LVDT Working Principle

Linear Variable Differential Transformer

LVDT stands for Linear Variable Differential Transformer. It is an important type of inductive transducer; those transducers that work on the principle of transduction mechanism are known as inductive transducers. LVDTs are considered the most accurate inductive transducer to measure the linear displacement from the polarity and magnitude of the net induced electromotive force (emf), which is why they are also known as the Linear Variable Displacement Transducer. Basically, LVDT is a position sensor that has the ability to sense and convert the linear motion or vibrations into electrical signals or a variable electrical current in the circuit. Here in this article, we’ll discuss the construction, working, and various parameters of LVDT.

Construction of LVDT

The Structure of LVDT is similar to the transformer, it consists of one primary winding, i.e., P and two secondary windings, i.e., S1 and S2. The primary and secondary windings are wounded on a hollow cylindrical shaped structure called former. The former is usually made of glass-reinforced polymer wrapped in a highly permeable material and then covered with cylindrical steel. The primary winding is at the centre of the cylindrical former and the secondary windings are present on both sides of the primary winding at an equal distance from the centre. Both the secondary windings consist of an equal number of turns, and they are linked with each other in series opposition, i.e., they are wounded in opposite directions but are connected in series with each other. The series-opposed connection ensures that the induced emf in both the secondary coils opposes each other. The primary winding is connected with the constant source of the AC power supply whose values ranges from 50 Hz to 20 kHz. This whole coil assembly remains stationary during the linear distance measurement process. The movable part of LVDT is a separate arm that is made up of a magnetic material. It is usually a soft iron core, which is laminated to reduce the losses due to eddy current. The core can freely move within the hollow coil (former), and the object whose displacement is to be measured is attached to the core through a non-magnetic rod. The hollow former has a larger radial diameter than that of the core to ensure zero physical contact between them and the coil can easily move within the former.

Construction of LVDT

Working Principle of LVDT

The working of LVDT is based on the principle of Faraday’s law of electromagnetic induction that states that “the net induced emf in the circuit is directly proportional to the rate of change of magnetic flux across the circuit, and the magnetic flux of the coil wounded with wires can be changed by moving a bar magnet through the coil.”As the primary winding of the LVDT is connected to the AC power supply, the alternating magnetic field is produced in the primary winding, which results in the induced emf the secondary windings. Let us assume that the induced voltages in the secondary windings S1 and S2 be E1 and E2 respectively. Now, according to Faraday’s Law the rate of change of magnetic flux, i.e., dØ/dt is directly proportional to the magnitude of induced emf’s, i.e., E1 and E2. Hence, the induced emf in the secondary windings will be more if the value of ‘dt’ will be low (dØ/dt ∝ E1 and E2), and the low value of ‘dt’ implies that the soft iron core present inside the LVDT is moving faster. Thus, emf of large magnitude will induce in the secondary windings S1 and S2 if the movement of the core is faster inside the LVDT.

As we have discussed in the construction above that both the secondary winding S1 and S2 are connected in series with each other but in opposite phases, due to this phase opposition connection, the total output voltage (Eo) in the circuit will be given by,

E0= E1 -E2

Working of LVDT

Characterstics of LVDT with respect to the Position of the Core

The net emf induced in the circuit depends upon the position of the movable core, let us discuss the three different cases according to the position of the core.

CASE 1: Core at the Null Position

As both of the secondary windings have an equal number of turns, and they are placed at an equal distance from the primary winding, hence at the normal position when the core is placed at the centre, the rate of change of magnetic flux will be the same in both the secondary windings. This implies that the induced emf’s E1 and E2 in the secondary windings S1 and S2 respectively will be the same, i.e., E1=E2. Hence, the net induced emf (Eo) in the circuit at the normal position of the core is zero (E1-E2=0). The normal position of the soft iron core at which the net induced emf is zero is called the ‘Null Position’ of the LVDT.

