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Namaskaram to all of you. We are going to talk about the subject mechanical measurements
which is one of the basic subjects for both engineers and scientists. Before we see how
the subject is important, we would like to see what these two words represent, before
we see mechanical let us see what are measurements.
A measurement is the process by which we assign a number to any parameter. What is a parameter?
Parameter is one which is surrounding us mainly feature, say it may be a displacement or any
atmospheric condition also say temperature or the pressure. When we say temperature is
too high or too low, people may not be able to appreciate how high or how low it is. So
it is important always that we assign a number, so the process of assigning a number to a
parameter is called measurement.
That is process of assigning a number to a feature, this is the process. Suppose we are
unable to give the number then what does it mean, then what we should do? We should say
probably the earlier man was also doing like that. He was telling that the weight is too
high or the distance is too much or the depth is too shallow. So that means he was telling
qualitatively that a parameter is high or low because probably he did not know how unique
by which you can measure a parameter. Later on we know for example, in length the standard
was accepted by all countries as meter. It is around 1889 that is at the end of the 19th
century the unit for distance is accepted for all countries that is the meter. What
is the meter according to the definition? Meter is a distance between 2 markings in
a bar.
That is something like a bar was there, even today it’s there somewhere near Paris, 2
markings was there. This bar is made up of a material which will not expand or contract.
It’s very stable material and in that 2 markings where made in which the marking looks
very thin and it was made and the distance between them is as agreed as 1 meter. Once
you have got a basic unit like this, any distance can easily be given a number in terms of meter.
That is multiplication of or sub multiple of this basic unit. That how we assign a number
to any distance, that is for a distance.
For example if you want to give a number for temperature, previously he was telling that
I cannot touch, it is too hot or ice is too cold. I cannot have it for so long; actually
it was called a qualitative statement. For assigning number what it was accepted is,
they measured the 0 to 100 degree water boiling. What is the total distance then divide it
into 100 parts and each part is the unit. So we call the temperature in terms of degree
centigrade so this is the basis of assigning a number. For assigning a number that means
you have to have a standard unless we have a standard we cannot assign a number. So 1
meter that is what was defined earlier but problem is we cannot go to Paris where the
standard is kept.
So in order to reproduce the distance in laboratories in 1960 they had another definition for meter.
That is so many wave lengths of krypton 86 whatever it is, an atomic resonance of that
with so many wave length, if you can make in a laboratory that distance is equal to
1 meter. But that is also a better version of that definition, which they got now around
1982. That is first one is 1889 and 1960, second definition. Now third definition for
meter is a distance traveled by light in a fraction of second that fraction is 1 over
3 into 10 to the power of something like that. So in that fraction of a second whatever the
light travels in vacuum that distance is 1 meter.
So that is now the basis for distance is we have time during the time whatever happens
for the light the distance traveled by the light is the unit for meter. Coincidentally
you will fine even today in Indian villages, people used to say how much distance one has
to walk. If you enquire somebody they may say, you walk through a better time, that
is time is taken as basis for telling distance. That is whatever we were using earlier in
our villages now that has become the basis for the most modern definition for displacement.
So thing is for making measurements we should have unit, without unit you cannot make measurements.
Similarly you have got unit for weight as Newton or for second we know there is again
second. In many wave lengths the duration is one second. So we have got standards for
different parameters. So measurements are the process of assigning number, numbers is
in terms of basic units. Now what is mechanical? Mechanical is telling the number of features
generally a mechanical engineer comes across. For example displacement, velocity, acceleration,
force, torque, flow, pressure, temperature, level etc. are the mechanical quantities.
Whereas in electrical engineering you have got current, voltage, electrical power, flux
density, gauss all these things are electrical quantities. So in order to differentiate the
field of measurements that pertains only to mechanical engineering we call the topic as
mechanical measurements. That is how the topic has evolved and under this topic we are going
to learn so many parameters and how important the topic is? How it is important for an engineer
or a scientist? For an engineer when he wants to select an instrument for measurement naturally
he should know how to select an instrument from the available instruments in the market
and for example if you want to make displace measurement there are about 10 or 20 different
type of instruments available where you have got different ranges, different accuracies
and working with different principals and among them if you want to select any one instrument
naturally you should know the characteristic of the instruments, so in that respect you
should learn the topics.
