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DESIGN AND FABRICATION OF MOTORIZED SCREW JACK
FOR A FOUR WHEELER
A PROJECT REPORT
Submitted in partial fulfillment for the award of the degree of
BACHELOR OF TECHNOLOGY
IN
MECHANICAL ENGINEERING
By
Mounika.Kandi.Reddy
(07241A0395)
Priyanka CH
(07241A03A3)
DEPARTMENT OF MECHANICAL ENGINEERING
Gokaraju Rangaraju Institute of Engineering and Technology
(Affiliated to Jawaharlal Nehru Technological University)
Bachupally, Kukatpally, Hyderabad-500072
April/May 2011
DEPARTMENT OF MECHANICAL ENGINEERING
GOKARAJU RANGARAJU INSTITUTE OF ENGINEERING AND TECHNOLOGY
(AFFILIATED TO JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY)
HYDERABAD
CERTIFICATE
This is to certify that this project entitled “design and fabrication of motorized screw jack
for a four wheeler” is a bonafide work carried out by Mounika Kandi Reddy (07241A0395)
and Priyanka Ch (07241A03A3) during the period 2010-2011 in partial fulfillment of the
requirements for the award of degree of “Bachelor of technology in Mechanical Engineering”
from Gokaraju Rangaraju Institute of Engineering and Technology, Hyderabad affiliated to
Jawaharlal Nehru Technological University, Hyderabad (JNTUH) under our guidance and
supervision.
The results embodied in the project work have not been submitted to any other University
or Institute for the award of any degree or diploma.
Dr.Kancha Sammaiah
PROJECT GUIDE
(Associate professor, Mech dept.)
GRIET
P.S.V KURMA RAO
PROJECT HEAD
(Professor, Mech dept.)
GRIET
K.G.K MURTI
(HOD)
MECHANICAL DEPT.
GRIET
ACKNOWLEDGEMENT
This project would have been a distant reality if not for the help and encouragement from
various people. We take immense pleasure in thanking Dr.Jandhyala N Murthy, Principal,
Gokaraju Rangaraju Institute of Engineering and Technology, Mr.P.S.Raju, Director,
Gokaraju Rangaraju Institute of Engineering and Technology, for having permitted us to
carry out this project work.
We wish to express our deep sense of gratitude to Mr.K.G.K Murti, HOD, GRIET, Dr.
P.S.V Kurma Rao, Professor, Mechanical Engineering Department, GRIET and our
project guide Dr.K.Sammaiah, Associate Professor, Mechanical Engineering Department,
GRIET for their able guidance, encouragement and useful suggestions, which helped us in
completing the project in time.
We would also like to mention Shantha Sivam Industries and Sai Engineering Works,
Fatehnagar for their encouragement and cooperation in carrying out the project work.
Finally, yet importantly, I would like to express my heartfelt thanks to my beloved
parents for their blessings, my friends for their help and wishes for the successful completion of
this project.
Mounika Kandi Reddy
Priyanka CH.
NOMENCLATURE
p
l
d
dc
dm
α
W
N
μ
P
θ
T
η
Fc
Ft
Fs
Ts
t
n
Tn
Pb
k
I
A
Pcr
E
Syt
M
WT
h
y
b
Fw
y
Fo
Cv
v
WD
WT
WI
C
K
EP
-
Pitch of screw thread (mm)
Lead of screw thread (mm)
Nominal diameter of screw (mm)
Core diameter of screw (mm)
Mean diameter of screw
Helix angle of screw (degree)
Load (kg)
Normal reaction
Coefficient of friction
Effort (N)
Friction angle (degree)
Torque (N.m)
Efficiency (%)
Direct compressive stress (N/mm2)
Torsional shear stress (N/mm2)
Principal shear stress (N/mm2)
Transverse shear stress (N/mm2)
Thread thickness at the core diameter (mm)
Number of threads in engagement with the nut.
Transverse shear stress at the root of the nut (N/mm²)
Unit bearing pressure (N/mm²)
Least radius of gyration of the cross-section about its axis (mm)
Least moment of inertia of the cross-section (mm4)
Area of the cross-section (mm2)
critical load (N).
Modulus of elasticity (N/mm²)
Yield strength of the material (N/mm2)
Maximum bending moment at the critical section
Tangential load acting at the tooth (N)
Length of the tooth (mm)
Half of the thickness of the tooth (t) at critical section (mm)
Width of gear face (mm)
Permissible working stress
Lewis form factor
allowable static stress (N/mm2)
velocity factor.
Pitch line velocity (m/s.)
Total dynamic load (N)
Steady transmitted load (N),
Incremental load due to dynamic action (N)
A deformation or dynamic factor (N/mm)
A factor depending upon the form of the teeth of a gear
Young‟s modulus for the material of the pinion in N/mm2
EG
e
WS
Wd
Ww
Dp
Q
K
N1
N2
D2
D1
-
Young‟s modulus for the material of the gear in N/mm2
Tooth error action in mm
Static tooth load (N)
Dynamic tooth load
Maximum or limiting load for wear (N)
Pitch circle diameter of the pinion in mm
Ratio factor
Load stress factor (N/mm2)
Surface endurance limit (N/mm²)
Pressure angle
Motor speed (RPM)
Output speed (RPM)
Diameter of the roller gear wheel (mm)
Diameter of the motor gear wheel (mm)
ABSTRACT
With the increasing levels of technology, the efforts being put to produce any kind of work has
been continuously decreasing. The efforts required in achieving the desired output can be
effectively and economically be decreased by the implementation of better designs.
Power screws are used to convert rotary motion into translatory motion. A screw jack is an
example of a power screw in which a small force applied in a horizontal plane is used to raise or
lower a large load. The principle on which it works is similar to that of an inclined plane. The
mechanical advantage of a screw jack is the ratio of the load applied to the effort applied. The
screw jack is operated by turning a lead screw. The height of the jack is adjusted by turning a
lead screw and this adjustment can be done either manually or by integrating an electric motor.
In this project, an electric motor will be integrated with the screw jack and the electricity needed
for the operation will be taken from the battery of the vehicle and thereby the mechanical
advantage will be increased.
CONTENTS
Page no.
1.0
Literature Survey
1
2.0
Power Screws
5
2.1
Applications
5
2.2
Advantages
5
2.3
Disadvantages
6
2.4
Forms of Thread
2.4.1 Advantages of Square Thread
6
2.4.2 Disadvantage of Square Thread
6
2.4.3 Advantages of Trapezoidal Threads
7
2.4.4 Disadvantages of Trapezoidal Threads
7
2.4.5 Advantages of Buttress Threads
8
Designation of Threads
9
2.5.1 Multiple Threaded Power Screws
9
2.6
Terminology of Power Screw
9
2.7
Torque Requirement- Lifting Load
12
2.8
Torque Requirement- Lowering Load
13
2.9
Self Locking Screw
14
2.10
Efficiency of Square Threaded Screw
16
2.11
Efficiency of Self-Locking Screw
17
2.12
Efficiency of Trapezoidal and Acme Threads
18
2.13
Coefficient of Friction
18
2.14
Stresses in Screw and Nut
18
2.15
Buckling of Columns
19
3.0
Screw Jack
21
2.5
3.1
The Screw
21
3.2
Operation
21
3.3
Construction of Screw Jack
22
3.4
Function
22
3.5
Features
22
3.6
Benefits
23
3.7
Types
23
3.7.1
3.8
Mechanical Jacks
23
3.7.1.1 Scissor Jacks
23
Construction
24
Design and Lift
24
3.7.1.2 Bottle (cylindrical) Jacks
24
3.7.2
25
Hydraulic Jacks
Design of Screw Jack
26
3.8.1 Loads and Stresses in Screw
26
3.8.2 Thrust Bearings
28
3.8.3 Operational Considerations of a screw jack
28
4.0
Motorized Screw Jack
30
4.1
Introduction
30
4.2
Need For Automation
31
4.3
Parts of Motorized Screw Jack
31
4.3.1
31
D.c.Motor (permanent magnet)
4.3.1.1 Design Of D.C. Motor
36
4.3.2
37
Batteries
4.3.2.1 Introduction
37
4.3.2.2 Lead-Acid Wet Cell
37
4.3.2.3 Construction
38
4.3.2.4 Chemical Action
38
4.3.2.5 Caring For Lead-Acid Batteries
40
4.3.2.6 Current Ratings
40
4.3.2.7 Specific Gravity
41
4.3.2.8 Charging the Lead-Acid Battery
42
4.3.3
Screw Jack
42
4.3.4
Spur Gear
44
4.3.4.1 Types
44
4.3.4.2 Design considerations for a gear drive
44
4.3.5
50
Switch
4.4
Working Principle
51
4.5
Advantages
51
4.6
Disadvantages
51
4.7
Applications
51
5.0
Design Calculations
53
5.1
Design calculations to check the safety of LEAD SCREW
53
5.2
Design calculations to check the safety of nut
54
5.3
Design calculations to check the buckling of screw
55
5.4
Design considerations for a gear drive
56
6.0
Conclusion
60
7.0
Bibliography
61
CHAPTER 1
LITERATURE SURVEY
Screw type mechanical jacks were very common for jeeps and trucks of World War II vintage.
For example, the World War II jeeps (Willys MB and Ford GPW) were issued the "Jack,
Automobile, Screw type, Capacity 1 1/2 ton", Ordnance part number 41-J-66. This jacks, and
similar jacks for trucks, were activated by using the lug wrench as a handle for the jack's ratchet
action to of the jack. The 41-J-66 jack was carried in the jeep's tool compartment. Screw type
jack's continued in use for small capacity requirements due to low cost of production raise or
lower it. A control tab is marked up/down and its position determines the direction of movement
and almost no maintenance.
The virtues of using a screw as a machine, essentially an inclined plane wound round a cylinder,
was first demonstrated by Archimedes in 200BC with his device used for pumping water.
There is evidence of the use of screws in the Ancient Roman world but it was the great Leonardo
da Vinci, in the late 1400s, who first demonstrated the use of a screw jack for lifting loads.
Leonardo‟s design used a threaded worm gear, supported on bearings, that rotated by the turning
of a worm shaft to drive a lifting screw to move the load - instantly recognisable as the principle
we use today.
1
We can‟t be sure of the intended application of his invention, but it seems to have been relegated
to the history books, along with the helicopter and tank, for almost four centuries. It is not until
the late 1800s that we have evidence of the product being developed further.
With the industrial revolution of the late 18th and 19th centuries came the first use of screws in
machine tools, via English inventors such as John Wilkinson and Henry Maudsley The most
notable inventor in mechanical engineering from the early 1800s was undoubtedly the
mechanical genius Joseph Whitworth, who recognised the need for precision had become as
important in industry as the provision of power.
