Mechanics - Сумський державний університет

liftdroveMechanics

Oct 24, 2013 (4 years and 2 months ago)

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Міністерство освіти і науки
,

молоді та спорту
України

Сумський державний університет










3186
Збірник текстів та завдань


з організації самостійного читання

з дисципліни «Англійська мова»


для студентів

спеціальності «Комп’ютерна механіка»

факультету
ТЕСЕТ

денної форми навчання


















Суми

Сумський державний університет

20
11

4


Збірник текстів та завдань

з організації самостійного читання з
дисципліни «Англійська мова»
/

у
кладач
Д. О. Марченко.


Суми

:
Сумський державний університет, 2011.


40 с.



Кафедра іноземних мов


































5


Mechanics

In its original sense, mechanics refers to the study of the behavior
of system under the action of forces. Statics deals with cases where the

forces either produce no motion or the motion is not of interest. Dynamics
deals properly with motions under forces. Mechanics is subdivided
according to the types of systems and phenomena involved.

An important distinction is based on the size of the
system. Those
systems that are large enough can be adequately described by the
Newtonian laws of classical mechanics. In this category, for example, are
celestial mechanics, the study of the motion of planets, stars, and other
heavenly bodies, and fluid me
chanics, which treats liquids and gases on a
macroscopic scale. Fluid mechanics is a part of a larger field called
continuum mechanics or (by some physicists) classical field theory,
involving any essentially continuous distribution of matter, whether rigi
d,
elastic, plastic, or fluid. On the other hand, the behavior of micro
scopic
system such as molecules

atoms, and nuclei can be interpreted only by the
concepts and mathematical methods of quantum mechanics.

From its inception, quantum mechanics had two ap
parentl
y
different mathematical forms


the wave mechanics of E. Schorodinger,
which emphasizes the spatial probability distributions in the quantum
states, and the matrix mechanics of W. Heisenberg, which emphasizes the
transitions between states. These
are now known to be equivalent.

Mechanics may also be classified as nonrelativistic or relativistic
mechanics, the latter applying to system with material velocities
comparable to the velocity of light. This distinction pertains to both
classical and quant
um mechanics.

Finally, statistical mechanics uses the methods of statistics for both
classical and quantum
systems containing ve
ry large numbers of similar
subsystems to obtain their

large
-
scale properties.


Words and word combinations

to deal with




мат
и

справу

з

property




властивість

motion





рух

fluid

mechanics



механіка

рідин

(
гідромеханіка
)

continuum

mechanics



механіка

суцільного

середовища

classical field theory



класична

теорія

поля

continuous

distribution

of

matter

безперервний

розподіл

матерії

to emphasize




підкреслювати

6


probability distribution


розподіл

ймовірностей

transition




перехід

to compare




порівнювати

velocity of light



швидкість

світла

to pertain




належати

similar





подібний

to obtain




отримати

large
-
scale




великомасштабний


Exercises

I. Read the text and decide if these statements are true or false:

1
.

Statics deals with motion studies under the action of forces.

2
.

Large systems can be described by the Newtonian laws.

3
.

Continuum mechanics is a part of a
larger field called fluid
mechanics.

4
.

E. Schorodinger is a progenitor of wave mechanics.

5
.

Relativistic mechanics describes systems with velocities
comparable to the velocity of sound.



II. Answer the questions:

1.

What cases does statics deal with?

2.

What theory can explain the behavior of microscopic system like
atoms and molecules?

3.

What does matrix mechanics of W. Heisenberg explain?

4.

How can mechanics be classified?

5.

Why does statistical mechanics use the methods of statistics?


III. Discuss

the following situations:

1
.

Tell about the difference between statics and dynamics.

2
.

Speak about the kinds of mechanics.

3
.

Compare the wave mechanics of Schorodinger and the matrix
mechanics of Heisenberg.








7


Dynamics

That branch of mechanics
which deals with the motion of a system
of

material particles under the influence of forces, especially those which
originate outside of the system

is

under consideration. From Newton's third
law of motion, namely, to every action there is an equal and opp
osite
reaction, the internal forces cancel in pairs and do not contribute to the
motion of the system as a whole, although they determine the relative
motion, if any, of the several parts.

Particle dynamics refers to the motion of a single particle under t
he
influence of external forces, particularly electromagnetic and gravitational
forces. The dynamics of a rigid body is the study of the motion, under
given forces, of a system of particles, the distances between which are
postulated to be constant through
out the motion.

In classical dynamics the basic relation that enables the motion to
be determined once the force is known is Newton's second law of motion,
which states that the resultant force on a particle is equal to the product of
the mass of the parti
cle times its acceleration. For a many
-
particle system it
becomes impracticable to write and solve this equation for each individual
particle and, in general, the motion may be computed only on a statistical
basis (that is, by the methods of statistical me
chanics) unless, as for a few
particles or a rigid body, the number of degrees of freedom is sufficiently
small.



Words and word combinations

under the influence of forces


під

впливом

сил

to originate




відбуватися

outside of the system



за

межами

системи

to considerate




розглядати

opposite reaction



протидія

internal




внутрішній

to contribute




сприяти

to determine




визначати

relative motion



відносний

рух

external




зовнішній

to postulate




бути
,
обумовлювати

resultant force




рівноді
й
н
а

сила

acceleration




прискорення

to compute




обчислювати

number of degrees of freedom

число

ступенів

свободи

8


Exercises

I. Read the text and decide if these statements are true or false:

1
.

Dynamics deals with the motion of a system of material
particles
without the influence of forces.

2
.

Newton's third law states that to every action is an equal and
opposite reaction.

3
.

Particle dynamics refers to the motion under the influence of
internal forces.

4
.

Electromagnetic and gravitational forces ar
e internal forces.

5
.

A many
-
particle system may be described and solved by Newton's
second law.


II. Answer the questions:

1.

How do the internal forces influence the motion of the whole
system according to Newton's third law?

2.

What forces does particle

dynamics deal with?

3.

What is the main postulate in dynamics of a rigid body?

4.

What does the basic relation in classical dynamics state?

5.

Why can Newton's second law equation not be solved?


III. Discuss the following situations:

1.

Compare the influ
ence of internal and external forces on the
system.

2.

Tell about the properties of a rigid body.

3.

Speak about the use of Newton's second law for a many
-
particle
system.


Continuum mechanics

Continuum mechanics is a branch of mechanics that deals with
the
analysis of the kinematics and mechanical behavior of materials modeled
as a continuum, i.e., solids and fluids (e.g., liquids and gases). A
continuum concept assumes that the substance of the body is distributed
throughout and completely fills the spa
ce it occupies.

Materials, such as solids, liquids and gases, are composed of
molecules separated by empty space. In a macroscopic scale, materials
have cracks and discontinuities. However, certain physical phenomena can
be modeled assuming the materials e
xist as a continuum, meaning the
matter in the body is continuously distributed and fills the entire region of
the
space it occupies. A continuum is a body that can be continually sub
-
9


divided into infinitesimal elements with properties being those of the b
ulk
material.

