ET NOTES, LVDT, PDF

# ELECTRICAL AND ELECTRONIC INSTRUMENTATION ## Example 25.19 In a variable reluctance type proximity inductive transducer the coil has an inductance of 2000 µH when the target made of ferromagnetic material is 1 mm away from the core. Calculate the value of inductance when a displacement of 0.02 mm...

# ELECTRICAL AND ELECTRONIC INSTRUMENTATION ## Example 25.19 In a variable reluctance type proximity inductive transducer the coil has an inductance of 2000 µH when the target made of ferromagnetic material is 1 mm away from the core. Calculate the value of inductance when a displacement of 0.02 mm is applied to the target in a direction moving it towards the core. Show that the change in inductance is linearly proportional to the displacement Neglect the reluctance of the iron parts. **Solution:** Inductance with gap length of 1 mm is L=2000 μH. Length of air gap when a displacement of 0.05 mm is applied to the target = 1.00 - 0.02 = 0.98 mm. Now inductance is inversely proportional to the length air gap. Inductance with gap length of 0.98 mm=L+AL=2000×(1/0.98)=2040 μH. Change in inductance AL=2040 - 2000 = 40 μH. Ratio AL/L = 40 / 2000 = 0.02 and Ratio displacement / normal gap length = 0.02 / 100 = 0.02. The two ratios are equal and hence the change in inductance is linearly proportional to the displacement. This, however, is true of only very small displacements. ## 25.27 Linear Variable Differential Transformer (LVDT) The most widely used inductive transducer to translate the linear motion into electrical signal is the linear variable differential transformer (LVDT). The basic construction of the LVDT is given in Fig. 25.37. The transformer consists of a single primary winding P1 and two secondary windings S1 and S2 wound on a cylindrical former. The secondary windings have equal number of turns and are identically placed on either side of the primary windings. The primary winding is connected to an alternating current source. A movable soft iron core is placed inside the former. The displacement to be measured is applied to an arm attached to the soft iron core. In practice the core is made of nickel iron alloy which is slotted longitudinally to reduce eddy current losses. When the core is in its normal (NULL) position equal voltages are induced in two secondary windings. The frequency of a.c. applied to primary winding may be between 50 Hz to 20 kHz. The output voltage of secondary, S1, is E1 and that of secondary, S2, is E2. In order to convert the outputs from S1 and S2 into a single voltage signal, the two secondaries S1 and S2 are connected in series opposition as shown in Fig. 25.38 (b). Thus the output voltage of the transducer is the difference of the two voltages. ### Differential output voltage Eo = E1 - E32 When the core is at its normal (NULL) position, the flux linking with both the secondary windings is equal and hence equal emfs are induced in them. Thus at null position E1=E32. Since the output voltage of the transducer is the difference of the two voltages, the output voltage Eo is zero at null position. Now if the core is moved to the left of the NULL position, more flux links with winding S1 and less with winding S2. Accordingly output voltage E1 of the secondary winding S1, is more than Es2, the output voltage of secondary winding S2. The magnitude of output voltage is, thus, E1-E2 and the output voltage is in phase with E1 i.e. the output voltage of secondary winding S1. Similarly, if the core is moved to the right of the null position, the flux linking with winding S2 becomes larger than that linking with winding S1. This results in Es2 becoming larger than Es1. The output voltage in this case is Eo=Es2-E1 and in phase with Es2 i.e. the output voltage of secondary winding S2. The amount of voltage change in either secondary winding is proportional to the amount of movement of the core. Hence, we have an indication of amount of linear motion. By noting which output voltage is increasing or decreasing, we can determine the direction of motion. In other words any physical displacement of the core causes the voltage of one secondary winding to increase while simultaneously reducing the voltage in the other secondary winding. The difference of the two voltages appears across the output terminals of the transducer and gives a measure of the physical position of core and hence the displacement. As the core is moved in one direction from the null position, the differential voltage i.e., the difference of the two secondary voltages, will increase while maintaining an in-phase relationship with the voltage from the input source. In the other direction from the null position, the differential voltage will also increase, but will be 180° out of phase with the voltage from the source. By comparing the magnitude and phase of the output (differential) voltage with that of the source, the amount and direction of the movement of the core and hence of displacement may be determined. The amount of output voltage may be measured to determine the displacement. The output signal may also be applied to a recorder or to a controller that can restore the moving system to its normal position. The output voltage of an LVDT is a linear function of core displacement within a limited range of motion, say, about 5 mm from the null position. Fig. 25.39 shows the variation of output voltage against displacement for various positions of core. The curve is practically linear for small displacements (upto about 5 mm as mentioned above). Beyond this range of displacement, the curve starts to deviate from a straight line. Fig. 25.40 shows the core of a LVDT at three different positions. In Fig. 25.40 (b), the core is at 0 which is the central zero or a null position. Therefore E1-E2 and hence the output Eo=0. When the core is moved to the left as in Fig. 25.40 (a) and is at A, E1 is more than Es2 and therefore