While he would eventually have over 50 British patents with titles ranging from knitting
machines to rifles, it was Whitworth‟s work on screw cutting machines, accurate measuring
instruments and standards covering the angle and pitch of screw threads that would most
influence our industry today.
Whitworth‟s tools had become internationally famous for their precision and quality and
dominated the market from the 1850s. Inspired young engineers began to put Whitworth‟s
machine tools to new uses. During the early 1880s in Coaticook, a small town near Quebec, a 24year-old inventor named Frank Henry Sleeper designed a lifting jack. Like da Vinci‟s jack, it
was a technological innovation because it was based on the principle of the ball bearing for
supporting a load and transferred rotary motion, through gearing and a screw, into linear motion
for moving the load. The device was efficient, reliable and easy to operate. It was used in the
construction of bridges, but mostly by the railroad industry, where it was able to lift locomotives
and railway cars.
Local Coaticook industrialist, Arthur Osmore Norton, spotted the potential for Sleeper‟s design
and in 1886 hired the young man and purchased the patent. The „Norton‟ jack was born. Over the
coming years the famous „Norton‟ jacks were manufactured at plants in Boston, Coaticook and
Moline, Illinois.
Meanwhile, in Alleghany County near Pittsburgh in 1883, an enterprising Mississippi river boat
captain named Josiah Barrett had an idea for a ratchet jack that would pull barges together to
form a „tow‟. The idea was based on the familiar lever and fulcrum principle and he needed
someone to manufacture it. That person was Samuel Duff, proprietor of a local machine shop.
2
Together, they created the Duff Manufacturing Company, which by 1890 had developed new
applications for the original „Barrett Jack‟ and extended the product line to seven models in
varying capacities.
Over the next 30 years the Duff Manufacturing Company became the largest manufacturer of
lifting jacks in the world, developing many new types of jack for various applications including
its own version of the ball bearing screw jack. It was only natural that in 1928, The Duff
Manufacturing Company Inc. merged with A.O. Norton to create the Duff-Norton
Manufacturing Company.
Both companies had offered manually operated screw jacks but the first new product
manufactured under the joint venture was the air motor-operated power jack that appeared in
1929. With the aid of the relatively new portable compressor technology, users now could move
and position loads without manual effort. The jack, used predominantly in the railway industry,
incorporated an air motor manufactured by The Chicago Pneumatic Tool Company.
Air Motor Power Jack
There was clearly potential for using this technology for other applications and only 10 years
later, in 1940, the first worm gear screw jack, that is instantly recognizable today, was offered by
Duff-Norton, for adjusting the heights of truck loading platforms and mill tables. With the ability
to be used individually or linked mechanically and driven by either air or electric motors or even
manually, the first model had a lifting capacity of 10 tons with raises of 2” or 4”.
Worm Gear Jack
3
Since then the product has evolved to push, pull, lift, lower and position loads of anything from a
few kilos to hundreds of tonnes. One of the biggest single screw jacks made to date is a special
Power Jacks E-Series unit that is rated for 350 tonnes –even in earthquake conditions for the
nuclear industry.
More recent developments have concentrated on improved efficiency and durability, resulting in
changes in both lead screw and gearbox design options for screw jacks.
A screw jack that has a built-in motor is now referred to as a linear actuator but is essentially still
a screw jack. Today, screw jacks can be linked mechanically or electronically and with the
advances in motion-control, loads can be positioned to within microns. Improvements in gear
technology together with the addition of precision ball screws and roller screws mean the
applications for screw jacks today are endless and a real alternative to hydraulics in terms of duty
cycles and speed at a time when industry demands cleaner, quieter and more reliable solutions.
4
CHAPTER 2
POWER SCREWS
A power screw is a mechanical device used for converting rotary motion into linear motion and
transmitting power. A power screw is also called translation screw. It uses helical translatory
motion of the screw thread in transmitting power rather than clamping the machine components.
2.1 Applications
The main applications of power screws are as follows:
(i) To raise the load, e.g. screw-jack,
(ii) To obtain accurate motion in machining operations, e.g. lead-screw of lathe,
(iii) To clamp a workpiece, e.g. vice, and
(iv) To load a specimen, e.g. universal testing machine.
There are three essential parts of a power screw, viz.screw, nut and a part to hold either the screw
or the nut in its place. Depending upon the holding arrangement, power screws operate in two
different ways. In some cases, the screw rotates in its bearing, while the nut has axial motion.
The lead screw of the lathe is an example of this category. In other applications, the nut is kept
stationary and the screw moves in axial direction. Screw-jack and machine vice are the examples
of this category.
2.2 Advantages
Power screws offer the following advantages:
(i) Power screw has large load carrying capacity.
(ii) The overall dimensions of the power screw are small, resulting in compact construction.
(iii) Power screw is simple to design
(iv) The manufacturing of power screw is easy without requiring specialized machinery. Square
threads are turned on lathe. Trapezoidal threads are manufactured on thread milling machine.
(v) Power screw provides large mechanical advantage. A load of 15 kN can be raised by
applying an effort as small as 400 N.Therefore, most of the power screws used in various
applications like screw-jacks, clamps, valves and vices are usually manually operated.
(vi) Power screws provide precisely controlled and highly accurate linear motion required in
machine tool applications.
(vii) Power screws give smooth and noiseless service without any maintenance.
(viii) There are only a few parts in power screw. This reduces cost and increases reliability.
5
(ix) Power screw can be designed with self-locking property. In screw-jack application, self
locking characteristic is required to prevent the load from descending on its own.
2.3 Disadvantages
The disadvantages of power screws are as follows:
(i) Power screws have very poor efficiency; as low as 40%.Therefore, it is not used in continuous
power transmission in machine tools, with the exception of the lead screw. Power screws are
mainly used for intermittent motion that is occasionally required for lifting the load or actuating
the mechanism.
(ii) High friction in threads causes rapid wear of the screw or the nut. In case of square threads,
the nut is usually made of soft material and replaced when worn out. In trapezoidal threads, a
split- type of nut is used to compensate for the wear. Therefore, wear is a serious problem in
power screws.
2.4 Forms of Threads
There are two popular types of threads used for power screws viz. square and I.S.O metric
trapezoidal.
2.4.1 Advantages of square threads
The advantages of square threads over trapezoidal threads are as follows:
(i) The efficiency of square threads is more than that of trapezoidal threads.
(ii) There is no radial pressure on the nut. Since there is no side thrust, the motion of the nut is
uniform. The life of the nut is also increased.
2.4.2 Disadvantages of square threads
The disadvantages of square threads are as follows:
(i) Square threads are difficult to manufacture. They are usually turned on lathe with single-point
cutting tool. Machining with single-point cutting tool is an expensive operation compared to
machining with multi-point cutting tool.
6
(ii) The strength of a screw depends upon the thread thickness at the core diameter. Square
threads have less thickness at core diameter than trapezoidal threads. This reduces the load
carrying capacity of the screw.
(iii) The wear of the thread surface becomes a serious problem in the service life of the power
screw. It is not possible to compensate for wear in square threads. Therefore, when worn out, the
nut or the screw requires replacement.
2.4.3 Advantages of Trapezoidal Threads
The advantages of trapezoidal threads over square threads are as follows:
(i) Trapezoidal threads are manufactured on thread milling machine. It employs multi-point
cutting tool. Machining with multi-point cutting tool is an economic operation compared to
machining with single point-cutting tool. Therefore, trapezoidal threads are economical to
manufacture.
(ii) Trapezoidal thread has more thickness at core diameter than that of square thread.Therfore; a
screw with trapezoidal threads is stronger than equivalent screw with square threads. Such a
screw has large load carrying capacity.
(iii) The axial wear on the surface of the trapezoidal threads can be compensated by means of a
split-type of nut. The nut is cut into two parts along the diameter. As wear progresses, the
looseness is prevented by tightening the two halves of the nut together, the split-type nut can be
used only for trapezoidal threads. It is used in lead-screw of lathe to compensate wear at periodic
intervals by tightening the two halves.
2.4.4 Disadvantages of Trapezoidal Threads
The disadvantages of trapezoidal threads are as follows:
(i) The efficiency of trapezoidal threads is less than that of square threads.
(ii) Trapezoidal threads result in side thrust or radial pressure on the nut. The radial pressure or
bursting pressure on nut affects its performance.
There is a special type of thread called acme thread. Trapezoidal and acme threads are identical
in all respects except the thread angle. In acme thread, the thread angle is 29° instead of 30°.The
relative advantages and disadvantages of acme threads are same as those of trapezoidal threads.
7
There is another type of thread called buttress thread. It combines the advantages of square and
trapezoidal threads. Buttress threads are used where heavy axial force acts along the screw axis
in one direction only.
2.4.5 Advantages of Buttress Threads
The advantages of buttress threads are as follows:
(i) It has higher efficiency compared to trapezoidal threads.
(ii) It can be economically manufactured on thread milling machine.
(iii) The axial wear at the thread surface can be compared by means of spit-type nut.
(iv) A screw with buttress threads is stronger than equivalent screw with either square threads or
trapezoidal threads. This is because of greater thickness at the base of the thread.
The buttress threads have one disadvantage. It can transmit power and motion only in one
direction. On the other hand, square and trapezoidal threads can transmit force and motion in
both directions.
Square threads are used for screw-jacks, presses and clamping devices. Trapezoidal and acme
threads are used for lead-screw and other power transmission devices in machine tools. Buttress
threads are used in vices, where force is applied only in one direction. Buttress threads are
ideally suited for connecting tubular components that must carry large forces such as connecting
the barrel to the housing in anti air-craft guns.
2.5 Designation of Threads
There is a particular method of designation for square and trapezoidal threads. A power screw
with single-start square threads is designated by the letters „Sq‟ followed by the nominal
diameter and the pitch expressed in millimeters and separated by the sign „x‟. For example,
Sq 30 x 6
It indicates single-start square threads with 30mm nominal diameter and 6mm pitch.
8
Similarly single-start I.S.O metric trapezoidal threads are designated by letters „Tr‟ followed by
the nominal diameter and the pitch expressed in millimeters and separated by the sign „x‟.For
example,
Tr 40x7
It indicates single-start trapezoidal threads with 40mm nominal diameter and 7mm pitch.
2.5.1 Multiple Threaded Power Screws
Multiple threaded power screws are used in certain applications where higher travelling speed is
required. They are also called multiple start screws such as double-start or triple-start screws.
These screws have two or more threads cut side by side, around the rod.
Multiple-start trapezoidal threads are designated by letters „Tr‟ followed by the nominal diameter
and the lead ,separated by sign „x‟ and in brackets the letter „P‟ followed by the pitch expressed
in millimetres. For example,
Tr 40 x 14 (P7)
In above designation,
Lead=14mm pitch=7mm
Therefore, No. of starts =14/7=2
It indicates two-start trapezoidal thread with 40mm nominal diameter and 7mm pitch. In case of
left handed threads. The letters „LH‟ are added to thread designation. For example,
Tr 40 x 14 (P7) LH
2.6 Terminology of Power Screw
The terminology of the screw thread is as follows:
9
(i) Pitch: The pitch is defined as the distance, measured parallel to the axis of the screw, from a
point on one thread to the corresponding point on the adjacent thread. It is denoted by the letter
„p‟.
