vehicle
wheels, and a charging means for supplying kinetic energy to the flywheel at relatively low
energy levels. The system provides substantial fuel economy and pollution relief through an
efficient energy-conversion system.

SUMMARY :-
In accordance with the principles of the present invention, an automobile is provided
which is driven by a stored power supply in the form of a flywheel. The flywheel is driven
through a range of speeds, with a maximum speed approximating 15,000 rpm and a minimum of
approximately 7,500 rpm. A flywheel “recharging” engine is employed which, when the
flywheel velocity drops below a low limit, such as, for example, the 7,500 rpm above noted, will
supply power to the flywheel until it reaches its design speed of 15,000 rpm or an intermediate
speed such as, for example, 12,000 rpm. In the system of the present invention, the supply of
recharging power operates substantially independently of the vehicle operator. The engine or
motor is controlled solely by the velocity of the flywheel and the operator is in control only of
the output of energy from the flywheel.



Fig. 12: Full Clutch Assembly

27. September 2017 27

2.2.5Patent 5:
“VARIABLE CAPACITY FLYWHEEL ”

ABSTRACT:-
A variable capacity flywheel comprises a main flywheel coupled with the rotating shaft
of an engine and at least one rotatable auxiliary flywheel. Both are selectively engaged and
disengaged with one another by means of an electromagnetic clutch. Both flywheels are engaged
with one another by an energizing member in the low speed range of Said enigmas Both are
disengaged from one another by means of excitation control of the electromagnetic clutch in the
high speed range of the engine. A generator driven by the engine rotating shaft is connected in
series with the electromagnetic clutch and a batter .

SUMMARY :-
This invention relates to improvements in a variable capacity flywheel to overcome the
drawbacks of prior art devices. This invention provides a lightweight and inexpensive device for
stabilizing engine operation over a range of operating conditions. In accordance with this
invention, a variable capacity flywheel is defined having a main flywheel coupled to the engine
shaft and at least one rotatable auxiliary flywheel. The flywheels are selectively engaged and
disengaged with each other by means of an electromagnetic clutch. Both flywheels are engaged
with each other at low engine speed ranges by an energizing member and are disengaged from
each other by means of excitation control of the electromagnetic clutch in the engine high speed
range. This invention will be described in greater detail relative to the drawing and the
description of the preferred embodiment that follows.

28. September 2017 28

Chapter 3
PROBLEM IDENTIFICATION
 A clutch is a mechanical device which engages and disengages power transmission especially
from driving shaft to drive shaft. In the simplest application, clutches connect and disconnect
two rotating shafts. In these devices, one shaft is typically attached to an engine or other
power unit (the driving member) while the other shaft provides output power for work. While
typically the motions involved are rotary, linear clutches are also possible.
 A flywheel is a mechanical device specifically designed to efficiently store rotational energy.
Flywheels resist changes in rotational speed by their moment of inertia. The amount of
energy stored in a flywheel is proportional to the square of its rotational speed. The way to
change a flywheel's stored energy is by increasing or decreasing its rotational speed applying
a torque aligned with its axis of symmetry.
 If the clutch cannot be disengaged or it fails to release, you cannot shift gears. In this
situation, when you stop the vehicle in gear (clutch pedal depressed), the engine stalls. This
condition is known as clutch drag.
 Clutch slippage is a condition wherein the full power of the engine does not reach the
transmission. The engine speeds up, but the vehicle speed does not increase as it should. The
clutch disc is not being gripped firmly, and it slips between the flywheel and pressure plate as
the members rotate.
 A grabbing clutch engages with a jerk or shudder no matter how slowly and carefully it is
applied. The effect may be a series of jerks, which is often described as bucking. This
problem may be severe enough to cause damage to universal joints or other drive train parts.
 Some clutch defects can result in a vibration that can be felt inside of the vehicle while the
clutch is fully engaged. This clutch vibration varies with engine speed. It differs from chatter,
which occurs when the clutch is in the process of being engaged or disengaged.
 Hard pedal effort is noticed when the clutch pedal is excessively hard to push down. If the
pedal is hard to depress, the problem is usually in the linkage. If the driver is strong enough
to depress the pedal, it may stay on the floor or rise very slowly when released. Components
may wear quickly.

