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We have seen until now the mechanical devices for measuring force or weight. They are normally
meant for smaller range few kilogram or for example compound lever mechanism. That is
our platform balance probably it may be 1 or 2 or 3 tons. Suppose hundreds of tons if
we want to measure, naturally people go for hydraulic or pneumatic load cells.
Hydraulic is for still higher range, medium range is pneumatic load cells. How a hydraulic
load cell and pneumatic load cells are functioning, we are going to see one or two principles.
First the hydraulic load cell, there is a diaphragm. The load button sits on the diaphragm
and below the diaphragm we have got incompressible liquid and which is connected to a pressure
gauge and we have got the chamber, suitable chamber at the bottom. So that when the force
F acts on the load button the liquid below the diaphragm gets compressed because of the
deformation of the diaphragm. So for a particular force a pressure is developed in the liquid
and that is being read by a pressure gauge, probably it may be a bourdon type pressure
gauge and that pressure reading is calibrated interms of hundreds of newton’s or few tons
in terms of tons. The working principle we can see the signal flow block diagram, diaphragm
plus oil converts this force into pressure. This pressure is read in the pressure gauge
and we have got the output signal as in the form of motion of a pointer over the scale
so that is our xo.
So how to ensure the moment you apply a force it is converted into pressure, for that is
achieved by having an initial pressure. We have got initial pressure of say 1 or 2 bar.
It’s of the order of 0.2 bar I mean 2 bar pressure, two times atmospheres or 0.2 newton
per millimeter square. A two bar pressure is built in that is our initial pressure.
So the pressure gauge may read two bar or some pressure that is written as input signals
with zero force that will be zero force. Further increase can be only from the applied force.
So that is a compact unit made up of hydraulic elements.
Next we should see the pneumatic load cell. In the pneumatic load cell we have the principle
nozzle I mean flapper nozzle principle that is this constitutes a flapper nozzle principle
is made use of in the pneumatic load cell. It is because the compressed air can be compressed,
it is a compressible medium whereas liquid is incompressible. So this is simple setup
whereas with pneumatic air or any gas since the fluid is compressible we are using the
flapper nozzle principle. So this is the flapper nozzle principle it is written there.
So that is we explain before we go to that load cell say here we have a fixed nozzle
and variable nozzle in the form of an imaginary cylinder, this nozzle being extended in this
gap that is the variable nozzle and in between these two fixed nozzles we have the pressure
gauge that is the chamber pressure is measured by a pressure gauge.
Now the distance between the end nozzle and the flapper, this is the flapper which can
rotate or move, varying the distance in front of that tipped nozzle and the chamber pressure
in between these two fixed nozzle we have got supply pressure. It is of the order of
1.2 bar, this is usual pressure for the flapper nozzle system, a gas or compressed air at
1.2 bar is the supply for this whole instrumentation. So as x varies the Po varies as per this curve,
when x is equal to zero Po is Ps. That is when the flapper fully closes then this pressure
becomes the supply pressure, for any other distance x then it varies, more or less you
have got some range as linear range in this instrumentation. Anyhow this is principle,
by giving a displacement x we covert that displacement into a pressure by the flapper
nozzle principle. That is what is being made use of in this pneumatic load cell, we have
got fixed nozzle similar to that fixed nozzles and variable nozzle between the extension
rod and the bottom valve we have this variable area. Now what is this variable area pi d,
if d is the diameter of this tipped nozzle, pi dx is the imaginary cylinder from the tip
of the nozzle to the flapper that is pi dx is area and that x will have effect on this
pressure Po until this cylindrical area becomes equal to the cross sectional area of this
whole. That is the maximum that you call if it is x maximum that is equal to pi d square
over 4.
