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c
Mechanical
Engineer’s
Reference
Book

Mechanical
Engineer’s
Reference
Book
Twelfth edition
Edited
by
FI
Mech
E
Head
of
Computing Services,
University
of
Central Lancashire
With specialist contributors
Edward
H.
Smith
BSC,
MSC,
P~D,

1999,2000
0
Reed Educational and Professional Publishing Limited
1994
All rights reserved.
No
part
of
this publication
may be reproduced in any material
form
(including
photocopying
or
storing in any medium by electronic
means and whether
or
not transiently or incidentally
to
some other use
of
this publication) without the
written permission
of
the copyright holder except
in accordance with the provisions
of
the Copyright,
Designs and Patents Act
1988

of
Congress
ISBN
0
7506
4218
1
Typeset by TecSet Ltd, Wallington, Surrey
Printed and bound in Great Britain by The Bath Press, Bath
~~
FOR EVERY
TIIU
THAT
WE
POBUSH,
EUI'IE8WORTH~HEW?MANR
WU
PAY
POR
BTCV
TO
PW
AN0
CARE
POR A
IREE.
Contents
Preface
8
Mechanics of solids

.
Rolling element bearings
.
Materials for unlubricated sliding
.
Wear and surface
treatment
.
Fretting
.
Surface topography
.
References
.
Further reading
10
Power units and transmission
Power units
.
Power transmission
.
Further reading
11
Fuels and combustion
Introduction
.
Major fuel groupings
.
Combustion
.

Heat transfer
.
References
2
Electrical and electronics principles
Basic electrica! technology
.
Electrical machines
.
Analogue
and digital electronics theory
.
Electrical safety
References
.
Further reading
3
Microprocessors, instrumentation and control
Summary of number systems
.
Microprocessors
.
Communication standards
.
Interfacing of computers to
systems
.
Instrumentation
.
Classical control theory and

Categories of
computer systems
Central processor unit
.
Memory
.
Peripherals
.
Output devices
.
Terminals
.
Direct input
.
Disk storage
.
Digital and analogue inputloutput
.
Data
communications
.
Computer networks
.
Data terminal
equipment
.
Software
.
Database management
.

References
roperties and selection
Engineering properties
of
materials
.
The principles
underlying materials selection
.
Ferrous metals
.
Non-ferrous metals
.
Composites
.
Polymers
.
Elastomers
.
Engineering ceramics and glasses
.
Corrosion
.
Non-destructive testing
.
References
.
Further reading
12
Alternative energy sources

Introduction
.
Nuclear radiation and energy
.
Mechanical
engineering aspects of nuclear power stations and associated
plant
.
Other applications of nuclear radiation
.
Elements of
health physics and shielding
.
Further reading
14
Offshore engineering
Historical review
.
Types of fixed and floating structures
.
Future development
.
Hydrodynamic loading
.
Structural
strength and fatigue
.
Dynamics
of
floating systems

Large-chip metal removal
.
Metal forming
.
Welding,
soldering and brazing
.
Adhesives
.
Casting and foundry
practice
.
References
.
Further reading
17
Engineering mathematics
Trigonometric functions and general formulae
.
Calculus
.
Series and transforms
.
Matrices and determinants
.
Differential equations
.
Statistics
.
Further reading

of lead at work
.
The Electricity at Work Regulations 1989
.
The Noise at Work Regulations 1989
.
Safety of machines
.
Personal protective equipment
.
Manual handling
.
Further
reading
19
Units, symbols and constants
SI
units
.
Conversion to existing imperial terms
.
Abbreviations
.
Physical and chemical constants
.
Further
reading
Index
Preface
I

that the aims of the book
are met and its weight is minimized!
I
hope
I
have
been
able to
do this,
so
that the information is neither cursory nor complex.
Any book of this size will inevitably contain errors, but
I
hope these will be minimal.
I
will he pleased to receive any
information from readers
SO
that the book can
be
improved.
To
see
this book in print is a considerable personal achieve-
ment, but
I
could not have done this without the help
of
others. First,
I

