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1. UNIVERSITY OF NAIROBI
SCHOOL OF ENGINEERING
DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
FINAL YEAR PROJECT REPORT
[FME 561 & 562]
PROJECT TITLE
COMPUTER AIDED MACHINE DESIGN: CASE STUDY ON THE DESIGN OF
A SCREW JACK
PROJECT CODE: MFO 02/2016
SUPERVISOR: PROF. ODUORI F. M.
COMPILED BY:
MOKORO ALBERT BORIGA - F18/1504/2011
NYABUTI JACK ONDARI - F18/44699/2012
IN PARTIAL FULFILLMENT OF THE AWARD OF THE DEGREE OF
BACHELOR OF SCIENCE IN MECHANICAL AND MANUFACTURING
ENGINEERING
APRIL 2016

2. ii
Declaration
We, the undersigned, declare that this project is of our original work and has not been
submitted for a degree award in any other institution of higher learning or published
anywhere else.
MOKORO BORIGA ALBERT - F18/1504/2011
Signature: ………………………
Date: …… May, 2016
NYABUTI JACK ONDARI - F18/44699/2012
Signature: ………..………….
Date: ….. May, 2016
This project has been submitted for examination with the approval of our project
supervisor
PROF. F.M ODUORI
Signature: ………………………
Date: ……. May, 2016

3. iii
Dedication
To our families, friends and the Academic Staff at the Department of Mechanical Engineering for
their guidance and support from the start to the end of our undergraduate studies successfully at
the University of Nairobi.

4. iv
Acknowledgement
We would like to acknowledge and appreciate the great guidance from our project
supervisor, Prof. F.M Oduori.
We would also like to thank our parents and classmates for their encouragement,
understanding and support throughout the entire project.
We would also like to thank the almighty God for bringing us this far and giving us the
strength to carry out the project.

5. v
Notations
𝑝 - Pitch of screw thread (𝑚𝑚)
𝑛 - Number of threads in contact with screwed spindle
𝑙 - Lead of screw thread (𝑚𝑚)
𝑡 - Thickness of screw
𝑑 - Nominal diameter of screw (𝑚𝑚)
𝑑 𝑐 - Core diameter of screw (𝑚𝑚)
𝑑 𝑚 - Mean diameter of screw (𝑚𝑚)
𝜃 - Friction angle (𝑑𝑒𝑔𝑟𝑒𝑒)
𝛼 - Helix angle of screw (𝑑𝑒𝑔𝑟𝑒𝑒)
𝑊- Load (𝑘𝑔)
𝑁 - Normal reaction (𝑁𝑒𝑤𝑡𝑜𝑛, 𝑁)
𝜇 − Coefficient of friction
𝑃 - Effort (𝑁𝑒𝑤𝑡𝑜𝑛, 𝑁)
𝑇 - Torque (𝑁. 𝑚)
𝜂 − Efficiency (%)
𝐹𝑙𝑜𝑎𝑑- The force the jack exerts on the load. (𝑁𝑒𝑤𝑡𝑜𝑛, 𝑁)
𝐹𝑒𝑓𝑓𝑜𝑟𝑡- The rotational force exerted on the handle of the jack. (𝑁𝑒𝑤𝑡𝑜𝑛, 𝑁)
𝑟-the length of the jack handle (𝑚𝑚)
𝑀. 𝐴 – Mechanical advantage
𝜋 = 3.141592654
BS – British standards
𝜎𝑐 - Pure compression stress
𝐴 𝑐 - Cross sectional area of the screw shaft
𝜎𝑐(𝑚𝑎𝑥) -Maximum principal stress
𝜏 𝑚𝑎𝑥 - Maximum shear stress
𝐽 - Polar moments
𝑃𝑏 - Bearing pressure on the nut

6. vi
𝑡1 - Thickness of nut collar
ℎ - Height of the nut
𝐷1- Outer diameter of nut collar
𝐷2- Outside diameter of nut collar
𝜎𝑡 - Tearing strength of the nut
𝜎𝑐 - Crushing strength of the nut
𝜏(𝑠𝑐𝑟𝑒𝑤) -Shearing stress on the screw
𝜏(𝑛𝑢𝑡)- Shearing stress on the nut
𝜏-Shearing stress of nut collar
𝐷3- Diameter of head on top of screw
𝐷4- Diameter of pin
𝑇-Total torque to which the handle is
subjected
𝑇1- Torque required to rotate the screw
𝑇2–Torque required to overcome
friction
𝑇- Total torque subjected to handle
𝜎 𝑦-Yield stress
𝐿 – Length of the handle
D - Diameter of handle
M - Bending moment
H - The height of head
𝜎𝑏- Bending stress
𝐿 𝑒𝑓𝑓 - Effective length of screw
𝐻1 – Lift of screw
𝑊𝑐𝑟 - Buckling or Critical load

7. vii
𝐸 – Young’s modulus or modulus of elasticity
𝐶 - End fixity coefficient
𝑅- Slenderness ratio
𝑘 - The radius of gyration
𝐻𝐵 – Hardness number
𝐼 − Moment of inertia of the cross section.
𝐷5- Diameter of body at the top
𝑡2- Thickness of body
𝑡3- Thickness of base
𝐷6- Inner Diameter at the bottom
𝐷7- Outer Diameter at the bottom
𝐻 𝑏- Height of the body

8. viii
Notations as Used In the Matlab Script
H1 - lift of screw
U - Coefficient of friction
y - Friction angle
Pb – Bearing Pressure
TstrYP – Tensile yield strength
CstrYP – Compressive yield strength
SHstrYP – Shear yield strength
p -pitch
f- Factor of safety
R - Slenderness ratio
Ac – cross-sectional area using core
diameter
Leff - Effective length
d1 – Minor diameter
d2 – Major diameter
dm – Mean diameter
h - Height of nut
Fm - Effort
D1 – Outer diameter of nut
D2 – Outer diameter of collar
D3 – Diameter of cup
D4 – Diameter of pin
D5 – Diameter of body at the top
D6 – Inside diameter at the bottom
D7 – Outside diameter at the bottom
Helix – Helix angle
CstrB - Compressive stress
SHstrB – Shear stress
SHstrmax – Maximum shear stress

9. ix
t1 – Collar thickness
t2 – Thickness of body
t3 – Thickness of base
Wcr – Critical load
Rcr – Critical slenderness ratio
disp - Display
Round–To round off to the nearest
whole number
Ceil-To round off towards the
positive infinity
Floor - To round of towards the
negative infinity

10. x
Abstract
A screw jack serves to give mechanical advantage by changing rotational force to linear force
thus allowing one to lift a load and support it at a given height.
The aim of the project was to come up with a design procedure for a simple screw jack and
coding in Matlab to form a program that would require one to enter the mechanical properties of
the materials to be used, lift and the desired load to be supported.
This case study is divided into various sections that describes classification of screw threads,
parts of the screw jack and selection of materials used for construction that are in agreement with
current industry practice of screw jack design.
The design procedure adopted here is from design of machine elements by V. B. Bhandari and
coded the design procedures using Matlab to serve the same function fast and efficient. This is
realized as we obtained the similar theoretical and Matlab solutions as coded. Application of the
procedure manually is tedious and extraneous since its lengthy and time consuming. Using
Matlab for the same makes work easier, efficient and fast for designers since only material
properties and specific design requirements such as lift and load are the only required input.
A factor of safety of 5 and above should be used in this design to reduce high chances of failure
due to dynamic loadings and impact loadings. Dynamics loading is as a result of external
interferences such as whirl wind, earth tremors and external forces while impact loading is such
as load is applied suddenly with a short time and results into high stresses which can cause failure
hence this calls for a high factor of safety.
Keywords: Screw Jack, Classification of threads, Square thread, Components, Design procedure,
Matlab script/code and Program run and Solution.

11. xi
List of Figures and Tables
Figure 2.1: Sample screw jack and parts.........................................................................................5
Figure 2.2: Examples of mechanical jacks (a) Floor Jack (b) Scissor jack ....................................7
Figure 3.1: Nomenclature of square thread ....................................................................................9
Figure 3.2: Nomenclature of ISO metric trapezoidal thread.........................................................10
Figure 3.3: Nomenclature of buttress thread.................................................................................11
Figure 3.4: Screw Nomenclature (Bhandari, 2010) ......................................................................12
Figure 3.5: Unwound thread..........................................................................................................14
Figure 3.6: Force diagram for lifting load ....................................................................................15
Figure 3.7: Force diagram for lowering load................................................................................16
Figure 3.8: Graph of efficiency against helix angle for various 𝝁................................................20
Table 3.1: Coefficient of friction under different conditions (Gupta, 2005)..................................22
Table 3.2: Coefficient of friction when thrust collars are used (Gupta, 2005)..............................22
Table 3.3: Values of end fixity coefficients(c) (Nisbet, 2015)........................................................23
Table 4.1: Mechanical Properties of Cast iron – Appendix A (Marshek, 2012) ...........................26
Table 4.2: Mechanical Properties of Plain carbon steel – Appendix B (Nyangasi, 18 December,
2006) .......................................................................................................................................27
Table 4.3: Safe Bearing Pressures for Power screws – Appendix C (Nyangasi, 18 December,
2006) & (Gupta,2005) ...........................................................................................................28
Table 5.1: Average Weight of Vehicles in USA..............................................................................29
Figure 5.1: Section of screw spindle..............................................................................................30
Figure 5.2: Section of Nut collar 1 ................................................................................................35
Figure 5.3: Section of Pin ..............................................................................................................36
Figure 5.4: Section of Cup.............................................................................................................37
Table 5.2: Maximal Isometric Force by General European Working Population for Whole Body
Work in a Standing Posture ....................................................................................................38
Figure 5.5: Section of Lever...........................................................................................................38
Figure 5.6: Section of Lever - Diameter ........................................................................................39
Figure 5.7: Section of Screw Head ................................................................................................40
Figure 5.8: Section of Frame (Body) .............................................................................................43