29. September 2017 29

Chapter 4
Analysis of Work & Possible Solution
(1) Clutch Adjustment
Clutch adjustment involves setting the correct amount of free play in the clutch linkage.
Too much free play can cause clutch drag, preventing the clutch from ever fully disengaging. In
this case, the power flow is not completely cut off from the clutch and the engine could continue
to propel the vehicle. Too little free play can cause the clutch to slip. In this case, the throwout
bearing rotates continually as it contacts the rotating pressure plate release levers or fingers, and
it quickly wears out. With enough pressure on the levers or fingers, the clutch slips, overheats,
and becomes damaged.
No matter what type of clutch linkage is used, the free play can be checked by pushing
the clutch pedal with your hand.
Begin with the pedal in a fully released position—that is, with the pedal all the way up.
Start pushing down on the pedal. The pedal should move easily for about 1″ (25 mm). In this
span, the only pressure you are working against is that of the return springs. Past this point, the
pedal becomes harder to push. This is where the throwout bearing contacts the pressure plate
release levers or fingers, and you are working against the force of the pressure plate apply
springs.
The distance that the pedal moved from the fully released position until it became hard to
push is the free lay. All vehicle manufacturers specify the proper amount of clutch free play. Free
play is adjusted at some place on the clutch linkage. On many vehicles, the clutch has a self-
adjusting feature that automatically adjusts free play whenever the clutch pedal is depressed.

(2) Hydraulic linkage adjustment
The hydraulic linkage uses hydraulic pressure to transfer pedal movement to the clutch
fork. As with the previous adjusters, adjustment is made by a threaded section on the linkage at
the clutch fork. Adjustment to this linkage changes the effective length of the pushrod at the
slave cylinder.
Measure the amount of free play at the clutch pedal. Use a ruler to obtain an accurate
reading, and compare it against specifications. If the specifications are not available, between 1″
and 1.5″ (25 mm and 38 mm) of free play is generally acceptable.
Before adjusting free play, check the master cylinder reservoir to make sure the fluid
level is sufficient. Add DOT 3 brake fluid if necessary.
Loosen the locknut holding the threaded rod to the adjuster. Turn the rod until you obtain
the proper free play as measured at the clutch pedal. Retighten the locknut. Recheck the free play
at the clutch pedal. Then, road test the car.

30. September 2017 30

Hydraulic linkage
Before adjusting a hydraulic linkage, always check the fluid level in the master cylinder
reservoir first. If the fluid level is low, check for leaks at the places. Leaks appear as dark stains
on hydraulic system parts. Sometimes the brake fluid used in the system is visible at the point of
the leak. Leaks can occur in the hydraulic lines or at loose connections. The most common leaks,
however, occur at the master or slave cylinder seals.
It is usually easier and cheaper to replace leaking master and slave cylinders. However, in
some cases, a replacement cylinder is not available, or the cost of replacement is excessive. If a
new or remanufactured master or slave cylinder cannot be located, the old cylinder can be rebuilt
with the proper seal kit.
The slave cylinder has a bleeder valve for bleeding air from the system. The valve looks
like a crew with a small hole running down its length. The hole is closed off when the bleeder
valve is tightened down. Loosening the valve a few turns will open the hole and permit system
bleeding. Note that some bleeder valves have a cap, as well.
There are two methods to manually bleed air from a hydraulic system. One method is
preferred over the other because it minimizes the chance of fluid contamination. This preferred
method is outlined as follows:
1. Fill the system reservoir with fresh brake fluid. Leave the cover off the reservoir.
(Bleeder valve is closed.)
2. If the bleeder valve has a cap, remove it at this time. Attach a hose to the end of the
bleeder valve. Place the free end of the hose in a clear container. Fill the container with enough
fluid to cover the bottom of the hose.
3. Have an assistant pump several times on the clutch pedal. Then, ask the assistant to
hold the pedal down.
4. Open the bleeder valve by loosening it about a quarter or half turn. Make sure your
assistant continues to keep his or her foot on the clutch pedal. The pedal will probably go all the
way to the floor. Air, or a mixture of air and brake fluid, will come out of the bleeder valve.
Keep the outlet of the hose submerged in the fluid as it begins to fill the container. Watch for air
bubbles.
5. Close the bleeder valve once the flow stops.
6. Let up on the clutch pedal.
7. Repeat the process until only brake fluid comes out of the bleeder valve. This can be
noted by watching the air bubbles emerging from the hose as the system is bled.
8. Top off the system reservoir with fresh brake fluid, and put the cover back on the
reservoir. Do not reuse fluid bled from the system, as it may be contaminated.
There is an alternative method of bleeding air from a hydraulic system. It can be done
without an assistant and without wasting brake fluid; however, expelled fluid, which may be
contaminated, is returned to the system. The method is outlined as follows:
1. Open the bleeder valve by loosening it about a quarter or half turn.
2. If the bleeder valve has a cap, remove it at this time. Attach a hose to the end of the
open bleeder valve. Place the free end of the hose in a clear container of brake fluid.
3. Fill the system reservoir with fresh brake fluid, and replace the cap.
4. Pump the clutch pedal until bubbles stop coming out of the hose in the container. You
might want to have an assistant watch for the bubbles for you to make the job easier.
5. With the clutch pedal released, close the bleeder valve.