BA, MA(Cantab)
Lecturer, Department
of
Engineering, University
of
Cambridge
Christopher Beards
BSc(Eng), PhD, CEng, MRAeS, MIOA
Consultant and technical author
Jonh
S.
Bevan
IEng, MPPlantE, ACIBSE
Formerly with British Telecom
Ronald
.J.
Blaen
Independent consultant
Tadeusz
2.
Bllazynski
PhD, BSc(Eng), MIMechE, CEng
Formerly Reader in Applied Plasticity, Department of
Mechanicaki Engineering, University
of
Leeds
James Carvill
WSc(MechE), BSc(E1ecEng)
Formerly Senior Lecturer in Mechanical Engineering,
University

Editor,
Materials and Manufacture
A.
Davi'es
National Centre of Tribology, Risley Nuclear Development
Laboratory
Raymond
J.
H.
Easton
CEng, MIR4echE
Chief Applications Engineer, James Walker
&
Co
Ltd
Philip
Eliades
BSc, AMIMechE
National Centre for Tribology, UKAEA, Risley,
Warrington
Duncan
S.
T.
Enright
BA: MA(Oxon), CertEd, GradInstP
Commissioning Editor, Butterworth-Heinemann, Oxford
Charles
J.
Fraser
BSc, PhD, CEng, FIMechE, MInstPet

Hntchinson
BSc, PhD, CEng, MICE
Deputy Head, Joining Technology Research Centre, School
of
Engineering, Oxford Brookes University
Jeffery
D.
Lewins
DSc(Eng), FINucE, CEng
Lecturer in Nuclear Engineering, University
of
Cambridge
and Director of Studies in Engineering and Management,
Magdalene College
Michael
W.
J.
Lewis
BSc, MSc
Senior Engineering Consultant, National Centre of
Tribology,
AE
Technology, Risley, Warrington
R. Ken Livesley
MA, PhD, MBCS
Lecturer Department of Engineering, University
of
Cambridge
J.
Cleland McVeigh

Engineering, Bolton Institute
Ben Noltingk BSc, PhD, CPhys, FInstP, CEng, FIEE
Consultant
Robert Paine BSc, MSc
Department of Engineering and Product Design, University
of Central Lancashire
John
R. Painter BSc(Eng), CEng, MRAes, CDipAF
Independent consultant (CAD/CAM)
Minoo
H.
Patel BSc(Eng), PhD, CEng, FIMechE, FRINA
Kennedy Professor of Mechanical Engineering and Head of
Department, University College, London
George E. Pritchard CEng, FCIBSE, FInst, FIPlantE
Consulting engineer
Donald B. Richardson MPhil, DIC, CEng, FIMechE, FIEE
Lecturer, Department of Mechanical and Manufacturing
Engineering, University of Brighton
Carl Riddiford MSc
Senior Technologist, MRPRA, Hertford
Ian Robertson MBCS
Change Management Consulatnt, Digital Equipment
Corporation
Roy Sharpe BSc, CEng,
FIM,
FInstP, FIQA, HonFInstNDT
Formerly Head
of
National Nondestructive Testing Centre,

C.
Webster BSc, MIEH
Roger Webster
&
Associates,
West
Bridgford, Nottingham
John
Weston-Hays
Managing Director, Noble Weston Hays Technical Services
Ltd, Dorking, Surrey
Leslie M. Wyatt FIM, CEng
Independent consultant and technical author
Mechanical
engineering
principles
Beards
(Section
I
.4.3)
Peter Tucker
(Section
i
.5
Dennis
H.
Bacon
(Sect
Contents
1.1

1/9
1.6.4 Work, heat, property values, procecs laws and
Further reading 1/15 1.6.5 Cycle analysis 1/37
British Standards 1/15
1.4
3
Random vibratio
Further reading 1/18
combustion 1/37

Strength
of
materials
113
i
=
ZSmg
.
zlZ6mg
where
Sm
is an element
of
mass at a distance
of
x,
y
or
z
from

w
then the following
relationship holds:
d2M
dF
dx2
dx
-W

Table
1.2
shows examples
of
bending moments. shear force
and maximum deflection for standard beams.
Bending equation:
If
a beam has two axes
of
symmetry in
the
xy
plane then the following equation holds:
MZIIz
=
EIRZ
=
dy
where
Mz

drawn, representing the system in space, with all the relevant
forces acting
on
that system.
Statics
of
rigid
bodies
When a set
of
forces act
on
a body they give rise to a resultant
force
or
moment or a combination of both. The situation may
be determined by considering three mutually perpendicular
directions on the ‘free body diagram’ and resolving the forces
and moment
in
these directions.
If
the three directions are
denoted by
n?
y
and
z
then the sum of forces may be
represented by

is
given by
The six conditions given in equations
(1.1)
and (1.2) satisfy
problems in three dimensions.
If
one
of
these dimensions is
not present (say: the
z
direction) the system reduces to
a
set of
cop1ana.r forces, and then
ZF,
=
.CM,
=
2My
=
0
are automatically satisfied, and the necessary conditions
of
equiiibrium
in
a two-dimensional system are
2Fx
=