12. xii
Table of Contents
Declaration....................................................................................................................................................ii
Dedication ....................................................................................................................................................iii
Acknowledgement .......................................................................................................................................iv
Notations .......................................................................................................................................................v
Notations as Used In the Matlab Script...................................................................................................viii
Abstract.........................................................................................................................................................x
List of Figures and Tables ..........................................................................................................................xi
CHAPTER ONE.......................................................................................................................................... 1
SCREW JACK ............................................................................................................................................ 1
1.0 Background............................................................................................................................................ 1
1.1 Problem Statement................................................................................................................................ 2
1.2 Objectives of the Study ..................................................................................................................... 2
CHAPTER 2 ................................................................................................................................................ 3
LITERATURE REVIEW........................................................................................................................... 3
2.0 Introduction ........................................................................................................................................... 3
2.1 Operation ............................................................................................................................................... 3
2.2 Construction of a Screw Jack............................................................................................................... 3
2.3 Advantages and Disadvantages of the Screw Jack............................................................................. 5
2.3.1 Advantages...................................................................................................................................... 5
2.3.2 Disadvantages ................................................................................................................................. 5
2.4 Mechanical Advantage (M.A)............................................................................................................... 6
2.5 Common Types of Screw Jack ............................................................................................................. 7
2.6 Factors to Consider in Selection of the Best Jack for Application Purposes ................................... 8
CHAPTER 3 ................................................................................................................................................ 9
CLASSIFICATION OF SCREW THREADS .......................................................................................... 9
3.1 Introduction ........................................................................................................................................... 9
3.1.1 Square Thread................................................................................................................................ 9
3.1.1.1 Nomenclature of Square Thread............................................................................................ 9
3.1.1.2 Advantages of the Square Thread.......................................................................................... 9
3.1.1.3 Disadvantages of Square Thread ........................................................................................... 9
3.1.2 ISO Metric Trapezoidal Threads................................................................................................ 10
3.1.2.1 Nomenclature of ISO Metric Trapezoidal Thread............................................................. 10

13. xiii
3.1.2.2 Advantages of the Trapezoidal Thread ............................................................................... 10
3.1.2.3 Disadvantages of Trapezoidal Threads ............................................................................... 11
3.1.3 Buttress Thread............................................................................................................................ 11
3.1.3.1 Advantages of Buttress Thread............................................................................................ 11
3.1.3.2 Disadvantages of Buttress Thread ....................................................................................... 11
3.2 Thread Series....................................................................................................................................... 12
3.3 Definition of Screw Thread Basic Terms .......................................................................................... 12
3.4 Torque Requirement - Lifting Load.................................................................................................. 14
3.5 Torque Requirement - Lowering Load ............................................................................................. 16
3.6 Over Hauling and Self-Locking Screws ............................................................................................ 17
3.7 Efficiency of the Square Threaded Screw......................................................................................... 19
3.8 Efficiency of Self-Locking Screw ....................................................................................................... 21
3.9 Coefficient of Friction, 𝝁..................................................................................................................... 21
3.10 Buckling of Columns......................................................................................................................... 22
CHAPTER 4 .............................................................................................................................................. 24
MATERIALS SELECTION .................................................................................................................... 24
4.0 Introduction ......................................................................................................................................... 24
4.1 Engineering Materials for Components ............................................................................................ 24
4.2 Steps for Selection of Materials for Components ............................................................................. 25
4.3 Components and their Specific Materials Selected .......................................................................... 26
4.3.1 Frame (Body)................................................................................................................................ 26
4.3.2 Screw ............................................................................................................................................. 27
4.3.3 Nut 27
4.3.4 Handle ........................................................................................................................................... 28
4.4.4 Cup 28
4.4.5 Set Screw and Lock nut + Washer.............................................................................................. 28
CHAPTER 5 .............................................................................................................................................. 29
DESIGN PROCEDURE FOR THE SCREW JACK............................................................................. 29
5.0 Introduction ......................................................................................................................................... 29
5.1 Design for Screw Shaft........................................................................................................................ 29
5.1.1 Core Diameter............................................................................................................................... 29
5.1.2 Torque Required to Rotate the Screw........................................................................................ 30
5.1.3 Screw Stresses............................................................................................................................... 31

14. xiv
5.1.4 Principal Stresses.......................................................................................................................... 31
5.2 Design for Nut...................................................................................................................................... 32
5.2.1 Height of the Nut .......................................................................................................................... 32
5.2.2 Stresses in the Screw and Nut...................................................................................................... 33
5.2.3 The outer diameter of Nut ........................................................................................................... 34
5.2.4 The outside diameter of Collar.................................................................................................... 34
5.2.5 Thickness of the Nut Collar......................................................................................................... 35
5.3 Design for Handle and Cup ................................................................................................................ 35
5.3.1 Dimensions of Diameter of Head on Top of Screw and for the Cup 𝑫𝟑 ................................. 35
5.3.2 Torque Required to Overcome Friction..................................................................................... 37
5.3.3 Total Torque Subjected to the Handle ....................................................................................... 37
5.3.4 Diameter of Handle/Lever ........................................................................................................... 38
5.3.5 Height of Head.............................................................................................................................. 39
5.3.6 Design Check against Instability/Buckling ................................................................................ 40
5.4 Design of Body ..................................................................................................................................... 41
5.4.1 Dimensions for the body of the screw......................................................................................... 41
5.5 Efficiency of the Screw Jack............................................................................................................... 43
5.6 Matlab Script File................................................................................................................................ 44
5.6.1 Screw Jack Matlab Design Script/Code ..................................................................................... 44
5.6.2 Program Run of the Design Script/Code & Solution ................................................................ 48
5.7 Recommendation................................................................................................................................. 49
6.0 APPENDICES ..................................................................................................................................... 50
6.1 Appendix A: Mechanical Properties of Cast Iron ............................................................................ 50
6.2 Appendix B: Mechanical Properties of Steels................................................................................... 51
6.3 Appendix C: Safe Bearing Pressure for Power Screws.................................................................... 52
6.4 Appendix D: Basic Dimensions for Square Threads in Mm (Fine Series) According To IS:
4694 -1968 (Reaffirmed 1996) (Gupta, 2005).......................................................................................... 53
References .................................................................................................................................................. 55

15. 1
CHAPTER ONE
SCREW JACK
1.0 Background
Engineers play a key role in the development of our society, contributing towards building the
economy and inspiring changes that improve on the quality of life. They possess the ability to
comprehend technological processes and creative thinking skills which can help in the solving of
the present problems in both business and the industrial world.
Due to global and technological changes in the world today there is a need for research and
development activities to help counter this, and this can be in terms of complete or slight changes
from the existing technology and all this work requires an engineer.
In an effort to improve the quality of life a power screw was invented, which is also called a
translational screw that converts rotary motion into translation motion. Power screws have many
applications such as in vices, fastening machines, screw jack and many others. The screw jack is
one of the power screws in which a small force is required to be applied to raise or lower a large
load (Bhandari, 2010).
A lifting jack was first designed by Leonardo da Vinci in the late 1400s who demonstrated the
use of a screw jack for lifting loads using a threaded worm gear that was supported in bearings
and rotated by turning the worm shaft to drive a lifting screw to move the load.
In the early 1880s Frank Henry Sleeper designed a lifting jack which was also based on the
principle of ball bearings for supporting a load and transforming rotary motion into translation
motion. This design patent was bought by Arthur Osmore Norton leading to the first Norton
jacks, which were produced in Boston.
In 1883 a Mississippi river boat captain named Josiah Barrett came up with an idea of the ratchet
jack which was based on the familiar lever and fulcrum principle. Duff manufacturing company
took up that chance and started the production of Barrett jacks. More recent screw jack designs
have concentrated on improved efficiency and durability (Collection, 2015).

16. 2
So many writers have come up with so many versions of the design procedures which are lengthy
and tedious to follow through. The design work can be made easy by coding the procedure in a
computer program (Matlab) to reduce the calculation time in designing and considering all design
constraints and factors.
1.1 Problem Statement
Many authors for example Eng. Nyangasi, Van Kudoth Naik, Gupta R.S. Khurmi, J.Keith
Nisbett, and Richard G. Budynas came up with varying procedures for the design of power
screws. These procedures are mostly lengthy and tedious to work with. The purpose of this
project is to come up with a software or program that can be used to design a power screw in this
case a screw jack, so as to save future designers from the tedious work involved in the procedures
available.
1.2 Objectives of the Study
This project is intended to help future designers of powers screws to easily come up with
dimensions of the required power screws by just keying in material properties and the load to be
supported to an available program.
The objectives of the project are:
 Select a material with desired properties for the design of a power screw more specifically
a screw jack.
 To come up with a design procedure for the design of a screw jack.
 To code the procedure above in a language most preferably Matlab.

17. 3
CHAPTER 2
LITERATURE REVIEW
2.0 Introduction
Screw jack is also called jack screw in other terms. A screw jack is an example of a power screw
and referred to as a mechanical device that can increase the magnitude of an effort force. Screw
jacks are used for raising and lowering platforms and they provide a high mechanical advantage
in order to move moderately heavy and large weights with minimum effort. They function by
turning the lead screw when raising or lowering of loads.
2.1 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/her 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 required level. To lower the jack the bar is turned in the
opposite direction.
2.2 Construction of a Screw Jack
A 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 from being completely turned out of the nut. Figure 2.1 below shows a screw
jack and its parts and description as labeled.

18. 4

19. 5
Figure 2.1: Sample screw jack and parts
2.3 Advantages and Disadvantages of the Screw Jack
2.3.1 Advantages
The load can be kept in lifted position since the screw jack is self-locking. This means it remains
motionless where it was left when the rotational force on the screw is withdrawn. It will not
rotate backwards regardless of size of the weight.
Screw jacks also lift or raise the moderate heavy weights against gravity and uses very small
handle force that can be applied manually.
2.3.2 Disadvantages
The major disadvantage of the screw jack is that chances of dropping, tipping or slipping of the
load are high and can cause serious accidents hence the device is termed as not safe fail.