The concept of

a

continuum is a macroscopic physical model, and
its validity depends on the type of problem
s

and the scale of the physical
phenomena under consideration. A material may be assumed to be a
continuum when the distance between th
e physical particles is very small
compared to the dimension of the problem. For example, such is the case
when analyzing the deformation be
havior of soil deposits in soil
mechanics. A given volume of soil is composed of discrete solid particles
(grains) o
f minerals that are packed in a certain manner with voids between
them. In this sense, soils evade the definition of a continuum. To simplify
the deformation analysis of the soil, the volume of soil can be assumed to
be a continuum because the grain partic
les are very small compared to the
scale of the problem.

The continuum concept ignores the fact that matter is made of
atoms, is not continuous, and that it commonly has some sort of
heterogeneous microstructure, allowing the approximation of physical
quantities, such as energy and momentum, at the infinitesimal limit.
Differential equations can thus be employed in solving problems in
continuum mechanics. Some of these differential equations are specific to
the materials being investigated and are calle
d constitutive equations, while
others capture fundamental physical laws, such as the conservation of mass
(the continuity equation), the conservation of momentum (the equations of
motion and equilibrium), and the conservation of energy (the first law

of

t
hermodynamics).

Continuum mechanics deals with physical quantities of solids and
fluids which are independent of any particular coordinate system in which
they are observed. These physical quantities are then represented by
tensors, which are mathematical
objects that are independent of coordinate
system. These tensors can be expressed in coordinate systems for
computational convenience.


Words and word combinations

continuum




суцільне

середовище

kinematics




кінематика

macroscopic

scale



макроскопічний

рівень

crack





тріщина

discontinuity




розрив

bulk





об
'
єм

10


soil

deposits




ос
іда
ння

ґрунту

to

evade




не

піддаватися

heterogeneous

microstructure

різнорідна

мікроструктура

approximation




наближення

momentum




імпульс

infinitesimal




нескінченно

малий

constitutive

equation



базове

рівняння

to

capture




завоювати
,
захоплювати

conservation




збереження

continuity

equation



рівняння

нерозривності

equilibrium




рівновага

coordinate

system




система

координат

physical

quantity



фізична

величина

tensor





тензор



Exercises

I. Read the text and decide if these statements are true or false:

1.

The substance doesn't fill all the space of the body in
a
continuum
concept.

2.

The matter in the body is continuously distributed when there are
cracks and discontinuities in the macroscopic scale of material.

3.

According to the continuum concept the matter is made of atoms.

4.

Some of these differential equations are called constitutive
equations.

5.

Physical quantities are then represented by ma
thematical objects.



II. Answer the questions:

1.

What is base of appearance of a continuum?

2.

In what way do
es

a continuum interact with the soil?

3.

What are the main factors which influence on the continuum?

4.

What does the main idea of a continuum s
tand for?

5.

What is the purpose of differential equation?



III. Discuss the following situations:

1.

Tell about the properties of molecules.

2.

Describe the material which may be assumed to be a continuum.

3.

Compare the coordinate systems you know.


11


Computational mechanics

Mechanics is the branch of physics concerned with the behaviour of
physical bodies when subjected to forces or displacements, and the
subsequent effect of the bodies on their environment. The discipline has its
roots in several anci
ent civilizations.

Computational mechanics emphasizes the development of
mathematical models representing physical phenomena including the
application of modern computing methods to analyze these phenomena. It
draws on the disciplines of physics,
mechanics, mathematics and computer
science, and encompasses numerical methods for application to various
civil engineering problems. Numerous application areas are being
investigated including constitutive modeling for structural and
geomaterials, advance
d computational methods for structural dynamics
problems, soil
-
structure interaction, and simulation of semiconductor
devices.

Work in computational mechanics is concerned with developing
numerical modeling and solution procedures for a broad variety of ph
ysical
problems in structural and geotechnical analysis. The general scope of this
work includes fundamental studies of the accuracy, stability, and efficiency
of finite element methods and finite difference techniques, as well as the
development of new cl
asses of methods. This work is important not only
for its utility in analysis and design, but also because it can develop
valuable tools for studying the fundamental mechanisms of complex and
often nonlinear phenomena important in many engineering problems
.

Some examples of research presently being undertaken in computational
mechanics include the development of new stabilized finite element
methods for transient dynamic analysis of fluid
-
soil
-
structure systems,
mathematical formulation and modeling of high
-
gradient problems in solid
mechanics, application of elastic and inelastic fracture mechanics to steel
structures, modeling of large deformation and instability in inelastic
materials, and multiscale modeling via the finite element method. Research
being
undertaken in the area of structural mechanics includes the
development of constitutive models for new high performance materials
such as ductile fiber
-
reinforced concrete, modeling of time
-
dependent
response including durability of advanced fiber
-
reinforc
ed composites, and
modeling of nonlinear response of structural systems that use high
performance composite materials. Emphasis is placed on developing
models that are based on micro
-
structural behavior and can be applied
efficiently to large
-
scale infrast
ructure simulations. In computational
12


plasticity, various numerical integration algorithms are currently being
developed for application to complex plasticity models such as those
encountered in geomechanics. Specific problems of interest include
damage an
d strain localization in metals, concrete, soils, and rocks, and
liquefaction instability in saturated granular materials.

In order for a computational technique to be competitive, it is
essential to consider not only the discretization procedure (e.g. fin
ite
elements), but also how the equations will be solved. While it is generally
acknowledged that parallel supercomputing offers considerable promise
for solving very large problems of practical interest, it is important to
recognize that new algorithms an
d data structures have to be developed to
exploit the new discretization methods and also to attack the intrinsic
difficulties of the physical problem being addressed. Adaptive solution
schemes based on error estimation also provide unique challenges for
s
olver technology. Current work in our group related to parallel and
distributed computing involves the development of new solution
algorithms for statics and dynamics problems, it is expected that research
in this area will continue to grow, as evidenced b
y the explosion of new
parallel computers, and networked workstations available in the last few
years. Philosophically, the objective of research in this area is to reexamine
traditional ways of thinking about computational mechanics and strategies
that wi
ll enable full utilization of state of the art computer technology.

We view this research area as a solution to problems usually faced by
engineers when dealing with very sophisticated analysis codes, and
involves the development of an intelligent front
-
en
d interface that can
guide the engineer to properly model the problem and select the
appropriate type of analysis procedure using applications which can easily
be understood, this computational mechanics issue is design
-
oriented and
can be suitably integra
ted in the form of geometric modeling, database
management, CAD, knowledge
-
based pre
-

and post
-

processors, and
adaptive methods.


Words and word combinations

constitutive modeling

конститутивне

моделювання

structural dynamics


динаміка

конструкції

soil
-
structure interaction

взаємодія

ґрунту

з

конструкцією

semiconductor device


напівпровідниковий

пристрій

to concern




пов
'
язувати

scope





сфера

діяльності

13


accuracy




точність

stability




стійкість

finite element method

метод

скінчених

елементів

finite difference technique

метод

скінчених

різниць

fracture mechanics


механіка

руйнувань

ductile




в
'
язкий

fiber
-
reinforce
d



волокноармований

concrete




бетон

durability




міцність

strain localization



локалізація

деформації


rock





порода

saturated granular material

насичений

сипучий

матеріал

error estimation


оцінка

похибки

to evidence



свідчити

response




реакція


Exercises

I. Read the text and decide if these statements are true or false:

1.