31. September 2017 31

4.1. Clutch Parts Inspection
(1) Bearing inspection
The clutch pilot bearing is not serviced until the clutch is removed. The bearing is often
worn out by then. The pilot bearing should be inspected for excessive wear or damage. Some
technicians will automatically replace the bearing as a matter of practice. If there is any doubt
about a pilot bearing’s condition, it should be replaced! Roller- or ball-type pilot bearings should
be inspected for lack of lubrication. To check this, turn the bearing and feel for roughness. If it
does not turn smoothly, it should be replaced. In a pilot bushing, wear will show up as looseness
between the bushing and the input shaft pilot. A good way to check for looseness is to insert a
used input shaft into the bearing and try to wiggle it. If it has too much play, the bushing is worn
out and it should be replaced.


Bearing removal
There are a couple ways to remove a pilot bearing. One way is to use a pilot bearing
puller tool One variation of this tool is the threaded-tip puller. The threaded-tip puller is used to
remove a pilot bushing, but it ruins the bearing in the process. The center shaft, or pilot, of this
tool has a self-tapping tip. The pilot is threaded into the bore of the bearing. When fully inserted,
the legs of the puller are adjusted to seat on the crankshaft flange. As the tool is tightened further,
it pulls the pilot bearing from the crankshaft bore. Another variation, called an expandable
finger-tip puller, is a similar tool used when ball or roller bearings are used.
Another way to remove the old pilot bearing is to pack the recess behind the bearing with
heavy grease. Then, install a driver into the pilot bearing—an old input shaft works nicely. Put
on eye protection and strike the exposed end of the input shaft with a hammer. The force from
the hammer will travel through the input shaft to the grease. The grease will push the bearing
from the crankshaft.


Bearing installation
Before installing the new pilot bearing, slip it over the pilot of the transmission input
shaft. This is done to ensure it is the proper bearing. If it will not slip over the shaft, or if the fit is
too loose, it is not the correct bearing. The next step is to drive the new bearing into the
crankshaft bore. Use a properly sized driver to avoid damage. Measure the installed depth of the
pilot bearing. If this depth is too shallow, the input shaft may contact the bearing. This will
damage the bearing, the input shaft, or both. If the bearing is driven in too deeply, it may not
make full contact with the input shaft pilot. This is not a problem with bushings, as they are
usually longer. If bushings are driven in too deeply, there is still usually adequate surface contact
with the input shaft pilot. Once the pilot bearing is properly installed, lubricate it with a small
quantity of high-temperature grease. Most bearings have a recess behind the bearing. A small
amount of grease stored in this recess will find its way to the bearing surface, helping to keep it
supplied with lubricant.

32. September 2017 32

(2) Flywheel Service
The flywheel is large and very heavy, and removing it can be difficult and even
dangerous. It should not be removed unless it is in need of resurfacing. It is rare to find a
flywheel that is not showing some sign of wear or overheating. Judgment is called for in
deciding if it must be resurfaced. In many cases, the flywheel can be reused without machining.
If the flywheel is not badly worn, it can be cleaned by light sanding.