20. 6
Accidents caused by screw jack are due to the following reasons:
(a) Improper securing of load on the jack.
(b) Overloading.
(c) Off center of axis of the jack with respect to center of gravity hence not ideal for side
loads.
(d) Placing the jack on a soft ground and unleveled surface.
(e) Using the jack for wrong purpose instead of using it for the purpose for which it is
designed.
Precaution: Long lifts should be avoided since they can cause serious overheating and generate
a large amount of heat. It should therefore be used under ambient temperatures with the
use of the required lubricants. Design and manufacturer’s instructions such as speed, load
capacity and recommended temperatures must be followed to avoid accidents. Always
keep the mating surfaces clean after use and check for wear and damage on the surfaces.
2.4 Mechanical Advantage (M.A)
The mechanical advantage of a screw jack can be referred to as the ratio of the force the jack
exerts on the load to the input force on the lever, neglecting friction. However, most screw jacks
have large amounts of friction which increase the required input force, so the actual mechanical
advantage is often only 30% to 50% of this figure (Bhandari, 2010).
𝑀. 𝐴 =
𝐹𝑙𝑜𝑎𝑑
𝐹𝑒𝑓𝑓𝑜𝑟𝑡
Where
𝐹𝑙𝑜𝑎𝑑 = 𝑇ℎ𝑒 𝑓𝑜𝑟𝑐𝑒 𝑡ℎ𝑒 𝑗𝑎𝑐𝑘 𝑒𝑥𝑒𝑟𝑡𝑠 𝑜𝑛 𝑡ℎ𝑒 𝑙𝑜𝑎𝑑
𝐹𝑒𝑓𝑓𝑜𝑟𝑡 = 𝑇ℎ𝑒 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑓𝑜𝑟𝑐𝑒 𝑒𝑥𝑒𝑟𝑡𝑒𝑑 𝑜𝑛 𝑡ℎ𝑒 ℎ𝑎𝑛𝑑𝑙𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑗𝑎𝑐𝑘

21. 7
2.5 Common Types of Screw Jack
Commonly used screw jacks are as shown below
(a)
(b)
Figure 2.2: Examples of mechanical jacks
(a) Floor Jack (b) Scissor jack

22. 8
A screw jack is a device that 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. Screw jacks
are usually rated for maximum lifting capacity. There are several types of mechanical jacks:
scissor jack, floor jack, scaffolds, bottle jack etc.
Advantages
 They are self-locking.
 They are simple to design.
 They are cheap and affordable.
 They can lifts moderately loads like cars with very less force.
Disadvantages
 They should always be lubricated.
 They cannot be used to lift or support very heavy loads.
2.6 Factors to Consider in Selection of the Best Jack for Application Purposes
1. Consider the load carrying capacity of the lifting screw (column load) when jacks are
loaded in compression. How high do you need to lift the load? One must choose a jack
whose lifting screw is stout enough to handle the load at full rise.
2. Consider the travel speed of the dynamic load. The speed at which the load will be moved
is a limiting factor. How fast do you need to move the load? Sometimes double lead
machine screw jacks or ball screw jacks are a better choice in a given application.
3. How frequently will the jack need to move the load? Remember that heat builds up
between the machine screw and nut during normal operation. Duty cycles for machine
screw jacks must include periods of rest to dissipate that heat.

23. 9
CHAPTER 3
CLASSIFICATION OF SCREW THREADS
3.1 Introduction
Screw jacks commonly use various forms of threads, namely; square threads, ISO metric
trapezoidal threads and buttress thread.
3.1.1 Square Thread
As the name suggest, it has a square cross section of the thread. It is the most common form used
by the screw jack and used especially in high load applications.
3.1.1.1 Nomenclature of Square Thread
`
Figure 3.1: Nomenclature of square thread
3.1.1.2 Advantages of the Square Thread
The advantages of square threads are as follows:
(i) They have high efficiency.
(ii) They have lower friction coefficient hence less power loss in lifting the load.
(iii)Motion of the nut is uniform since there is no side thrust and radial pressure on the nut.
3.1.1.3 Disadvantages of Square Thread
The disadvantages of square threads are as follows:
(i) The threads are usually turned on a lathe machine with a single point cutting tool hence
expensive compared to machining with multi-point cutting tools. This makes them more
difficult to manufacture.
(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.

24. 10
(iii) It is not possible to compensate for wear in square threads since wear of the thread
surface becomes a serious problem in the service life of the power screw. Therefore,
replacement of the nut or the screw is required when worn out.
Applications: Square threads are used for screw-jacks and presses.
3.1.2 ISO Metric Trapezoidal Threads
These are threads with trapezoidal outline profile. They are most commonly used for lead screws.
They offer high strength and ease of manufacture.
3.1.2.1 Nomenclature of ISO Metric Trapezoidal Thread
Figure 3.2: Nomenclature of ISO metric trapezoidal thread
3.1.2.2 Advantages of the Trapezoidal Thread
(i) They are cheap to manufacture as compared to square threads. Multi-point cutting
tools are employed for machining compared to single point cutting tools that are
used in machining square threads.
(ii) The trapezoidal thread has greater thickness at core diameter than that of the
square thread. Therefore, a screw with trapezoidal threads is stronger than an
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

25. 11
lead-screw of lathe to compensate wear at periodic intervals by tightening the two
halves.
3.1.2.3 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 the nut affects its performance.
Application: Trapezoidal and acme threads are used for lead-screw and other power transmission
devices in machine tools.
3.1.3 Buttress Thread
Figure 3.3: Nomenclature of buttress thread
3.1.3.1 Advantages of Buttress Thread
The advantages of buttress threads are as follows:
(i) It has higher efficiency compared to trapezoidal threads.
(ii) It can be economically manufactured on a thread milling machine.
(iii) The axial wear at the thread surface can be compensated by means of split-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.
3.1.3.2 Disadvantages of Buttress Thread
The buttress threads have one disadvantage. They can transmit power and motion only in one
direction as compared to square and ISO metric trapezoidal threads, which can transmit force and
motion in both directions.
Application: Buttress threads are used in vices, where force is applied only in one direction.

26. 12
3.2 Thread Series
There are three standard thread series in the unified screw thread system;
 Fine series
 Coarse series
 Normal series
Fine thread series have more threads per axial distance and thus have a smaller pitch while coarse
thread series have a large pitch (fewer threads per axial distance). This shows that fine series
threads are stronger as compared to coarse thread series of the same dimensions (diameter)
(Fasteners, 2005).
Fine series has advantages over the other series, these are;
 They have large stress areas hence are strong in compression.
 They have a larger minor diameter which develops higher torsional and shear strength.
 They have smaller helix angle therefore permitting closer adjustment accuracy.
3.3 Definition of Screw Thread Basic Terms
Figure 3.4: Screw Nomenclature (Bhandari, 2010)

27. 13
The terminologies of the screw thread are defined as follows (Gupta, 2005):
(i) Pitch (𝒑)
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.
(ii) Lead (𝒍)
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.
For a single threaded screw 𝒍 = 𝒑
For a double threaded screw 𝒍 = 𝟐𝒑
(iii) Nominal or Outside Diameter (𝒅 𝒐)
It is the largest diameter of the screw. It is also called major diameter.
(iv) Core or Minor Diameter(𝒅 𝒄)
It is the smallest diameter of the screw thread.
𝑑 𝑐 = 𝑑 𝑜 − 𝑝
(v) Mean Diameter (𝒅 𝒎)
𝑑 𝑚 =
(𝑑 𝑜 + 𝑑𝑐)
2
𝑑 𝑚 = 𝑑 𝑜 − 0.5𝑝
(vi) Helix Angle(𝜶)
It is defined as the angle made by the helix of the thread with a plane perpendicular to
the axis of the screw. The helix angle is related to the lead and the mean diameter of
the screw.
Taking one thread of the screw and unwinding, one complete turn is developed. The thread will
become the hypotenuse of a right-angled triangle with the base 𝜋𝑑 𝑚 and height being equal to the
lead 𝑙.

28. 14
Figure 3.5: Unwound thread
This right-angled triangle gives the relationship between the helix angle, mean diameter and lead,
which can be expressed in the following form:
tan 𝛼 =
𝑙
𝜋𝑑 𝑚
Where
𝛼 = 𝑇ℎ𝑒 ℎ𝑒𝑙𝑖𝑥 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑟𝑒𝑎𝑑.
The following conclusions can be drawn on the basis of the development of thread:
 The screw can be considered as an inclined plane with 𝛼 as the angle of inclination.
 The load 𝑊 always acts in the vertical 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.
 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 (𝑑 𝑚/2) gives the torque
𝑇 required to raise or lower the load. Force 𝑃 is perpendicular to load 𝑊.
3.4 Torque Requirement - Lifting Load
The screw is considered as an inclined plane with inclination 𝛼 when the load is being raised. The
following forces act at a point on this inclined plane:

29. 15
Figure 3.6: Force diagram for lifting load
Load 𝑾: It always acts in the vertical downward direction.
Normal reaction 𝑵: It acts perpendicular (normal) to the inclined plane.
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.
Effort 𝑷: The effort 𝑃 acts in a direction perpendicular to the load 𝑊. It may act towards the
right to overcome the friction and raise the load.
Resolving forces horizontally,
𝑃 = 𝜇𝑁 cos 𝛼 + 𝑁 sin 𝛼 (3.0)
Resolving forces vertically,
𝑊 = 𝑁 cos 𝛼 − 𝜇𝑁 sin 𝛼 (3.1)
Dividing equation (3.0) 𝑏𝑦 (3.1) we get:
𝑃 =
𝑊(𝜇 cos 𝛼+sin 𝛼)
(cos 𝛼−𝜇 sin 𝛼)
(3.2)
Dividing the numerator and denominator of the right hand side of equation (3.2) by 𝑐𝑜𝑠 𝛼 we
get:
𝑃 =
𝑊(𝜇+tan 𝛼)
(1−𝜇 tan 𝛼)
(3.3)
The coefficient of friction μ can be expressed as follows:
𝜇 = tan 𝜃 (3.4)

30. 16
Where
𝜃 = the friction angle.
Substituting (3.4) into equation (3.3),
𝑃 =
𝑊(tan 𝜃+tan 𝛼)
(1−tan 𝜃 tan 𝛼)
(3.5)
𝑃 = 𝑊 tan(𝛼 + 𝜃) (3.6)
The torque 𝑇 required to raise the load is given by:
𝑇 = 𝑃 ×
𝑑 𝑚
2
Whence
𝑇 =
[𝑊 tan(𝛼+𝜃)]𝑑 𝑚
2
(3.7)
3.5 Torque Requirement - Lowering Load
When the load is being lowered, the following forces act at a point on the inclined plane:
Load 𝑾: It always acts in the vertical downward direction.
Normal reaction 𝑵: It acts perpendicular (normal) to the inclined plane.
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 the upward direction.
Figure 3.7: Force diagram for lowering load