Until this cylinder surface area equal to this cross sectional area of the nozzle, you
will have the effect of x on Po. Later on you will not have, that is both the area is
equal. Now you find pi d they cancels out then you will find x maximum is equal to d
by 4 that is the maximum distance one can have. So such a distance is given to this
extension rod by the diaphragm, when the diaphragm is acted upon by a force F. So the force F,
see the block diagram or signal flow diagram, force given to the diaphragm then diaphragm
gets deformed. This deformation is carried to this nozzle to this opening by this extension
rod. So the amount of opening is varied when the diaphragm deforms that is our variable
area analogous to variable nozzle. So this distance is converted because this is fixed
nozzle, this is a variable nozzle in between these two nozzle we call it chamber here.
So chamber pressure now that is chamber pressure is a function of the amount of opening here.
So the amount of opening is given which is nothing but our displacement in the extension
rod. So that is proportional to that extension rod, so d is converted into Po by this flapper
nozzle system. This Po is read by a pressure gauge and we have got the signal here.
So this pressure gauge reading will be calibrated in terms of force we have applied. So known
force we can give and calibrate it by having dead weights or something like that. Later
on the machine member will act on this and then unknown force can be read from this pressure
gauge which is calibrated in terms of tons or newton’s, whatever it is. So these are
the two principles under the hydraulic pneumatic principles. Next we are going to see elastic
elements. How elastic elements are made use of in force measurement? A typical elastic
element is an ordinary spring, helical spring. This is helical spring, we call we call it
spring balance domestically used, I mean normally used there. So there you will have the hook
and here you hang your weight whatever weight you want to measure and from the other end
a pointer is taken, this will be moving over a scale.
Only scale we see, all the things are covered by a cylinder or a cover. This pointer mechanism
analog will be inside. So you see the outside of the pointer moves over these scales. So
normally we may have up to zero to 20 kilogram force is normal range domestic spring balance
and with a least count of 0.5 kilograms. We can read point up to 0.5 kilogram force, this
is a very convenient to measure the household articles. So this is the first foremost elastic
element that is a spring itself is made use of in the form of spring balance and other
is elastic element is the foremost and often used is the column type strain gauge load
cell.
This is very often made use of and it has got fairly high capacity so up to few tons
we can measure. The main advantage of all this instrumentation is this spring balance
is purely mechanical instrument because only static, no dynamic measurements can be made
but in case of this column type strain gauge load cell we are converting the mechanical
signal force into an electrical signal. So you can use it for both static as well as
dynamic measurement, force can be varying and still you can measure it. As you find
this is a typically a second order instruments we have got a particular I mean spring constants
that is the force per unit deflections. So spring is there and air is the surrounding
medium damping medium and the mass here will be the force transmitting element. Suppose
this is being transmitted by a machine member that must also we have to consider in finding
out the natural frequency of the whole instrumentations.
So the mass of the transducer alone is not sufficient, the force transmitting member
that weight also you have to add to this machine, to this instrumentation of this column. So
it is a typical second order instrument here what you are doing is we take a length for
suppose this we are using for a compressive force. When you want to use it for tensile,
you have two cups or whatever it is with the screw threads you can make suitable fittings
and then apply a tensile force. So same instrumentation we can use it for tensile for same column
also. Here we want to stick strain gauges so if it is sufficient to large diameter,
surface area we need not make the flat surface, we cannot make a square surface inside, just
on the cylindrical surface itself you can place a strain gauges. So this may be 1, the
2 is at perpendicular directions, this is 2, 3 are just diametrically behind this. So
this is our 3, this is our strain gauge 1 and this is 2 because in transverse directions
it is pasted 2 and 4. So 1, 2, 3, 4 these are the, that is if the column is having,
if the cylinder has a sufficiently large surface then we can paste the strain gauges on surface
itself but if it is a smaller diameter then the curvature may not allow us.
The small curvature may not allow us to paste this strain gauge rigidly. So in that case
we make a square cross sections or flat surface we machine it and then paste the strain gauges
for better bonding. So after fixing the strain gauges on the column then it becomes part
of the column and this column material you have to carefully select. You should reduce
the hysteresis effect of the spring material. So some alloy steel or spring steel with some
additions will make a large elastic limit as well as less hysteresis. This is what is
important for long time usage or long life. The calibration should not change. So once
if we know for a column type we cannot paste all the strain gauges along the axis, this
we have learnt already under bridge network, the sensitivity of bridge network. So two
strain gauges along the axial direction that is the strain gauge loop will be along the
axis. Then the other strain gauges it 90 degree perpendicular to the axial, two in axial directions
two strain gauges in transverse directions that will make 2 into 1 plus nu where that
is the total sensitivity of this instrumentation where nu is the Poisson’s ratio.