(ii) Lead: The lead is defined as the distance, measured parallel to the axis of the screw, that the
nut will advance in one revolution of the screw. It is denoted by the letter „l‟. For a singlethreaded screw, the lead is same as the pitch, for a double-threaded screw, the lead is twice that
of the pitch, and so on.
(iii) Nominal diameter: It is the largest diameter of the screw. It is also called major diameter. It
is denoted by the letter„d‟.
(iv) Core diameter: It is the smallest diameter of the screw thread. It is also called minor
diameter. It is denoted by the letters „dc‟.
(v) Helix angle: It is defined as the angle made by the helix of the thread with a plane
perpendicular to the axis of the screw. Helix angle is related to the lead and the mean diameter of
the screw. It is also called lead angle. It is denoted by α.
From the figure,
dc = d- [ + ]
or,
dc= (d-p)
The mean diameter of the screw is denoted by dm and it is given by,
dm= [d +dc]
= [d + (d-p)]
Or,
dm= (d-0.5p)
10
Imagine that one thread of the screw is unwound and developed for one complete turn. The
thread will become the hypotenuse of a right-angled triangle, whose base is (πdm) and whose
height is the lead (l).Considering this right-angle triangle, the relationship between helix angle,
mean diameter and lead can be expressed in the following form,
Tan α =
where α is the helix angle of the thread.
The following conclusions can be drawn on the basis of the development of thread:
(i) The screw can be considered as an inclined plane with α as inclination.
(ii) The load W always acts in vertically downward direction. When the load W is raised, it
moves up the inclined plane. When the load W is lowered, it moves down the inclined plane.
(iii) The load W is raised or lowered by means of an imaginary force P acting at the mean radius
of the screw. The force P multiplied by the mean radius (dm/2) gives the torque required to raise
or lower the load. Force P is perpendicular to load W.
11
2.7 Torque Requirement- Lifting Load
The screw is considered as an inclined plane with inclination α.When the load is being raised,
following forces act at a point on this inclined plane:
(i) Load W: It always acts in vertically downward direction.
(ii) Normal reaction N: It acts perpendicular (normal) to the inclined plane.
(iii) Frictional force μN: Frictional force acts opposite to the motion. Since the load is moving
up the inclined plane, frictional force acts along the inclined plane in downward direction.
Fig.
(iv) Effort P: The effort P acts in a direction perpendicular to the load W.It may act towards right
to overcome the friction and raise the load.
For an equilibrium of horizontal forces,
P = μ N cos α + N sin α
(a)
For an equilibrium of vertical forces,
W = N cos α – μ N sin α
(b)
Dividing expression (a) by (b),
P=
Dividing the numerator and denominator of the right hand side by cos α,
P=
(c)
The coefficient of friction μ is expressed as,
μ = tan θ
(d)
where θ is the friction angle.
12
Substituting μ = tan θ in Eq. (c),
P=
or
P = W tan (θ + α)
(e)
The torque „T‟ required to raise the load is given by,
T=
T=
tan (θ + α)
(f)
2.8 Torque Requirement- Lowering Load
When the load is being lowered, the following forces act at a point on the inclined plane:
(i) Load W: It always acts in vertically downward direction.
(ii) Normal reaction N: It acts perpendicular (normal) to the inclined plane.
(iii) Frictional force μN: Frictional force acts opposite to the motion. Since the load is moving
down the inclined plane, frictional force acts along the inclined plane in upward direction.
(iv) Effort P: The effort P acts in a direction perpendicular to the load W.It should act towards
left to overcome the friction and lower the load.
For an equilibrium of horizontal forces,
P = μ N cos α - N sin α
(a)
For an equilibrium of vertical forces,
W = N cos α + μ N sin α
(b)
Dividing expression (a) by (b),
13
P=
Dividing the numerator and denominator of the right hand side by cos α,
P=
(c)
The coefficient of friction μ is expressed as,
μ = tan θ
(d)
where θ is the friction angle.
Substituting μ = tan θ in Eq. (c),
P=
or
P = W tan (θ - α)
(e)
The torque „T‟ required to raise the load is given by,
T=
T=
tan (θ - α)
2.9 Self Locking Screw
The torque required to lower the load can be given by,
T=
tan (θ - α)
It can be seen that when,
θ
the torque required to lower the load is negative. It indicates a condition that no force is required
to lower the load. The load itself will begin to turn the screw and descend down, unless a
restraining torque is applied. This condition is called „overhauling‟ of screw.
14
When,
θ
a positive torque is required to lower the load. Under this condition, the load will not turn the
screw and will not descend on its own unless effort P is applied. In this case, the screw is said to
be „self-locking‟. The rule for self-locking screw is as follows:
A screw will be self-locking if the coefficient of friction ids equal to or greater than the tangent
of the helix angle.
For self locking screw,
θ>α
tan θ > tan α
μ>
Therefore, the following conclusions can be made:
(i) Self-locking of screw is not possible when the coefficient of friction (μ) is low. The
coefficient of friction between the surfaces of the screw and the nut is reduced by lubrication.
Excessive lubrication may cause the load to descend on its own.
(ii) Self-locking property of the screw is lost when the lead is large. The lead increases with
number of starts. For double-start thread, lead is twice of the pitch and for triple threaded screw,
three times of pitch. Therefore, single threaded is better than multiple threaded screw from selflocking considerations.
Self-locking condition is essential in applications like screw-jack.
15
2.10 Efficiency of Square Threaded Screw
Refer to the force diagram for lifting the load, illustrated in Fig.
.Suppose the load W moves
from the lower end to the upper end of the inclined plane. The output consists of raising the load.
Therefore,
Work output = force x distance travelled in the direction of force
=Wxl
The input consists of rotating the screw by means of an effort P.
Work output = force x distance travelled in the direction of force
= P x (π dm)
The efficiency η of the screw is given by,
η=
=
=
tan α
Substituting P = W tan (θ + α) in the above equation,
η=
From the above equation, it is evident that the efficiency of the square threaded screw depends
upon the helix angle α and the friction angle θ.The following figure shows the variation of the
efficiency of square threaded screw against the helix angle for various values of coefficient of
friction. The graph is applicable when the load is lifted.
16
Following conclusions can be derived from the observation of these graphs,
(i) The efficiency of square threaded screw increase rapidly up to helix angle of 20°.
(ii) The efficiency is maximum when the helix angle between 40 to 45°.
(iii) The efficiency decreases after the maximum value is reached.
(iv) The efficiency decreases rapidly when the helix angle exceeds 60°
(v) The efficiency decreases as the coefficient of friction increases.
There are two ways to increase the efficiency of square threaded screws. They are as follows:
(i) Reduce the coefficient of friction between the screw and the nut by proper lubrication, and
(ii) Increase the helix angle up to 40 to 45° by using multiple start threads.
However, a screw with such helix angle has other disadvantages like loss of self-locking
property.
2.11 Efficiency of Self-Locking Screw
The efficiency of square threaded screw is given by,
η=
(a)
For self-locking screw,
θ
α
Substituting the limiting value (θ = α) in (a),
η
η
Substituting,
tan (2θ) =
in the above expression,
η
Or,
η
[ -
]
17
Therefore, efficiency of self-locking square threaded power screw is less than ½ or 50%.
2.12 Efficiency of Trapezoidal and Acme Threads
The thread angle is 2θ.For isometric I.S.O metric trapezoidal thread,
2θ = 30°
For acme thread,
2θ = 29°
There is a basic difference between the force acting on the thread of square and trapezoidal
threads. In case of square threads, W is the axial load raised by the screw. It is also the normal
force acting on the thread surface. In case of trapezoidal or acme threads, these two forces are
different. The axial force on the screw is W, while the normal force on the thread surface is
(W/cos θ) or (Wsec θ).The frictional force depends upon the normal force.Therefore; the effect of
thread angle is to increase the frictional force by a term (sec θ).This is because of the wedging
action of the threads. The coefficient of friction is taken as (μ sec θ) instead of μ in case of
trapezoidal threads and the equations derived for square threaded screw are modified and used
for trapezoidal or acme threads.
2.13 Coefficient of Friction
It has been found that the coefficient of friction (μ) at the thread surface depends upon the
workmanship in cutting the threads and on the type of the lubricant. It is practically independent
of the load, rubbing velocity or materials. An average of 0.15 can be taken for the coefficient of
friction, when the screw is lubricated with mineral oil.
2.14 Stresses in Screw and Nut
The body of a screw is subjected to an axial force W and torsional moment (T).The direct
compressive stress Fc is given by,
Fc =
The torsional shear stress is given by,
Ft =
The principal shear stress is given by,
Fs =
18
The threads of the screw which are engaged with the nut are subjected to transverse shear
stresses. The screw will tend to shear off the threads at the core diameter under the action of load
W.The shear area of one thread is πdc t. The transverse shear stress in the screw is given by,
Ts =
Where,
Ts = transverse shear stress at the root of the screw (N/mm²)
t = thread thickness at the core diameter (mm)
n = number of threads in engagement with the nut.
The transverse shear stresses in the nut are determined in a similar way. Under the action of load
W, the thread of the nut will tend to shear off at the nominal diameter. The shear area of one
thread is πdt.Therefore,
Tn =
where,
Tn = transverse shear stress at the root of the nut (N/mm²)
t = thread thickness at the root of the nut (mm).
The bearing pressure between the contacting surfaces of the screw and the nut is an important
consideration in design. The bearing area between the screw and the nut for one thread is
[
Pb =
].Therefore,
(
)
where Pb = unit bearing pressure(N/mm²)
The permissible bearing pressure depends upon the materials of the screw and the nut and the
rubbing velocity.
2.15 Buckling of Columns
When a short member is subjected to axial compressive force, it shortens according to the
Hooke‟s law. As the load is gradually increased, the compression of the member increases.
When the compressive stress reaches the elastic limit of the material, the failure occurs in the
form of bulging.However, when the length of the component is large compared to the crosssectional dimensions, the component may fail by lateral buckling. Buckling indicates elastic
instability. The load at which the buckling starts is called critical load, which is denoted by Pcr.
When the axial load on the column reaches Pcr, there is sudden buckling and a relatively large
lateral deflection occurs.
An important parameter affecting the critical load is the slenderness ratio. It is defined as,
Slenderness ratio =
19
where,
l = length of column (mm)
k = least radius of gyration of the cross-section about its axis (mm)
The radius of gyration is given by,
k=
where,
I = least moment of inertia of the cross-section (mm4)
A = area of the cross-section (mm2)
When the slenderness ratio is less than 30, there is no effect of buckling and such components
are designed on the basis of compressive stresses. Columns, with slenderness ratio greater than
30 are designed on the basis of critical load. There are two methods to calculate the critical loadEuler‟s equation and Johnson‟s equation.