31. 17
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.
Resolving horizontally,
𝑃 = 𝜇 𝑁 𝑐𝑜𝑠 𝛼 − 𝑁 𝑠𝑖𝑛 𝛼 (3.8)
Resolving vertically,
𝑊 = 𝑁 𝑐𝑜𝑠 𝛼 + 𝜇 𝑁 𝑠𝑖𝑛 𝛼 (3.9)
Dividing expression (3.8) by (3.9) we get as follows:
𝑃 =
𝑊(𝜇 cos 𝛼−sin 𝛼)
(cos 𝛼+𝜇 sin 𝛼)
(3.10)
Dividing the numerator and denominator of the right hand side of equation (3.10) by cos α:
𝑃 =
𝑊(𝜇−tan 𝛼)
(1+𝜇 tan 𝛼)
(3.11)
Substituting equation (3.4) into Equation (3.11),
𝑃 =
𝑊(tan 𝜃−tan 𝛼)
(1+tan 𝜃 tan 𝛼)
(3.12)
Whence
𝑃 = 𝑊 𝑡𝑎𝑛 (𝜃 − 𝛼) (3.13)
The torque 𝑇 required to lower the load is given by,
𝑇 = 𝑃 ×
𝑑 𝑚
2
Whence
𝑇 =
[𝑊 tan(𝜃−𝛼)]𝑑 𝑚
2
(3.14)
3.6 Over Hauling and Self-Locking Screws
From equation (3.14), we know torque required to lower load is given by:
𝑇 =
[𝑊 tan(𝜃 − 𝛼)]𝑑 𝑚
2

32. 18
Case 1: When 𝜽 < 𝛼
The torque required to lower the load becomes negative. This indicates a condition that no force
is required to lower the load and the load itself will begin to turn the screw and descend down,
unless a restraining torque is applied. This condition is called overhauling of the screw.
Case 2: When 𝜽 > 𝛼
The torque required to lower the load becomes positive. Under this condition, the load will not
turn the screw and will not descend on its own unless effort 𝑃 is applied. This condition is called
self- locking.
The rule for self-locking screw states that: A screw will be self-locking if the coefficient of friction
is equal to or greater than the tangent of the helix angle.
For self-locking screw,
tan 𝜃 ≥ tan 𝛼
Or
𝜇 ≥
𝑙
𝜋𝑑 𝑚
Therefore, the following conclusion are made:
(i) Self-locking of the 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) The 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, the single threaded screw is better than multiple threaded
screws from self-locking considerations.
Self-locking condition is essential in applications like screw jack (Naik, Apr 15, 2015).

33. 19
3.7 Efficiency of the Square Threaded Screw
Referring to Figure 3.6: Force diagram for lifting the load, the output consists of raising the load
if the load 𝑊 moves from the lower end to the upper end of the inclined plane.
Therefore,
𝑊𝑜𝑟𝑘 𝑜𝑢𝑡𝑝𝑢𝑡 = 𝐹𝑜𝑟𝑐𝑒 𝑥 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑓𝑜𝑟𝑐𝑒
𝑊𝑜𝑟𝑘 𝑜𝑢𝑡𝑝𝑢𝑡 = 𝑊 𝑥 𝑙
The input consists of rotating the screw by means of an effort P.
𝑊𝑜𝑟𝑘 𝑖𝑛𝑝𝑢𝑡 = 𝐹𝑜𝑟𝑐𝑒 𝑥 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑓𝑜𝑟𝑐𝑒
𝑊𝑜𝑟𝑘 𝑖𝑛𝑝𝑢𝑡 = 𝑃 𝑥 (𝜋𝑑 𝑚)
The efficiency 𝜂 of the screw is given by,
𝜂 =
𝑤𝑜𝑟𝑘 𝑜𝑢𝑡𝑝𝑢𝑡
𝑤𝑜𝑟𝑘 𝑖𝑛𝑝𝑢𝑡
(3.15a)
𝜂 =
𝑊𝑙
𝑃𝜋𝑑 𝑚
(3.15b)
This equation can also be expressed as:
𝜂 =
𝑤
𝑃
(
𝑙
𝜋𝑑 𝑚
) (3.15c)
And
tan 𝛼 =
𝑙
𝜋𝑑 𝑚
Therefore
𝜂 =
𝑊
𝑃
tan 𝛼 (3.15d)
Substituting for 𝑃 = 𝑊 tan(𝛼 + 𝜃) we get;
𝜂 =
tan 𝛼
tan(𝛼+𝜃)
(3.15e)
From the above equation, it is evident that the efficiency of the square threaded screw depends
upon the helix angle 𝛼 and the friction angle𝜃. The following figure shows the variation of the

34. 20
efficiency of the square threaded screw against the helix angle for various values of the coefficient
of friction. The graph is applicable when the load is being lifted.
Figure 3.8: Graph of efficiency against helix angle for various 𝝁
From the graph the following observations are made (Gupta, 2005):
i The efficiency of the square threaded screw increase rapidly up to a helix
angle of 20°.
ii The efficiency is maximum when the helix angle is between 40o
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:
i Reduce the coefficient of friction between the screw and the nut by proper
lubrication.
ii Increase the helix angle up to 40o
to 45° by using multiple start threads. However, a
screw with such a large helix angle has other disadvantages like loss of the self-
locking property.

35. 21
3.8 Efficiency of Self-Locking Screw
The efficiency of square threaded screw is given by (From equation 3.15e):
𝜂 =
tan 𝛼
tan(𝛼+𝜃)
For self-locking screw 𝜃 ≥ 𝛼
Substituting the limiting value (𝜃 = 𝛼) into the equation above
𝜂 ≤
tan 𝜃
tan(𝜃+𝜃)
(3.16a)
𝜂 ≤
tan 𝜃
tan(2𝜃)
(3.16b)
And from trigonometric identities
tan 2𝜃 =
2 tan 𝜃
1−𝑡𝑎𝑛2 𝜃
Substituting for tan 2𝜃 into the above expression,
𝜂 ≤
tan 𝜃(1−𝑡𝑎𝑛2 𝜃)
tan(2𝜃)
(3.16c)
Simplifying
𝜂 ≤
1
2
(1 − 𝑡𝑎𝑛2
𝜃) (3.16d)
From the above expression we can deduce that the efficiency of self-locking square threaded
power screw is less than 0.5 or 50%. If the efficiency is more than 50%, then the screw is said to
be overhauling (Gupta, 2005).
3.9 Coefficient of Friction, 𝝁
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 used. It is practically
independent of the load and dependent on rubbing velocity or materials. An average of 0.1 can be
taken for the coefficient of friction when the screw is lubricated with mineral oil (Gupta, 2005).

36. 22
No. Condition
Average coefficient of friction
Starting Running
1 High grade material and workmanship and best
running conditions.
0.14 0.10
2 Average quality of materials and workmanship
and average running conditions.
0.18 0.13
3 Poor workmanship or very slow and in frequent
motion with indifferent lubrication or newly
machined surface.
0.21 0.15
Table 3.1: Coefficient of friction under different conditions (Gupta, 2005)
No.
Materials
Average coefficient of friction
Starting Running
1 Soft Steel on Cast Iron 0.17 0.12
2 Hardened Steel on Cast Iron 0.15 0.09
3 Soft Steel on Bronze 0.10 0.08
4 Hardened Steel on Bronze 0.08 0.06
Table 3.2: Coefficient of friction when thrust collars are used (Gupta, 2005)
3.10 Buckling of Columns
According to Johnson’s Formula for columns, a short member subjected to axial compressive force
shortens. Compression for the member increases with gradual increase in load. Therefore, the
member fails by buckling when the compressive stress reaches the elastic limit of the material.
Buckling indicates elastic instability. The load at which the buckling starts is called critical load,

37. 23
which is denoted by 𝑊𝑐𝑟. When the axial load on the column reaches 𝑊𝑐𝑟 there is sudden buckling
and a relatively large lateral deflection occurs. An important parameter affecting the critical load
is the slenderness ratio 𝑅 =
𝑙
𝑘
. Mathematical expression for buckling is as shown below (Gupta,
2005), (Marshek, 2012) & (Nisbet, 2015):
𝑊𝑐𝑟 = 𝐴 𝑐. 𝜎 𝑦 [1 −
𝜎 𝑦
4𝐶𝜋2 𝐸
(
𝐿 𝑒𝑓𝑓
𝑘
)
2
] (3.17)
Where
𝜎 𝑦 = Yield stress = 385𝑀𝑃𝑎
𝐶 = End fixity coefficient. The screw is considered to be strut with lower end
fixed and load end free. Therefore 𝐶 = 0.25
𝑘 = The radius of gyration = √
𝐼
𝐴
= 0.25𝑑 𝑐= 0.007
𝐼 = Moment of inertia of the cross section.
This is a parabolic formula that was proposed by Johnson to determine the crippling or the
critical load of straight column.
The following table shows the values of end fixity coefficient (C) for various end conditions
No.
End conditions End fixity coefficient (C)
1 Both ends pinned or hinged 1
2 Both ends fixed 4
3 One end fixed and the other pinned or hinged 2
4 One end fixed and one end free 0.25
Table 3.3: Values of end fixity coefficients(c) (Nisbet, 2015)

38. 24
CHAPTER 4
MATERIALS SELECTION
4.0 Introduction
Material selection is an important process in design processes. Selecting materials is a process
that is design-led in that the material selection process uses the design requirements as the input
so as to come up with materials that have the desired properties for the part to be designed to
function well.
4.1 Engineering Materials for Components
The common engineering materials used in making machine components include;
 Cast iron,
 Steel (all types of steel),
 Copper and its alloys,
 Aluminum and its alloys,
 Plastics.
Therefore, the right materials for the design of the screw jack parts should be selected. Selection
requires one to consider the following factors which give the best material fit for the design job:
a) Specific strength and mass.
It is preferable to select a material of high yield stress with ability to carry external load
without failure and low density in order to realize a screw shaft of high strength and low
mass. Therefore, the material selection process should aim to maximize the quantity
termed as the specific strength.
b) Resistance to abrasive wear.
Most of engineering materials in contact with one another are subjected to surface wear
due to relative motion. It is therefore desirable to select a material from the candidate
materials with low wear rate or capacity to resist abrasive wear at the thread surfaces.
c) Resistance to buckling.
Heavy loads may cause the screw to buckle once the critical load is exceeded. It is
preferable to select a material with high resistance to buckling of the screw, that is,
excellent elasticity and deflection behavior in response to application of an external load.