We learnt that time Poisson’s ratio where s is the sensitivity of a quarter bridge.
So with such instrumentation we will have the twice the, suppose if it is 0.3 then you
will find 1.3 so 2.6 times the sensitivity of a quarter bridge that will be total sensitivity.
Higher sensitivity means we can have larger signal output eo. So now the four stain gauges
are connected in the bridge network R1, R2, R3, R4. R1 and R3 are axial strain and R2
and R4 takes transverse strain, Poisson's strain so is called Poisson’s configuration,
we have learnt already earlier so it should be like this. If all of them in the axial
direction, the output will be zero so to avoid it we put to two in Poisson's and two in transverse
directions and so. Now this instrumentation we find it is insensitive for the temperature
variations because it’s a full bridge, all the 4 strain gauges are under the same temperature
conditions. So we find temperature compensation is already there. There is no need for any
dummy gauge. Because all temperature brings same effect in all the strain gauges, any
same effect and all the strain gauges will give rise to zero output which we know already.
So temperature is taken care of regarding the coefficient of linear expansion that aspect
of it but temperature will affect the Young’s modulus of this column material. That is when
temperature is higher then Young’s modulus will come down that is for a given force we
may have larger deformations, when Young’s modulus comes down then that is to be accounted
for that is done by having a resistance in series with the excitations to the bridge.
How this will be compensated for this change in Young’s modulus? Suppose temperature
is increased then Young’s modulus comes down then large strain is there so larger
output voltage will be there in the bridge network.
So this we want to reduce it, that is done by having Rc in series this is also in the
same atmospheric conditions, same temperature. So when temperature increases Rc will increase
when Rc increases voltage drop here will increase so net voltage coming to the bridge will be
reducing. We know the sensitivity of a bridge is proportional to the excitation voltage
when excitation voltage comes down then the voltage output reduce. If you so select the
value of Rc this reduction is equal to the increase due to the reduction in the Young’s
modulus. So you will find more or less that net may be very small, if they are not equal
it may be very small so error may be within tolerable limit. So that is for temperature
compensation for change in Young’s modulus we put a resistance in series and you will
find one more advantage of this instrumentation is this will be sensitive only for this axial
loading.
Suppose there is a bending movement due to some eccentric loading, suppose it is here
and you apply like it so we find a small couple or movement is there. In such situation what
will happen, suppose the 1 will be tilted in this way so 1 will be in tension and 3
is opposite face, 3 will be in compression. Now 1 and 3 they are subjected to opposite
strains and that means they should be put in adjacent terms for maximum sensitivity
but you find they are put in opposite arms. So opposite strain in opposite arms gets nullified
as per the rule of the bridge. So even if there is bending, there is no output
due to the bending strain. Similarly if this way excitation is there and 2 will be in tension
and 4 will be in compression and 2 and 4 on opposite arms and opposite strains gives rise
to zero output voltage. So we will find this instrumentation is insensitive for both bending
load and temperature effects.
So that is advantage but one should be careful when we design this column, column height
should be sufficiently short so that under this compressive load it doesn’t buckle
that is one thing. Secondly the place where we are going to fix the strain gauges should
be sufficiently weak to produce sufficient strain in the member. If we fix the strain
gauges on the existing member which has been designed for strength then you will find the
strain produced will be very small of 0.1 or 0.2 micro strain which will not give rise
to any output voltage. So when we want to fix the strain gauges in existing member then
at that place you have to weaken it so that there is sufficient strain but you should
not weaken in a way it goes to plastic region but still the loading range should be just
above the elastic region. So it will produce at least a 200 micro strain that is what we
expect at least 200 micro strain should be there for the maximum loading. If it is 0.1
or 0.2 microns then it will not produce any effect.