Secondly, not always the instrument is available in the market and some research purposes he
has to design his own instrument. Unless he knows the field of instrumentation the problem
of designing doesn’t arise at all. So it is very important for an engineer to know
the measurement topics either to select or to design himself the instrumentation. So
thus there is a necessity for an engineer or scientist to learn the topic. One more
point is how this field of instrumentation is important in engineering field?
If we take any power plant which processes 3 quantities, a power plant processes material,
energy and signal. These are the three quantities a power plant or any engineering system deals
with. How important these three quantities are? Now if you take a power plant itself,
we find material is coal which is to be transported at different stages. So from storage to cleaning,
to remove the foreign materials from coal and then it is to be transported to the top
of the furnace, blast or some furnace whatever it is.
So it has to be properly transported and also during transportation, it has to be measured
what is the flow rate. So any how the coal is to be handled properly that is one material
coal or oil whatever it is, depending upon the power plant. In a hydraulic plant, water
is to be properly transported and energy is to be extracted. These are the material dealt
by that power plant and energy. Now energy is converted from say chemical energy to electrical
energy that is what is being processed in a power plant. Chemical energy of the coal
is burnt in the furnace and then it is converted into heat energy that is being absorbed by
the steam and from steam it is made into mechanical energy by the engine and the engine drives
an alternator or generator and electrical power is made. So the energy is changed from
one form to another form.
Now what is signal? In both of the above cases signal plays a vital role. The size of the
coal which is being taken to the furnace should be a proper size of proper distribution and
it should be at particular flow rate, the measurement should be made that is signal.
Signal processing is nothing but measuring. What is the size? That is the signal, it is
to the measured and oil flow rate for different power generations, a water inlet to the turbine
should be controlled. So all these things controlling of different parameters is dealt
by signal also energy. Energy conversion, amount of energy that is coming out its also
measured how much energy we give inside and say if steam boiler is there in the power
plant then we see that pressure and temperature of the boiler should be maintained constant.
So control systems are based on the measurements or signal.
Unless we properly measure the size or the pressure or temperature of steam turbine or
steam boiler we cannot have the proper control over the energy output. So controlling the
temperature and controlling the pressure and all is achieved by control system which is
again based on measurement. In order to maintain a parameter at a particular level naturally
you have to measure that level unless we measure it, we cannot maintain it. Thus you find measurement
is the basis of any control system. How control system is important in these power
plants or any engines? Just like human body the nervous system is important for you to
actuate any muscles. Suppose I want to move my hand the signal comes from brain to the
muscle and then the muscle acts. That is the signal coming from the brain to the nervous
system. Similarly you find control system which measures and controls maintains every
parameter there is analogous to our nervous system. Suppose the nerve fails here in our
human system then muscle stop functioning. See this side of the brain controls all actions
on the opposite side, so when something happens due to accident you will find the other side
is paralyzed. That is signal is not taken which means the nervous system fail, the power
system fails or energy system fails.
Similarly you will find in a power plant when its control system fails, the whole power
plant stops that is the importance of control systems. Now control system is based on measurements
hence we find the topic of the measurement is very important. So this is the introduction
for the whole topic of mechanical measurements. Now we go into detail of some of the important
parameters.
Now we are going to see the device what is made use for the measurement. The device used
for measurement is called instrument. Instrument is the device used for measurement. Now what
is it made up of? The instrument is made up of so called basic functional element. It
is something like a brick which is used to build a big building. Big building is made
up of arranging bricks and joining them together. Similarly you will find the instrument also
is made up of by joining different basic functional element and here we have got different types
of such basic elements. What are they? One transducer, transformer, power amplifier,
converter, modulator, demodulator, differentiator, integrator, etc. What is the definition of the basic function element?
It is a unit when we divide further, you cannot do any function. That is it is a basic I mean
when we divide further for example if we take a lever mechanism.
