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Explain LVDT and define its application in displacement measurement.
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THE LVDT :THE BASICS OF LVDT:

• The linear variable differential transformer (LVDT) (also called just a differential transformer, linear variable displacement transformer, or linear variable displacement transducer ) is a type of electrical transformer used for measuring linear displacement (position).
• A counterpart to this device that is used for measuring rotary displacement is called a rotary variable differential transformer (RVDT).
• LVDTs are robust, absolute linear position/displacement transducers; inherently frictionless, they have a virtually infinite cycle life when properly used.
• As AC operated LVDTs do not contain any electronics, they can be designed to operate at cryogenic temperatures or up to 1200 °F (650 °C), in harsh environments, under high vibration and shock levels.
• LVDTs have been widely used in applications such as power turbines, hydraulics, automation, aircraft, satellites, nuclear reactors, and many others. These transducers have low hysteresis and excellent repeatability.
• The LVDT converts a position or linear displacement from a mechanical reference (zero, or null position) into a proportional electrical signal containing phase (for direction) and amplitude (for distance) information.
• The LVDT operation does not require an electrical contact between the moving part (probe or core assembly) and the coil assembly, but instead relies on electromagnetic coupling.

OPERATION OF THE LVDT:

• The LVDT closely models an ideal zeroth-order displacement sensor structure at low frequency, where the output is a direct and linear function of the input.
• It is a variable-reluctance device, where a primary center coil establishes a magnetic flux that is coupled through a center core (mobile armature) to a symmetrically wound secondary coil on either side of the primary.
• Thus, by measurement of the voltage amplitude and phase, one can determine the extent of the core motion and the direction, that is, the displacement.
• The below Figure shows the linearity of the device within a range of core displacement.
• We can note that the output is not linear as the core travels near the boundaries of its range.
• This is because less magnetic flux is coupled to the core from the primary.
• However, because LVDTs have excellent repeatability, nonlinearity near the boundaries of the range of the device can be predicted by a table or polynomial curve-fitting function, thus extending the range of the device.
• The linear variable differential transformer has three solenoidal coils placed end-to-end around a tube. The center coil is the primary, and the two outer coils are the top and bottom secondaries.
• A cylindrical ferromagnetic core, attached to the object whose position is to be measured, slides along the axis of the tube.
• An alternating current drives the primary and causes a voltage to be induced in each secondary proportional to the length of the core linking to the secondary.
• The frequency is usually in the range 1 to 10 kHz.As the core moves, the primary's linkage to the two secondary coils changes and causes the induced voltages to change.
• The coils are connected so that the output voltage is the difference (hence "differential") between the top secondary voltage and the bottom secondary voltage.
• When the core is in its central position, equidistant between the two secondaries, equal voltages are induced in the two secondary coils, but the two signals cancel, so the output voltage is theoretically zero.
• In practice minor variations in the way in which the primary is coupled to each secondary means that a small voltage is output when the core is central.
• When the core is displaced toward the top, the voltage in the top secondary coil increases as the voltage in the bottom decreases. The resulting output voltage increases from zero.
• This voltage is in phase with the primary voltage. When the core moves in the other direction, the output voltage also increases from zero, but its phase is opposite to that of the primary.
• The phase of the output voltage determines the direction of the displacement (up or down) and amplitude indicates the amount of displacement.
• A synchronous detector can determine a signed output voltage that relates to the displacement.
• The LVDT is designed with long slender coils to make the output voltage essentially linear over displacement up to several inches (several hundred millimetres) long.The LVDT can be used as an absolute position sensor.
• Even if the power is switched off, on restarting it, the LVDT shows the same measurement, and no positional information is lost.
• Its biggest advantages are repeatability and reproducibility once it is properly configured.
• Also, apart from the uni-axial linear motion of the core, any other movements such as the rotation of the core around the axis will not affect its measurements.
• Because the sliding core does not touch the inside of the tube, it can move without friction, making the LVDT a highly reliable device.
• The absence of any sliding or rotating contacts allows the LVDT to be completely sealed against the environment.
• LVDTs are commonly used for position feedback in servomechanisms, and for automated measurement in machine tools and many other industrial and scientific applications.