(m)
of
the body:
W
=
mg,
where
g
is the acceleration due to gravity.
Centre
of
gravity:
This
is
a point, which may or may not be
within the body, at which the total weight
of
the body may be
considered to act as a single force. The position
of
the centre
of gravity may be found experimentally or by analysis. When
using analysis the moment
of
each element of weight, within
the body, about a fixed axis is equated to the moment
of
the
complete weight about that axis:
x

Rectangular area
yb:
Circular sector
gx
Slender rod
G
I
j
=
hi3
IGG
=
bh3136
I,,
=
bh3112
2r
sin
a
r4
1
3a
4
x
=
-__
I,,
=
-
(a

=
h14
I,,
=
3m3110
3m2
mh’
20
10
I,,
=
-
+
~
Torsion equation:
If
a circular shaft is subject to a torque
(T)
1.3
Dynamics
of
rigid
bodies
1.3.1
Basic definitions
1.3.1.1
Newton’s Laws
of
Motion
First Law

T
the shear stress
and
Y
the radius of the shaft.
Table
1.2
Dynamics
of
rigid
bodies
115
Second Law
The sum of all the external forces acting on a
particle
is
proportional to the rate
of
change of momentum.
Third Law
The forces
of
action and reaction between inter-
acting bodies are equal in magnitude and opposite in direc-
tion.
Newton's law
of
gravitation,
which governs the mutual
interaction between bodies, states

(m)
is a measure of the amount
of
matter present
in
a
body.
Velocity
is the rate
of
change of distance
(n)
with time
(t):
v
=
dxldt or
k
Acceleration
is the rate
of
change
of
velocity
(v)
with time
(4
:
a
=

=
m
dvldt, i.e. Force
=
mass
X
acceleration, and
it
is
measured in Newtons.
Impulse
(I)
is the product of the force and the time that
force acts. Since
I
=
Ft
=
mat
=
m(v2
-
vl),
impulse is also
said to be the change in momentum.
Energy:
There are several different forms
of
energy which
may exist in a system. These may be converted from one type

W
=
F
.
x.
Power (P)
is the rate of doing work with respect to time and
is measured in watts.
Moment
of
inertia
(I):
The moment of inertia is that
property in a rotational system which may be considered
equivalent
to
the mass in a translational system. It
is
defined
about an axis
xx
as
Ixx
=
Smx'
=
mk2m,
where
x
is

6
velocity
(0)
with time:
=
dwldt or d28/d$ or
0
Angular acceleration
(a)
is the rate
of
change
of
acgular
B
One concentrated load
W
MatA=
Wx,QatA=
W
M
greatest at
B,
and
=
WL
Q
uniform throughout
Maximum deflection
=

concentrated load at the
centre
oi
a beam
L-
Mat A
="(&
-
x),
22
Q
at A
=
W12
M
greatest at B
=
WLl4
Q
uniform throughout
Maximum deflection
=
WL3148El
at the centre
Uniform load
W
W
Q
at A
=

B
and
=
WLl12
Maximum deflection at
C
=
WL31384EI
One
concentrated load
W
Reaction
R
=
SWl16
M
maxiinum at
A,
and
=
3WLl16
M
at C
=
5WLl32
Maximum deflection is
LIVS
from
the free end, and
=