Mechanics is a science concerned with
forces and displacements.

2.

Transient dynamic analysis needed new stabilised finite element
methods.

3.

Ductile fiber
-
reinforced concrete is a high performance material.

4.

Finite element methods are not used for solving engineering
problems in computatio
nal

mechanics.

5.

Computational mechanics is a completely new discipline.


II. Answer the questions:

1.

Why is the computation mechanics considered to be an integral part
of different investigation?

2.

What is the principal concept of computational mechani
cs?

3.

Where can the application of computational mechanics be bserved?

4.

What consequences of being incompetent are taken under
consideration?

5.

What tasks do
es

the computational mechanics solve?


III. Discuss the following situations:

1.

Compare
mathematical and dynamical models.

2.

Describe a finite element method.

3.

Tell about the numerical methods you know.

14


Turbulence

In fluid dynamics, turbulence or turbulent flow is a fluid regime
characterized by chaotic, stochastic property changes. This
includes low
momentum diffusion, high momentum convection, and rapid variation of
pressure and velocity in space and time. Flow that is not turbulent is called
laminar flow. While there is no theorem relating Reynolds number to
turbulence, flows with high
Reynolds numbers usually become turbulent,
while those with low Reynolds numbers usually remain laminar. For pipe
flow, a Reynolds number above about 4000 (
a

Reynolds number between
2100 and 4000 is known as transitional flow) will most likely be turbulent
.
At very low speeds the flow is laminar, i.e., the flow is smooth (though it
may involve vortices on a large scale). As the speed increases, at some
point the transition is made to turbulent flow. In turbulent flow, unsteady
vortices appear on many scales

and interact with each other. Drag due to
boundary layer skin friction increases. The structure and location of
boundary layer separation often changes, sometimes resulting in a
reduction of overall drag. Although laminar
-
turbulent transition is not
gover
ned by Reynolds number, the same transition occurs if the size of the
object is gradually increased, or the viscosity of the fluid is decreased, or if
the density of the fluid is increased.

Turbulence causes the formation of eddies. Most of the kinetic
ene
rgy of the turbulent motion is contained in the large scale structures.
The energy "cascades" from these large scale structures to smaller scale
structures by an inertia! and essentially inviscid mechanism. This process
continues, creating smaller and s
mal
ler structures which produce

a
hierarchy of eddies. Eventually this process creates structures that are
small enough that molecular diffusion becomes important and viscous
dissipation of energy finally takes place. The scale at which this happens is
the Ko
lmogorov length scale.

Turbulent diffusion is usually described by a turbulent diffusion
coefficient. This turbulent diffusion coefficient is defined in a
phenomenologica
l

sense, by analogy with the molecular diffusivities, but it
does not have a true phys
ical meaning, being dependent on the flow
conditions, and not a property of the fluid, itself. In addition, the turbulent
diffusivity concept assumes a constitutive relation between a turbulent flux
and the gradient of a mean variable similar to the relati
on between flux and
gradient that exists for molecular transport. In the best case, this
assumption is only an approximation. Nevertheless, the turbulent
diffusivity is the simplest approach for quantitative analysis of turbulent
15


flows, and many models hav
e been postulated to calculate it. For instance,
in large bodies of water like oceans this coefficient can be found using
Richardson's law and is governed by the random walk principle. In rivers
and large ocean currents, the diffusion coefficient is given
by variations of
Elder's formula.

When designing piping systems, turbulent flow requires a higher
input of energy from a pump than laminar flow. However, for applications
such as heat exchangers and reaction vessels, turbulent flow is essential for
good he
at transfer and mixing.

While it is possible to find some particular solutions of the Navier
-
Stokes equations governing fluid motion, all such solutions are unstable at
large Reynolds numbers. Sensitive dependence on the initial and boundary
conditions mak
es fluid flow irregular both in time and in space so that a
statistical description is needed. Russian mathematician Andrey
Kolmogorov proposed the first statistical theory of turbulence, based on
the aforementioned notion of the energy cascade (an idea or
iginally
introduced by Richardson) and the concept of self
-
similarity. It is now
known that the self
-
similarity is broken so the statistical description is
presently modified. Still, the complete description of turbulence remains
one of the unsolved proble
ms in physics. According to an apocryphal story
Werner Heisenberg was asked what he would ask God, given the
opportunity. His reply was: "When I meet God, I am going to ask him two
questions: Why relativity? And why turbulence? I really believe he wi
ll
hav
e an answer for the first
"
.

A similar witticism has been attributed to
Horace Lamb (who had published a noted text book on Hydrodynamics)



his choice being quantum electrodynamics (instead of relativity) and
turbulence. Lamb was quoted as saying in a spee
ch to the British
Association for the Advancement of Science, "I am an old man now, and
when I die and go to heaven there are two matters on which I hope for
enlightenment. One is quantum electrodynamics, and the other is the
turbulent motion of fluids. An
d about the former I am rathe
r optimistic
"
.


Words and word combinations

momentum diffusion



імпульсна

дифузія

smooth




однорідний
,
плавний

vortex





вихор


unsteady




нестаціонарний

interact




взаємодіяти

drag





опір

16


boundary layer


граничний

шар

reduction



скорочення
,
зменшення

eddy




вихор

viscous




в
'
язкий

molecular diffusion


молекулярна

дифузія

dissipation




дисипація
,
розсіяння

constitutive

relations



конститутивні

відносини

flux





потік

assumption




припущення

quantitative

analysis



кількісний

аналіз

to

require



потребувати
,
вимагати

heat

exchanger



теплообмінник

heat

transfer




теплообмін

self
-
similarity



самоподібність

hydrodynamics



гідродинаміка

quantum

electrodynamics


квантова

електродинаміка


Exercises

I. Read

the text and decide if these statements are true or false:

1.

Turbulent flow has high Reynolds numbers.

2.

Eddies are formed in the laminar flow.

3.

Turbulent diffusion coefficient does not depend on the flow
conditions.

4.

All particular solutions of the

Navier
-
Stokes equations are stable at
large Reynolds numbers.

5.

Werner Heisenberg proposed the first statistical theory of
turbulence



II. Answer the questions:

1.

What is understood by Laminar flow?

2.

What process is caused by means of turbulence?

3.

What do
es

the turbulence diffusion stand for?

4.

Where can the diffusion coefficient be observed?

5.

What are the reasons of the turbulence

statistical description?


III. Discuss the following situations:

1.

Try to describe turbulent and laminar flows.

2.

Tell about a Reynolds number and its properties.

3.

Speak about the kinds of energy you know.

17


ADDITIONAL TEXTS


Bearings

A bearing is a device to allow constrained relative motion between
two or more parts, typically rotation or linear movement. Bearings
may be
classified broadly according to the motions they allow and according to
their principle of operation as well as by the directions of applied loads
they can handle.