According to the Euler‟s equation,
Pcr =
where,
Pcr = critical load (N).
n = end fixity coefficient
E = modulus of elasticity (N/mm²)
A = area of cross-section (mm²)
The load carrying capacity of the column depends upon the condition of restraints at the two
ends of the column. It is accounted by means of a dimensionless quantity called end fixity
coefficient (n).
According to Johnson‟s equation,
Pcr = Syt A [1 -
]
where Syt is the yield strength of the material.
20
CHAPTER 3
SCREW JACK
A screw jack is a portable device consisting of a screw mechanism used to raise or lower the
load. The principle on which the screw jack works is similar to that of an inclined plane. There
are mainly two types of jacks-hydraulic and mechanical. A hydraulic jack consists of a cylinder
and piston mechanism. The movement of the piston rod is used to raise or lower the load.
Mechanical jacks can be either hand operated or power driven.
Jacks are used frequently in raising cars so that a tire can be changed. A screw jack is commonly
used with cars but is also used in many other ways, including industrial machinery and even
airplanes. They can be short, tall, fat, or thin depending on the amount of pressure they will be
under and the space that they need to fit into. The jack is made out of various types of metal, but
the screw itself is generally made out of lead.
While screw jacks are designed purposely for raising and lowering loads, they are not ideal for
side loads, although some can withstand side loads depending on the diameter and size of the
lifting screw. Shock loads should also be avoided or minimized. Some screw jacks are built with
anti-backlash. The anti-backlash device moderates the axial backlash in the lifting screw and nut
assembly to a regulated minimum.
A large amount of heat is generated in the screw jack and long lifts can cause serious
overheating. To retain the efficiency of the screw jack, it must be used under ambient
temperatures, otherwise lubricants must be applied. There are oil lubricants intended to enhance
the equipment‟s capabilities. Apart from proper maintenance, to optimize the capability and
usefulness of a screw jack it is imperative to employ it according to its design and
manufacturer‟s instruction. Ensure that you follow the speed, load capacity, temperature
recommendation and other relevant factors for application
3.1 The Screw
The screw has a thread designed to withstand an enormous amount of pressure. This is due to the
fact that it is generally holding up heavy objects for an extended amount of time. Once up, they
normally self lock so that they won't fall if the operator lets go, and they hold up well to the wear
of repeated use. If they are made with a ball nut, they will last longer because there is less
friction created with this type of jack. However, they will not self lock. This can be dangerous
and handled carefully.
3.2 Operation
The jack can be raised and lowered with a metal bar that is inserted into the jack. The operator
turns the bar with his hands in a clockwise direction. This turns the screw inside the jack and
makes it go up. The screw lifts the small metal cylinder and platform that are above it. As the
jack goes up, whatever is placed above it will raise as well, once the jack makes contact. The bar
is turned until the jack is raised to the level needed. To lower the jack the bar is turned in the
21
opposite direction. An automatic screw jack has gears inside the jack that are connected to the
screw. Theses gears are connected by other gears and bars that are turned by a power source to
raise and lower the jack.
Although a jack is a simple and widely used device, the use of any lifting device is subject to
certain hazards. In screw-jack applications, the hazards are dropping, tipping or slipping of
machines or their parts during the operation. These hazards may result in serious accidents. The
main reasons of such accidents are as follows:
(i) The load is improperly secured on the jack
(ii) The screw-jack is over loaded.
(iii) The centre of gravity of the load is off centre with respect to the axis of the jack
(iv) The screw-jack is not placed on hard and level surface.
(v) The screw-jack is used for a purpose, for which it is not designed.
Proper size, strength and stability are the essential requirements for the design of the screw-jack
from safety considerations.
3.3 Construction of Screw Jack
Screw jack consists of a screw and a nut. The nut is fixed in a cast iron frame and remains
stationary. The rotation of the nut inside the frame is prevented by pressing a set screw against it.
The screw is rotated in the nut by means of a handle, which passes through a hole in the head of
the screw. The head carries a platform, which supports the load and remains stationary while the
screw is being rotated. A washer is fixed to the other end of the screw inside the frame, which
prevents the screw to be completely turned out of the nut.
3.4 Function
The basic function of a screw jack is to lift a portion of a vehicle. Typically this is used to change
a tire although other maintenance is sometimes performed.
3.5 Features
All jacks have safety features to protect the user from accidental injury. Wide bases help to
stabilize a jack and prevent tilting or sinking into soft soil. Most car jacks also come equipped
with their own handle or cranking mechanism, but alternately many of these also will accept the
flat end of a tire tool to jack up a vehicle. When in the extended position, jacks will have a stop
point that prevents the user from overextending the jack beyond its rated capabilities. When in
the contracted position, jacks that are provided by the manufacturer will have a storage area
specially formed or designed for the jack to rest in when not in use.
22
3.6 Benefits
Equipping motorists with car jacks has provided many benefits to those who are on the road.
Most importantly, jacks have equipped drivers with the ability to change a tire in an emergency
situation without having to call for assistance, which can save service fees and potential towing
fees as well. Car jacks also provide the home auto enthusiast with a tool to use in maintenance of
their own vehicle with the simpler tasks such as changing brake pads, oil and belts. When used
appropriately with safety in mind, car jacks are an essential resource for anyone owning or
operating a motorized vehicle.
3.7 Types
Jacks are of mainly two types- mechanical and hydraulic. They vary in size depending on the
load that they are used to lift.
3.7.1 Mechanical Jacks
A mechanical jack is a device which lifts heavy equipment. The most common form is a car jack,
floor jack or garage jack which lifts vehicles so that maintenance can be performed. Car jacks
usually use mechanical advantage to allow a human to lift a vehicle by manual force alone. More
powerful jacks use hydraulic power to provide more lift over greater distances. Mechanical jacks
are usually rated for maximum lifting capacity. There are two types of mechanical jacks:
3.7.1.1 Scissor Jacks

Scissors jacks are also mechanical and have been in use at least since the 1930s.

A scissor jack is a device constructed with a cross-hatch mechanism, much like a scissor,
to lift up a vehicle for repair or storage. It typically works in just a vertical manner. The
jack opens and folds closed, applying pressure to the bottom supports along the crossed
pattern to move the lift. When closed, they have a diamond shape.

Scissor jacks are simple mechanisms used to drive large loads short distances. The
power screw design of a common scissor jack reduces the amount of force required by
the user to drive the mechanism. Most scissor jacks are similar in design, consisting of
four main members driven by a power screw.

A scissor jack is operated simply by turning a small crank that is inserted into one end of
the scissor jack. This crank is usually "Z" shaped. The end fits into a ring hole mounted
on the end of the screw, which is the object of force on the scissor jack. When this crank
is turned, the screw turns, and this raises the jack. The screw acts like a gear mechanism.
It has teeth (the screw thread), which turn and move the two arms, producing work. Just
by turning this screw thread, the scissor jack can lift a vehicle that is several thousand
pounds.
23
Construction
A scissor jack has four main pieces of metal and two base ends. The four metal pieces are all
connected at the corners with a bolt that allows the corners to swivel. A screw thread runs across
this assembly and through the corners. As the screw thread is turned, the jack arms travel across
it and collapse or come together, forming a straight line when closed. Then, moving back the
other way, they raise and come together. When opened, the four metal arms contract together,
coming together at the middle, raising the jack. When closed, the arms spread back apart and the
jack closes or flattens out again.
Design and Lift
A scissor jack uses a simple theory of gears to get its power. As the screw section is turned, two
ends of the jack move closer together. Because the gears of the screw are pushing up the arms,
the amount of force being applied is multiplied. It takes a very small amount of force to turn the
crank handle, yet that action causes the brace arms to slide across and together. As this happens
the arms extend upward. The car's gravitational weight is not enough to prevent the jack from
opening or to stop the screw from turning, since it is not applying force directly to it. If you were
to put pressure directly on the crank, or lean your weight against the crank, the person would not
be able to turn it, even though your weight is a small percentage of the cars.
3.7.1.2 Bottle (cylindrical) Jacks
Bottle screws may operate by either
(i)
(ii)
Rotating the screw when the nut is fixed; or
Rotating the nut and preventing rotation of the screw.
24
Bottle jacks mainly consist of a screw, a nut, thrust bearings, and a body. A stationary platform is
attached to the top of the screw. This platform acts as a support for the load and also assists it in
lifting or lowering of the load. These jacks are sturdier than the scissor jacks and can lift heavier
loads.
(i)
(ii)
3.7.2 Hydraulic Jacks
Hydraulic jacks are typically used for shop work, rather than as an emergency jack to be carried
with the vehicle. Use of jacks not designed for a specific vehicle requires more than the usual
care in selecting ground conditions, the jacking point on the vehicle, and to ensure stability when
the jack is extended. Hydraulic jacks are often used to lift elevators in low and medium rise
buildings.
A hydraulic jack uses a fluid, which is incompressible, that is forced into a cylinder by a pump
plunger. Oil is used since it is self lubricating and stable. When the plunger pulls back, it draws
oil out of the reservoir through a suction check valve into the pump chamber. When the plunger
moves forward, it pushes the oil through a discharge check valve into the cylinder. The suction
valve ball is within the chamber and opens with each draw of the plunger. The discharge valve
ball is outside the chamber and opens when the oil is pushed into the cylinder. At this point the
suction ball within the chamber is forced shut and oil pressure builds in the cylinder.
25
In a bottle jack the piston is vertical and directly supports a bearing pad that contacts the object
being lifted. With a single action piston the lift is somewhat less than twice the collapsed height
of the jack, making it suitable only for vehicles with a relatively high clearance. For lifting
structures such as houses the hydraulic interconnection of multiple vertical jacks through valves
enables the even distribution of forces while enabling close control of the lift.
In a floor jack a horizontal piston pushes on the short end of a bellcrank, with the long arm
providing the vertical motion to a lifting pad, kept horizontal with a horizontal linkage. Floor
jacks usually include castors and wheels, allowing compensation for the arc taken by the lifting
pad. This mechanism provide a low profile when collapsed, for easy maneuvering underneath the
vehicle, while allowing considerable extension
3.8 Design of Screw Jack
3.8.1 Loads and Stresses in Screw
The load on the screw is the load which is to be lifted W, twisting moment M, between the screw
threads and force F at the handle to rotate the screw.
The load W is compressive in nature and induces the compressive stress in the screw. It may also
lead the screw to buckle.
The load F produces bending and it is maximum, when the screw is at its maximum lift. The
screw also experiences twisting moment due to F. the shear stress is also induced in the screw
due to the twisting moment between the threads of screw and nut.