39. 25
d) Availability, Cost and Affordability.
It is also preferable to choose a material with the highest affordability rating. Relative cost
of the materials is used in finding or calculating the affordable rates. Therefore, the
availability of the material and the cost of processing the material into the finished
product need to be taken into account and considered as supporting information when
making the final choice of the material.
e) Heat transmission properties.
As we know there always a relative motion between screw and nut, which cause a friction
that generates heat which can cause change in the mechanical properties of the material.
f) Other relevant properties include; resistance to corrosion, electrical and mechanical
properties, heat transmission properties etc.
4.2 Steps for Selection of Materials for Components
Selection of materials in engineering design involves the following steps (Prof. F.M. Oduori,
2016):
 Translation of design requirements into specifications for a material.
 Screening out those materials that do not meet the specifications in order to leave only the
viable candidates.
 Ranking of the surviving materials to identify those that have the greatest potential.
 Using supporting information to finally arrive at the choice of material to be used.
The first three steps involve mathematical analysis, use of various charts and graphs of specific
property such as specific strength, wear resistance, buckling resistance and affordability. The
materials are compared, ranked as per the indices of merit and available supporting information is
used to reach the final decision (Ashby, 2005).
In this project, information from case studies on previous designs of similar products is used in
material selection for the screw jack components/parts. However, other factors such as
availability of the candidate materials, purchase price of the candidate materials, manufacturing
processes and properties, forms and sizes in which the materials are available are also considered.

40. 26
4.3 Components and their Specific Materials Selected
The goal of material selection is to come up with an appropriate material that best meets the
design requirements. The approach is to identify the connection between functional requirements
and the material properties so as to help us reduce the number of candidate materials from which
to select from.
The following are components and materials required in the design of a power screw (screw
jack):
4.3.1 Frame (Body)
Most of the frames are in conical shape and hollow internally to accommodate both the nut and
screw assembly. The frame works to ensure that the screw jack is safe and has a complete rest on
the ground. The purpose of the frame is to support the screw jack and enable it to withstand
compressive load exerted on it.
The frame is a bit complex and thus requires casting as a manufacturing process. For this reason,
grey cast iron as a material is selected for the frame. This is also evident from the case study on
previous design of the same product (Nyangasi, 18 December, 2006). Cast iron is cheap and it
can give any complex shape without involving costly machining operations. Cast iron has higher
compressive strength compared to steel. Therefore, it is technically and economically
advantageous to use cast iron for the frame. Graphite flakes cast iron with an ultimate tensile
strength of 220MPa is considered suitable for the design of the frame. The graphite flakes
improve the ability to resist compressive load.
Mechanical properties British Standard Specification
Tensile strength (MPa) 220
Compressive strength (MPa) 766
Shear strength (MPa) 284
Endurance limit (MPa) 96
Young’s modulus (GPa) 89 – 114
Modulus of rigidity (GPa) 36 – 45
Hardness number (HB) 196
Table 4.1: Mechanical Properties of Cast iron – Appendix A (Marshek, 2012)

41. 27
4.3.2 Screw
The screw is subjected to torsional moment, compressive force and bending moment. The screw
profile is square type because of its higher efficiency and self-locking but not compared to
trapezoidal threads. Square threads are usually turned on lathes using a single point cutting tool
also square threads are weak at the root and this leads to use of free cutting steel. Screws are
usually made of steel where great resistance to weather or corrosion is required. Most fasteners
close to 90% use carbon steel because steel has excellent workability, offers abroad range of
attainable combinations of strength properties and it is less expensive. Medium plain carbon steel
can be heat treated for the purpose of improving properties such as hardness, strength (tensile and
yield), the desired results are therefore obtained (Fasteners, 2005). This leads to the use of plain
carbon steels.
Material British
standard
Production
in process
Maximum
section
size, mm
Yield
strength
MPa
Tensile
strength,
MPa
Elon
gatio
n %
Hardness
Number,
HB
0.30C 080M30 Hardened &
Tempered
63 385 550 – 700 13 152 - 207
Table 4.2: Mechanical Properties of Plain carbon steel – Appendix B (Nyangasi, 18 December,
2006)
4.3.3 Nut
There exists a relative motion between the screw and the nut which causes friction, friction in
turn causes wear of the material used for screw and nut. Therefore, it requires one of the two
members to be softer. A suitable material for the nut is therefore phosphor bronze which is a
copper alloy with small percentage of lead and has the following advantages;
 Good corrosion resistance.
 Low coefficient of friction.
 High tensile strength.
Bronze has 0.2% phosphor to increase tensile strength and the yield stresses may be taken as;
tension = 125MPa, compression = 150MPa, yield stress in shear = 105MPa with safe bearing
pressure of 15MPa, ultimate tensile strength is 190MPa and a coefficient of friction of 0.1.

42. 28
Type of power
screw
Screw material Nut
material
Bearing
pressures
Rubbing speed
Screw jack Steel Bronze 11-17MPa 3m/s
Table 4.3: Safe Bearing Pressures for Power screws – Appendix C (Nyangasi, 18 December,
2006) & (Gupta, 2005)
4.3.4 Handle
The handle is subjected to bending moments so plain carbon steel of BS 080M30 with yield
strength of 385MPa can also be used. It has the same mechanical properties and process as in
Table 4.2.
4.4.4 Cup
Shape of cup is complex and thus requires casting process. It also has the same properties as in
Table 4.1. Taking graphite flakes cast iron with an ultimate tensile strength of 200MPa. The
graphite flakes improve the ability to resist compressive load.
4.4.5 Set Screw and Lock nut + Washer
The purpose of the set screw is to resist motion of nut with screw. The lock nut + washer on the
other hand is used to provide uniform force by enlarging the area under the action of the force.
We can use plain carbon steel for both and they have the same manufacturing process and
properties as in Table 4.2.

43. 29
CHAPTER 5
DESIGN PROCEDURE FOR THE SCREW JACK
5.0 Introduction
The generalized adopted design procedure for a screw jack to raise a load of 2460 kg for example
a large truck to a height of 200 mm.
The table below shows average weight of vehicles according to USA Today.
Vehicle Class Curb weight in kg
Compact car 1354
Midsize car 1590
Large Car 1985
Compact truck 1577
Midsize truck 1936
Large truck 2460
Table 5.1: Average Weight of Vehicles in USA
5.1 Design for Screw Shaft
Material specification selected for the screw shaft is plain carbon steel to British Standard
specification BS 970 080M30, Hardened and Tempered, whose properties are as shown in
Appendix B and the material yield strength is 700 MPa both in tension and pure compression
and 450 MPa in shear.
5.1.1 Core Diameter
The core diameter is determined by considering the screw to be under pure compression. That is;
𝑊 = 𝜎𝑐 × 𝐴 𝑐 (5.1)
Where
𝜎𝑐 = Pure compression stress = 700MPa
𝐴 𝑐 = Cross sectional area of the screw shaft =
𝜋
4
(𝑑 𝑐)2
𝑑 𝑐= Core diameter
Whence

44. 30
𝑊 = 𝜎𝑐 ×
𝜋
4
(𝑑 𝑐)2
(5.1a)
𝑑 𝑐 = √
4𝑊
𝜎 𝑐×𝜋
(5.1b)
Taking factor of safety 𝑓. 𝑠 = 5
𝑑 𝑐 = √
4𝑊
𝜎 𝑐
𝑓.𝑠
×𝜋
(5.1c)
𝑑 𝑐 = √
4 × 2460 × 9.81
700 × 106
5
× 𝜋
𝑑 𝑐 = 0.0148147𝑚 = 14.8147𝑚𝑚
For square threads of fine series, the following dimensions of screw are selected from Appendix
D (Gupta, 2005) hence,
The core diameter 𝑑 𝑐 = 16𝑚𝑚, 𝑑 𝑜 = 18𝑚𝑚 and pitch 𝑝 = 𝑙 = 2𝑚𝑚.
Figure 5.1: Section of screw spindle
5.1.2 Torque Required to Rotate the Screw
We know that torque required to rotate the screw is the same torque required to lift the load
which is given by;

45. 31
𝑇1 = 𝑃 ×
𝑑 𝑚
2
=
[𝑊 tan(𝛼+𝜃)]𝑑 𝑚
2
(5.2)
We know that
𝑑 𝑚 =
(𝑑 𝑜 + 𝑑 𝑐)
2
=
(18 + 16)
2
= 17𝑚𝑚
And
tan 𝛼 =
𝑙
𝜋𝑑 𝑚
=
2
𝜋 × 17
= 0.03745
Assuming coefficient of friction between screw and nut,
𝜇 = tan 𝜃 = 0.1
Then
𝑇1 =
[24132.60 tan(2.1447 + 5.71)]0.017
2
= 28.298𝑁𝑚
5.1.3 Screw Stresses
Compressive Stress due to axial load using the new core diameter is,
𝜎𝑐 =
𝑊
𝐴 𝐶
=
𝑊
𝜋
(𝑑 𝑐)2
4
=
4 × 24132.60
𝜋 × 0.0162
= 120.025𝑀𝑃𝑎
And the shear stress due to this torque using the new core diameter is given by;
𝜏 =
𝑇1 𝑑 𝑐
2𝐽
(5.3)
Where
𝐽 = 𝑃𝑜𝑙𝑎𝑟 𝑚𝑜𝑚𝑒𝑛𝑡𝑠 =
𝜋𝑑 𝑐
4
32
(5.4)
Whence
𝜏 =
16𝑇1
𝜋(𝑑 𝑐)3
=
16 × 28.298
𝜋 × 0.0163
= 35.186𝑀𝑃𝑎
5.1.4 Principal Stresses
Maximum principal stress is as follows:

46. 32
𝜎𝑐(𝑚𝑎𝑥) =
1
2
[𝜎𝑐 + √(𝜎𝑐)2 + 4𝜏2] (5.5)
Substituting the stresses we get;
𝜎𝑐(𝑚𝑎𝑥) =
1
2
[120.025 + √(120.025)2 + 4(35.186)2]
𝜎𝑐(𝑚𝑎𝑥) = 129.579𝑀𝑃𝑎
The design value of 𝜎𝑐 =
700
5
= 140𝑀𝑃𝑎
And maximum shear stresses as follows:
𝜏 𝑚𝑎𝑥 =
1
2
√(𝜎𝑐)2 + 4𝜏2 (5.6)
𝜏 𝑚𝑎𝑥 =
1
2
√(120.025)2 + 4(35.186)2
𝜏 𝑚𝑎𝑥 = 69.567𝑀𝑃𝑎
The design value of 𝜏 =
450
5
= 90𝑀𝑃𝑎
Check: These maximum shear and compressive stresses are less than the permissible stresses,
hence the spindle or shaft is safe.
5.2 Design for Nut
5.2.1 Height of the Nut
We find the height of the nut (h) by considering the bearing pressure 𝑃𝑏 on the nut. The bearing
pressure on the nut is given by;
𝑃𝑏 =
𝑊
𝜋
4
[(𝑑 𝑜)2−(𝑑 𝑐)2]𝑛
(5.7)
Where
𝑛 = Number of threads in contact with screwed spindle
Material specification for the nut is phosphor bronze which has tensile stress = 150MPa,
compressive stress = 125MPa, shear stress = 105MPa, safe bearing pressure not exceed 17MPa
and a coefficient of friction of 0.1.