Reducing friction in bearings is often important for efficiency, to
reduce wear and t
o facilitate extended use at high speeds and to avoid
overheating and premature failure of the bearing. Essentially, a bearing can
reduce friction by virtue of its shape, by its material, or by introducing and
containing fluid between surfaces or by separa
ting the surfaces with an
electromagnetic field.

Bearings vary greatly over the size and directions of forces that
they can support. Forces can be predominately radial, axial or
b
ending
moments perpendicular to the main axis.

There are many types of bearin
gs, with varying shape, material,
lubrication, principal of operation, and so on.

Plain bearings use surfaces in rubbing contact, often with a
lubricant such as oil or graphite. A plain bearing may or may not be a
discrete device. It may be nothing more th
an the bearing surface of a hole
with a shaft passing through it, or of a planar surface that bears another (in
these cases, not a discrete device); or it may be a layer of bearing metal
either fused to the substrate (semi
-
discrete) or in the form of a sep
arable
sleeve (discrete). With suitable lubrication, plain bearings often give
entirely acceptable accuracy, life, and friction at minimal cost. Therefore,
they are very widely used.

Ball bearings are probably the most common type of bearing
s
.
They are fou
nd in everything from inline skates to hard drives. These
bearings can handle both radial and thrust loads, and are usually found in
applications where the load is relatively small.

In a ball bearing, the load is transmitted from the outer race to the
ball
, and from the ball to the inner race. Since the ball is a sphere, it only
contacts the inner and outer race at a very small point, which helps it spin
very smoothly. But it also means that there is not very much contact area
holding that load, so if the b
earing is overloaded, the balls can deform or
squish, ruining the bearing.

18


Roller bearings are used in applications like conveyer belt rollers,
where they must hold heavy radial loads. In these bearings, the roller is a
cylinder, so the contact between the

inner and outer race is not a point but a
line. This spreads the load out over a larger area, allowing the bearing to
handle much greater loads than a ball bearing. However, this type of
bearing
s

is not designed to handle much thrust loading.

A variation
of this type of bearing
s
, called a needle bearing, uses
cylinders with a very small diameter. This allows the bearing to fit into
tight places.

Ball thrust bearings are mostly used for low
-
speed applications and
cannot handle much radial load. Barstools us
e this type of bearing.

Roller thrust bearings can support large thrust loads. They are often
found in gearsets like car transmissions between gears, and between the
housing and the rotating shafts. The helical gears used in most
transmissions have angled
teeth


this causes a thrust load that must be
supported by a bearing.

Tapered roller bearings can support large radial and large thrust
loads. Tapered roller bearings are used in car hubs, where they are usually
mounted in pairs facing opposite directions

so that they can handle thrust
in both directions.

Different bearing types have different operating speed limits. Speed
is typically specified as maximum relative surface speeds, often specified
ft/s or m/s. Generally there is considerable speed range ove
rlap between
bearing types. Plain bearings typically handle only lower speeds, rolling
element bearings are faster, followed by fluid bearings and finally
magnetic bearings which are limited ultimately by centripetal force
overcoming material strength.

The

oldest instance of the bearing principle dates to the Egyptians
when they used tree trunks under sleds. There are also Egyptian drawings
of bearings used with hand drills. The earliest recovered example of a
bearing is a wooden ball bearing supporting a r
otating table from the
remains of the Roman Nemi ships in Lake Nemi, Italy. The wrecks were
dated to 40 AD. Leonardo da Vinci is often credited with drawing the first
roller bearing around the year 1500. However, Agostino Ramelli is the first
to have publi
shed sketches of roller and thrust bearings.

Bearings saw use for holding wheel and axles. The bearings used
there were plain bearings that were used to greatly reduce friction over that
of dragging an object by making the friction act over a shorter dista
nce as
the wheel turned. Watch makers produced "jeweled" pocket watches using
19


sapphire plain bearings to reduce friction thus allowing more precise time
keeping.

Friedrich Fischer's idea from the year 1883 for milling and grinding
balls of equal size and e
xact roundness by means of a suitable production
machine formed the foundation for creation of an independent bearing
industry. Henry Timken, a 19th century visionary and innovator in carriage
manufacturing, patented the tapered roller bearing, in 1898. Th
e following
year, he formed a company to produce his innovation. Through a century,
the company grew to make bearings of all types, specialty steel and an
array of related products and services.

Today ball and roller bearings are used in many applications
which
include a rotating component. Examples include ultra high speed bearings
in dental drills, aerospace bearings in the Mars Rover, gearbox and wheel
bearings on automobiles, flexure bearings in optical alignment systems and
bicycle wheel hubs.


Combat
cavitation

To anyone who works with pumps, the symptoms of cavitation are
relatively familiar. They are a unique rumbling/rattling noise, and high
vibration levels. Closer inspection will also reveal pitting damage to the
impeller and a slight reduction in

the total head being developed by the
pump. In order to avoid or cure these problems consistently, it is important
to understand what cavitation really is and what causes it in a centrifugal
pump.

Cavitation is a two
-
part process caused by the changes in
pressure
as the liquid moves through the impeller. As the liquid enters the suction
nozzle of the pump and progresses through the impeller, there are a
number of pressure changes that take place (
f
igure 1).

As the liquid enters the pump through the suction

nozzle, the
pressure drops slightly. The liquid then moves into the eye of the rotating
impeller where an even more significant drop in pressure occurs. The first
part of the cavitation process occurs if the pressure falls below the liquid's
vapour pressu
re in the eye of the impeller. This causes vapour bubbles to
be created in that area (in other words, it boils!). The second part of the
process occurs as the centrifugal action of the impeller moves the bubbles
onto the vanes where they are instantly re
-
p
ressurized and thus collapsed in
a series of implosions.

While

such a single implosion would be insignificant, their
increasing
repetition and severity develop

energy levels well beyond the
20


yield strength of most impeller materials. At this stage, the impe
ller starts
to disintegrate and small cavities are created in the metal. This condition is
also responsible for the noise and high vibration levels mentioned earlier.
When considering
f
igure 1, it is evident that cavitation can be avoided or
stopped simply

by increasing the pressure of the liquid before it enters the
suction nozzle of the pump. This will ensure that the pressure in the eye
area does not fall below the vapour pressure, and therefore no vapour
bubbles will be created and no cavitation will ex
ist.

Much of the critical pressure drop that is created as the liquid
moves into the eye of the impeller can be attributed simply to the loss of
energy of a liquid moving from a static environment (the pump suction) to
a dynamic environment in the rotating

impeller. However, other design
factors may occasionally play a part, such as the entrance angles of the
impeller vanes as they relate to the velocity of the liquid.





Figure 1


Pressure changes in the pump




There is a tendency in many areas to try
to combat cavitation by
reducing the NPSH (net positive suction head) required by the pump. It is
worthwhile to realize that, to accomplish this, there are only a limited
number of possibilities. Two of these require significant hydraulic design
changes to

the impeller's eye, while the others require the installation of at
21


least one new pump. Therefore to stop cavitation in most instances, the
only really practical solution is to increase the NPSH available (NPSHA)
from the system.

The NPSH available from t
he system comprises only four absolute
values (
f
igure 2).