We give input here we get output here; say xi is input xo is the output. The lever plus
the pivot is a unit, this is the lever and this is the pivot. Pivot is nothing but a
bearing; it allows the lever to tilt like this. So these two put together is the mechanism
which achieves the function of changing xi into xo. Suppose we have got lever edge here
1 mm here, 3 mm from here and any distance given say about 1 mm we give at xi it is made
into 3 mm at xo. This is the basic lever mechanism which you all know and in this case the lever
and pivot constitutes the basic functional element. If we divide it further what will
be there? Pivot will be in one place, lever will be in another place and it cannot achieve
any function, pivot and lever individually cannot do any function. So we can divide the
instruments until a basic unity is obtained which can achieve a function, if we divide
further it cannot achieve a function that is called basic functional element.
So we have got so many types in such a basic functional element. So many types and more
also in instrumentation and we are going to see what are these basic functional element,
what do they achieve when they are part of a big instrumentation. Now the transducer
is one which changes one physical quantity to another physical quantity. That is the transducer
changes one physical quantity to another physical quantity. For example a thermocouple. What
it does? It changes the temperature into a voltage. We know what is thermocouple, the
voltmeter is there and this is wire A, this is wire B the similar materials, homogeneous
material is immersed in one box T1 and another box T2. So temperature difference that is
temperature is converted or changed into a voltage.
That is the temperature quantity is changed into a voltage quantity. Hence it is a transducer,
a basic functional element. As per our definition can you divide this further? That is basic
function element is one which cannot be divided further. Suppose if we divide further what
will happen? Wire A will be different, B will be different they will not achieve; they will
not achieve any function. Hence the thermocouple pair is a basic functional element converting
the temperature quantity into a voltage quantity.
Similarly you find, we have spring. Second example we have spring. Spring is a single
unit, what it can achieve? It changes the force into a displacements say a spring is
there, you got spring and it is supported at the bottom, now you can apply a force and
when you apply a force what happens? It deforms into a shorter length. So much is the deformation,
deflection of the spring. That is what it achieves is, function is force is changed
into a displacement. Similarly you find spring; also you can use it for a reverse action.
That is we give you a displacement instead of a, you can also give d displacement and
you will realize a force that is reverse way. Force to displacement or displacement to force
both things are possible by using a spring. So such elements are called transducer that
is it changes one physical parameter into another physical parameter. Now what is the
transformer?
Transformer maintains a physical nature of the quantity same that is it changes magnitude
of the input parameter or input quantity. That is what it achieves, transformer the
signal is same or we say the quality is same, input say displacement typical example we
have already seen a lever. It is a displacement say d1 and converted into xo as d2. Here both
of them are displacement only but what has happened, the magnitude has changed from d1
to d2. So in transformer the physical quantity remains same and magnitude alone is changed
or increase or decrease whatever it is, magnitude is changed that is a transformer. A transformer
doesn’t change the physical nature of the signal; it changes only the magnitude of the
signal that is the transformer.
Third is power amplifier. What it achieves? In many instrumentation we find that energy
available at different stages of instrumentation, is not sufficient to actuate the next stage.
For example if you take a bourdon gauze somewhat like this bourdon tube where we can give pressure
signal, pressure as input and we find the closed end of the bourdon tube is moving in
this direction.
So normally what is done is it is taken through leverage like this and a gear is there and
pinion and it is moving over a scale. This is your working of bourdon gauze. Now we find
amount of energy available at the bourdon tube end is so small, you can use it only
for moving a pointer over a scale. Suppose you want to use this motion d to actuate a
valve, suppose bourdon gauze is used to control the flow of fuel in any power plant suppose
pressure increase in the boiler you have to reduce the fuel to the furnace. So naturally
you have to close the valve to reduce the flow into the furnace and if you want to connect
this signal itself directly to the valve naturally you will find valve is in the pipe line where
we require lot of energy.
The energy here is not sufficient to actuate that valve. In such instances what you should
do? You interpose or this is given to a power amplifier as input signal and power amplifier
puts lot of energy. Such a power amplifier, hydraulic power amplifier is such a one for
mechanical signal it’s just like a displacement signal. If you want to inject energy we go
for hydraulic power amplifier, by using a hydraulic power amplifier for small motion
of 1 mm or here it may be few grams, the force available may be of the order of few grams
but with that few grams force, we actuate hydraulic power amplifier and hydraulic power
gives out so many 100 of Newton of force. So with that force naturally we can actuate
any valve.