26
Step I Problem Specification
It is required to design a screw jack for supporting the machine parts during their repair and
maintenance. It should be a general purpose jack with a load carrying capacity of 50KN and a
maximum lifting height of 0.3m. The jack is to be operated by means of a D.C motor.
Step II Selection of Materials
(i)
(ii)
The frame of the screw jack has complex shape. It is subjected to compressive stress.
Grey cast iron is selected as the material for the frame. Cast iron is cheap and it can
be given any complex shape without involving costly machining operations. Cast iron
has higher compressive strength compared with steel. Therefore, it is technically and
economically advantageous to use cast iron for the frame.
The screw is subjected to torsional moment, compressive force and bending moment.
From strength consideration, EN8 is selected as material for screw.
Screw
(iii)
There is a relative motion between the screw and the nut, which results in friction.
The friction causes wear at the contacting surfaces. When the same material is used
for these two components, the surfaces of both components get worn out, requiring
replacement. This is undesirable. The size and shape of the screw make it costly
compared with the nut. The material used for the nut is stainless steel.
Nut
Step III Design of Screw
(i)
The screw jack is an intermittently used device and wear of threads is not an
important consideration. Therefore, instead of trapezoidal threads, the screw is
provided with square threads. Square threads have higher efficiency and provision
can be made for self-locking arrangement. When the condition of self-locking is
27
fulfilled, the load itself will not turn the screw and descend down, unless an effort in
the reverse direction is applied.
3.8.2 Thrust Bearings
Thrust ball bearings are used to replace the sliding force with rolling friction. The friction torque
is so small, that it can be neglected.
Thrust ball bearing is suitable for a purely axial load. It is a single-direction thrust ball bearing,
because it can support axial load in one direction only, i.e., vertically downward. This ball
bearing should not be subjected to radial load.
Single-direction thrust ball bearings are separable and the mounting is simple as the components
can be mounted individually. There are three separable parts of this bearing known as shaft
washer, a housing washer and the ball and cage assembly. The mounting of thrust bearing I
shown in the figure below
Thrust Bearing
The inner diameter of the shaft washer is press fitted in the screw body. The outer diameter of
the housing washer is press fitted in the cup. These two components are separately mounted
before final assembly. The life of thrust bearing is assumed to be 3000 hours.
3.8.3 Operational Considerations of a screw jack



Maintain low surface contact pressure
Increasing the screw size and nut size will reduce thread contact pressure for the same
working load. The higher the unit pressure and the higher the surface speed, the more
rapid the wear will be.
Maintain low surface speed
Increasing the screw head will reduce the surface speed for the same linear speed.
Keep the mating surfaces well lubricated
The better the lubrication, the longer is the service life. Grease fittings or other
lubrication means must be provided for the power screw and nut.
28


Keep the mating surfaces clean
Dirt can easily embed itself in the soft nut material. It will act as a file and abrade the
mating screw surface. The soft nut material backs away during contact leaving the hard
dirt particles to scrap away the mating screw material.
Keep heat away
When the mating surfaces heat up, they become much softer and are more easily worn
away. Means to remove the heat such as limited duty cycles or heat sinks must be
provided so that rapid wear of over-heated materials can be avoided.
29
CHAPTER 4
MOTORIZED SCREW JACK
Our survey in the regard in several automobile garages, revealed the facts that mostly some
difficult methods were adopted in lifting the vehicles for reconditioning.
Now the project has mainly concentrated on this difficulty, and hence a suitable device has been
designed, such that the vehicle can be lifted from the floor land without application of any
impact force.
The fabrication part of it has been considered with almost case for its simplicity and economy,
such that this can be accommodated as one of the essential tools on automobile garages.
4.1 Introduction
The motorized screw jack has been developed to cater to the needs of small and medium
automobile garages, which are normally man powered with minimum skilled labor. In most of
the garages the vehicles are lifted by using screw jack. This needs high man power and skilled
labour.
In order to avoid all such disadvantages, the motorized jack has been designed in such a way that
it can be used to lift the vehicle very smoothly without any impact force. The operation is made
simple so that even unskilled labour can use it with ease.
The d.c motor is coupled with the screw jack by gear arrangement. The screw jack shaft‟s
rotation depends upon the rotation of D.C motor. This is a simple type of automation project.
This is an era of automation where it is broadly defined as replacement of manual effort by
mechanical power in all degrees of automation. The operation remains to be an essential part of
the system although with changing demands on physical input, the degree of mechanization is
increased.
Degrees of automation are of two types, viz.


Full automation.
Semi automation.
In semi automation a combination of manual effort and mechanical power is required
whereas in full automation human participation is very negligible.
30
4.2 Need for Automation
Automation can be achieved through computers, hydraulics, pneumatics, robotics, etc.
Automation plays an important role in mass production.
For mass production of the product, the machining operations decide the sequence of
machining. The machines designed for producing a particular product are called transfer
machines. The components must be moved automatically from the bins to various machines
sequentially and the final component can be placed separately for packaging. Materials can also
be repeatedly transferred from the moving conveyors to the work place and vice versa.
Nowadays, almost all the manufacturing processes are being atomized in order to deliver the
products at a faster rate. The manufacturing operation is being atomized for the following
reasons:

To achieve mass production









To reduce man power
To increase the efficiency of the plant
To reduce the work load
To reduce the production cost
To reduce the production time
To reduce the material handling
To reduce the fatigue of workers
To achieve good product quality
Less Maintenance
4.3 Parts of Motorized Screw Jack
The main parts of the motorized screw jack are as follows:
4.3.1 D.c. motor (permanent magnet)
Description of dc motor
An electric motor is a machine which converts electrical energy to mechanical energy. Its action
is based on the principle that when a current-carrying conductor is placed in a magnetic field, it
experiences a magnetic force whose direction is given by Fleming‟s left hand rule.
When a motor is in operation, it develops torque. This torque can produce mechanical
rotation. DC motors are also like generators classified into shunt wound or series wound or
compound wound motors.
31
Fleming’s Left Hand Rule
Keep the force finger, middle finger and thumb of the left hand mutually perpendicular to one
another. If the fore finger indicates the direction of magnetic field and middle finger indicates
direction of current in the conductor, then the thumb indicates the direction of the motion of
conductor.
Principle of Operation of Dc Motor
A uniform magnetic field in which a straight conductor carrying no current is placed. The
conductor is perpendicular to the direction of the magnetic field.
The conductor is shown as carrying a current away from the viewer, but the field due to the N
and S poles has been removed. There is no movement of the conductor during the above two
conditions. When the current carrying conductor is placed in the magnetic field, the field due to
the current in the conductor supports the main field above the conductor, but opposes the main
field below the conductor.
Movement of
Conductor
N
Magnetic flux
S
current carrying Conductor
32
The result is to increase the flux density in to the region directly above the conductor and
to reduce the flux density in the region directly below the conductor. It is found that a force acts
on the conductor, trying to push the conductor downwards as shown by the arrow. If the current
in the conductor is reversed, the strengthening of flux lines occurs below the conductor, and the
conductor will be pushed upwards.
Now consider a single turn coil carrying a current. In view of the reasons given above,
thone side of the coil will be forced to move downwards, whereas the other side will be forced to
move upwards. The forces acting on both the coil sides will be of same magnitude. But their
direction is opposite to one another. As the coil is wound on the armature core which is
supported by the bearings, the armature will now rotate. The commutator periodically reverses
the direction of current flow through the armature. Therefore the armature will have a
continuous rotation.
A simplified model of such a motor is shown in figure VI. The conductors are wound
over a soft iron core. DC supply is given to the field poles for producing flux. The conductors
are connected to the DC supply through brushes
A simple 2-pole DC electric motor has 6 parts, as shown in the diagram below.






An armature or rotor
A commutator
Brushes
An axle
A field magnet
A DC power supply of some sort
33
An electric motor is all about magnets and magnetism: a motor uses magnets to create
motion. Opposites attract and likes repel.
So if there are 2 bar magnets with their ends marked north and south, then the North end
of one magnet will attract the South end of the other. On the other hand, the North end of one
magnet will repel the North end of the other (and similarly south will repel south). Inside an
electric motor these attracting and repelling forces create rotational motion.
In the diagram above, you can see two magnets in the motor, the armature (or rotor) is an
electromagnet, while the field magnet is a permanent magnet (the field magnet could be an
electromagnet as well, but in most small motors it is not to save power).
Electromagnets and Motors
An electromagnet is the basis of an electric motor. You can understand how things work
in the motor by imagining the following scenario. Say that you created a simple electromagnet
by wrapping 100 loops of wire around a nail and connecting it to a battery. The nail would
become a magnet and have a North and South pole while the battery is connected.
Now say that you take your nail electromagnet, run an axle through the middle of it, and
you suspended it in the middle of a horseshoe magnet as shown in the figure below. If you were
to attach a battery to the electromagnet so that the North end of the nail appeared as shown, the
basic law of magnetism tells you what would happen: The North end of the electromagnet would
be repelled from the north end of the horseshoe magnet and attracted to the south end of the
horseshoe magnet.
The South end of the electromagnet would be repelled in a similar way. The nail would
move about half a turn and then stop in the position shown.
You can see that this half-turn of motion is simple and obvious because of the way
magnets naturally attract and repel one
another. The key to an electric motor is to
then go one step further so that, at the
moment that this half-turn of motion
completes, the field of the electromagnet
flips. The flip causes the electromagnet to
complete another half-turn of motion. You
flip the magnetic field simply by changing
the direction of the electrons flowing in the
wire (you do that by flipping the battery
over). If the field of the electromagnet
flipped at just the right moment at the end of
34
each half-turn of motion, the electric motor would spin freely.
The Armature
The armature takes the place of the nail in an electric motor. The
armature is an electromagnet made by coiling thin wire around two or
more poles of a metal core. The armature has an axle, and the
commutator is attached to the axle. In the diagram above you can see
three different views of the same armature: front, side and end-on. In
the end-on view the winding is eliminated to make the commutator
more obvious. The commutator is simply a pair of plates attached to the
axle. These plates provide the two connections for the coil of the
electromagnet.
The Commutator and brushes
The "flipping the electric field" part of an electric motor is accomplished
by two parts: the commutator and the brushes. The diagram at the
right shows how the commutator and brushes work together to let
current flow to the electromagnet, and also to flip the direction that the
electrons are flowing at just the right moment. The contacts of the
commutator are attached to the axle of the electromagnet, so they spin
with the magnet. The brushes are just two pieces of springy metal or
carbon that make contact with the contacts of the commutator.
