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Mechanical Engineering
BTEC National Engineering Specialist Units
Third Edition
Alan Darbyshire
AMSTERDAM • BOSTON • HEIDELBERG • LONDON • NEW YORK • OXFORD
PARIS • SAN DIEGO • SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO
Newnes is an imprint of Elsevier
Newnes is an imprint of Elsevier
Linacre House, Jordan Hill, Oxford OX2 8DP, UK
30 Corporate Drive, Suite 400, Burlington, MA 01803, USA
First edition 2003
Second edition 2008
Third edition 2010
Copyright © 2010 Alan Darbyshire, except Chapter 6 © 2010
Elsevier Ltd. All rights reserved
The right of Alan Darbyshire to be identifi ed as the author of this work
has been asserted in accordance with the Copyright, Designs and Patents
Act 1988
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A catalog record for this book is available from the Library of Congress
ISBN: 978-0-08-096577-2
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10 11 12 13 14 10 9 8 7 6 5 4 3 2 1
iii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .v
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii
Chapter 1 Further Mechanical Principles and
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Engineering Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
Engineering Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Rotating Systems with Uniform Angular Acceleration . . . . . . . . . . . . . . . . . . . . . 41
Moment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Centripetal Acceleration and Centripetal Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Simple Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Chapter 2 Advanced Mechanical Principles and
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Uni-axial and Complex Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Bending in Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Torsion in Power Transmission Shafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Resultant and Relative Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Plane Linkage Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Natural Vibrations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Chapter 3 Applications of Mechanical Systems and
Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Lubricants and Lubrication Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Engineering Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Mechanical Power Transmission Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Plant Equipment and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Chapter 4 Properties and Applications of
Engineering Materials . . . . . . . . . . . . . . . . . . . . 219
Atomic Structure of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
Material Properties and Eff ects of Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
Material Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
Selection of Engineering Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Chapter 5 Engineering Design . . . . . . . . . . . . . . . . . . . . . . 287
Knowing How the Design Process Operates When Dealing
with Customers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
Understanding the Impact of Legislation, Standards and
Environmental and Manufacturing Constraints on the Design
Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
Be Able to Prepare Design Proposals That Meet the
Requirements of a Product Design Specifi cation . . . . . . . . . . . . . . . . . . . . . . . . . 303
Be Able to Produce and Present a Final Design Solution . . . . . . . . . . . . . . . . . . 317
Contents
iv
Chapter 6 Electro, Pneumatic and Hydraulic
Engineering Materials . . . . . . . . . . . . . . . . . . . . 333
Industrial Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
Legislation, Regulations and Safety Precautions . . . . . . . . . . . . . . . . . . . . . . . . . . 335
Fluid Power Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
Fluid Power Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
Maintenance of Fluid Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
Contents
Unit 6
v
The author and publisher would like to thank the following people for
their contribution to the second edition:
W Bolton for writing chapter 6 “ Electro, Pneumatic and Hydraulic
Systems and Devices ”
Mike Tooley for allowing us to adapt his chapters in Engineering
A Level and Higher National Engineering for use as chapter 5
“ Engineering Design ”
Chapter opener and cover illustrations
Photo of train (chapter 1) courtesy of iStockphoto, Remus Eserblom,
Image # 4619117
Photo of racing car (chapter 2) courtesy of iStockphoto, Jan Paul
Schrage, Image # 4955692
Photo of turbine (chapter 3) courtesy of iStockphoto, Tomas Bercic,
Image # 4056469
Photo of aircraft (chapter 4) courtesy of iStockphoto, Dan Barnes,
Image # 4941515
Photo of CNC machine (chapter 5) courtesy of iStockphoto,
Shawn Gearhart, Image # 1798391
Photo of robotic system (chapter 6) courtesy of iStockphoto,
Paul Mckeown, Image # 5129181
Acknowledgements
This page intentionally left blank
Unit 6
vii
Welcome to the challenging and exciting world of engineering! This
book has been written to help get you through six specialist units of the
revised BTEC National Certificate and Diploma awards in Engineering.
It provides the essential underpinning knowledge required of a student
who wishes to pursue a career in engineering.
The book has been written by a highly experienced further education
lecturer, who has over 30 years of practical teaching experience, with
contributions from specialist lecturers in Engineering Design and
Pneumatics and Hydraulics. Throughout the book I have adopted
a common format and approach with numerous student activities,
examples, end of chapter review questions and key points.
About the BTEC National Certifi cate and Diploma
The BTEC National Certificate and National Diploma qualifications
have long been accepted by industry as appropriate qualifications for
those who are about to enter industry or who are receiving training at
the early stages of employment in industry. At the same time, these
qualifications have become increasingly acceptable as a means of
gaining entry into higher education.