NPSH A = Hs + Ha


Hvp


Hf;

where: Hs is the static head over the impeller centreline;


Ha is the head on the surface of the liquid in the suction tank;


Hvp equals the vapour pressure of the l
iquid;


Hf is the friction losses in the suction line.

In the simple system shown it is apparent that, if a pump is
cavitating, we should strive to increase the first two factors in the equation,
and/or decrease the second two factors. It should be stres
sed that a huge
difference is not normally needed to eliminate cavitation. A few feet of
NPSH will usually be enough to stop cavitation. With this in mind, we can
consider the four factors as they relate to a typical pump inlet system.




Figure 2


Typical pump inlet system


As pump inlet piping is notoriously bad in the vast majority of
installations throughout the world, this is the area where significant
improvements can often be realized. However, the tendency to shorten the
22


length of suction pip
ing simply to reduce friction losses should be resisted
as it could deny the liquid the opportunity of a smooth flow path to the eye
of the impeller. This, in turn, could cause turbulence and result in air
entrainment difficulties that create the same symp
toms as cavitation. To
avoid this, the pump should be provided with a straight run of suction line
in a length equivalent to 5 to 10 times the diameter of the pipe. The smaller
multiplier should be used on the larger pipe diameters and vice versa.

The most

effective way of reducing the friction losses on the
suction side is to inrease the size of the line. Reduction in friction losses
can also be achieved even with the same line size by incorporating long
sweep elbows, changing valve types and reducing thei
r number.

Suction strainers that are left over from the commissioning stage of
a new plant can also be a problem. The blockage in the strainer basket
steadily increases the friction loss to an unacceptable level.

Air entrainment describes a variety of cond
itions where the vapour
bubbles are already in the liquid before it reaches the pump. When they
arrive in the eye of the impeller, exactly the same thing happens as if they
were created at that point. In other words, the vapour bubbles are subjected
to the

increasing pressure at the start of the vanes and are then imploded,
causing the identical damage as cavitation, and at the same location.

Vapour bubbles can be created in the system by a variety of
conditions:

-

f
ermenting liquids or foaming agents
;

-

l
i
quids operating close to their boiling point
;

-

t
urbulence in suction the supply tank or suction line.

The last of these can cause pockets of low pressure in the liquid
flow in which vaporization can occur. As air entrainment causes the same
pitting damage

to the impeller in precisely the same location as cavitation,
it can be a little confusing, particularly as both can occur simultaneously in
the same service. However, a quick comparison of the NPSHA and
NPSHR, combined with a visual review of the piping
characteristics, will
usually help identify the root cause of th
e so
-
called “cavitation”

and solve
the air entrainment problem.


23




Figure
3



Typical damage location in impeller


Solution of problem concerning elastohydrodynamic lubrication for
friction p
air of face packing seal

Among the contact seals, which are used for sealing shafts of
chemical and centrifugal pumps for general industrial purpose, the face
packing seals possess substantial advantages as for their technical and
economical activities.

To

increase life time and tightness of the face packing seals, it is
necessary to influence on distributing contact pressure in friction pair
through their design features. For this purpose, there is need in applying
the seal designs with a flexible bottom a
nd a special form of grooves in the
working surface of the supporting ring, providing for uniform distributing
and reducing contact pressure, and also decreasing leakages due to
hydrodynamic unloading and reverse pumping a portion of the stream from
the fr
iction pair into the medium to be sealed.

From the art, there are known publications on receaches of different
seal designs, foremost face and lip ones, wherein the principles of
hydrodynamic unloading for friction pair and reverse pumping of sealed
medium

are realized. The methods of numerical and analytical calculations
of such seals have been developed. The problem of hydroelasticity for the
24


flexible bearing with the shaft texture surface has been solved. Therefore
creating the calculation method procedu
re of various designs of the face
packing seals is enough an actual problem for today.

The face packing seal represents a mechanical face seal having a
friction pair, which consists of stationary supporting ring made of hard
material and flexible packing r
ing located in sleeve. In the friction pair,
under the action of preliminary compressive loads by springs and sealing
pressure force as well, there is created necessary contact load providing the
tightness of the sealing unit at the station. While the seal

operating, the
packing is wrung out from the supporting ring under the action of the
sealed pressure, and the external load is perceived substantially by
essentially smaller contact area at the outlet from the seal, which appears
considerably overloaded.
At the expense of deformation of flexible bottom
and under the action of axial load, there is provided redistribution and
alignment of the contact pressure over the width of the friction pair of the
face packing seal.

To create the additional hydrodynamic
unloading and reduce the
average contact pressure in the friction pair, in the surface of the
supporting ring, the grooves of two types are executed: grooves, which are
opened on the side of sealed medium to generate, as compared to the
sealed medium press
ure, the increased hydrodynamic pressure for
unloading the contact of the face packing seal friction pair; and closed
grooves, which due to compressing the flow in circumferential direction
provide for returning a portion of leakages back into the sealed c
hamber.
At compressing the sleeve with the packing to the supporting ring, the
packing deflects in the places of grooves with forming the necessary
profile on the contact surface. At the shaft rotation, this profile generates
excessive hydrodynamic pressur
e in the friction pair. It should be noted
that in the face packing seals, an additional hydrodynamic effect is
achieved due to the packing flexibility and extension of its surface layer.

To obtain hydrodynamic pressure distribution in the friction pair
be
tween the flexible packing and the supporting ring with the special
grooves, it is necessary jointly to resolve the Reynolds equation for a
viscous incompressible Newtonian fluid at laminar flow.

In this paper, to solve the hydroelasticity problem of face
packing
seal, the numerical possibilities of the Ansys Program were used. The
conjugate problem of Fluid Solid Interaction (FSI) was modeled. This
problem algorithm consists in the iterative calculation of separate problems
for fluid and deformed solid dom
ains. ANSYS Structural and CFX solvers
25


can be run both simultaneously and end
-
to
-
end at performing the inner
loop. The outer loop (MF Time Step) describes the process of conjugate
problem solution in time, and inner loops (Stagger Iteration) control
conver
gence of the ANSYS and CFX solutions and monitor the process of
data exchange. There is used an implicit procedure of conjugating two
solvers at solving FSI problem. In our case, in FSI, the dependent variables
are the displacement of the packing and the h
ydrodynamic pressure force
acting on the packing surface element.

The Navier
-
Stokes equations for the laminar isothermal flow of
incompressible fluid were solved in the ANSYS CFX Program. The
volume forces are neglected in the equations. There are consider
ed
constant viscous and density.

The numerical calculation results showed that in a static position,
without taking into account the action of the sealed medium pressure in the
gap, the packing is pressed by the external load to the supporting ring and,
as

a result of the deformation of the flexible bottom, there is the
redistribution of the contact pressure over the width of the friction pair of
the face packing seal occurs. Thus the contact pressure is increased on the
side of the sealed medium, and at th
e outlet of the seal, it is reduced. At the
joint action of the hydrodynamic pressure in the gap and the action of the
external load onto the seal sleeve, there is occurred aligning and reducing
the contact pressure in the friction pair. At the outlet of t
he grooves in the
convergent area of the gap to the direction of the motion, there is generated
excessive pressure to provide for the necessary load
-
carrying capacity of
the friction pair with minimum contact pressure and minimum leakages
corresponding to
the mixed friction condition.