MEASURMENT OF DISPLACEMENT USING THE LVDT:

• The main advantage of the LVDT transducer over other types of displacement transducer is the high degree of robustness. Because there is no physical contact across the sensing element, there is no wear in the sensing element.Because the device relies on the coupling of magnetic flux, an LVDT can have infinite resolution.
• Therefore the smallest fraction of movement can be detected by suitable signal conditioning hardware, and the resolution of the transducer is solely determined by the resolution of the data acquisition system.An LVDT measures displacement by associating a specific signal value for any given position of the core.
• This association of a signal value to a position occurs through electromagnetic coupling of an AC excitation signal on the primary winding to the core and back to the secondary windings. The position of the core determines how tightly the signal of the primary coil is coupled to each of the secondary coils.
• The two secondary coils are series-opposed, which means wound in series but in opposite directions. This results in the two signals on each secondary being 180 deg out of phase. Therefore phase of the output signal determines direction and its amplitude, distance.
• The core causes the magnetic field generated by the primary winding to be coupled to the secondaries. When the core is centered perfectly between both secondaries and the primary, as shown, the voltage induced in each secondary is equal in amplitude and 180 deg out of phase. Thus the LVDT output (for the series-opposed connection shown in this case) is zero because the voltages cancel each other.
• To summarize, “The LVDT closely models an ideal zeroth-order displacement sensor structure at low frequency, where the output is a direct and linear function of the input. It is a variable-reluctance device, where a primary center coil establishes a magnetic flux that is coupled through a center core (mobile armature) to a symmetrically wound secondary coil on either side of the primary.
• Thus, by measurement of the voltage amplitude and phase, one can determine the extent of the core motion and the direction, that is, the displacement.” Note that the output is not linear as the core travels near the boundaries of its range. This is because less magnetic flux is coupled to the core from the primary.
• However, because LVDTs have excellent repeatability, nonlinearity near the boundaries of the range of the device can be predicted by a table or polynomial curve-fitting function, thus extending the range of the device.

APPLIATION OF LVDT IN DISPLACEMENT MEASUREMENT:

• Although the LVDT is a displacement sensor, many other physical quantities can be sensed by converting displacement to the desired quantity via thoughtful arrangements.
• In field of Displacement measurent it is used in extensometers, temperature transducers, butterfly valve control, servo valve displacement sensing.
• In field of Deflection of Beams, Strings, or Rings it can be used as load cells, force transducers, pressure transducers.
• In field of Thickness Variation of Work LVDT is used as Pieces dimension gages, thickness and profile measurements, product sorting by size.
• In field of Fluid Level LVDT is used to measure fluid level and fluid flow measurement, position sensing in hydraulic cylinders

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Answer: Linear Variable Differential Transducer( LVDT) - It is a variable inductance displacement transducer.

Construction - It consists of a primary and two identical secondary winding. These windings are axially spaced and wound on a cylindrical core former. A rod shaped core is positioned centrally inside the coil assembly. This rod provides a low reluctance path for the magnetic flux linking the coils. The displacement pf which is to be measured is coupled to this movable rod.

Since , the two secondary winding are connected in series so the voltages induced into winding are of opposite polarities. The output voltage is given as

$e_0=e_{01}-e_{02}$

where, $e_{01} \ and \ e_{02}$ are the emf induced in two secondary windings.

Operation - The primary winding is connected to the ac source. According to the position of the core , three cases are developed which are given below.

Case 1 : When the core is exactly in center of the coil assembly.Then , the flux linked to both the coils of secondary are equal. Due to this the secondary induced voltages are equal but with opposite polarities.The output voltage is zero and this position is called as Null position.

Case 2 : When the core is displaced towards secondary 1 , then the flux linkage to secondary 1 increases and flux linkage to secondary 2 decreases. Therefore, $e_{01}$ is greater than $e_{02}$ . Hence, the output voltage is positive.

Case3 : When the core is displaced towards secondary 2 , then the flux linkage to secondary 2 increases and flux linkage to secondary 1 decreases. Therefore, $e_{02}$  is greater than $e_{01}$  Hence, the output voltage is negative.

Thus , a voltage proportional to the displacement of core is obtained at the LVDT output. Hence , LVDT helps to measure the displacement of the moving object.