Core at the Null Position

CASE 2: Core at the Left of Null Position

When the position of the core is displaced from the null position, it will result in the electromagnetic imbalance between the secondary windings, and a differential AC voltage will generate across the output terminal of the secondary coils. If the core is moved towards the left from the null position the magnetic flux associated with the secondary coil S1 will become larger than the magnetic flux associated with the coil S2, i.e., the induced emf in coil S1 will be larger than the induced emf in coil S2.

Hence, the tool output voltage (E0) of LVDT is given by,

E0= E1 – E2 = Postive (E1 > E2)

This implies that the total output voltage of the LVDT is positive, i.e., in-phase with that of the primary voltage.

Core at the Left of Null Position

 

CASE 3: Core at the Right of Null Position

If the core is displaced from the null position and moved towards the right, the magnetic flux associated with the winding S1 will be more than that of the winding S2, i.e., induced emf in winding S2 will become more than the emf induced in winding S2.

Hence, the tool output voltage (E0) of LVDT is given by,

Eo= E1 – E2 = Negative (E2 > E1)

This implies that the total output voltage of the LVDT is negative, i.e., out of phase (Φ={180}^{0}) with that of the primary voltage.

Core at the Right of Null Position

From all the three cases discussed above, it can be concluded that the displacement of the body is directly proportional to the output voltage, i.e., the more the displacement of the body, the more will be the output voltage of LVDT. Hence, the direction of the movement of the body attached to the core of the LVDT can find out with the help of net output voltage obtained across the output terminal of the LVDT. One can analyse that the body is moving away from the null position towards the left direction if the output voltage of LVDT is positive; however, if the output voltage of the LVDT is negative it means that the body is moving towards the right from the null position. However, if we take the core out of the hollow structure then the output voltage of the LVDT will become zero. It is observed that when the core is displaced from the null position either towards the left or towards the right, up to the 5 mm displacement, the output voltage increases linearly but after 5mm, it becomes non-linear. Let us understand the linear range and linearity error from the following graph, which shows the variations of the output voltage with respect to the displacement of the body.

Graphical Representation of the Output Voltage of LVDT with respect to the Displacement

Graphical Representation of the Output Voltage of LVDT with respect to the Displacement

Graphical Representation of the Output Voltage of LVDT with respect to the Displacement

The above graph indicates the transfer function of the linear variable differential transducer. The x-axis represents the displacement of the body, and the y-axis represents the magnitude of the output voltage of LVDT. Ideally, when the displacement is zero, the output voltage should also be zero, but there exists a small output voltage even when the core is at the null position because of the residual magnetism of the soft iron core, hence it is called residual voltage of LVDT. When the core is moved away from the null position to either right or to the left the output voltage increases linearly with respect to the displacement of the core to a certain value, and after that non-linear increase of output voltage is observed.

Linear Range: As shown in the graph above, LVDT shows the linear increase in the output voltage only for a limited range of displacement of the core, the range up to which linear transfer function is observed is called the linear range of LVDT. Now, let us understand that why the output voltage is observed non-linear after a certain range of displacement. The maximum distance that can be travelled by the core from the null position up to which the linear transfer function can be observed is known as the full-scale displacement. When the core is displaced further after full-scale displacement, the magnetic flux associated with the core due to the primary winding P becomes low, which eventually results in the reduction of the voltage across the secondary windings S1 and S2.

Linearity Error: Linearity error is the maximum deviation of the output voltage from the expected straight line in the output versus displacement graph. It is clearly observed from the graph, that the variation of the output voltage with respect to the displacement in the linear range does not give a perfectly straight line. The reason behind the non-linear curve even in the linear range is due to the saturation of the soft iron core, which results in the third harmonic component even when the core is at the null position. The harmonic components can be repressed by using the low-output filter at the output terminal of the LVDT.

Sensitivity: The sensitivity of the LVDT tells about the relation between the output voltage of LVDT and the displacement of the core. It is also known as the transference ratio of the LVDT. The sensitivity of the LVDT is measured when the primary AC source is kept at the particular voltage (3 Vrms) and when the core is displaced by the full-scale displacement from the null position, and then the voltage across the windings S1 and S2 is measured to find out the net output voltage of the LVDT. The sensitivity of the LVDt is then calculated by substituting the obtained values in the following equation.