Putting It All Together
When you put all of these parts together, what you have is a complete
electric motor:
35
In this figure, the armature winding has been left out so that it is easier to see the commutator in
action. The key thing to notice is that as the armature passes through the horizontal position, the
poles of the electromagnet flip. Because of the flip, the North pole of the electromagnet is always
above the axle so it can repel the field magnet's North pole and attract the field magnet's South
pole. If you ever take apart an electric motor you will find that it contains the same pieces
described above: two small permanent magnets, a commutator, two brushes and an
electromagnet made by winding wire around a piece of metal. Almost always, however, the rotor
will have three poles rather than the two poles as shown in this article. There are two good
reasons for a motor to have three poles:
It causes the motor to have better dynamics. In a two-pole motor, if the electromagnet is
at the balance point, perfectly horizontal between the two poles of the field magnet when
the motor starts; you can imagine the armature getting "stuck" there. That never happens
in a three-pole motor.
Each time the commutator hits the point where it flips the field in a two-pole motor, the
commutator shorts out the battery (directly connects the positive and negative terminals)
for a moment. This shorting wastes energy and drains the battery needlessly. A three-pole
motor solves this problem as well.
It is possible to have any number of poles, depending on the size of the motor and the
specific application it is being used in.
4.3.1.1 Design of d.c. motor
Torque in a motor
By the term torque, it is meant the turning or twisting moment of a force about an axis. It
is measured by the product of the force and the radius at which this force acts.
For an armature of a motor, to rotate about its centre, a tangential force is necessary. This
force is developed within the motor itself.
Torque (T)
=
½ ( Ia / A ) BDC Z Newton meters
=
φ/a
=
φ/(ΠD/P)ł
=
φ x P / ( Π Dł )
=
½ x (Ia / A) x Z x φ x {P/ (ΠDł) } x Dł
=
φ Z P Ia / ( 2ΠA ) Newton meters
=
0.159 x φ x Z x Ia X (P/A) Newton meters
Using the relation,
B
T
36
=
0.162 x φ x Z x Ia x (P/A) Kg-m
The torque given by the above equation is the developed torque in the machine. But the
output torque is less than the developed torque due to friction and windage losses.
4.3.2 Batteries
4.3.2.1 Introduction
In isolated systems away from the grid, batteries are used for storage of excess solar
energy which can be converted into electrical energy. In fact for small units with output less
than one kilowatt, batteries seem to be the only technically and economically available storage
means. Since both the photo-voltaic system and batteries are high in capital costs, it is necessary
that the overall system be optimized with respect to available energy and local demand pattern.
To be economically attractive the storage of solar electricity requires a battery with a particular
combination of properties:
(1)
(2)
(3)
(4)
(5)
(6)
Low cost
Long life
High reliability
High overall efficiency
Low discharge
Minimum maintenance
(A)
Ampere hour efficiency
(B)
Watt hour efficiency
4.3.2.2 Lead-acid wet cell
Where high values of load current are necessary, the lead-acid cell is the type most
commonly used. The electrolyte is a dilute solution of sulfuric acid (H₂SO₄). In the application
of battery power to start the engine in an auto mobile, for example, the load current to the starter
motor is typically 200 to 400A. One cell has a nominal output of 2.1V, but lead-acid cells are
often used in a series combination of three for a 6-V battery and six for a 12-V battery.
The lead acid cell type is a secondary cell or storage cell, which can be recharged. The
charge and discharge cycle can be repeated many times to restore the output voltage, as long as
the cell is in good physical condition. However, heat with excessive charge and discharge
currents shortens the useful life to about 3 to 5 years for an automobile battery. Of the different
types of secondary cells, the lead-acid type has the highest output voltage, which allows fewer
cells for a specified battery voltage.
37
4.3.2.3 Construction
Inside a lead-acid battery, the positive and negative electrodes consist of a group of plates
welded to a connecting strap. The plates are immersed in the electrolyte, consisting of 8 parts of
water to 3 parts of concentrated sulfuric acid. Each plate is a grid or framework, made of a leadantimony alloy. This construction enables the active material, which is lead oxide, to be pasted
into the grid. In manufacture of the cell, a forming charge produces the positive and negative
electrodes. In the forming process, the active material in the positive plate is changed to lead
peroxide (pbo₂). The negative electrode is spongy lead (pb).
Automobile batteries are usually shipped dry from the manufacturer. The electrolyte is
put in at the time of installation, and then the battery is charged.With maintenance-free batteries,
little or no water is needed to be added in normal service. Some types are sealed, except for a
pressure vent, without provision for adding water.
4.3.2.4 Chemical action
Sulfuric acid is a combination of hydrogen and sulfate ions. When the cell discharges,
lead peroxide from the positive electrode combines with hydrogen ions to form water and with
sulfate ions to form lead sulfate. Combining lead on the negative plate with sulfate ions also
produces sulfate. Therefore, the net result of discharge is to produce more water, which dilutes
the electrolyte, and to form lead sulfate on the plates.
As the discharge continues, the sulfate fills the pores of the grids, retarding circulation of
acid in the active material. Lead sulfate is the powder often seen on the outside terminals of old
batteries. When the combination of weak electrolyte and sulfating on the plate lowers the output
of the battery, charging is necessary.
38
On charge, the external D.C. source reverses the current in the battery. The reversed
direction of flow of ions in the electrolyte results in a reversal of the chemical reactions. Now
the lead sulfates on the positive plate reacts with the water and sulfate ions to produce lead
peroxide and sulfuric acid. This action re-forms the positive plates and makes the electrolyte
stronger by adding sulfuric acid.
At the same time, charging enables the lead sulfate on the negative plate to react with
hydrogen ions; this also forms sulfuric acid while reforming lead on the negative plate to react
with hydrogen ions. It also results in formation of current which can restore the cell to full
output, with lead peroxide on the positive plates, spongy lead on the negative plate, and the
required concentration of sulfuric acid in the electrolyte.
The chemical equation for the lead-acid cell is
Charge
Pb + pbO₂ + 2H₂SO₄
2pbSO₄ + 2H₂O
Discharge
39
On discharge, the pb and pbo₂ combine with the SO₄ ions at the left side of the equation to
formlead sulfate (pbSO₄) and water (H₂O) at the right side of the equation.
One battery consists of 6 cells, each having an output voltage of 2.1V, which are
connected in series to get a voltage of 12V and the same 12V battery is connected in series, to
get an 24 V battery. They are placed in the water proof iron casing box.
4.3.2.5 Caring For Lead-Acid Batteries
Always use extreme caution when handling batteries and electrolyte. Wear gloves,
goggles and old clothes. “Battery acid” will burn skin and eyes and destroy cotton and wool
clothing.
The quickest way of ruining lead-acid batteries is to discharge them deeply and leave
them stand “dead” for an extended period of time. When they discharge, there is a chemical
change in the positive plates of the battery. They change from lead oxide (when charged) to lead
sulfate when discharged. If they remain in the lead sulfate state for a few days, some part of the
plate does not return to lead oxide when the battery is recharged. If the battery remains in a
discharged state for a longer time, a greater amount of the positive plate will remain lead sulfate.
The parts of the plates that become “sulfate”, no longer store energy. Batteries that are deeply
discharged, and then charged partially on a regular basis can fail in less then one year.
Check your batteries on a regular basis to be sure they are getting charged. Use a
hydrometer to check the specific gravity of your lead acid batteries. If batteries are cycled very
deeply and then recharged quickly, the specific gravity reading will be lower than it should be
because the electrolyte at the top of the battery may not have mixed with the “charged”
electrolyte.
Check the electrolyte level in the wet-cell batteries at least four times a year and top each
cell with distilled water. Do not add water to discharged batteries. Electrolyte is absorbed when
batteries are discharged. If you add water at this time, and then recharge the battery, electrolyte
will overflow and make a mess.
Keep the top of your batteries clean and check that cables are tight. Do not tighten or
remove cables while charging or discharging. Any spark around batteries can cause a hydrogen
explosion inside, and ruin one of the cells.
On charge, with reverse current through the electrolyte, the chemical action is reversed.
Then the pb ions from the lead sulfate on the right side of the equation re-form the lead and lead
peroxide electrodes. Also the SO₄ ions combine with H₂ ions from the water to produce more
sulfuric acid at the left side of the equation.
4.3.2.6 Current Ratings
Lead-acid batteries are generally rated in terms of how much discharge currents they can
supply for a specified period of time; the output voltage must be maintained above a minimum
40
level, which is 1.5 to 1.8V per cell. A common rating is ampere-hours (A.h.) based on a specific
discharge time. Typical values for automobile batteries are 100 to 300 A.h.
As an example, a 200 A.h battery can supply a load current of 200/8 or 25A, used on 8h
discharge. The battery can supply less current for a longer time or more current for a shorter
time. Automobile batteries may be rated for “cold cranking power”, which is related to the job
of starting the engine. A typical rating is 450A for 30s at a temperature of 0 degree F.
The ratings for lead-acid batteries are given for a temperature range of 77 to 80ºF.
Higher temperature increases the chemical reaction, but operation above 110ºF shortens the
battery life.
Low temperatures reduce the current capacity and voltage output. The ampere-hour
capacity is reduced approximately 0.75% for each decreases of 1º F below normal temperature
rating. At 0ºF the available output is only 60 % of the ampere-hour battery rating.
In cold weather, therefore, it is very important to have an automobile battery unto full
charge. In addition, the electrolyte freezes more easily when diluted by water in the discharged
condition.
4.3.2.7 Specific Gravity
Measuring the specific gravity of the electrolyte generally checks the state of discharge
for a lead-acid cell. For instance, concentrated sulfuric acid is 1.835 times as heavy as water for
the same volume. Therefore, its specific gravity equals 1.835. The specific gravity of water is 1,
since it is the reference.
In a fully charged automotive cell, mixture of sulfuric acid and water results in a specific
gravity of 1.280 at room temperatures of 70 to 80ºF. As the cell discharges, more water is
formed, lowering the specific gravity. When it is down to about 1.150, the cell is completely
discharged.
Specific-gravity readings are taken with a battery hydrometer.Note that the calibrated
float with the specific gravity marks will rest higher in an electrolyte of higher specific gravity.
The importance of the specific gravity can be seen from the fact that the open-circuit
voltage of the lead-acid cell is approximately equal to
V
=
Specific gravity + 0.84
For the specific gravity of 1.280, the voltage is 1.280 = 0.84 = 2.12V, as an example.
These values are for a fully charged battery.
41
4.3.2.8 Charging the Lead-Acid Battery
An external D.C. voltage source is necessary to produce current in one direction. Also,
the charging voltage must be more than the battery e.m.f. Approximately 2.5 per cell are enough
to produce current opposite to the direction of discharge current.
Note that the reversal of current is obtained just by connecting the battery VB and
charging source VG with + to + and –to. The charging current is reversed because the battery
effectively becomes a load resistance for VG when it higher than VB. In this example, the net
voltage available to produce charging currents is 15-12=3V.
A commercial charger for automobile batteries is essentially a D.C. power supply,
rectifying input from the AC power line to provide D.C. output for charging batteries.