Eo is +ve. By convention, this movement represents a positive value of Eo and therefore the phase angle 0. When the core is moved to the right towards B as shown in Fig. 25.40 (c), Es2 is greater than E1 and hen e E1 is negative. Therefore, the output voltage is 180° out of the phase with the voltage which is obtained when the core is moved to the left. Thus 0=180°. The characteristics are linear up to 0-A and 0-B but after that they become non-linear and flatten out as shown in Fig. 25.39. Ideally the output voltage at the null position should be equal to zero. However, in actual practice there exists a small voltage at the null position. This may be on account of presence of harmonics in the input supply voltage and also due to harmonics produced in the output voltage on account of use iron core. There may be either an incomplete magnetic or electrical balance or both which result in a finite output voltage at the null position. This finite residual voltage is generally less than 1% of the maximum output voltage in the linear range. Other causes of residual voltage are stray magnetic fields and temperature effects. The residual voltage is shown in Fig. 25.4!. However, with improved technological methods and with the use of better a.c. sources, the residual voltage can be reduced to almost a negligible value. ## 25.27.1 Advantages of LVDTs. The advantages of a LVDT are: 1. Linearity. The output voltage of this transducer is practically linear for displacements up to 5 mm. A linearity of 0.05% is available in commercial LVDTs. 2. Infinite resolution. The change in output voltage is stepless as there are no mechanical elements to change the output voltage in discrete steps. The effective resolution depends more on test equipment than on the transducer It is possible to build a transducer with a resolution as fine as 1 x 10-3 mm. 3. High output. It gives a high output and therefore many a times there is no need for intermediate amplification devices. 4. High sensitivity. The transducer possesses a high sensitivity as high as 40 V/mm. 5. Ruggedness. These transducers can usually tolerate a high degree of shock and vibration without any adverse effects. They are simple anl by virtue of being small and light in weight, they are stable and easy to align and maintain. 6. Less friction. There are no sliding contacts and hence there is less friction and less noise. 7. Low hysteresis. This transducer shows a low hysteresis and hence repeatability is excellent under all conditions. 8. Low power consumption. Most of the LVDTs consume a power of less than 1 W. ## 25.28 Disadvantages of LVDTs. 1. Relatively large displacements are required for appreciable differential output. 2. They are sensitive to stray magnetic fields but shielding is possible. This is done by providing magnetic shields with longitudinal slots. 3. Many a times, the transducer performance is affected by vibrations. 4. The receiving instrument must be selected to operate on a.c. signals or a demodulator network must be used if a d.c. output is required. 5. The dynamic response is limited mechanically by the mass che core and electrically by the frequency of applied voltage. The frequency of the carrier should be at least ten times the highest frequency component to be measured. 6. Temperature affects the performance of the transducer. But when temperature effects are expected to affect the performance, manganin wire may be used instead of copper wire. Unfortunately manganin has a high resistivity and therefore its use results in loss of sensitivity. The sensitivity with manganin coils may be as low as 1/5 of that with copper coils. Temperature also causes phase shifting effects which may be minimized by using a capacitor across one of the secondary windings. ## 25.27.3. Use of LVDTs The uses of LVDTs are numerous. Some of the major applications of LVDTs are listed below: 1. The LVDT can be used in all applications where displacement ranging from fractions of a mm to a few cm have to be measured. The LVDT acting as a primary transducer converts the displacement directly into an electrical output proportional to displacement. This is a fundamental conversion i.e. the mechanical variable (displacement in this case) is directly converted into an analogous signal (voltage in this case) in one stage only. In contrast, the electrical strain gauge requires the assistance of some form of a material to act as primary transducer to convert the mechanical displacement into strain which in turn is converted into an electrical signal by the stre gauge acting as a secondary transducer. Therefore two stages of signal conversion are involved in strain gauge while there is only one in case of LVDT when displacement is being measured. 2. Acting as a secondary transducer it can be used as a device to measure force, weight and pressure etc. The force measurement can be done by using a load cell as the primary transducer while fluid pressure can be measured by using Bourdon tube which acts as primary transducer. The force or the pressure is converted into a displacement which when applied to an LVDT (that acts as a secondary transducer) is converted into a voltage. In these applications the high sensitivity of LVDTs is a major attraction. As explained earlier, the LVDT is not suited for fast dynamic measurements on account of mass of the core. ## Example 25.20 The output voltage of a LVDT is 1'5 V at maximum displacement. At a load of 0'5 M2, the deviation from linearity is maximum and it is ±0.003 V from a straight line through origin. Find the linearity at the given load. **Solution:** %age linearity=±( 0.003 / 1.5) ×100 = ±0.2%. # Eddy current Eddy current is a loop of electric carrent that forms in a conductor when the magnetic field around it changes. Eddy current is created when: * A conductor is placed in a changing magnetic field * A conductor moves relative to a magnetic field