So you find for this load cell where we want to fix the strain gauges there should be sufficient
strain to that extend we have to weaken that place and then only fix the strain gauges,
this is what is important. So here you find in the column type, the spring constant since
it is a solid member it is fairly large and deformation will be very small, to have some
more sensitivity but advantage is since Ks is large and omegan which is root of Ks by
M will be larger omegan.
So it will have naturally larger bandwidth but the problem here is since it is a column
it may have the smaller deflections or sensitivity may be small. To increase sensitivity what
we can do is; see one disadvantage is when we reduce the cross section then it becomes
too narrower or you may have very small area for the strain gauges. To avoid the problem
what people do, we can have a hollow constructions, at the place where we want to fix the strain
gauges have the hallow construction small valve thickness. So inside it will be hollow
so that we find it is weak at same time sufficient area is there for fixing the strain gauges.
So all these measures we can observe so that sufficient sensitivity comes but another better
design is going for the proving ring transducer. Here we have much more sensitivity than this
but problem here is Ks spring constant is reduced and bandwidth is reduced.So this always
the case instrumentation when you want to increase one characteristic value and some
other characteristics gets affected that’s why you have to come to compromise. Anyhow
this is the proving ring load cell or transducer is widely used in places, industries and laboratories.
It is made up of just you have a ring and the inside and outside surface and in the
surfaces we place the four strain gauges as it is shown here and this is end view of it.
So you find when the load is applied F, the ring is compressed. So this compressive load
converted into bending strains at the surfaces, 1 and 3 will be subjected to tensile strain
2 and 4 will be subjected to compressive strain. Then the same bridge holds good 1 and 3 in
compressive, 2 and 4 in tensile, 1 and 3 tensile, 2 and 4 in compressions. So bridge we can
use again you can have this compensation for elastic modulus change due to the temperature.
So the same circuit we can use it for this one also.
Advantage is here more sensitivity but the load capacity is reduced so probably 1 or
2 ton. Here you may go up to say for 50 or 100 tons we can go for column type, here it
is a small it will be reduced. The disadvantage of the set up is if you unknowingly load more
then these points may go into plastic deformations. It may not come back to original because we
might have exceeded the elastic limit that is danger; to avoid this we have some other
design. That is a load cell with overload production; see here the special construction
with a gap s so in one circle we have got 2 circles with the central gap. So when you
put the load here F and this is a fixed surface when it is compressed and when the gap is
reduced to zero any further loading will go to the floor or the ground directly, it will
not stress or strain the elastic member.
So until it becomes zero you have got strain here, it will be within the elastic limit.
So you will find beyond elastic limit, the force will go not through this element but
directly to the floor through this bulging. So that is the overload protection here. So
if you want to have still higher sensitivity and say for smaller load range, the natural
its a few gram onwards we can measure by having the cantilever type of load cell. Say it is
written is cantilever transducer but cantilever load cells, this we have made use of for explaining
many principles, bridge network principles we are using this example very often. So you
find at the top surfaces are two strain gauges 1 and 3, same bridge network whatever we have
learnt earlier same thing holds good.
So this is 1, 2 this is 3, 4 that is 1 and 3 will be in say for this type of loading
its tensile strain 2 and 4 will be in compressive strain and for I mean 2 polarities we have
got. So all the four will give rise to 4 times sensitivity of a quarter bridge. So this is
a full bridge and temperature compensation is there and for counting for the Young’s
modulus change due to temperature we connected Rc see it’s a circuit we can have it. So
this is for smaller load range we can go for this cantilever type. By having the different
thickness and different length we can have different load ranges in this, it’s very
versatile useful a principle. Then next one is using diaphragm and using LVDT diaphragm
type of load cell.