In future, to create a calculation method for such seals, it is
necessary to take into account the mechanism of the mixed lubrication in
the friction pair, which is thoroughly developed for the contact seals in
works. To achie
ve maximal effect of hydrodynamic unloading and
upstream pumping in the friction pair, the analysis of grooves with
different geometry as well as optimization of their geometrical form are
required.



Cavitation

Cavitation is the formation of gas bubbles o
f a flowing liquid in a
region where the pressure of the liquid falls below its vapor pressure.
Cavitation is usually divided into t
wo classes of behavior: inertial

(or
transient) cavitation, and noninertial cavitation. Inertial cavitation is the
26


process w
here a void or bubble in a liquid rapidly collapses, producing a
shock wave. Such cavitation often occurs in control valves, pumps,
propellers, impellers, the strike of a mantis shrimp and in the vascular
tissues of plants. Noninertial cavitation is the pr
ocess in which a bubble in
a fluid is forced to oscillate in size or shape due to some form of energy
input, such as an acoustic field. Such cavitation is often employed in
ultrasonic cleaning baths and can also be observed in pumps, propellers,
etc.

Since

the shock waves formed by cavitation are strong enough to
significantly damage moving parts, cavitation is usually an undesirable
phenomenon. It is specifically avoided in the design of machines such as
turbines or propellers, and eliminating cavitation i
s a major field in the
study of fluid dynamics.




Figure 4


Cavitating propeller mod
el in a water tunnel experiment


27




Figure 5


High speed jet of
fluid impact on a fixed surface


Inertial

cavitation


Inertial cavitation was first studied by Lord
Rayleigh in the late
19th century, when he considered the collapse of a spherical void within a
liquid. When a volume of liquid is subjected to a sufficiently low pressure,
it may rupture and form a cavity. This phenomenon is termed cavitation
inception an
d may occur behind the blade of a rapidly rotating propeller or
on any surface vibrating underwater with sufficient amplitude and
acceleration. A fast
-
flowing river can cause cavitation on rock surfaces,
particularly when there is a drop
-
off, such as on a
waterfall.

Other ways of generating cavitation voids involve the local
deposition of energy, such as an intense focused laser pulse (optic
cavitation) or with an electrical discharge through a spark. Vapor gases
evaporate into the cavity from the
surrounding medium; thus, the cavity is
not a perfect vacuum, but has a relatively low gas pressure. Such a low
-
pressure cavitation bubble in a liquid begins to collapse due to the higher
pressure of the surrounding medium. As the bubble collapses, the pre
ssure
and temperature of the vapor within increases. The bubble eventually
collapses to a minute fraction of its original size, at which point the gas
within dissipates into the surrounding liquid via a rather violent
mechanism, which releases a significan
t amount of energy in the form of
an acoustic shock wave and as visible light. At the point of total collapse,
the temperature of the vapor within the bubble may be several thousand
kelvin, and the pressure several hundred atmospheres.

Inertial cavitation
can also occur in the presence of an acoustic
field. Microscopic gas bubbles that are generally present in a liquid will be
forced to oscillate due to an applied acoustic field. If the acoustic intensity
is sufficiently high, the bubbles will first grow in

size and then rapidly
collapse. Hence, inertial cavitation can occur even if the rarefaction in the
28


liquid is insufficient for a Rayleigh like void to occur. High
-
power
ultrasonics usually utilize the inertial cavitation of microscopic vacuum
bubbles for
treatment of surfaces, liquids, and slurries.

The physical process of cavitation inception is similar to boiling.
The major difference between the two is the thermodynamic paths that
precede the formation of the vapor. Boiling occurs when the local vapor
p
ressure of the liquid rises above its local ambient pressure and sufficient
energy is present to cause the phase change to a gas. Cavitation inception
occurs when the local pressure falls sufficiently far below the saturated
vapor pressure, a value given b
y the tensile strength of the liquid.

In order for cavitation inception to occur, the cavitation "bubbles"
generally need a surface on which they can nucleate. This surface can be
provided by the sides of a container, by impurities in the liquid, or by sma
ll
undissolved microbubbles within the liquid. It is generally accepted that
hydrophobic surfaces stabilize small bubbles. These pre
-
existing bubbles
start to grow unbounded when they are exposed to a pressure below the
threshold pressure, termed Blake's t
hreshold.

The vapor pressure here differs from the meteorological definition
of vapor pressure, which describes the partial pressure of water in the
atmosphere at some value less than 100% saturation. Vapor pressure as
relating to cavitation refers to the
vapor pressure in equilibrium conditions
and can therefore be more accurately defined as the equilibrium (or
saturated) vapor pressure.


Noninertial cavitation

Noninertial cavitation is the process in which small bubbles in a
liquid are forced to oscillate

in the presence of an acoustic field, when the
intensity of the acoustic field is insufficient to cause total bubble collapse.
This form of cavitation causes significantly less erosion than inertial
cavitation, and is often used for the cleaning of delica
te materials, such as
silicon wafers.


Cavitation damage

Cavitation is, in many cases, an undesirable occurrence. In devices
such as propellers and pumps, cavitation causes a great deal of noise,
damage to components, vibrations, and a loss of efficiency.

When the cavitation bubbles collapse, they force energetic liquid
into very small volumes, thereby creating spots of high temperature and
emitting shock waves, the latter of which are a source of noise. The noise
29


created by cavitation is a particular probl
em for military submarines, as it
increases the chances of being detected by passive sonar.

Although the collapse of a cavity is a relatively low
-
energy event,
highly localized collapses can erode metals, such as steel, over time. The
pitting caused by the

collapse of cavities produces great wear on
components and can dramatically shorten a propeller or pump's lifetime.

After a surface is initially affected by cavitation, it tends to erode at
an accelerating pace. The cavitation pits increase the turbulence

of the fluid
flow and create crevasses that act as nucleation sites for additional
cavitation bubbles. The pits also increase the components' surface area and
leave behind residual stresses. This makes the surface more prone to stress
corrosion.




Figure 6


Cavitation damages on a valve plate for an axial piston
hydraulic pump


30




Figure 7


Cavitation damage

to a Francis turbine



Figure 8


Cavitation
p
ropeller
d
amage

31


Hydr
o
dynamic cavitation

Hydrodynamic cavitation describes the process of
vaporisation,
bubble generation and bubble implosion which occurs in a flowing liquid
as a result of a decrease and subsequent increase in pressure. Cavitation
will only occur if the pressure declines to some point below the saturated
vapor pressure of the

liquid. In pipe systems, cavitation typically occurs
either as the result of an increase in the kinetic energy (through an area
constriction) or an increase in the pipe elevation.

Hydrodynamic cavitation can be produced by passing a liquid
through a const
ricted channel at a specific velocity or by mechanical
rotation through a liquid. In the case of the constricted channel and based
on the specific (or unique) geometry of the system, the combination of
pressure and kinetic energy can be created when the hy
drodynamic
cavitation cavern
s

downstream of the local constriction generating high
energy cavitation bubbles.