So what is done is, since signal here is not able to actuate the valve, we interpose or
bring a power amplifier into the instrumentation. So that the next stage the valve is moved,
pressure is increased say 100 bars to 120 then the valve is moved down say to the distance
of say at a few millimeters that is possible only by using a power amplifier. So wherever
we have less power in the instrumentation go for amplifier, thus we find it is again
an important basic element in building a whole instrumentation.
Next is converter. Nowadays the instrumentation as we have got so many instrumentation in a system, in a power plant and simultaneously
a person noting down all the readings is not possible. Hence we find so called data logging.
It’s in use by the help of the computers. So computer will collect all the data from
different instrumentation in a power plant and store it or it can compute different quantities
from the measured parameters. So there is a need for us to give the input of the measured
parameter to a computer. When you want to use computer naturally the signal should be
in digital form, analog signals cannot be fed directly into the computer. So in such
instances we go for analog to digital converter.
The conversion is required and also when the computer gives output that also cannot be
digital because that cannot be appreciated always. We require for main precise purposes
how the parameter varies over a certain period. So for such instances we want output also
in analog form. So naturally the output side of the computer we have got the necessity
to change the signal from digital to, basically it is digital but we want analog display.
So we should have again a converter which should be digital to analog, both of them
are converters that is digital to analog. So these are the two functions achieved by
converter. In such instrumentation where data logging is involved these conversion should
be done by the converter.
In modulator we have two types, amplitude modulation and frequency modulation. These
are the two types of modulations which are used in instrumentation and the amplitude
modulation very often adopted even our radio transmission from the radio station which
propagates our music or talk to different places and you have got receiver in our houses,
so the signal there whatever a person talks is converted into that is sound, sound is
converted into voltage. So that is the signal which should be carried to different houses,
different localities. So what is done there is to cover a distance
the sound signal which varies say 20 hertz to 20 kilo hertz. So it varies the sound signal
is varying when we talk that is the mechanical vibrations taking place in air.
This vibration is in terms of pressure, pressure varies like this, in atmospheric air pressure
varies and this variation is converted into electrical signal by so called microphone.
Microphone changes the sound waves into electrical waves and this electrical wave is to be carried
to long distances and for that purpose they use so called amplitude modulation. So the
amplitude modulator functions like this. So this is our input signal or the desired signal
xs that is our voltage signal coming out of microphone which is corresponding to a sound
signal and now we have got so called carrier signal xc and these two things are combine
together by so called modulator. This modulator combines these two signals carrier signal
as well as desired signal and its modulated signal comes out.
In achieving this modulation there are certain characteristics which are necessary for successful
modulation. That is xc the frequency of the carrier signal should be at least 10 times
more than the highest frequency of the desired signal and the amplitude of the carrier signal
should be also much larger than the amplitude of the desired signal. Under this condition
you can connect to them to a, for example suppose I take a simple form. So suppose sinusoidal
variation this is t versus xi. The xi varies with reference to time sinusoidally that is
our xs. So to say I will call it xs x into xi will call it xs. That is our input signal
and the carrier signal for such an input signal should be of this order. This is your carrier
signal xc versus time and these two things are combined together by modulator and you
will find the output signal that is xm will be of this order that is will be as follows.
It is obtained like this; you super impose the amplitude that’s why it’s called amplitude
modulation. The modulation of the desired signal is super imposed over the carrier signal
and mirror image also is drawn and whatever is held in between that gives rise to the
so called the modulated signal.
So modulated signal will be somewhat like this, I will show by different color. So it
will be like this, within the boundaries the signal is varying. So this is the shape of
a modulator signal that is the amplitude of the desired signal is put into the carrier
signal and finally you get this modulate signal. This is the amplitude modulation whereas frequency
modulation we have got constant frequency again for the carrier signal but the output
say xm this is xm for the modulated signal and xm for the frequency for this I will call
xfm will be somewhat like this. So when the signal is having a larger voltage like this
and a smaller voltage it will be varying like this again higher voltage. That is depending
upon the value of the desired signal the frequency will vary but amplitude remains constant.
For frequency modulation amplitude remains constant, frequency is varying depending upon
the amplitude of the desired signal whereas in the amplitude modulation the amplitude
of the carrier signal is varied this is the difference but any how the modulation process
is combining two signal and obtaining a modulated signal.