47. 33
Assuming the load is uniformly distributed over the entire cross section of the nut and
substituting for the known values we get the number of threads in contact,
17 × 106
=
24132.60
𝜋
4
[(0.018)2 − (0.016)2]𝑛
=
451.861 × 106
𝑛
𝑛 = 26.58
Say 𝑛 = 27
Then height of the nut is as follows;
ℎ = 𝑛 × 𝑝 (5.8)
ℎ = 27 × 2 = 54𝑚𝑚
Check: For a safe nut height ℎ ≤ 4𝑑 𝑐 = 64𝑚𝑚 (Gupta, 2005)
5.2.2 Stresses in the Screw and Nut
Shear stress in the screw is as follows;
𝜏(𝑠𝑐𝑟𝑒𝑤) =
𝑊
𝜋𝑛.𝑑 𝑐.𝑡
(5.9)
Where
𝑡 = 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑠𝑐𝑟𝑒𝑤 =
𝑝
2
= 1𝑚𝑚
𝜏(𝑠𝑐𝑟𝑒𝑤) =
24132.60
𝜋 × 27 × 0.016 × 0.001
= 17.782𝑀𝑃𝑎
And shear stress in the nut is as follows;
𝜏(𝑛𝑢𝑡) =
𝑊
𝜋𝑛.𝑑 𝑜.𝑡
(5.10)
Where
𝑡 = 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑠𝑐𝑟𝑒𝑤 =
𝑝
2
= 1𝑚𝑚
𝜏(𝑛𝑢𝑡) =
24132.60
𝜋 × 27 × 0.018 × 0.001
= 15.806𝑀𝑃𝑎

48. 34
The given value of 𝜏 =
105
5
= 21𝑀𝑃𝑎
Check: These stresses are within permissible limit, hence, design for the nut is safe.
5.2.3 The outer diameter of Nut
Outer diameter 𝐷1 is found by considering the tearing strength of the nut.
𝜎𝑡 =
𝑊
𝜋
4
[(𝐷1)2−(𝑑 𝑜)2]
(5.11)
Where
𝜎𝑡 = 𝑇𝑒𝑎𝑟𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑢𝑡 = 𝑇𝑒𝑛𝑠𝑖𝑙𝑒 𝑠𝑡𝑟𝑒𝑠𝑠
𝜎𝑡 =
150
5
= 30𝑀𝑃𝑎
Then we get 𝐷1 as follows;
30 =
24132.60
𝜋
4
[(𝐷1)2 − (18)2]
𝐷1 = 36.718𝑚𝑚, Say 𝐷1 = 37𝑚𝑚
5.2.4 The outside diameter of Collar
Outside diameter 𝐷2 is found by considering the crushing strength of the nut collar.
𝜎𝑐 =
𝑊
𝜋
4
[(𝐷2)2−(𝐷1)2]
(5.12)
Where
𝜎𝑐 = 𝐶𝑟𝑢𝑠ℎ𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑢𝑡 = 𝐶𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒 𝑠𝑡𝑟𝑒𝑠𝑠
𝜎𝑐 =
125
5
= 25𝑀𝑃𝑎
Then we get 𝐷2 as follows;
25 =
24132.60
𝜋
4
[(𝐷2)2 − (37)2]
𝐷2 = 50.971𝑚𝑚, Say 𝐷2 = 51𝑚𝑚

49. 35
Figure 5.2: Section of Nut collar 1
5.2.5 Thickness of the Nut Collar
The thickness of nut collar 𝒕 𝟏 is found by considering the shearing strength of the nut collar.
𝑡1 =
𝑊
𝜋𝐷1.𝜏
(5.13)
Shearing strength of nut collar =
105
5
= 21𝑀𝑃𝑎
Therefore
𝑡1 =
24132.60
𝜋 × 37 × 21
𝑡1 = 9.88𝑚𝑚, 𝑆𝑎𝑦 𝑡1 = 10𝑚𝑚
5.3 Design for Head and Cup
5.3.1 Dimensions of Diameter of Head on Top of Screw and for the Cup 𝑫 𝟑
Assuming

50. 36
𝐷3 = 1.75𝑑 𝑜 (5.14)
Then
𝐷3 = 1.75 × 18 = 31.50𝑚𝑚, 𝑆𝑎𝑦 32𝑚𝑚
The seat for the cup is made equal to the diameter of the head and then chamfered at the top. The
cup prevents the load from rotating and is fitted with pin of diameter 𝐷4 =
𝐷3
4⁄ approximately
(Gupta, 2005). Therefore 𝐷4 = 8𝑚𝑚.
The pin should remain loose fit in the cup.
Figure 5.3: Section of Pin
Take length of pin to be 9mm.
Other dimensions for the cup are taken as:
Diameter at the top of the cup = Diameter of the head = 52mm
Height of cup = 9mm
Thickness of cup = 3mm
Fillet radii = 1mm

51. 37
Figure 5.4: Section of Cup
5.3.2 Torque Required to Overcome Friction
We know that by assuming uniform pressure condition torque required to overcome friction is
given as follows;
𝑇2 =
1
3
× 𝜇1 𝑊 [
(𝐷3)3−(𝐷4)3
(𝐷3)2−(𝐷4)2
] (5.15)
Where
𝐷3= Diameter of head = 32mm
𝐷4= Diameter of pin = 8mm
Substituting for the known values we get;
𝑇2 =
1
3
× 0.1 × 24132.60 [
(0.032)3
− (0.008)3
(0.032)2 − (0.008)2
] = 27.0285𝑁𝑚
5.3.3 Total Torque Subjected to the Handle
Total torque to which the handle is subjected is given by
𝑇 = 𝑇1 + 𝑇2 (5.16)
𝑇 = 28.298 + 27.0285 = 55.326𝑁𝑚

52. 38
Activity Professional use Domestic use
Pushing 200N (20.4kg) 119N (12.1kg)
Pulling 145N (14.8kg) 96N (9.8kg)
Table 5.2: Maximal Isometric Force by General European Working Population for Whole
Body Work in a Standing Posture
Therefore taking the force of 96N in domestic use (J.J. Fereira, 2004) then the length of the
handle required is
𝐿 = 𝑇/96
Then
𝐿 =
55.326
96
= 0.5763𝑚 = 576.30𝑚𝑚
𝑆𝑎𝑦 𝐿 = 580𝑚𝑚
The length of the handle may be fixed by giving some allowance for gripping 70mm.
Therefore, the length of the handle/lever is 646.30mm.
Figure 5.5: Section of Lever
5.3.4 Diameter of Handle/Lever
The diameter of the handle/lever, 𝐷 may be obtained by considering bending effects. We know
that bending moment;
𝑀 =
𝜋
32
× 𝜎𝑏 × 𝐷3
(5.17)

53. 39
While 𝜎𝑏 = 𝜎𝑡 = 𝜎𝑐 =
700
5
= 140𝑀𝑃𝑎
and maximum bending moment on the lever/handle
𝑀 = 𝐹𝑜𝑟𝑐𝑒 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 × 𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑒𝑣𝑒𝑟
𝑀 = 96 × 0.6463 = 62.0448𝑁𝑚
Then
62.0448 =
𝜋
32
× 140 × 106
× 𝐷3
𝐷 = 16.5269𝑚𝑚, Say 𝐷 = 17𝑚𝑚
Figure 5.6: Section of Lever - Diameter
5.3.5 Height of Head
The height of head is usually taken as twice the diameter of handle.
𝐻 = 2𝐷 (5.18)
Therefore 𝐻 = 2 × 17 = 34𝑚𝑚

54. 40
Figure 5.7: Section of Screw Head
5.3.6 Design Check against Instability/Buckling
Effective length of screw,
𝐿 𝑒𝑓𝑓 = 𝐿𝑖𝑓𝑡 𝑜𝑓 𝑠𝑐𝑟𝑒𝑤 +
1
2
𝑜𝑓 ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑛𝑢𝑡
𝐿 𝑒𝑓𝑓 = 𝐻1 +
ℎ
2
(5.19)
𝐿 𝑒𝑓𝑓 = 200 +
54
2
𝐿 𝑒𝑓𝑓 = 227𝑚𝑚
When the screw reaches the maximum lift, it can be regarded as strut whose lower end is fixed
and the load end is free. Therefore, buckling or critical load for this given condition is as follows
(Gupta, 2005);
𝑊𝑐𝑟 = 𝐴 𝑐. 𝜎 𝑦 [1 −
𝜎 𝑦
4𝐶𝜋2 𝐸
(
𝐿 𝑒𝑓𝑓
𝑘
)
2
] (5.20)
Where
𝜎 𝑦 = Yield stress = 385𝑀𝑃𝑎
𝐶 = End fixity coefficient. The screw is considered to be strut with lower end
fixed and load end free. Therefore 𝐶 = 0.25