So two diaphragms are there and at the middle of the diaphragm one rod is connected and
at the end of the rod we give the force which we want to measure. It is supported in the
say it can be supported on the floor, now give the load and the diaphragms deforms like
this. So this deformation is maximum at the middle so the rod comes down at the bottom
end of the rod we connected the core of an LVDT or of self inductance pickup, here it
is LVDT. So this is your supply voltage, two secondary connected in oppositions so the
output voltage eo is a modulated voltage, a modulated signal modulated modulation between
es and the magnitude of the displacement of the core and further we process it as we have
learnt earlier in LVDT by giving amplifying or without amplification give into phase sensitivity
demodulator and low pass filter and finally we get a displacement. This displacement there,
that displacement is written in terms of Newton or kilogram force. That is how the displacement
reading is calibrated in terms of force unit.
So here we have two transducer one to transduce the force into deformation and this deformation
back to voltage that voltage is written in terms of Newton, so 2 transducers in essence.
That is the case in almost all the type of the elastic members with strain gauges; we
use a one member elastic member to transduce the force into strain that is the block diagram.
That is the force converted into strain either in the cantilever or in the proving ring or
in the load cell, we use that primary this is a primary transducer load member. So this
has to be properly designed so that sufficient stress and strain is there and then later
on we give this to a bridge network that is our bridge network and from there we get an
output voltage. This is the instrumentation; this output voltage is further amplified or
read according to the situations. So two transducers more or less we will find 2 transducers are
there epsilon to e0, either the LVDT or strain gauge anything we can use.
The one problem in the cantilever type of transducer is suppose this is load button
this is a place where you are supposed to apply the load or force. If it is little bit
changed say it is little bit changed then you will find for the same force, little bit
earlier in this cantilever we have the less strain here. Then the instrument will show
a less reading, smaller reading the force may be 10 or 100 Newton but the instrument
will show only about 90 Newton it is because it is shifted from its original place by due
to some error or something like that little bit earlier.
So to that extent the instrumentation gives rise to that is it is very sensitive to the
proper placing of the load on the instrumentation in the load cell. That problem is solved once
you go for the shear type of load cell.
Here we can apply it here or here, nothing will happen it will give the same reading.
It is non-sensitive for the location of the load, more or less this is the loading point
say about the loading point if you vary it is not affecting the instrumentation where
it is in cantilever type it is very sensitive for this small error in applying the load.
How it is non-sensitive? It is because this instrumentation based on shear type, we know
the bending movement diagram for this cantilever is, it goes like this. From tip is zero bending
movement and at the bottom is of the near about fixed end, we got the maximum bending
movement, it varies linearly. Whereas shear force diagram for the same cantilever shear
force diagram is rectangle, from this point up to the fixed point shear force remains
same.
It is same as applied load that means shear force doesn’t change with distance of the
application of the load so that is the property what is made use of it. Load is supplied area
and we know shear force is same throughout so we can select any place but here we have
to be careful because from shear force we have to go for the maximum stress or strain
that is principle strain, the compressive or tensile strain that is at 45 degrees to
these axis of this one. So if the one then the other one at the back
side you can put of 90 degree to this orientations. So that will be in dotted line I am drawing
so it will be like that. So if one is in tension, due to shearing in this axis, so compressive
tensile will be available at 40 degrees to this one which we have learnt in machine design.
So 1 will be in tension and 2 will be in compression then you connect so in the same bridge 1 is
in tension this is tension and the other 2 is in compression. So adjacent arms you connect
and if we want 4, 3 also we can have 1 and 3 in the same way, you can have another parallel
and you can have 4 strain gauges also. This will be 3 behind at 90 degree to that it will
be 4. So that full of full bridge, if 1 and 2 alone half bridge we have got which we are
making use of.So that problem of loading exact place or if we make I mean if this is an instrumentation
which is not sensitive for the loading point. So it is nowadays very often used, shear type
load is often used and next what we are going to see is three dimensional load cell. Suppose
you have force F acts in some random direction like this.
This is a random directions which a component which is Fx, Fy and Fz along the three coordinate
axis. This is a three dimensional one so it is not vertical or horizontal or x direction,
y direction so some random directions. So for that we use a column like this, this column
should be little bit sturdy or a strong column because due to this application if it bends
it gives rise to lot of error. So the amount of deformations should be limited, to that
extent we should have a strong beam fixed at the bottom end. Now the Fx and Fy they
will bend the beam having a cantilever, having a fixed end at this bottom. The beam will
function as a cantilever for Fx and Fy, for Fz it is again a column.