Flywheel inspection
Visually inspect the flywheel for obvious signs of damage. Check the flywheel machined
surface for discoloration (caused by overheating), scoring, or extremely shiny surfaces. In some
cases, the flywheel may have deep heat cracks. Look for warping. Inspect the threads in the holes
for the clutch cover attaching bolts. If they are stripped, they can be restored by installing a
thread repair insert. Also, check the flywheel ring gear for damage. If even one ring gear tooth is
broken, the ring gear must be replaced. Note that if the ring gear teeth are damaged, you should
also check the teeth of the starter drive pinion for damage. If the flywheel is not obviously
damaged, use a straightedge and feeler gauge to check for warped contact surfaces.
Manufacturers’ specifications as to maximum warpage vary.
As mentioned, the surface of the flywheel should also be checked for runout. This is a
condition of a rotating object, such as a shaft or flywheel, in which the surface is not rotating in a
true circle or plane. Radial runout is a measure of out-of-roundness. It is measured at right angles
to the centerline of an object. Excessive radial runout may be caused, for example, by a bent
shaft. Lateral runout is a measure of in-and-out movement, or wobble. It is measured in the
direction that is lengthwise to the centerline of the rotating object. In other words, it is measured
on the plane surface of the rotating object.
Determine the lowest point on the flywheel, which corresponds to the lowest reading on
the dial. Zero the indicator at this point. Move the flywheel until the highest reading is recorded.
This measurement is the lateral runout. Lateral runout should not exceed the manufacturer’s
specifications. If it does, the flywheel may not be mounted properly. Remove it and check for
burrs between the flywheel and the face of the crankshaft flange. If no burrs exist, check the
runout of the crankshaft flange. Note that while the dial indicator is mounted, you can also
measure crankshaft endplay. Push the flywheel forward and rearward and note the displacement
on the dial.
Flywheel removal
The easiest way to remove the flywheel attaching bolts is with an impact wrench. If you
do not have an impact wrench to remove the flywheel, it must be kept from rotating so the
attaching bolts can be loosened. While the bolts are being removed, the flywheel can be held in
place using a flywheel turner or locked in place with a flywheel holder; alternatively, a block of
wood can be placed between the flywheel and a stationary part of the engine. A flywheel is very
heavy. It can cause injury or severe damage if dropped. Do not remove the bolts completely until
you have the flywheel secured so that it cannot fall. Once the flywheel is securely held, the bolts
can be loosened and the flywheel can be removed. Sometimes there is a flat metal spacer
between the flywheel and the crankshaft flange. The spacer should be saved for reassembly.
After removing the flywheel, check the rear main bearing seal for leaks. If the seal is leaking, oil
could reach the new clutch disc and ruin it, just as it may have ruined the old disc. A leaking seal
must be replaced.

33. September 2017 33


Flywheel repair
Some flywheels may be damaged beyond repair. Others may be repaired and then
reinstalled. Some of these may be fixed by replacing the ring gear or by resurfacing. Flywheels
with damaged ring gears are usually replaced. Some ring gears can be removed from the
flywheel and replaced, Some flywheel ring gears are welded into position; others are a shrink fit.
After the ring gear is placed on the flywheel, it should be checked for proper seating.
Make sure the gear is not warped; warpage will cause the starter to jam. Once you have
determined that the ring gear is properly installed, stake it or weld it in place, as necessary.
Resurfacing a flywheel is a job for a machine shop. Generally speaking, any machine
shop that can resurface cylinder heads can resurface a flywheel. The machining process for
flywheels is similar to that for cylinder heads.
Flywheels can be resurfaced by turning on a lathe (including a brake lathe), cutting on a
milling machine, or grinding on a table with a special grinding wheel. No matter what method is
used, the basic process is the same: material is removed until the surface is totally clean and
damage-free.
Only a certain amount of metal can be removed, however. If too much is removed, the
flywheel will not have sufficient metal to absorb heat. Some flywheels are marked to indicate the
maximum amount of metal that can be removed. If the flywheel is not marked, the machine shop
will usually be able to tell you if there is enough good metal left in the flywheel. As a general
rule, about 0.2″ (5 mm) can be removed from a flywheel that has not been machined before.

Flywheel installation
Once the flywheel is resurfaced, it should be reinstalled in its original position. First,
reinstall any alignment dowels. Solid dowels are installed by driving them in squarely with a
soft-faced mallet. A special tool with a shoulder is needed to drive hollow dowels. Drive the
dowels in carefully until they are fully seated. If there was a spacer plate between the flywheel
and the crankshaft flange, reinstall it before replacing the flywheel.
Align the crankshaft flange and flywheel bolt holes. They are usually spaced so they will
line up at only one location. After the bolt holes are aligned, start the flywheel attaching bolts.
Torque the bolts to the proper tension in a crisscross pattern. Use a flywheel holder or a wood
block to hold the flywheel during the tightening operation.

(4) Clutch Disc Service
In most cases, the clutch disc is replaced when any kind of clutch teardown is done, since
it is relatively inexpensive. If the disc was recently replaced or appears to be in excellent
condition, it can be reused. Before deciding to reuse the disc, it should be carefully checked.
If you intend to reuse the clutch disc, do not wash it in any kind of cleaning solvent.
Solvent will ruin the clutch disc friction facings.
Inspect the clutch disc for thin or cracked friction material. The disc thickness can be
checked with a sliding caliper. Usually, however, other indications will be obvious and this step
will be unnecessary. Check the disc for loose rivets, oil-soaked friction facings, or broken
cushion springs. Make sure the hub flange splines are not worn and they slide freely on the
splines of the transmission input shaft. If the clutch disc shows any wear or damage, it should be
replaced.