BTEC National programmes in engineering attract a very large number
of registrations per annum such that there are in excess of 35,000
students currently studying these qualifications in the UK by both
part-time and full-time modes of study.
The BTEC National syllabus was recently reviewed and extensively
updated and new programmes have been launched with effect from
September 2007. The new scheme is likely to be adopted by all
institutions that currently offer the programme as well as a number of
others who will be offering BTEC qualifications for the first time.
Many organizations have contributed to the design of the new BTEC
National Engineering programme including the Qualifications and
Curriculum Authority (QCA), the Engineering Council and several
Sector Skills Councils (SSC).
The Engineering Council continues to view the BTEC National
Certificate/Diploma as a key qualification for the sector. They also
recognize that BTEC National qualifications are frequently used as
a means of entry to higher education courses, such as HNC/HND
programmes and Foundation Degree courses.
How to use this book
This book covers six of the most popular specialist units that are
common to many of the BTEC Engineering programmes. Each chapter
Introduction
viii
covers one unit and contains Text , Key points , Test your knowledge
questions , Examples , Activities and Review questions .
The Test your knowledge questions are interspersed with the text
throughout the book. These questions allow you to check your
understanding of the preceding text. They also provide you with an
opportunity to reflect on what you have learned and consolidate this in
manageable chunks.
Most Test your knowledge questions can be answered in only a few
minutes and the necessary information, formulae, etc., can be gleaned
from the surrounding text. Activities , on the other hand, make excellent
vehicles for gathering the necessary evidence to demonstrate that you
are competent in key skills. Consequently, they normally require a
significantly greater amount of time to complete. They may also require
additional library or resource area research time coupled with access to
computing and other information technology resources.
Many tutors will use Test your knowledge questions as a means of
reinforcing work done in class while Activities are more likely to be
‘ set work ’ for students to do outside the classroom. Whether or not this
approach is taken, it is important to be aware that this student-centred
work is designed to complement a programme of lectures and tutorials
based on the BTEC syllabus. Independent learners (i.e. those not taking a
formal course) will find complete syllabus coverage in the text.
The Examples not only show you how to solve simple problems but
also help put the subject matter into context with typical illustrative
examples. In order to successfully tackle this work you will need to have
a good scientific calculator (and get to know how to use it).
Finally, here are some general points to help you with your studies:
● Allow regular time for reading – get into the habit of setting aside
an hour, or two, at the weekend. Use this time to take a second look
at the topics that you have covered during the week or that you may
have not completely understood.
● Make notes and fi le these away neatly for future reference – lists of
facts, defi nitions and formulae are particularly useful for revision!
● Look out for the inter-relationship between subjects and units – you
will fi nd many ideas and a number of themes that crop up in different
places and in different units. These can often help to reinforce your
understanding.
● Don’t expect to fi nd all subjects and topics within the course equally
interesting. There may be parts that, for a whole variety of reasons,
don’t immediately fi re your enthusiasm. There is nothing unusual
in this; however, do remember that something that may not appear
particularly useful now may become crucial at some point in the
future!
● However diffi cult things seem to get – don’t be tempted to give up!
Engineering is not, in itself, a diffi cult subject, rather it is a subject
Introduction
ix
that demands logical thinking and an approach in which each new
concept builds upon those that have gone before.
● Finally, don’t be afraid to put your new ideas into practice.
Engineering is about doing – get out there and do it!
Good luck with your BTEC Engineering studies!
Alan Darbyshire
Introduction
x
Trains travelling at speeds in excess of 200 kmh 1
have greatly
reduced the journey time to continental cities. Mechanical
principles are applied in the calculation of the tractive eff ort
required to maintain these speeds and the braking forces
required to bring the trains to rest. Mechanical principles are
also applied in the design of tilting mechanisms and the track
infrastructure.
Photo courtesy of iStockphoto, Remus Eserblom, Image# 4619117
Further Mechanical
Principles and
Applications
T
he design, manufacture and servicing of engineered products are important to
the nation ’ s economy and well-being. One has only to think of the information
technology (IT) hardware, aircraft, motor vehicles and domestic appliances
we use in everyday life to realise how reliant we have become on engineered
products. A product must be fi t for its purpose. It must do the job for which it was
designed for a reasonable length of time and with a minimum of maintenance. The
term ‘ mechatronics ’ is often used to describe products which contain mechanical,
electrical, electronic and IT systems. It is the aim of this chapter to broaden your
knowledge of the underpinning mechanical principles which are fundamental to
engineering design, manufacturing and servicing.
Chapter 1
1
Further Mechanical Principles and Applications
CHAPTER 1
2
Engineering Structures
Loading systems
Forces whose lines of action lie in a single plane are called coplanar
forces . If the lines of action pass through a single point, the forces are
said to be concurrent and the point through which they pass is called
the point of concurrence ( Figure 1.1 ).