Float charging refers to a method in which the charger and the battery are always
connected to each other for supplying current to the load. In figure the charger provides current
for the load and the current necessary to keep the battery fully charged. The battery here is an
auxiliary source for D.C. power.
It may be of interest to note that an automobile battery is in a floating-charge circuit. The
battery charger is an AC generator or alternator with rectifier diodes, driven by a belt from the
engine.When you start the car, the battery supplies the cranking power. Once the engine is
running, the alternator charges the battery. It is not necessary for the car to be moving. A
voltage regulator is used in this system to maintain the output at approximately 13 to 15 V.It is a
good idea to equalize charge when some cells show a variation of 0.05 specific gravity from each
other. With proper care, lead-acid batteries will have a long service life and work very well in
almost any power system.
4.3.3 Screw Jack
The screw jack used in this project is a 5 tonne bottle (cylindrical) jack. It mainly consists of the
body, screw, nut and thrust bearings. In this type of a jack, the nut remains stationary while the
screw rotates and helps in lifting or lowering of the load.
42
Capacity: 5Ton
Min height: 200MM
Max height: 300MM
Net Weight: 8KG
Lifting height: 100 mm
43
4.3.4 Spur Gear
The spur gears, which are designed to transmit motion and power between parallel shafts,
are the most economical gears in the power transmission industry.
Application





Material handling
Feed drives
Machine tools
Conveyors
Marine hoists
4.3.4.1 Types
Internal Spur Gear
The internal gears are spur gears turned "inside out." In other words, the teeth are cut into
the inside diameter while the outside diameter is kept smooth. This design allows for the driving
pinion to rotate internal to the gear, which, in turn, allows for clean operation. Intended for light
duty applications, these gears are available only in brass. When choosing a mating spur gear,
always remember that the difference in the number of teeth between the internal gear and pinion
should not be less than 15 or 12.
Applications





Light duty applications
Timing
Positioning
Rollers
Indexing
External Spur Gear
Perhaps the most often used and simplest gear system, external spur gears are cylindrical
gears with straight teeth parallel to the axis. They are used to transmit rotary motion between
parallel shafts and the shafts that rotate in opposite directions. They tend to be noisy at high
speeds as the two gear surfaces come into contact at once.
4.3.4.2 Design considerations for a gear drive
In the design of a gear drive, the following data is usually given:
1. The power to be transmitted,
44
2. The speed of the driving gear,
3. The speed of the driven gear or the velocity ratio, and
4. The centre distance.
The following requirements must be met in the design of a gear drive:
(a) The gear teeth should have sufficient strength so that they will not fail under static loading or
dynamic loading during normal running conditions.
(b) The gear teeth should have wear characteristics so that there life is satisfactory.
(c) The use of space and material should be economical.
(d) The alignment of the gears and deflections of the shafts must be considered because they
affect the performance of the gears
(e) The lubrication of the gears must be satisfactory.
Beam strength of gear teeth –Lewis Equation
The beam strength of gear teeth and the load carrying ability is determined from an equation,
known as Lewis equation. In the investigation, Lewis assumed that as the load is being
transmitted from one gear to another it is all given and taken by one tooth because it is not
always safe to assume that the load is distributed among several teeth. When contact begins, the
load is assumed to be at the end of the driven teeth and as the contact ceases, it is at the end of
the driving teeth. This may not be true when the number of teeth in a pair of mating gears is large
because the load may be distributed among several teeth. But it is almost certain that at some
time during contact of teeth, the proper distribution of load does not exist and that one tooth must
transmit the full load. In any pair of gears having unlike number of teeth, the gear which has
fewer teeth (i.e., pinion) will be weaker because the tendency toward undercutting of the teeth
becomes more pronounced in gears as the number of teeth becomes smaller.
Consider each tooth as a cantilever beam loaded by a normal load (WN). It is resolved into two
components i.e., tangential component (WT) and radial component (WR) acting perpendicular
and parallel to the centre line of the tooth respectively. The tangential component (W T) induces a
bending stress which tends to break the tooth. The radial component (WR) induces a compressive
stress of relatively small magnitude; therefore its effect on the tooth may be neglected. Hence,
the bending stress is used as the basis for design calculations.
45
The critical section or the section of maximum bending stress may be obtained by drawing a
parabola through A and tangential to the tooth curves at B and C. this parabola outlines a beam
of uniform strength, i.e., if the teeth are shaped like the parabola, it will have the same stress at
all the sections. But the tooth is larger than the parabola at every section except BC.Therefore,
section BC is the section of maximum stress or the critical section. The maximum value of the
bending stress (or the permissible working stress), at the section BC is given by
Fw = M.y / I
where
M = Maximum bending moment at the critical section, BC = WT x h,
WT = Tangential load acting at the tooth,
h = Length of the tooth,
y = Half of the thickness of the tooth (t) at critical section BC = t/2,
I = moment of inertia about the centre line of the tooth = b.t2/12,
b = width of gear face.
Substituting the values for M, y, I in equation, we get
Fw =
=
46
WT = Fw x b x t²/6h
In this expression, t and h are variables depending upon the size of the tooth and its profile.
Let t = x x pc and h = k x pc; where x and k are constants.
= F w x b x pc x
W T = Fw x b x
Substituting x²/6k = y, another constant,
WT = Fw x b x pc x y= Fw.b.πm.y
The quantity y is known as Lewis form factor or tooth form factor and WT is called the beam
strength of the tooth. The value of y in terms of the number of teeth may be expressed as follows:
y = 0.154 –
, for 20° full depth involute system.
Permissible working stresses for gear teeth in the Lewis equation
The permissible working stress (FW) in the Lewis equation depends upon the material for which
an allowable static stress (Fo) may be determined. The allowable static stress is the stress at the
elastic limit of the material. It is also called the basic stress. In order to account for the dynamic
effects which become more severe as the pitch line velocity increases, the value of F W is
reduced.
According to the Barth formula, the permissible working stress is given by,
FW = Fo x C v
where Fo = allowable static stress, and
Cv = velocity factor.
The value of the velocity factor for very accurately cut and ground metallic gears operating at
velocities upto 20m/s is given by,
Cv =
where v = pitch line velocity in m/s.
Dynamic Tooth Load
The dynamic loads are due to the following reasons:
1. Inaccuracies of tooth spacing,
2. Irregularities in tooth profiles, and
3. Deflections of teeth under load.
47
4. A closer approximation to the actual conditions may be made by the use of equations
based on extensive series of the teeth, as follows:
WD = WT + W I
Where WD = Total dynamic load,
WT = Steady transmitted load in Newton,
WI = Incremental load due to dynamic action.
The incremental load (WI) depends upon the pitch line velocity, face width, material of the gears,
and accuracy of cut and tangential load. For average conditions, the dynamic load is determined
by using the following Buckingham equation, i.e.
WD = WT + W I = WT +
Where
√
WD = Total dynamic load in Newton,
WT = Steady transmitted load in Newton,
V = Pitch line velocity in m/s,
b = Face width of gears in mm, and
C = A deformation or dynamic factor in N/mm.
A deformation factor (C) depends upon the error in action between teeth, the class of out of the
gears, the tooth form and the material of the gears.
The value of C in N/mm may be determined by using the following relation:
C=
Where K = A factor depending upon the form of the teeth.
= 0.111 for 20° full depth involute system.
EP = Young‟s modulus for the material of the pinion in N/mm2
EG = Young‟s modulus for the material of the gear in N/mm2
e = Tooth error action in mm.
The maximum allowable tooth error in action (e) depends upon the pitch line velocity (v) and
the class of cut of the gears.
Static Tooth Load
The static tooth load is obtained by Lewis formula by substituting flexural endurance limit or
elastic limit stress (fs) in place of permissible working stress (fw).
The static tooth load or beam strength of the tooth,
WS = fe.b.pc.y = fe.b.πm.y
For safety, against tooth breakage, the static tooth load (Ws) should be greater than the dynamic
load (WD).Buckingham suggests the following relationship between Ws and WD.
For steady loads, Ws≥1.25WD
48
For shock loads, Ws≥1.5WD
Wear Tooth Load
The maximum load that gear teeth can carry, without premature wear, depends upon the radii of
curvature of the tooth profiles and on the elasticity and surface fatigue limits of the materials.
The maximum of the limiting load for satisfactory wear of gear teeth, is obtained by using the
following Buckingham equation, i.e.
Ww = Dp.b.Q.K
Where Ww = Maximum or limiting load for wear in Newton,
Dp = Pitch circle diameter of the pinion in mm,
b = Face width of the pinion in mm,
Q = Ratio factor
=
=
, for external gears.
V.R = Velocity ratio =
K = Load stress factor in N/mm2.
The load stress factor depends upon the maximum fatigue limit of compressive stress, the
pressure angle and the modulus of elasticity of the materials of the gears. According to
Buckingham, the load stress factor is given by the following relation:
)
K=
Where
= Surface endurance limit in N/mm²
= Pressure angle
EP = Young‟s modulus for the material of the pinion in N/mm2
EG = Young‟s modulus for the material of the gear in N/mm2
Speeds In Gear Box:
Measured Specifications:
N1/N2
=
D2/D1
N1
=
Motor speed in RPM---40 RPM
N2
=
Output speed
D2
=
Diameter of the roller gear wheel
Where,
= 160 mm
D1
=
Diameter of the motor gear wheel
= 48 mm
49
∴ N2
=
(D1/D2) x N1
=
(48 / 160) X40
=
12 Rpm
4.3.5 Switch
A switch is used in order to start or stop the entire operation of the screw jack. The type of
switch that is used is known as a toggle switch.A toggle switch is a class of electrical switches
that are manually actuated by a mechanical lever, handle, or rocking mechanism.
Toggle switches are available in many different styles and sizes, and are used in countless
applications. Many are designed to provide, e.g., the simultaneous actuation of multiple sets of
electrical contacts, or the control of large amounts of electric current or mains voltages.
The word "toggle" is a reference to a kind of mechanism or joint consisting of two arms, which
are almost in line with each other, connected with an elbow-like pivot. However, the phrase
"toggle switch" is applied to a switch with a short handle and a positive snap-action, whether it
actually contains a toggle mechanism or not. Similarly, a switch where a definitive click is heard,
is called a "positive on-off switch".
Control cables are used in order to connect the battery to the motor and the switch.
A base for the entire set-up has also been used. The motor is mounted on an inverted U shaped
support frame.
.
50
4.4 Working Principle
The lead-acid battery is used to drive the d.c motor. The d.c motor shaft is connected
to the spur gear. If power is given to the D.c motor, it will run so that the spur gear also runs to
slow down the speed of the D.C motor. The screw jack moves the screw upward, so that the
vehicle lifts from ground.