Sensitivity = V output / (Vprimary × Core Displacement)

It is expressed in the terms of mV/V/mm or mV/V/in, i.e., millivolt output per volt of excitation per displacement of the core in millimetres/inches.

Applications of LVDT

  • Apart from the measurement of displacement, LVDT can also be used to measure other physical quantities like force, pressure, and weight if it is used as a secondary transducer. For example, a Bourdon tube can be used as a primary transducer that can measure the pressure by converting it into linear displacement, and then we can get the pressure reading using LVDT that converts the linear displacement into the voltage or electrical signals.
  • LVDT is used in civil engineering to test the strength of the various soil samples and rocks to be used in the construction of buildings or bridges and to measure other factors like spring tensions, weight, and displacement.
  • It is also used in the medical field for the manufacturing of pills. A computer-controlled hybrid mechanism consisting of primary and secondary windings transducers are used for this purpose, it reduces human errors and accurately measures the weight and thickness of the pills.
  • They also find its applications in inspecting the quality of flat display panels by monitoring the waveform at the output terminal of LVDT.
  • It is used in ṭhe aerospace industry to monitor various mechanisms like flight control and pilot control. Various mini-positon transducers are mounted at the fixed positions, and the moving core is attached to the moving parts, for example, landing gears. when the landing gears are moved the core also displaces from the null position and various output electrical signals will provide the angles, lengths, motion, and rate of the moving depending upon the sensitivity of LVDT and the mounting system.
  • It is used in hydraulics for the detection of any leaks or damage to objects that are submerged in non-corrosive and non-conductive fluids. LVDT sensors are also used in robotic manipulators.

Advantages of LVDT

  • LVDT is a frictionless device as there is no direct contact between the moving core and the fixed coil structure (former). This reduces the damage to the device due to the absence of water and tear because of friction. Hence, the mechanical life of LVDT is quite longer than the other devices that have friction during the working process.
  • It can be used to estimate the displacement of the object ranges from a fraction of millimetres to few centimetres. LVDTs that have the ability to measure the displacement of broad ranges (±100μm to ±25 cm) are widely used in laboratories and for industrial purposes.
  • LVDT does not require the application of an amplifier to enlarge the signals as LVDT provides high output signal and is highly sensitive to even small displacements.
  • They consume very low electricity, usually less than 1 W, and they also show less hysteresis loss, which increases their reliability.
  • LVDT are of small size and are very lightweight, hence they can be easily managed and aligned as per the requirements, and despite their small size and lightweight nature, they have the ability to bear mechanical shocks and vibrations.
  • The coil and core of the LVDT are magnetically coupled with each other and there does not exist any direct connection, hence they can be separate from each other. This can be done by inserting a tube, made of non-magnetic material, between the core and the former. This assembly is usually utilized in hydraulics for various measurements, here, the pressurized fluid is added to the inserted tube.
  • LVDT’s are built of quality materials and techniques that can easily withstand corrosion, pressure and extreme temperatures. The Null point of the LVDT usually remains stable even at temperatures above its operating temperature.
  • As there is no friction during the operation of LVDT, hence the position of the core can be changed rapidly which results in the dynamic responses of the LVDT. The only thing that is considered to limits the dynamic responsive nature of the LVDT is the mass of the core.
  • The LVDT provides the absolute value. It means that the LVDT does not lose its position data in case of abrupt power failure. The value of the output remains the same if the measurement is restarted as it was measured before the power failure.

Disadvantages of LVDT

  • The major disadvantage of the LVDt is that an additional circuit is required to deal with the stray magnetic field produces across the electric circuit. The stray magnetic field arises due to the inductive transducer mechanism of the LVDT.
  • The performance of the LVDT may lag due to the unwanted vibrations or temperature changes in the device.
  • The output obtained by the LVDT is AC, hence, a demodulator is required to get the DC output.
  • The fast dynamic responses of the LVDT may get limited due to the mass of the movable core or due to the frequency of the applied primary voltage.

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