F1
F2
F2
F3
F1
F3
Point of concurrence
Concurrent forces Non-concurrent forces
Figure 1.1 Coplanar force systems
A concurrent system of coplanar forces can be reduced to a single force
acting at the point of concurrence. This is called the resultant force .
If a body is subjected to a system of concurrent coplanar forces and is
not constrained, it will move in the direction of the resultant force. To
prevent this from happening, a force must be applied which is equal and
opposite to the resultant. This balancing force, which will hold the body
in a state of static equilibrium, is called the equilibrant of the system.
When a body is subjected to a system of non-concurrent coplanar forces,
there is a tendency for the forces not only to make it move in a particular
direction, but also to make it rotate. Such a non-concurrent system can
be reduced to a single resultant force and a resultant couple .
If the body is to be held at rest, an equilibrant must again be applied
which is equal and opposite to the resultant force. This alone however
will not be suffi cient. A balancing couple or turning moment must also
be applied which is equal and opposite to the resultant couple.
If you have completed the BTEC First Diploma unit Mathematics and
Science for Technicians and the BTEC National Certifi cate/Diploma
unit Mechanical Principles and Applications, you will know how to fi nd
the resultant and equilibrant of a coplanar force system graphically by
means of a force vector diagram, and also by using mathematics. We
will shortly be using both methods again but applied to more complex
engineering structures. Here is a reminder of some of the main points of
the mathematical or analytical method.
Sign convention
When you are using mathematics to solve coplanar force system
problems you need to adopt a method of describing the action of the
KEY POINT
A system of concurrent coplanar forces
can be reduced to a single resultant
force.
KEY POINT
A system of non-concurrent coplanar
forces can be reduced to a single
resultant force and a resultant couple
or turning moment.
Further Mechanical Principles and Applications
CHAPTER 1
3
forces and couples. The following sign convention is that which is most
often used:
(i) Upward forces are positive and downward forces are negative.
(ii) Horizontal forces acting to the right are positive and horizontal
forces acting to the left are negative.
(iii) Clockwise acting moments and couples are positive and
anticlockwise acting moments and couples are negative.
+
− +
−
M M
+ −
Figure 1.2 Sign convention
F
(a)
FH
FH
FV FV
(b)
F
θ
θ
Figure 1.3 Resolution of forces
Resolution of forces
Forces which act at an angle exert a pull which is part horizontal and
part vertical. They can be split into their horizontal and vertical parts or
components , by the use of trigonometry. When you are doing this, it is a
useful rule to always measure angles to the horizontal ( Figure 1.3 ).
In Figure 1.3(a) the horizontal and vertical components are both acting
in the positive directions and will be:
F F FF H v cos sin and
In Figure 1.3(b) the horizontal and vertical components are both acting
in the negative directions and will be:
F F FF H v cos sin and
Forces which act upwards to the left or downwards to the right will have
one component which is positive and one which is negative. Having
resolved all of the forces in a coplanar system into their horizontal
and vertical components, each set can then be added algebraically to
determine the resultant horizontal pull, FH , and the resultant vertical
Further Mechanical Principles and Applications
CHAPTER 1
4
pull, FV . The Greek letter (sigma) means ‘ the sum or total ’ of the
components. Pythagoras ’ theorem can then be used to fi nd the single
resultant force R of the system.
i.e. 2 2 RF F 2
H V ( )( )
RF F ( )( ) H V
2 2 (1.1)
The angle which the resultant makes with the horizontal can also be
found using:
tan V
H
F
F
(1.2)
With non-concurrent force systems, the algebraic sum of the moments
of the vertical and horizontal components of the forces, taken about
some convenient point, gives the resultant couple or turning moment. Its
sign, positive or negative, indicates whether its direction is clockwise or
anticlockwise. This in turn can be used to fi nd the perpendicular distance
of the line of action of the resultant from the chosen point.
Example 1.1
Find the magnitude and direction of the resultant and equilibrant of the
concurrent coplanar force system shown in Figure 1.4 .
Space diagram
(Not to scale)
F5 = 3N
F4 = 10N F3 = 6N
F2 = 8N
F1 = 5N
60° 60°
30°
Figure 1.4
When you resolve the forces into their horizontal and vertical components it is
essential to use the sign convention. A logical way is to draw up a table as follows
with the forces and their horizontal and vertical components, set out in rows and
columns.
Force Horizontal component Vertical component
F1 5 N 0 5.0 N
F2 8 N 8 cos 30 6.93 N 8 sin 30 4.0 N
F3 6 N 6 cos 30 3.0 N 6 sin 60 5.2 N
F4 10 N 10 cos 60 5.0 N 10 sin 60 8.66 N
F5 3 N 3.0 N 0
Totals FH 1.93 N FV 4.86 N