The vehicle is lifted by using the lifting platform at the top of the screw jack. The motor
draws power supply from the battery. The lifting and uplifting is done by changing the battery
supply to the motor.
4.5 Advantages
1.
2.
3.
4.
5.
6.
The loaded light vehicles can be easily lifted.
Checking and cleaning are easy, because the main parts are screwed.
Handling is easy
No Manual power required.
Easy to Repair.
Replacement of parts are easy
4.6 Disadvantages
 Cost of the equipment is high when compared to ordinary hand jack.
 Care must be taken for the handling the equipment such as proper wiring
connection, battery charging checkup, etc.
4.7 Applications
1. It is useful in auto-garages.
2. This motorized screw jack is used for lifting the vehicles. Thus it can be useful for the
following types of vehicles in future;
 Maruti, Ambassador, Fiat, Mahindra
51
52
CHAPTER 5
DESIGN CALCULATIONS
5.1 Design calculations to check the safety of LEAD SCREW
Maximum Load to be lifted
= 5 Ton
= 50 x 103 N
= 50KN
For a 5 Ton capacity screw jack, the suitable screw is the one whose nominal (major) diameter is
36mm.
Corresponding to the nominal diameter 36mm, the pitch (p) selected is 6mm.
The core diameter (dc)
= 30mm
The mean diameter (dm)
= 33mm
EN8 material is used for lead screw. The ultimate and yield stresses are 450N/mm2 and
230N/mm2 respectively.
The compressive stresses induced in lead screw due to load of 50KN is given by
Fc =
= (50 x 103 x 4)/ (π x 302)
= 70.73N/mm2
Safety factor = 230/70.73= 3.25
Hence lead screw will bear 50KN easily
The helix angle of screw = tanα =
= 6/ (πx33)
53
= 0.057
Therefore, α = 3.31°
Assuming coefficient of friction between screw and nut,
µ = tanθ = 0.14
θ = tan-1(0.14) = 7.96°
α < θ, hence it is a self locking screw.
The turning moment required to rotate screw under design load is given by
T = W (dm/2) tan (α+θ)
= (50x103) (33/2) tan (3.31°+7.96°)
=164.40KN.mm
The shear stress due to torque,
Ft = 16T/ (πdc3)
= (16x164.40x103)/π(30)3
= 31.01N/mm2
Direct stress is given by
Fs = ½√ (Fc2 + 4Ft2)
= ½√70.732 + 4(31.01)2
= 47.03N/mm2
The lead screw material has 115N/mm2 shear strength.
Safety factor = 115/47.03
= 2.44
5.2. Design calculations to check the safety of nut
The material of the nut used is stainless steel. The yield stress in tension and compression are
216 N/mm2 and 294N/mm2 respectively.
Shear stress = 186N/mm2
Bearing pressure between lead screw material and nut material is Pb =15N/mm2
n = Number of threads in contact with the screwed spindle.
54
H = height of nut = n x p
t = thickness of screw = p/2 = 6/2 = 3mm
The number of internal thread (n) in nut for the load 50KN is given by
n=
(
)
= (4 x 50 x 103)/ (π (362-302) (15))
≈ 11
H=nxp
= 11x6 = 66mm
The outer diameter of the nut, D1 = 54mm
The inner diameter of the nut, D0 =36mm
The tensile stresses induced in the nut is given by
Ft =
= (4x50x103)/π (542- 36²)
=39.29 N/mm² which is less than 216 N/mm²
Safety factor=216/39.29
= 5.49
5.3. Design calculations to check the buckling of screw
The maximum length of the screw above the nut when lifting the load is 100mm.
Radius of gyration (K) = ¼ dс = ¼ x 30 = 7.5mm
Area =
dc2
= (30)2 =706.85mm2
L/K=slenderness ratio=100/7.5=13.33
55
Slenderness ratio is less than 30, therefore there is no effect of buckling and such components are
designed on the basis of compressive stresses.
5.4 Design considerations for a gear drive
Beam strength of gear teeth –Lewis Equation
Consider each tooth as a cantilever beam loaded by a normal load (WN). It is resolved into two
components i.e., tangential component (WT) and radial component (WR) acting perpendicular
and parallel to the centre line of the tooth respectively.
The tangential component (WT) induces a bending stress which tends to break the tooth.
The radial component (WR) induces a compressive stress of relatively small magnitude; therefore
its effect on the tooth may be neglected. Hence, the bending stress is used as the basis for design
The maximum value of the bending stress (or the permissible working stress), at the section BC
is given by
Fw = M.y / I
where
M = Maximum bending moment at the critical section, BC = WT x h,
WT = Tangential load acting at the tooth,
h = Length of the tooth = 5mm
y = Half of the thickness of the tooth (t) at critical section BC = t/2 = 4/2 = 2mm
I = moment of inertia about the centre line of the tooth = b.t2/12 =33.33
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b = width of gear face = 25mm
Bearing strength of teeth WT = Fw x b x pc x y = Fw.b.πm.y
The quantity y is known as lewis form factor or tooth form factor and WT is called the beam
strength of the tooth. The value of y in terms of the number of teeth may be expressed as follows:
y = 0.154 –
, for 20° full depth involute system.
Permissible working stresses for gear teeth in the Lewis equation
The permissible working stress (FW) in the Lewis equation depends upon the material for which
an allowable static stress (Fo) may be determined.
According to the Barth formula, the permissible working stress is given by,
FW = Fo x C v
where Fo = allowable static stress, for cast steel heat treated- 196N/mm2
Cv = velocity factor.
The value of the velocity factor for very accurately cut and ground metallic gears operating at
velocities upto 20m/s is given by,
Cv =
where v = pitch line velocity in m/s =
(D= Pitch circle diameter = 150mm,Speed = 40)
v =188.495m/min
= 3.141m/s
Cv = 0.656
FW = 196 x 0.656 = 128.576 N/mm2
WT = 128.576 x 25 x 16/30
= 1714.266N = 174.806 kgf
Dynamic Tooth Load
Dynamic tooth load is given by
WD = WT + W I
Where WD = Total dynamic load,
WT = Steady transmitted load in Newton,
WI = Incremental load due to dynamic action.
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For average conditions, the dynamic load is determined by using the following Buckingham
equation, i.e.
WD = WT + W I = WT +
√
Where WD = Total dynamic load in Newton,
WT = Steady transmitted load in Newton =
V = Pitch line velocity in m/s = 3.141 m/s
b = Face width of gears in mm = 25mm
C = A deformation or dynamic factor in N/mm.
A deformation factor (C) depends upon the error in action between teeth, the class of out of the
gears, the tooth form and the material of the gears.
The value of C in N/mm may be determined by using the following relation:
C=
Where K = A factor depending upon the form of the teeth.
= 0.111 for 20° full depth involute system.
EP = Young‟s modulus for the material of the pinion in N/mm2 = 2 x 103 N/mm2
EG = Young‟s modulus for the material of the gear in N/mm2 = 2 x 103 N/mm2
e = Tooth error action in mm = 0.0700 for 3.141m/s
The maximum allowable tooth error in action (e) depends upon the pitch line velocity (v) and
the class of cut of the gears
C=
C
= 7.77
WD = 174.806 + WI = 174.806 +
= 2862.456N = 291.889 kgf
Wear Tooth Load
The maximum load that gear teeth can carry,without premature wear,depends upon the radii of
curvature of the tooth profiles and on the elasticity and surface fatigue limits of the materials.
The maximum of the limiting load for satisfactory wear of gear teeth, is obtained by using the
following Buckingham equation, i.e.
Ww = Dp.b.Q.K
Where Ww = Maximum or limiting load for wear in Newton,
Dp = Pitch circle diameter of the pinion in mm = 48mm
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b = Face width of the pinion in mm = 16mm
Q = Ratio factor = 1.56
=
=
, for external gears.
V.R = Velocity ratio =
K = Load stress factor in N/mm2.
The load stress factor depends upon the maximum fatigue limit of compressive stress, the
pressure angle and the modulus of elasticity of the materials of the gears. According to
Buckingham, the load stress factor is given by the following relation:
)
K=
Where
= Surface endurance limit in N/mm² =630N/mm2
= Pressure angle= 20°
EP = Young‟s modulus for the material of the pinion in N/mm2 =
EG = Young‟s modulus for the material of the gear in N/mm2 =
K=
(
)
²N/mm2
N/mm2
)
= 96.9627
Wear Tooth Load
Ww = Dp.b.Q.K
= 48 x 16 x 1.56 x 96.9627
Ww = 116,169.907N
= 11846 kgf
Static Tooth Load
The static tooth load is obtained by lewis formula by substituting flexural endurance limit or
elastic limit stress (fs) in place of permissible working stress (fw).
The static tooth load or beam strength of the tooth,
WS = fe.b.pc.y
= fe.b.πm.y
= 84 x 16 x π x 1.92 x (0.152-0.192/25)
= 3854.9N
= 393.09 kgf
For safety, against tooth breakage, the static tooth load (Ws) should be greater than the dynamic
load (WD).Buckingham suggests the following relationship between Ws and WD.
For steady loads, Ws≥1.25WD
For shock loads, Ws≥1.5WD
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CONCLUSION
Screw Jacks are the ideal product to push, pull, lift, lower and position loads of anything from a
couple of kilograms to hundreds of tonnes.The need has long existed for an improved portable
jack for automotive vehicles. It is highly desirable that a jack become available that can be
operated alternatively from inside the vehicle or from a location of safety off the road on which
the vehicle is located. Such a jack should desirably be light enough and be compact enough so
that it can be stored in an automobile trunk, can be lifted up and carried by most adults to its
position of use, and yet be capable of lifting a wheel of a 4,000-5,000 pound vehicle off the
ground. Further, it should be stable and easily controllable by a switch so that jacking can be
done from a position of safety. It should be easily movable either to a position underneath the
axle of the vehicle or some other reinforced support surface designed to be engaged by a jack.
Thus, the product has been developed considering all the above requirements. This particular
design of the motorized screw jack will prove to be beneficial in lifting and lowering of loads.

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BIBLIOGRAPHY
1. Design of machine elements by V.B.Bhandari
2. A text book of machine design by Rajendra Karwa
3. Analysis and Design of Machine Elements by V K Jadon, Suresh Verma
4. Tribology in Machine Design by T. A. Stolarski
5. A text book of Machine Design by R.S.Khurmi,J.K.Gupta
6. Design of Machine Elements by Farazdak Haideri
7. Machine Design by S.G.Kulkarni
8. Design of machine elements by K.Rao
http://en.wikipedia.org/wiki/Jack_(device)
http://hubpages.com/hub/Automobile-Jacks
http://www.powerjacks-de.com/Screw-Jacks-FAQ.html
http://www.radicon.com/screw-jacks.php
http://www.powerjacks.com/PowerJacks-History-The-Screw-Jack-Story.php
http://www.scribd.com/doc/38577261/Screw-Jack-Design
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