Both angular velocity and accleration are related to linear
motion by the equations
v
=
wx
and
a
=
LYX
(see Figure
1.2).
Torque
(T)
is the moment of force about the axis of
rotation:
T
=
IOU
A
torque may also be equal to a
couple,
which is two forces
equal in magnitude acting some distance apart in opposite
directions.
Parallel axis theorem:
if
IGG
is the moment
of
inertia

axes
x,
y
and
z
for a plane figure in the
xy
plane (see Figure
1.3)
then
Izz
=
Ixx
+
Iyy.
Angular momentum
(Ho)
of a body about a point
0
is the
moment of the linear momentum about that point and is
wZOo.
The angular momentum of a system remains constant unless
acted on by an external torque.
Angular impulse
is
the produce of torque by time, i.e.
angular impulse
=
Tt

to torque
is the rate of angular work with respect
to
time and is given by
Td0ldt
=
Tw.
Friction:
Whenever two surfaces, which remain in contact,
move one relative to the other there is a force which acts
tangentially to the surfaces
so
as to oppose motion. This is
known as the force of friction. The magnitude of this force is
pR,
where
R
is the normal reaction and
p
is a constant known
as the coefficient of friction. The coefficient of friction de-
pends
on
the nature
of
the surfaces in contact.
1.3.2
Linear and angular motion in
two
dimensions

4
=
w:
+
2a8
Variable acceleration:
If the acceleration is a function of
time then the area under the acceleration time curve repre-
sents the change in velocity.
If
the acceleration is a function of
displacement then the area under the acceleration distance
curve represents half the difference of the square of the
velocities (see Figure
1.4).
Curvilinear motion
is when both linear and angular motions
are present.
If a particle has a velocity
v
and an acceleration
a
then its
motion may be described
in
the following ways:
1.
Cartesian components
which represent the velocity and
acceleration along two mutually perpendicular axes

vdv
X
Figure
1.4
Dynamics
of
rigid bodies
1/7
Figure
1.5
I
Normal
vx
=
v
cos
6,
vy
=
v
sin
8,
ax
=
a
cos
+,
ay
:=
a

the
link
F
is
on
the slider
3.
Pobzr
coordinates:
see Figure 1.5(c):
vr
=
i,
"8
=
~8
a,
=
i
-
rV,
as
=
4
+
2i.i
1.3.3 Circular motion
Circular motion is a special case
of
curvilinear motion in which

A
is
moving with
a
different velocity to the end
B,
then the velocity
of
A
relative
to
B
is in a direction perpendicular
to
AB
(see
Figure
1.6).
When a block slides on a rotating link the velocity is made
up
of
two components, one being the velocity of the block
relative to the link and the other the velocity
of
the link.
Accelerations:
If
the link has an angular acceleration
01
then

Coriolis acceleration. The direction
of
Coriolis acceleration is
determined
by
rotating the sliding velocity vector through
90"
in
the diirection
of
the
link
angular velocity
w.
1.3.4
1.3.4.1
xyz
is a moving coordinate system, with
its
origin at
0
which
has a position vector
R,
a translational velocity vector
R
and
an
angular velocity vector
w

Figure
1.6
r
=
1
+
pr
+
w x
p
r
=
R
+
w
x
p
+
w
x
(w
x
p)
+
2w
x
p,
+
pr
where

ir;
2.
3.
and
r
is the sum
of:
1.
The relative acceleration
Br;
2.
3.
4.
5.
The absolute velocity
R
of the moving origin
0;
The velocity
w
x
p
due to the angular velocity
of
the
moving axes
xyz.
The absolute acceleration
R
of

due
to
the inter-
action of coordinate angular velocity and relative velocity.
1/8
Mechanical engineering principles
1.3.6
Balancing
of
rotating
masses
't
1.3.6.1
Single out-of-balance
mass
P
Y
Figure
1.7
V
Precession axis
Spin
5%
axis
One mass
(m)
at a distance
r
from the centre of rotation and
rotating at a constant angular velocity

and angles
(el,
e,,
. .
.
)
(see Figure
1.9)
then the balancing
mass
M
must be placed at a radius
R
such that
MR
is
the vector
sum of all the
mr
terms.
1.3.6.3 Masses in different transverse planes
If
the balancing mass in the case of a single out-of-balance
mass were placed in a different plane then the centrifugal force
would be balanced. This is known as
static balancing.
However, the moment of the balancing mass about the
't
axis
X

on
the axle to form a torque
T,
whose vector is along
the
x
axis, will produce a rotation about the
y
axis. This is
known as precession, and it has an angular velocity
0.
It
is
also
the case that
if
the rotor is precessed then a torque Twill be
produced, where
T
is given by
T
=
IXxwf2.
When this is
observed it is the effect
of
gyroscopic reaction torque that is
seen, which is in the opposite direction to the gyroscopic
torq~e.~
1.3.5