That is your modulator and the demodulator is done actually in the receiver, we have
got radios in our house that is actually receiver. It receives this modulated signal and then
it amplifies because for a longer distance the signal will be very weak so amplify it,
power amplifier then the amplified signal will also be of the same shape and this signal
is being demodulated. That is demodulates the process by which we extract because we
find in modulated signal both carrier signal proportional to our desired signal as well
as carrier way both are there and we want only the sound signal alone. So remove the
carrier signal from the modulated signal so that is called extraction of the desired signal
from the modulated signal is called the demodulation. So demodulator extracts the desired signal
from the modulate signal and that extracted signal will be say for a sound it will be
of this shape and it is given to a speaker.
Now speaker comes into picture. What speaker does? Speaker changes the voltage variations
into a mechanical vibration of the diaphragm. When any movement in air within the frequency
of 20 hertz to 20 kilo hertz will make sound. So the sound is made in speaker that is reproduction
of the talk, whatever the person is doing at the broadcasting station that is reproduced
in our radios. So that is the modulator and demodulator. Now differentiator, we will see
differentiator, integrator together because one operation is just like modulator and demodulator
and differentiator and opposite is our integrator. Now in case of electrical signals, the differentiation
is normally achieved by an electronic circuit.
For example this displacement given to a transducer and it gives rise to a voltage say e, e is
the output of the transducer and this output can be given to a differentiator which gives
rise to signal a xo proportional to v or I call it as xi, xi is the input signal which
is displacement. Now here we get dxi by dt which is equal to velocity. So such things
are there in electronic circuit but in mechanical we use the moving body, moving body is a unit
by which we differentiate, displacement or we integrate any acceleration or any velocity
whatever is given we can use a moving body, moving body or rotating body. Moving body
is in linear line or rotating body, body in rotation that can differentiate or it can
also integrate. These two functions can be achieved by a moving body or rotating body.
For example there is a shaft rotating like this and if you want to note what is the displacement
that has taken place that is in terms of number of rotations. If you are interested you just
connect a bevel gear unit to the rotating system and connect a mechanical counter, there
it will be recorded what is the number of rotation it has made. That is our displacement,
number of rotations it’s recorded in a counter and suppose if we are interested to differentiate
this and find out what is omega. This is theta, if you are interested to find out the rotating
speed radian per second then we can get it by having another instrumentation because
the differentiate quantity is there in the rotating shaft.
The problem is how to tap that signal? Displacement is there, that we have tapped through by using
a bevel gear unit and counter that is the instrumentation for measuring the displacement.
If you want to find out the differentiate quantity of the displacement then go for different
instrumentation that is what we call it as fly ball mechanism, omega squared r. Suppose
omega is the rotating speed and m omega squared r is the force available at the fly ball.
This force is made use of to make the instrumentation you have the leverage, a different linkage
and a caller and put a spring here. By this instrumentation we can also tap a signal proportional
to the velocity.
Now this is the force proportional to omega square and the same force is transmitted to
this caller. This is the moving caller which can move up and down and when there is a force
here, force is acting, moving the caller up against the spring. So when this moves up,
you find a signal proportional to omega square is available in the scale so root of that
will give the signal proportional to a velocity, radian per second. So thing is, in the same
shaft we have got a displacement and we have got velocity also. Suppose if you give velocity
as input signal to this shaft, if we want to integrate then connect a counter that is
from a velocity you can get the displacement as number of rotations or from rotations to
velocity both of them are there in the rotating shaft.
Similarly you find, if you have to have a body of mass moving on a line, we connect
a displacement transducer it will give the, suppose it moves to and fro, this is transducer
it can give the displacement at any instance suppose it’s a starting zero point at any
distance it moves. You can get the reading here and suppose you connect here in the same
body you have also velocity problem is the solution is you have to connect instead displacement
transducer is the displacement transducer. If you connect a velocity transducer that
can check and find out the velocity of the moving body.
So the integrated quantity or the differentiate quantity are available in any moving body.
So hence you find moving bodies are used sometimes as the differentiators and integrators. So
these are the basic functional somehow the basic functional unit which will be used in
building and big instrumentations.