55. 41
𝑘 = The radius of gyration = √
𝐼
𝐴
= 0.25𝑑 𝑐= 0.004
𝐼 = Moment of inertia of the cross section.
The buckling load as obtained by the above expression and must be higher than the load at which
the screw is designed. Substituting for the known values:
𝑊𝑐𝑟 =
𝜋
4
(𝑑 𝑐)2
. 𝜎 𝑦 [1 −
𝜎 𝑦
4𝐶𝜋2 𝐸
(
𝐿 𝑒𝑓𝑓
𝑘
)
2
] (5.21)
𝑊𝑐𝑟 =
𝜋
4
(0.016)2
× 385 × 106
[1 −
385 × 106
4 × 0.25 × 𝜋2 × 200 × 109
(
0.227
0.004
)
2
]
𝑊𝑐𝑟 = 28784.55𝑁
While
𝑊 = 24132.60𝑁
𝑊𝑐𝑟 > 𝑊 , hence there is no chance for the screw to buckle.
5.4 Design of Body
5.4.1 Dimensions for the body of the screw
The dimension of the body may be fixed and given as in shown in the figure above (Gupta,
2005):
1. Diameter of the Body at the Top
𝐷5 = 1.5𝐷2 (5.22)
𝐷5 = 1.5 × 51 = 76.50𝑚𝑚
2. Thickness of the body
𝑡2 = 0.25𝑑 𝑜 (5.23)
𝑡2 = 0.25 × 18 = 4.5𝑚𝑚, 𝑆𝑎𝑦 𝑡3 = 5𝑚𝑚
3. Inside Diameter at the Bottom
𝐷6 = 2.25𝐷2 (5.24)
𝐷6 = 2.25 × 51 = 114.75𝑚𝑚

56. 42
4. Outer Diameter at the Bottom
𝐷7 = 1.75𝐷6 (5.25)
𝐷7 = 1.75 × 114.75 = 200.8125𝑚𝑚
5. Thickness of Base
𝑡3 = 2𝑡1 (5.26)
𝑡3 = 2 × 10 = 20𝑚𝑚
6. Height of the Body 𝐻 𝑏
𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑏𝑜𝑑𝑦 = Max 𝑙𝑖𝑓𝑡 + 𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑛𝑢𝑡 + 𝐸𝑥𝑡𝑟𝑎 50𝑚𝑚
𝐻 𝑏 = 200 + 54 + 50 = 304𝑚𝑚
Finally, the body is tapered in order to achieve stability of the jack.

57. 43
Figure 5.8: Section of Frame (Body)
5.5 Efficiency of the Screw Jack
Efficiency of screw jack is given as follows:
𝜂 =
𝑇𝑜𝑟𝑞𝑢𝑒 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑡𝑜 𝑟𝑜𝑡𝑎𝑡𝑒 𝑠𝑐𝑟𝑒𝑤 𝑤𝑖𝑡ℎ 𝑛𝑜 𝑓𝑟𝑖𝑐𝑡𝑖𝑜𝑛
𝑇𝑜𝑡𝑎𝑙 𝑡𝑜𝑟𝑞𝑢𝑟𝑒 𝑜𝑢𝑡𝑝𝑢𝑡
=
𝑇𝑜
𝑇
(5.27a)
𝜂 =
𝑇𝑜
𝑇
(5.27b)
But
𝑇𝑜 = 𝑊 tan 𝛼 ×
𝑑 𝑚
2

58. 44
𝑇𝑜 = 24132.60 × 0.03745 ×
0.017
2
𝑇𝑜 = 7.682𝑁𝑚
And
𝑇 = 55.326𝑁𝑚
Therefore
𝜂 =
7.682
55.326
= 0.1388 𝑜𝑟 13.88%
5.6 Matlab Script File
5.6.1 Screw Jack Matlab Design Script/Code
% MATERIAL PROPERTIES %
W = input ('Enter load capacity of the screw jack in kg');
W = W * 9.81;
H1 = input ('Enter the required lift of the screw jack in mm');
u = input ('Enter coefficient of friction between materials');
E = input ('Enter the modulus of elasticity of the screw material in MPa');
y = atan (u);
TstrYP = input ('Enter yield point for tension in MPa for screw and nut material as 1*2 matrix
respectively');
CstrYP = input ('Enter yield point for compression in MPa for screw and nut material as 1*2
matrix respectively');
SHstrYP = input ('Enter yield point for shear in MPa for screw and nut material as 1*2 matrix
respectively');
% DESIGN FOR SCREW SHAFT %
d1 = (4*W/(pi*CstrYP(1,1)/5))^0.5; % Minor Diameter %
disp ('CALCULATED VALUE OF MINOR DIAMETER in mm =')
d1 = (d1) %#ok<NOPTS>
d2 = input ('SELECT A STANDARD MAJOR DIAMETER FROM LIST 10 12 14 16 18 20 22
24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 55 58 60 62 65 68 70 72 75 78 80 82 85 88 90 92
95 98 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175');
disp ('STANDARD MAJOR DIAMETER in mm =')
disp (d2)
if 10<=d2 && d2<20 % Pitch %
p = 2;
elseif 22<=d2 && d2<62
p = 3;
elseif 65<=d2 && d2<110

59. 45
p = 4;
elseif 115<=d2 && d2<175
p = 6;
else disp ('SELECT CORRECT NOMINAL DIAMETER in mm =')
break
end
disp ('PITCH')
disp (p)
d1 = d2 - p; % Standard Minor Diameter %
disp ('STANDARD MINOR DIAMETER in mm =')
disp (d1)
dm = (d2+d1)/2; % Mean Diameter %
helix = atan (p/(pi*dm)); % Helix Angle %
disp ('HELIX ANGLE in radians =')
disp (helix)
if helix >= y
disp ('Screw Nut Pair is Not Self Locking')
break
end
T1 = W*(dm/2)*tan (helix + y); % Torque Required to Rotate the Screw %
disp ('TORQUE TO ROTATE THE SCREW in Nmm =')
disp (T1)
% DESIGN FOR NUT %
Pb = input ('Enter Allowable Bearing Pressure in MPa');
if Pb == [] %#ok<BDSCA>
Pb = 17; % Default value for Pb for the Phosphor Bronze %
end
n =4*W/ (pi*(d2^2-d1^2)*Pb); % Number of Screw Thread %
n = round (n);
disp ('NUMBER OF THREAD =')
disp (n)
h = n*p; % Height of the Nut %
disp ('HEIGHT OF THE NUT in mm =')
disp (h)
% CHECKING FOR SAFE NUT HEIGHT %
if n <= 27 && h <= 4.0*d1
disp ('NUT DESIGN CHECK IS SATISFIED')
else
disp ('NUT DESIGN CHECK IS NOT SATISFIED')
break
end
% CHECKING FOR SCREW STRESSES %
CstrB = 4*W/ (pi*d1^2); % Compressive stress %
SHstrB = 16*T1/ (pi*d1^3); % Shear stress %

60. 46
SHstrmax = ((CstrB/2) ^2 + SHstrB^2) ^0.5; % Maximum shear stress %
f = SHstrYP (1, 1)/SHstrmax; % Factor of safety %
if f >= 5
disp ('SCREW DESIGN IS SAFE')
else
disp ('SCREW DESIGN IS NOT SAFE')
break
end
% OTHER ASPECTS OF NUT DESIGN %
D1 = ((4*W/ (pi*TstrYP (1, 2)/5)) +d2^2) ^0.5; % Outer diameter of the nut %
D1 = ceil (D1);
disp ('OUTER DIAMETER OF THE NUT in mm =')
disp (D1)
D2 = ((4*W/(pi*CstrYP(1,2)/5))+D1^2)^0.5; % Outside diameter of the collar %
D2 = ceil (D2);
disp ('OUTSIDE DIAMETER OF THE COLLAR in mm =')
disp (D2)
t1 = W/ (pi*D1*SHstrYP (1, 2)/5); % Collar thickness %
t1 = round (t1);
disp ('COLLAR THICKNESS in mm =')
disp (t1)
%CHECKING FOR SCREW AGAINST INSTABILITY %
Leff = H1+h/2; % Length of column considered %
k = 0.25*d1; % Radius of gyration %
R = Leff/k; % Slenderness ratio%
C = 0.25; % End condition for fixed free column %
Ac = (pi*d1^2)/4;
Rcr = ((2*C*pi^2*E)/TstrYP (1, 1)) ^0.5; % Critical slenderness ratio%
if R < Rcr
Wcr = Ac*TstrYP*(1-0.5*(R/Rcr) ^2); % Short column formula%
else
Wcr = pi^2*E*k^2*Ac/ (4*Leff^2); % Long column formula%
end
if Wcr >= W
disp ('THE SCREW IS STABLE')
else
disp ('THE SCREW IS NOT STABLE REDUCE THE LIFT ')
break
end
% DESIGN FOR HANDLE, PIN AND CUP %
D3 = 1.75*d2; % Diameter for the Cup %
D3 = round (D3);
disp ('CUP DIAMETER in mm =')
disp (D3)

61. 47
D4 = D3/4; % Diameter of Pin %
disp ('PIN DIAMETER in mm =')
disp (D4)
T2 = 1/3*u*W*((D3^3-D4^3)/ (D3^2-D4^2)); % Torque required to overcome friction %
disp ('TORQUE TO OVERCOME FRICTION in Nmm =')
disp (T2)
T = T1 + T2; % Total Torque the handle is subjected to %
disp ('TOTAL TORQUE in Nmm =')
disp (T)
L = T/96; % Length of the Handle %
L = L+70; % Length of handle + Allowance for gripping 70mm %
disp ('LENGTH OF THE HANDLE in mm =')
disp (L)
M = 96*L; % Maximum bending moment on the lever%
disp ('MAXIMUM BENDING MOMENT in Nmm =')
disp (M)
D = ((32*M*5)/ (pi*CstrYP (1, 1))) ^0.33; %Diameter of handle%
D = round (D+1);
disp ('DIAMETER OF HANDLE in mm =')
disp (D)
H = 2*D; % Height of Head %
disp ('HEIGHT OF HEAD in mm =')
disp (H)
% DESIGN OF BODY %
D5 = 1.5*D2; % Diameter of the body at the top %
disp ('DIAMETER OF BODY AT THE TOP in mm =')
disp (D5)
t2 = 0.25*d2; % Thickness of the Body %
t2 = round (t2);
disp ('THICKNESS OF BODY in mm =')
disp (t2)
D6 = 2.25*D2; % Inside Diameter at the Bottom %
disp ('INSIDE DIAMETER AT THE BOTTOM in mm =')
disp (D6)
D7 = 1.75*D6; % Outside Diameter at the Bottom %
disp ('OUTSIDE DIAMETER AT THE BOTTOM in mm =')
disp (D7)
t3 = 2*t1; % Thickness of Base %
disp ('BASE THICKNESS in mm =')
disp (t3)
Hb = H1+h+50; % Height of body %
disp ('HEIGHT OF BODY in mm =')
disp (Hb)