also
ZM~
=
Zrnw2r
sin
e
.
a
=
o
zMy
=
Crnw2r
cos
e
.a
=
0
Figure
1.10
Vibrations
119
1.4
Vibrations
1.4.1
Single-degree-of-freedom systems
The term degrees of freedom in an elastic vibrating system
is
the number
of

is
known as dynamic
unbalan,ce.
To overcome this, the vector sum
of
all the moments about
the reference plane must also be zero.
In
general, this requires
two
masses placed in convenient planes (see Figure 1.10).
1.3.6.4
Balancing
of
reciprocating masses in single-cylinder
machines
The accderation
of
a piston-as shown in Figure 1.11 may be
represented by the equation>
i
=
-w’r[cos
B
+
(1in)cos
28
+
(Mn)
(cos

as the secondary force. Partial primary
balance
is
achieved in a single-cylinder machine by an extra
mass
M
at a radius
R
rotating at the crankshaft speed. Partial
secondary balance could be achieved by a mass rotating at
2w.
As
this is not practical this
is
not attempted. When partial
primary balance is attempted a transverse component
Mw’Rsin
B
is
introduced. The values of
M
and
R
are chosen to
produce a compromise between the reciprocating and the
transvense components.
1.3.6.5
When considering multi-cylinder machines account must be
taken
of

F
=
Zm,w2(r/n) cos 20
=
&~(2w)~(r/4n) cos 20
=
o
and
M
=
Sm(2~)~(r/4n) cos 20
.
a
=
0
The addition
of
extra masses to give secondary balance is not
attempted in practical situations.
Balancing of reciprocating masses in multi-cylinder
machines
Y>
W
I
Mass
m
\
1R
\
LM

-
-
ww2y/g
=
0
dx4
where
o
is the natural frequency. The general solution of this
equation is given by
y
=
A
cos
px
+
B sin
px
+
C
cosh
px
+
D
sinh
px
where
p”
=
ww2igEI.

of vibration of the beam due to its weight alone
is
found
(fo).
*
Consider the equation
of
motion
for
an
undamped system (Figure
1.13):
dzx
d?
rn +lur=O
but
Therefore equation
(1.4)
becomes
Integrating gives
krn
($)’+’,?
2
=
Constant
the term &(dx/dt)* represents the kinetic energy and
&xz
the
potential energy.
1/10

y‘
=
0
x
=
0,
y
=
0,
y‘
=
0
COS
pl
.
cash
pl
=
-1
1.875 4.694 7.855
x
=
1,
y“
=
0,
y”’
=
0
x

tanh
Pl
3.927 7.069
10.210
Then the natural frequency of vibration
of
the complete
system
U,
is given by
11111
1
-
+-+-+-+
_-_
f2
f;
f?
f:
fS
fi
(see reference
7
for a more detailed explanation).
Whirling of shafts:
If
the speed
of
a shaft or rotor is slowly
increased from rest there will be a speed where the deflection

-1)
When
(k/mw2)
=
1, y
is
then infinite and the shaft is said to be
at its critical whirling speed
wc.
At any other angular velocity
w
the deflection
y
is given by
When
w
<
w,,
y
is the same sign as
e
and as
w
increases
towards
wc
the deflection theoretically approaches infinity.
When
w
>

8
the angular displacement and
m
by
I,
the moment
of
inertia.
1.4.1.2
Undamped
free
vibrations
The equation of motion is given by
mi!
+
kx
=
0 or
x
+
wix
=
0,
where
m
is the mass,
k
the stiffness and
w:
=

T
=
2?r/w,.
1.4.1.3
Damped free vibrations
The equation of motion is given by
mi!
+
d
+
kx
=
0
(see
Figure
1.14),
where
c
is the viscous damping coefficient, or
x
+
(c/m).i
+
OJ;X
=
0.
The solution to this equation and the
resulting motion depends
on
the amount of damping.

