The linear variable differential transformer (LVDT) is used to measure the translational displacement of the object which is in physical contact with it.
Construction:
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 only moving part in an LVDT is the central iron core.
Principle and Working:
The object whose translational displacement is to be measured is physically attached to the central iron core of the transformer, so that all motions of the body are transferred to the core. 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 between the top secondary voltage and the bottom secondary voltage.
The parameters Ka and Kb, depend on the amount of coupling between the respective secondary and primary windings and hence on the position of the iron core. With the core in the central position, Ka = Kb, and we have: Va =Vb = K sin (ωt - ɸ)
Because of the series opposition mode of connection of the secondary windings, V0 = Va - Vb, and hence with the core in the central position, V0 = 0. Suppose now that the core is displaced upwards (i.e. towards winding A) by a distance x. If then Ka = K1 and Kb = K2, we have:
V0 = (K1 - K2) sin (ωt - ɸ)
If, alternatively, the core was displaced downwards from the null position (i.e. towards winding B) by a distance x, the values of Ka and Kb would then be Ka = K2 and Kb = K1, and we would have:
V0 = (K2 – K1) sin (ωt - ɸ) = (K1 – K2) sin (ωt + [π - ɸ])
Thus for equal magnitude displacements +x and -x of the core away from the central (null) position, the magnitude of the output voltage V0 is the same in both cases. The only information about the direction of movement of the core is contained in the phase of the output voltage, which differs between the two cases by 180°. If, therefore, measurements of core position on both sides of the null position are required, it is necessary to measure the phase as well as the magnitude of the output voltage. The relationship between the magnitude of the output voltage and the core position is approximately linear over a reasonable range of movement of the core on either side of the null position, and is expressed using a constant of proportionality C as V0 = Cx.Measurement:
As the core is only moving in the air gap between the windings, there is no friction or wear during operation. For this reason, the instrument is a very popular one for measuring linear displacements and has a quoted life expectancy of 200 years. The typical inaccuracy is ±0.5% of full scale reading and measurement resolution is almost infinite. Instruments are available to measure a wide span of measurements from ±100µm to ±100mm. The instrument can be made suitable for operation in corrosive environments by enclosing the windings within a non-metallic barrier, which leaves the magnetic flux paths between the core and windings undisturbed. An epoxy resin is commonly used to encapsulate the coils for this purpose. One further operational advantage of the instrument is its insensitivity to mechanical shock and vibration.
Limitations:
Some problems that affect the accuracy of the LVDT are the presence of harmonics in the excitation voltage and stray capacitances, both of which cause a non-zero output of low magnitude when the core is in the null position. It is also impossible in practice to produce two identical secondary windings, and the small asymmetry that invariably exists between the secondary windings adds to this non-zero null output. The magnitude of this is always less than 1% of the full-scale output and in many measurement situations is of little consequence. Where necessary, the magnitude of these effects can be measured by applying known displacements to the instrument. Following this, appropriate compensation can be applied to subsequent measurements.