62. 48
5.6.2 Program Run of the Design Script/Code & Solution
Enter load capacity of the screw jack in kg 2460
Enter the required lift of the screw jack in mm 200
Enter coefficient of friction between materials 0.1
Enter the modulus of elasticity of the screw material in MPa 200000
Enter yield point for tension in MPa for screw and nut material as 1*2 matrix respectively [700
150]
Enter yield point for compression in MPa for screw and nut material as 1*2 matrix respectively
[700 125]
Enter yield point for shear in MPa for screw and nut material as 1*2 matrix respectively [450
105]
CALCULATED VALUE OF MINOR DIAMETER in mm =d1 = 14.8147
SELECT A STANDARD MAJOR DIAMETER FROM LIST 10 12 14 16 18 20 22 24 26 28 30
32 34 36 38 40 42 44 46 48 50 52 55 58 60 62 65 68 70 72 75 78 80 82 85 88 90 92 95 98 100
105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 18
STANDARD MAJOR DIAMETER in mm =18
PITCH = 2
STANDARD MINOR DIAMETER in mm = 16
HELIX ANGLE in radians = 0.0374
TORQUE TO ROTATE THE SCREW in Nmm = 2.8300e+04
Enter Allowable Bearing Pressure in MPa = 17
NUMBER OF THREAD = 27
HEIGHT OF THE NUT in mm = 54
NUT DESIGN CHECK IS SATISFIED
SCREW DESIGN IS SAFE
OUTER DIAMETER OF THE NUT in mm = 37
OUTSIDE DIAMETER OF THE COLLAR in mm = 51
COLLAR THICKNESS in mm = 10
THE SCREW IS STABLE
CUP DIAMETER in mm = 32

63. 49
PIN DIAMETER in mm = 8
TORQUE TO OVERCOME FRICTION in Nmm = 2.7029e+04
TOTAL TORQUE in Nmm = 5.5329e+04
LENGTH OF THE HANDLE in mm = 646.3422
MAXIMUM BENDING MOMENT in Nmm = 6.2049e+04
DIAMETER OF HANDLE in mm = 17
HEIGHT OF HEAD in mm = 34
DIAMETER OF BODY AT THE TOP in mm = 76.5000
THICKNESS OF BODY in mm = 5
INSIDE DIAMETER AT THE BOTTOM in mm = 114.7500
OUTSIDE DIAMETER AT THE BOTTOM in mm = 200.8125
BASE THICKNESS in mm = 20
HEIGHT OF BODY in mm = 304
5.7 Recommendation
From the case study, we concentrated on design of a simple mechanical screw jack where the nut
is fixed in a cast iron frame and remains stationary while the spindle is being rotated by the lever.
This design can only work for light loads hence when a screw jack is needed for heavy load
application a different design is required where the nut is rotated as the spindles moves.
We therefore recommend design of a screw jack for the heavy loads.

64. 50
6.0 APPENDICES
6.1 Appendix A: Mechanical Properties of Cast Iron (Nyangasi, 18 December, 2006)
Mechanical
Properties
Grade Designation(British Standards)
150 180 220 260 300 350 400
Tensile
Strength
(MPa)
150 180 220 260 300 350 400
Compressive
Strength
(MPa)
587 663 766 868 970 1097 1225
Shear
Strength
(MPa)
176 222 284 346 407 484 562
Endurance
Limit (MPa) 71 82 96 111 125 143 161
Young’s
Modulus
(MPa)
71-96 70-104 89-114 100-135 110-135 124-147 137-160
Modulus Of
Elasticity
(GPa)
29-40 32-42 36-45 43-51 43-51 48-55 53-58
Hardness
(HB) 160 176 196 236 236 261 286

65. 51
6.2 Appendix B: Mechanical Properties of Steels (Nyangasi, 18 December, 2006)
Materials British
standards
Production
process
Maximum
section size,
mm
Yield
Strength
MPa
Tensile
Strength,
MPa
Elongation
%
Hardness
number, HB
0.20C 070M20 HR
152 215 430 22 126 – 179
254 200 400 20 116 – 170
CD
13 385 530 12 154
76 340 430 14 125
0.30C 080M30 HR
152 245 490 20 143 – 192
254 230 460 19 134 – 183
CD
13 470 600 10 174
63 385 530 12 154
H&T 63 385 550 - 700 13 152 – 207
0.40C 080M40
HR 150 280 550 16 152 – 207
CD 63 430 570 10 165
H&T 63 385 625 - 775 16 179 – 229
0.50C 080M50
HR 150 310 620 14 179 – 229
CD 63 510 650 10 202 – 255
H&T 150 430 625 – 775 11 248 – 302
1Cr 530M40 H&T
100 525 700 – 850 17 202 – 255
29 680 850 - 1000 13 248 – 302
1.5MnMo 605M36 H&T
150 525 700 – 850 17 202 – 255
29 755 925 - 1075 12 269 – 331
1.25NiCr 640M40 H&T
152 525 700 – 850 17 202 – 255
102 585 770 – 930 15 223 – 277
64 680 850 - 1000 13 248 – 302
29 755 930 - 1080 12 269 – 331
3NiCr 653M31 H&T
64 755 930 - 1080 12 269 – 331
- 680 850 – 000 12 248 – 302

66. 52
1CrMo 708M40 H&T 150 525 700 – 850 17 201 – 255
13 940 1075-1225 12 311 – 375
3CrMo 722M24 H&T
152 680 850-1000 13 269 – 331
- 755 930-1080 12 269 – 331
2.5NiCr
Mo
826M40 H&T
150 755 925-1075 12 269 – 331
- 850 1000-1150 12 293 – 352
- 1020 1150-1300 10 341 – 401
3NiCrMo 830 H&T
254 650 850 - 1000 13 248 – 302
152 680 850 - 1000 12 248 – 302
64 940 1080-1240 11 311 – 375
1.5MnNi
CrMo
945M38 H&T
152 525 690 – 850 17 201 - 255
64 680 850 –
1000
13 248 - 302
29 850 1000-1160 12 293 - 352
Key: HR - Hot- Hot rolled and normalized
CD - Cold drawn
H&T - Hardened and tempered
6.3 Appendix C: Safe Bearing Pressure for Power Screws (Gupta, 2005)
Type of power
screw
Material Safe bearing
pressure,(𝑷 𝒃)
MPa
Rubbing speed
m/sscrew Nut
Hand press Steel Bronze 17.0-24.1 Low speed ,well lubricated
Screw jack Steel Cast Iron 12.0-17.0 Low speed < 2.5
Screw jack Steel Bronze 11.0-17.0 Low speed < 3
Hoisting screw Steel Cast Iron 4.0-7.0 Medium speed (6-12)
Hoisting screw Steel Bronze 5.5-10.0 Medium speed (6-12)
Load screw Steel Bronze 1.0-1.6 High speed > 15

67. 53
6.4 Appendix D: Basic Dimensions for Square Threads in Mm (Fine Series) According
To IS: 4694 -1968 (Reaffirmed 1996) (Gupta, 2005)
Nominal/
Major
Diameter
(𝒅 𝒐), mm
Major Diameter
Minor
Diameter
(𝒅 𝒄), mm
Pitch
(𝒑)
Depth of Thread
Area of Core,
(𝑨 𝒄) 𝒎𝒎 𝟐
Bolt
(d)
Nut
(D)
Bolt
(Hb)
Nut
(h)
10
12
14
16
18
20
10
12
14
16
18
20
10.5
12.5
14.5
16.5
18.5
20.5
8
10
12
14
16
18
2 1 1.25
50.3
78.5
113
154
201
254
22
24
26
28
30
32
34
36
(38)
40
42
44
(46)
48
50
52
55
(58)
60
(62)
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
52
55
58
60
62
22.5
24.5
26.5
28.5
30.5
32.5
34.5
36.5
38.5
40.5
42.5
44.5
46.5
48.5
50.5
52.5
55.5
58.5
60.5
62.5
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
52
55
57
59
3 1.5 1.75
284
346
415
491
573
661
755
855
962
1075
1195
1320
1452
1590
1735
1886
2124
2376
2552
2734

68. 54
65
(68)
70
(72)
75
(78)
80
(82)
85
(88)
90
(92)
95
(98)
100
(105)
110
65
68
70
72
75
78
80
82
85
88
90
92
95
98
100
105
110
65.5
68.5
70.5
72.5
75.5
78.5
80.5
82.5
85.5
88.5
90.5
92.5
95.5
98.5
100.5
105.5
110.5
61
64
66
68
71
74
76
78
81
84
86
88
91
94
96
101
106
4 2 2.25
2922
3217
3421
3632
3959
4301
4536
4778
5153
5542
5809
6082
6504
6960
7238
8012
8825
(115)
120
(125)
130
(135)
140
(145)
150
(155)
160
(165)
170
(175)
115
120
125
130
135
140
145
150
155
160
165
170
175
115.5
120.5
125.5
130.5
135.5
140.5
145.5
150.5
155.5
160.5
165.5
170.5
175.5
109
114
119
124
129
134
139
144
149
154
159
164
169
6 3 3.25
9331
10207
11122
12076
13070
14103
15175
16286
17437
18627
19856
21124
22432
Note: Diameter in brackets are of second preference.

69. 55
References
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Pergamon Press .
2. Bhandari, V. B., 2010. Design of Machine Elements. Third Edition ed. New Delhi: Tata
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[Accessed 11 November 2015].
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Chand and Company.
6. J.J. Fereira, M. B. M. G., 2004. Review of the risks associated with pushing and pulling
heavy loads.. first ed. Shefield: Health and sfety Laboratory.
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[Accessed 3 December 2015].
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11. Nyangasi, 18 December, 2006. http://webcache.googleusercontent.com/search. [Online]
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http://mechanical.uonbi.ac.ke/sites/default/files/cae/engineering/mechanical/POWER%20
SCREWS.doc.
[Accessed 4 February 2016].
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