We know instrumentation for bending; for bending top surface 1 and 3 tension, bottom surface
2 and 4 compression. Similarly if we consider Fx when it is this way, this layer will be
under tension the other layer will be that is the bottom layer will be under compression.
So X1 and X3 are in tension and Y2 and Y4 are in compression I mean X2 and X4 are compression.
So I have drawn one bridge network and I am supposed to draw 3 bridge networks, one for
X another for Y separately but nomenclature will be more or less same that’s why I indicated
here but we should have 3 independent bridges. One for X instrumentation in X direction and
another one for Y instrumentation and another one for Z instrumentation, three bridges we
should build for each component force and this is eo, you will have eox from the x bridge,
eoy for the Y bridge and eoz for the Z bridge. So three different bridges, they are added
finally in algebraic fashion and final output voltage will be proportional to F. So algebraic
addition of these three independent voltages from three bridges will be proportionate to
the final three dimensional force F but we should be careful, the instrumentation for
X direction Fx should not be influenced by Y direction force or the instrumentation,
the strain gauges meant for F measuring Fy should not be affected by the Fx. That is
possible only when you fix the strain gauges about the neutral axis, symmetrical distance
from the neutral axis.
For example you consider this face ABCD; this is the phase and neutral axis more or less
at the middle. So we find Y1 and Y3 will be at equidistance from the neutral axis. In
that case we will find the instrumentation for Y will not be affected by the other two
forces. For example you can see Y1, Y3 and Fx is this direction. So we find this is above
the neutral axis Y1 will be in tension, Y3 will be in compression, Y1 Y3 should be in
adjacent arms for Fx but Y1, Y3 are in opposite arms, so it gets canceled out. Similarly you
can analyze in all the strain gauges, Z1 is at the middle and you will find top side will
be in tension and bottom side from the neutral axis compression within the strain gauge itself
it gets canceled out. So instrumentation for one direction force will not be influenced
by the other direction provided the strain gauges are fixed symmetrical about the neutral
axis on each face. So for Fx and Fy we have got 4 strain gauges similarly for Fz, Fz is
column type. So you cannot have all the four axial directions. So here we have the four
times sensitivity for Fy and Fx as the quarter bridge whereas for Fz we have the 2.6 times
sensitivity of the quarter bridge because it is the axial force.
So two in axial direction two strain gauges, other two strain gauges should be transverse
in Poisson’s configuration. So sensitivity for Z will be little small, it does not matter
we are going to add these forces and then later on we are going to calibrate. So this
is the way all the three components and finally we add the output of individual bridges and
get the signal proportional, algebraic addition and get the signal proportional to F.
Next we see the piezoelectric force transducer. We know the piezoelectric crystals and they
respond to dynamic loads. So we can have this piezoelectric crystal apply the load either
I mean given displacement signal or we can give force signal also. Displacement signal
alone we cannot give without a force because the crystal will not deform, it has got very
high spring constant. So we now use it for measuring force, supply the force then it
deforms that deformation is producing a charge and that charge we take into a charge amplifier
this can be taken to a charge amplifier and the voltage output can be read with the help
of a voltmeter.
So instead of displacement we can use it for force also, known force to calibrate the readings
and later on allow the unknown force to act and then from the calibrated curve we can
find the force. As we know this crystal can be used only for
a dynamic load that omega being between say 3.04 over tau and 0.2 times omegan. That is
for plus or minus 5% error and also when size equal to zero that is crystal works more or
less air damping; air damping can be assumed zero. So we will find under these conditions
the bandwidth for this instrumentation is 0.4, tau is the time constant of the electrical
circuit, it is 3.04 over tau that is it functions like a simple capacitor transducer because
this is a metallic plate at the bottom and at the top. So this is a dielectric medium
insulating material so it is typical capacitor circuit, we already learnt 5% error, omega
should be larger than this value 3.04 over tau and considering second order system we
have found out, it should be less than 0.2 omegan for 5% error psi being zero, these
all we have arrived already. So this is the working range for this piezoelectric transducer.