The process of bubble generation, subsequent growth and collapse
of the cavitation bubbles results in very high energy densities, resulting in
ver
y high temperatures and pressures at the surface of the bubbles for a
very short time. The overall liquid medium environment, therefore,
remains at ambient conditions. When uncontrolled, cavitation is damaging;
however, by controlling the flow of the cavit
ation the power is harnessed
and non
-
destructive. Controlled cavitation can be used to enhance chemical
reactions or propagate certain unexpected reactions because free radicals
are generated in the process due to disassociation of vapors trapped in the
ca
vitating bubbles.



Vibration

Passive vibration isolation systems consist essentially of a mass,
spring and damper (dash
-
pot).

Negative
-
Stiffness Vibration Isolator

Negative
-
Stiffness
-
Mechanism (NSM) vibration isolation systems
offer a unique passive appr
oach for achieving low vibration environments
and isolation against sub
-
Hertz vibrations. "Snap
-
through" or "over
-
center"
NSM devices are used to reduce the stiffness of elastic suspensions and
create compact six
-
degree
-
of
-
freedom systems with low natural
frequencies. Practical systems with vertical and horizontal natural
frequencies as low as 0.2 to 0.5 Hz provide isolation efficiencies one to
two orders of magnitude better than top
-
performance air tables and
pneumatic isolation systems. Electro
-
mechanical

auto
-
adjust mechanisms
32


compensate for varying weight loads and provide automatic leveling in
multiple
-
isolator systems, similar to the function of leveling valves in
pneumatic systems. All
-
metal systems can be configured which are
compatible with high vac
uums and other adverse environments such as
high temperatures.

These isolation systems enable vibration
-
sensitive instruments such
as scanning probe microscopes, micro
-
hardness testers and scanning
electron microscopes to operate in severe vibration enviro
nments
sometimes encountered, for example, on upper floors of buildings and in
clean rooms. Such operation would not be practical with pneumatic
isolation systems. Similarly, they enable vibration
-
sensitive instruments to
produce better images and data tha
n those achievable with pneumatic
isolators. The theory of operation of NSM vibration isolation systems is
summarized, some typical systems and applications are described, and data
on measured performance is presented.


Vertical
-
Motion Isolation

A vertica
l
-
motion isolator is shown in
f
igure
9
. It uses a
conventional spring connected to an NSM consisting of two bars hinged at
the center, supported at their outer ends on pivots, and loaded in
compression by forces P. The spring is compressed by weight W to t
he
operating position of the isolator, as shown in
f
igure
9
. The stiffness of the
isolator is K

=

KS



KN where KS is the spring stiffness and KN is the
magnitude of a negative stiffness which is a function of the length of the
bars and the load P. The iso
lator stiffness can be made to approach zero
while the spring supports the weight W.



Figure 9


Vertical
-
Motion Isolator

33




A horizontal
-
motion isolator consisting of two
beam
-
columns is
illustrated in figure

10
. Each beam
-
column behaves like two
fixed
-
free
beam columns loaded axially by a weight load W. Without the weight load
the beam
-
columns have horizontal stiffness KS With the weight load the
lateral bending stiffness is reduced by the "beam
-
column" effect. This
behavior is equivalent to a hor
izontal spring combined with an NSM so
that the horizontal stiffness is K

=

KS



KN, and KN is the magnitude of
the beam
-
column effect. Horizontal stiffness can be made to approach zero
by loading the beam
-
columns to approach their critical buckling load.





Figure 10
-

Horizontal
-
Motion Isolator


Six
-
Degree
-
of
-
Freedom (six
-
DOF) Isolation

A six
-
DOF NSM isolator typically uses three isolators stacked in
series: a tilt
-
motion isolator on top of a horizontal
-
motion isolator on top of
a vertical
-
motion isolat
or.
f
igure
11

shows a schematic of a vibration
isolation system consisting of a weighted platform supported by a single
six
-
DOF isolator incorporating the isolators of
f
igures
9

and
10
. Flexures
are used in place of the hinged bars shown in
f
igure
9
. A til
t flexure serves
as the tilt
-
motion isolator. A vertical
-
stiffness adjustment screw is used to
adjust the compression force on the negative
-
stiffness flexures thereby
changing the vertical stiffness. A vertical load adjustment screw is used to
adjust for v
arying weight loads by raising or lowering the base of the
support spring to keep the flexures in their straight, unbent operating
position.


34




Figure 11


Schematic of Six
-
DOF Single
-
Isolator System



Figure 12


Vibration
-
isolation of supporting joint

35


The equipment and gears have joint with surrounding objects (the
supporting joint


with the support; the unsupporting joint


the pipe duct
or cable). Vibration
-
isolation of supporting joint is realized in the device
named vibration
-
isolator (absorber). O
n an illustration presented
dependence of difference is levels of vibrations which are measured before
installation of the functioning gear on vibration
-
isolator and after
installation in a wide range of frequencies.




Figure 13


Vibration
-
isolator



Vibration
-
isolator
is a

device that reflects and absorbs waves of
oscillatory energy, extending from the working gear or an electrical
equipment, with the aid of effect of a vibration insulation. Vibration
-
isolator is established between a body transferrin
g fluctuations and a body
which defend (for example, between the gear and the foundation). On an
illustration is presented the image vibration
-
isolator a series «B
И
» which
are applied in shipbuilding of Russia. Shown «B
И
» allow loadings 5, 40
and 300 kg. T
hey differ in the size
s, but have a similar structure
. In a
structure is used the rubber envelope, which is reinforced by a spring.
Rubber and a spring are strongly connected during transformation of crude
rubber into rubber envelope by a method of vulcani
zation. Under action of
36


weight loading of the gear the ru
bber envelope is of deformation
, and a
spring are compressed or stretch. Thus, in springs cross section, occurs the
twig twist with a material of rubber envelope, causing deformation of shift
in rubb
er envelope. It is known, that the vibration insulation basically
cannot be carried out without presence of vibration absorption. The size of
deformation of shift
in elastic material of isolator



vibration it basis for
definition of size of absorption of
fluctuations. At action of vibration or
shock loadings of deformation increase. Being thus cyclic, it considerably
strengthens efficiency of the given device. In the upper part of a design the
sleeve, and in the lower part a flange by means of which the vi
bration
-
isolator fastens to the gear and the foundation.

Vibration
-
isolation of unsupporting joint

Vibration
-
isolation of unsupporting joint is realized in the device
named branch pipe a of vibration
-
isolating.


Figure
14



V
ibration
-
isolating branch pipe


A vibration
-
isolating branch pipe is a part of a tube with elastic
walls for reflection and absorption of waves of the oscillatory energy
extending from the working pump over wall of the pipe duct. Is established
between the pump and the pipe duct. On an

illustration is presented the
image a vibration
-
isolating branch pipe of a series «
ВИПБ
». In a structure
is used the rubber envelope, which is reinforced by a spring. Properties of
an envelope are similar envelope to a vibration
-
isolator. Has the device
r
educing axial effort from action of internal pressure up to zero.