34. September 2017 34

If a replacement disc is to be used, it must be carefully compared to the old one before it
is installed. Many clutch problems are caused by installing the wrong replacement disc. It is
especially important to check the hub flange size against the old disc. A hub flange that is too
large will contact the flywheel and pressure plate, causing clutch disc damage and gear clash. As
a final check, slip the replacement disc over the transmission input shaft to make sure it has the
correct splines.


(5) Pressure Plate Assembly Service
The pressure plate assembly is another clutch component that is almost always replaced
when the clutch is repaired. You should spend a few moments checking the pressure plate
assembly. This will help you determine the cause of the clutch problem and learn how it can be
prevented in the future.

Pressure plate assembly inspection
The pressure plate machined surface develops the same problems as the flywheel surface.
Check for wear, scoring, signs of overheating, cracks, and warpage. The pressure plate will
usually show more heat damage than the flywheel.
Retaining rivets for diaphragm-spring pivot rings should be checked for looseness. Loose
rivets indicate long usage or rough clutch treatment.
Elongation of the bolt holes in the clutch cover is an indication the clutch cover attaching
bolts were loose. The pressure plate assembly may bounce against the flywheel if these bolts are
loose, which would cause the holes to elongate.
Check for weak pressure plate springs and for signs of overheated springs. The release
fingers or levers should be checked for wear and misadjustment. If any fingers or levers are
lower than the others, the pressure plate application will be uneven. The clutch may grab or
chatter. Severe wear at the contact point with the throw out bearing indicates the clutch has seen
much use or there was no free play.
This damage may range from chatter marks on the pressure plate to a scored pressure
plate or broken release levers. Being able to readily identify the damage will result in better
service times.



Pressure plate assembly repair
Most repair shops choose to completely replace pressure plate assemblies, rather than
rebuild them. It is possible, however, with the proper equipment, to take apart a pressure plate
assembly and replace just the parts that are worn. This is typically done on an assembly line by
large automotive rebuilders. As a general rule, pressure plate assemblies that are put together
with nuts and bolts can be rebuilt, while pressure plates held by rivets cannot be rebuilt. If a shop
decides to rebuild a pressure plate assembly, it must closely follow the manufacturer’s directions.

35. September 2017 35

Chapter 5
Conclusion


 These is the clutch assembly layout which is use in present vehicle .

 To solve the problems related to clutch assembly, we’ll change these mechanism and
solve the problems.

 We can modify this project by doing some following changes like –

1. Replacement of Clutch and Flywheel

2. We can modify the shaft by adding displacement clutch so the strength and stiffness of
spring is also change.

5.1. Future Scope

In future, we can make simple design and construction of clutch assembly.

 We’ll modify clutch for gaining more torque.

 We can make easing working mechanism of the clutch.

 We can improve more safety than present mechanism.

36. September 2017 36

Chapter 6
References

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[2] Timoshenko S., Element of Strength of Materials, Part I and II, Van Nastrond , New Jersey,
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[4] Richards, T H, Energy Methods in Structural Analysis with an Introduction to Finite Element
Techniques, Ellis Harwood Ltd., Chichester,1977.
[5] Argyris J H and S Kelsey, Energy Theorom and Structural analysis, Butlerworth, London,
1960.
[6] Zeinkiewicz O C and R L Taylor, The Finite element method , vol.I., Basic Formulation and
Linear problems, Mc Graw Hill, ( UK ) Limited, 1989.
[7] Zeinkiewicz O C and K.Morgan, Finite element and approximation, John Wiley and Son,
Inc., New York.1983.
[8] Reddy J N , An Introduction to the finite element Method , Mc Graw Hill Book Co,
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[9] Desai C S and J F Wilson, Numerical method in FEA, Prentice-Hall of India Private limited,
New Delhi, 1978.
[10] Strang G and B J F ix, An Analysis of the finite element method, prentice Hall, Englewood
cliffs,N.J,1973.
[11] Desai C S and J F Abel, Introduction to the Finite Element method, Affiliated East-West
press pvt. Ltd.,1970.
New Delhi, East West student Edition, 1977.