Otherwise it is a very good dynamic measuring instrument, a force measuring instrument.
Next method is force by acceleration measurement. That is a member is there, this is a machine
member and we want to find out what is the force acting on this member. So we can connect
a load cell and find the force but many instances it may not be possible to connect to bring
a load cell here. So people what they do, they put an accelerometer here. They will
measure the acceleration a and now we know force F is equal to, if M is the mass so mass
into acceleration. So measuring the acceleration and knowing the mass of the body of machine
member on which the force is acting, we can find out the force. It is indirect way of
measuring. So by measuring the acceleration we measure actually a force but what is the
drawback in this. It will measure only the resultant force, suppose there is friction
force. It is moving over a surface suppose that a friction force Ff, the net force is
F minus Ff. Now instead of F, F minus Ff.
F minus Ff will be equal to equal to Ma that means you should know the friction force.
If you do not know the friction force you will be assuming that to be force so that
will be error. so you are measuring a smaller force but you will be calibrating as a bigger
force. Suppose you have 10 newton and here 1 newton then only 9 newton alone accelerate
this mass. So accordingly this acceleration will be smaller and that will be writing it
as 10 newton because you do not know the friction force so that is the error component. So that
means the acceleration will be proportional to the net force or resultant force and you
cannot find out the different forces constituting the resultant force. So this instrumentation
we can use it only when the resultant force is one or if there is another force that force
amount should be known to avoid the error in the measurements. Drawback is if acceleration
is a result of the resultant force that is the point what you have to measure. The next
what we are going to measure is closed loop instrument, it's called electromagnetic balance
that is the electromagnetic balance what I have written here electromagnetic balance.
This is a closed loop instrument. So far what we have seen all these instrumentation, earlier
version whatever we have seen they are all in open loop instrumentation but now it is
closed loop instrumentation that general advantage whatever it is there in closed loop instrument,
it is here for this instrument also. That means they have got higher accuracy say 0.1%
accuracy we can get, whereas in open loop we can get 1 or 2% accuracy alone we can get.
So it is functional like this, this is one of the versions there are many versions one
of the versions of such instrument is we have got a lever at the end of which we apply a
force F and the other end we have got this inductive pickups and this is a force coil
and we can call it a force coil, this is force coil are arranged.
The functioning is like this we can explain with a help of the signal flow diagram also,
we apply a force F and at the end of a lever this is a lever so a moment is there that
moment say mi this is mb. There will be some force on the force coil that is acting at
a distance so there will be some mb, the resultant of these two movements is me, me acts over
this coil spring. So that moment is converted into angular rotation theta. This theta at
a distance of another distance we have got a pickup at some other distance. So theta
times the distance will be displacement at this tip that is this is the tip, displacement
inductive pickups for measuring displacement. So that much displacement will be sensed by
this pickup and it is given to carrier frequency amplifier, the current will be flowing here
i due to this current. This current is taken to the force coil; the force coil gives rise
to a force bringing the lever back to its original positions. So amount of current required
to bring it back it’s a measure of the force. A force is larger it will tilt more and it
has to brought back a higher current will be going.
So the amount of force required in the coil to bring the lever back is a measure and proportional
to that force, you have got current flow in this system. So you find a current flowing
through that constant resistor R gives rise to a voltage drop eo so that is why it is
taken here. So i following flowing through R gives rise to eo this output signal and
this i is taken to force coil to give rise the feedback movement. So now eo read here
with a help of voltmeter can be calibrated in terms of force here. So that is how the
closed loop instrument is functioning. Any error, any temperature rise and all will not
affect this instrumentation accuracy because if a coil spring constant is changed due to
temperature, the same coil resistance that same spring constant is valid for the feedback
also. So that softening of the spring will not because softened spring will require only
a less force here in the coil also, so you find it gets stabilized this error source
gets nullified. So that is how it is having a larger accuracy. We will close it with this
one.