37


Another technique used to increase isolation is to use an isolated
subframe. This splits the system with an additional mass/spring/damper
system. This doubles the high frequency attenuation
rolloff, at the cost of
introducing additional low frequency modes which may cause the low
frequency behaviour to deteriorate. This is commonly used in the rear
suspensions of cars with Independent Rear Suspension (IRS), and in the
front subframes of some
cars. The graph (see illustration) shows the force
into the body for a subframe that is rigidly bolted to the body compared
with the red curve that shows a compliantly mounted subframe. Above 42
Hz the compliantly mounted subframe is superior, but below th
at
frequency the bolted in subframe is better.


Spectrum

A spectrum (plural spectra or spectrums) is a condition that is not
limited to a specific set of values but can vary infinitely within a
continuum. The word saw its first scientific use within the fi
eld of optics to
describe the rainbow of colors in visible light when separated using a
prism; it has since been applied by analogy to many fields other than
optics. Thus, one might talk about the spectrum of political opinion, or the
spectrum of activity
of a drug, or the autism spectrum. In these uses, values
within a spectrum may not be associated with precisely quantifiable
numbers or definitions. Such uses imply a broad range of conditions or
behaviors grouped together and studied under a single title
for ease of
discussion.



Figure 15


The spectrum in a rainbow

38


In Latin spectrum means "image" or "apparition", including the
meaning "spectre". It was used to convict a number of persons of
witchcraft at Salem, Massachusetts in the late 17th century. Th
e word
"spectrum" was strictly used to designate a ghostly optical afterimage by
Goethe in his Theory of Colors and Schopenhauer in On Vision and
Colors.

In the 17th century the word spectrum was introduced into optics,
referring to the range of colors obs
erved when white light was dispersed
through a prism. Soon the term referred to a plot of light intensity or power
as a function of frequency or wavelength, also known as a spectral density.

The term spectrum was soon applied to other waves, such as sound
waves, and now applies to any signal that can be decomposed into
frequency components. A spectrum is a usually 2
-
dimensional plot, of a
compound signal, depicting the components by another me
asure.
Sometimes, the word spectrum refers to the compound signal itself, such as
the "spectrum of visible light", a reference to those electromagnetic waves
which are visible to the human eye. Looking at light through a prism
separates visible light into
its colors according to wavelength. It separates
them according to its dispersion relation and a grating separates according
to the grating equation and if massive particles are measured often their
speed is measured. To get a spectrum, the measured functi
on has to be
transformed in their independent variable to frequencies and the dependent
variable has to be reduced in regions, where the independent variable is
stretched. For this imagine that the spectrum of pulse with a finite number
of particles is mea
sured on a film or a CCD. Assuming no particles are
lost, any nonlinearity (compared to frequency) on the spectral separation
concentrates particles at some points of the film. The same is true for
taking a spectrum by scanning a monochromator with a fixed

slit width.
Violet at one end has the shortest wavelength and red at the other end has
the longest wavelength of visible light. The colors in order are violet, blue,
green, yellow, orange, red. As the wavelengths get bigger below the red
visible light the
y become infrared, microwave, and radio. As the
wavelengths get smaller above violet light, they become ultra
-
violet,

X
-
ray, and gamma ray.

Spectrogram

A spectrogram is a time
-
varying spectral representation (forming an
image) that shows how the spe
ctral density of a signal varies with time. In
the field of time
-
frequency signal processing, it is one of the most popular
quadratic Time
-
Frequency Distribution that represents a signal in a joint
39


time
-
frequency domain and that has the property of being p
ositive. Also
known as spectral waterfalls, sonograms, voiceprints, or voicegrams,
spectrograms are used to identify phonetic sounds, to analyse the cries of
animals; they were also used in many other fields including music,
sonar/radar, speech processing,

seismology, etc. The instrument that
generates a spectrogram is called a spectrograph and is equivalent to a
sonograph.

The most common format is a graph with two geometric
dimensions: the horizontal axis represents time, the vertical axis is
frequency; a

third dimension indicating the amplitude of a particular
frequency at a particular time is represented by the intensity or colour of
each point in the image.

There are many variations of format: sometimes the vertical and
horizontal axes are switched, so
time runs up and down; sometimes the
amplitude is represented as the height of a 3D surface instead of color or
intensity. The frequency and amplitude axes can be either linear or
logarithmic, depending on what the graph is being used for. Audio would
usua
lly be represented with a logarithmic amplitude axis (probably in
decibels, or dB), and frequency would be linear to emphasize harmonic
relationships, or logarithmic to emphasize musical, tonal relationships.




Figure 16


3D surface spectrogram of a par
t from a music piece


Spectrograms are usually created in one of two ways: approximated
as a filterbank that results from a series of bandpass filters (this was the
only way before the advent of modern digital signal processing), or
calculated from the tim
e signal using the short
-
time Fourier transform
40


(STFT). These two methods actually form two different quadratic Time
-
Frequency Distributions, but are equivalent under some conditions.

The bandpass filters method usually uses analog processing to
divide the

input signal into frequency bands; the magnitude of each filter's
output controls a transducer that records the spectrogram as an image on
paper.

Creating a spectrogram using the STFT is usually a digital process.
Digitally sampled data, in the time domai
n, is broken up into chunks,
which usually overlap, and Fourier transformed to calculate the magnitude
of the frequency spectrum for each chunk. Each chunk then corresponds to
a vertical line in the image; a measurement of magnitude versus frequency
for a
specific moment in time. The spectrums or time plots are then "laid
side by side" to form the image or a three
-
dimensional surface.




Figure 17


Spectrogram of an FM signal (In this case the signal
frequency

is modulated with a
sinusoidal

frequency vs.
time profile)




41


Applications:

Early analog spectrograms were applied to a wide range of areas
including the study of bird calls, with current research continuing using
modern digital equipment and applied to all animal sounds. Contemporary
use of the
digital spectrogram is especially useful for studying frequency
modulation (FM) in animal calls. Specifically, the distinguishing
characteristics of FM chirps, broadband clicks, and social harmonizing are
most easily visualized with the spectrogram. A part
icularly interesting
example for the use of the spectrogram is in analysis of the vocalizations of
a pod of Dolphins.

Spectrograms are useful in assisting in overcoming speech defects
and in speech training for the portion of the population that is
profoundly
deaf.

The studies of phonetics and speech synthesis are often facilitated
through the use of spectrograms.

By reversing the process of producing a spectrogram, it is possible
to create a signal whose spectrogram is an arbitrary image. This techn
ique
can be used to hide a picture in a piece of audio and has been employed by
several electronic music artists. See also steganography.

Some modern music is created using spectrograms as an
intermediate medium; changing the intensity of different frequen
cies over
time, or even creating new ones, by drawing them and then inverse
transforming. See Audio timescale
-
pitch modification and Phase vocoder.

Spectrograms can be used to analyze the results of passing a test
signal through a signal processor such as
a filter in order to check its
performance.

High definition spectrograms are used in the development of RF
and microwave systems

Spectrograms are now used to display S
-
parameters measured with
vector network analyzers

The US Geological Survey now provides
real
-
time spectrogram
displays from seismic stations.