### Measurement of Displacement & Strain

Measurement of Displacement & Strain

Now we will see what is displacement and Strain and how to measure them through the various electrical transducer, so let's first define the displacement "  The displacement is defined as the motion of a body in the straight line between the two points OR in simple word the distance between the two points is called as displacement.
here we use displacement transducers to measure the translational motion and used as secondary components in measurement systems, it is sometimes said that the measurement of displacement - linear or angular is fundamental to all measurement many measurements, such as force, strain, pressure, temperature, level, etc,
we can broadly classify the displacement transducer in the following categories.
1. Electrical:- Resistive, Capacitive, and Indictive transducers
2. Optical  transducer
3. Ultrasonic transducer
4 magnetostrictive transducer
5. Digital transducer
Apart from these electrical devices, we commonly use mechanical devices such as scales, vernier, measuring tapes, micrometers, spherometers, etc but now a day these are not preferred to automation and electrical operation. here we will only discuss that transducers can be used as electrical components in an instrumentation system.

1. Electrical Transducers:- During the measurement of any physical parameter our main goal is to convert a non_electrical or mechanical signal into an electrical signal and our all electrical circuit consists of three main passive components as  Resistor, Capacitor, and Inductor, so we can use this three passive components to construct a device for measuring displacement

Resistive Transducers: Potentiometer
As we all are already familiar with the potentiometer and sometimes also called pot in common parlance, this potentiometer is widely used as a transducer to measure the distance or displacement.
The potentiometer consists of a variable resistance element provided with a movable or adjustable strip or contact, the motion of this strip can be in the form of translational, rotational, and helical.

Single slide wire potentiometer :-The single slide wire potentiometer offers the stepless variation of resistance as the wiper travels over it, and the length of the single slide wire potentiometer is limited so we can measure log distance or displacement. Although the resistance of the potentiometer per length can be increased or decreased by changing the cross-section area of the wire, we can understand it as simple formula and single slide wire potentiometer.
R= ρL/A

Single slide wire potentiometer

Wire-wound Potentiometer:- In this type of potentiometer, the resistance wire is wound on a circular strip or mandrel, depending on the type of the device translational or Rotational used. The wire-wound potentiometer has a long length so we can measure more s displacement, here displacement is measured using the contact wiper which moves as per the physical displacement of anybody, and due to a change in the position of the contact wiper on the resistive element the resistance varies and the value of voltage and current value also increase or decrease. the wire-wound construction produces a stepwise increase in resistance as the wiper moves from one turn of the wire to another, thus restricting the resolution of the transducer.
The resistive wire is made of nickel-chromium(nichrome), nickel-copper, silver-palladium, or some other precious metals that are used as resistive elements, and the diameters vary between 25 and 50 micrometers.

Circular Potentiometer

•    This is inexpensive and simple to set
•   It produces sufficient output to drive output
• Frequency response and resolution are limited for the wire-wound, but unlimited for others.
•   We can easily amplify its output signal

• Mechanical loading owing to wiper friction
• It produces some electrical noise due to sliding contact or wiper and misalignment owing to friction
• There need for some electrical circuit arrangements to measure variation in resistance like bridges.
• Quick Manipulation generates heat and associated problems.

Inductive Transducers:- here we can divide inductive transducers in again various types. we will consider only two namely

• Linear Variable differential transformer (LVDT):- The working mechanism of the LVDT transducer is similar to our Tranduformer now let's see how this transducer work. The linear variable differential transducer (LVDT) is the most commonly used variable inductance transducer in the industry,  this is an electromechanical device designed to produce an ac voltage output that is directly proportional to the relative displacement of a transducer and movable iron core in the magnetic field.

The construction of LVDT is simple it consists of one primary winding and two secondary winding which are wounded on the transformer, the secondary winding is identical in respect of their number of turns and their placement on both sides of the primary winding. when we applied a sinusoidal voltage of amplitude 1v to 15v and frequency range is 50Hz to 20kHz so it's excited the primary winding and produced some magnetic field, and when we move the iron core this produces a magnetic field, so due to the mutual inductance .there is some volage generate in the secondary winding. the strength of emf in the secondary winding depends on the position of the iron core and at the last end, we will take the difference of both secondary winding produced emf as a resulted output.

Linear Variable diffrential Transformer

Equation for the output emf on the secondary winding
So Ei is the applied input voltage on the primary winding
(sLp+Rp)Ip=Ei
If es1 and es2 are the voltage generated in the secondary coil owing to their mutual inductances of coefficients M1 and M2 equation for the secondaries and their Laplace transforms
es1=M1dip/dt                                         es2=M2dip/dt
Es1=sM1Tp                                           Es2=sM2Tp
Therefore the final output is a difference of secondary winding emf is
Eo=Es1-Es2