to
a
disturbance by returning to its equilibrium
position in the shortest possible time. In this case (see Figure
1.15(b))
=
e-(c/2m)r(A+Br)
where
A
and
B
are constants.
If
c
<
2mw,
the system has a
transient oscillatory motion given by
=
e-(</2m)r
[C
sin(w;
-
c2i4m2)’”t
+
cos
w:
-
~~/4m~)”~t]
where

of
any
two
successive amplitudes (see Figure
1.16):
6
=
log&1/x2)
c
=
Zmw,
Figure 1.15
where
x
is given by
x
=
ecnm sin
[(J
Therefore
112
=
cr12rn
If
the amount
of
damping present
is
small compared to the
where

F\
\
I
.
t
4
/
/
/
/
Figure
1.16
1.4.1.5
Forced undamped vibrations
The equation
of
motion is given by (see Figure 1.17)
mx
+
kx
=
Fo
sin
wt
or
x
+
w,2
=
(Fdm)

sin
wt
Fo
sin
at
(a)
Figure
1.17
The term
wt/(w;
-
w2)
is
known
as the dynamic magnifier
and it gives the ratio of the amplitude
of
the vibration to the
static deflection under the load
Fo.
When
w
=
on
the ampli-
tude becomes infinite and resonance is said to occur.
1.4.1.6
Forced damped vibrations
The equation of motion is given by (see Figure 1.17(b))
mx

The term
sin(ot
-
4
[(wt
-
w2)’
+
(c~/m)]~]~’~
is called the dynamic magnifier. Resonance occurs when
w
=
w,.
As
the damping is increased the value of
w
for which
resonance occurs is reduced. There is also a phase shift as
w
increases tending to a maximum
of
7~
radians. It can be seen in
Figure 1.18(a) that when the forcing frequency is high com-
pared to the natural frequency the amplitude
of
vibration is
minimized.
1.4.1.7
Forced damped vibrations due

-
MJ)2
+
(cw)2]
In representing this information graphically it is convenient to
plot
MXlme
against
wlw,
for various levels of damping (see
Figure l.20(a)). From this figure it can be seen that for small
values of
w
the displacement is small, and as
w
is increased the
displacement reaches a maximum when
w
is slightly greater
than
w,.
As
w
is further increased the displacement tends to a
constant value such that the centre
of
gravity
of
the total mass
M

(cw)’
where
x
is the ampiitude of motion of the system.
1
k2
+
(cw)’
Vibrations
1/13
No
damping
I
Moderate damping
Figure
1.18
1
.o
2.0
3.0
Frequency ratio
(w/w,)
(a)
/
No
damping
Critical damping
1
2
3

Figure
1.20
Moderate damping
1.0
2.0
3.0
4.0
Frequency ratio
(w/w,)
(b)
m
Figure
1.19
Figure
1.21
1/14
Mechanical engineering principles
When this information is plotted as in Figure 1.22 it can be
seen that for very small values
of
w
the output amplitude Xis
equal to the input amplitude
Y.
As
w
is increased towards
w,
the output reaches a maximum. When
w

mf1
+
(kl
+
k2)xl
-
kzxz
=
0
m2Xz
+
(k3
+
k2)x2
-
kzxl
=
0
or in matrix form:
L
0
1
.o
0
d
////
//
/
/
///

vibration may be found along with the appropriate mode
shapes. This is a slow and tedious process, especially for
systems with large numbers of degrees of freedom, and is best
performed by a computer program.
1.4.2.2
The
Holtzer method
When only one degree
of
freedom is associated with each mass
in a multi-mass system then a solution can be found by
proceeding numerically from one end of the system to the
other.
If
the system is being forced to vibrate at a particular
frequency then there must be a specific external force
to
produce this situation. A frequency and a unit deflection is
assumed at the first mass and from this the inertia and spring
forces are calculated at the second mass. This process is
repeated until the force at the final mass is found.
If
this force
is zero then the assumed frequency is a natural frequency.
Computer analysis is most suitable for solving problems of this
type.
Consider several springs and masses as shown in Figure
1.24. Then with a unit deflection at the mass
ml
and an

m2w2x2,
thus iving the total force acting on the spring
Critical
1.0
d2
2.0
3.0
of
stiffness
k2
as
fmlw
4
+
m202xz}/kz.
Hence the displacement
Frequency ratio
(w/w,)
(a)
0
Low
damping
Moderate
1800w
1234 damping
Frequency ratio
(w/w,)
(
b)
~~~