 Good day everyone. I'm assistant professor Ruchad Mistry from the Mechanical Engineering Department, Walsh Institute of Technology, Sholapur, and for today's class, I'll be discussing inductive sensors. The learning outcome of this session is that the learner will be able to list features of inductive sensors, explain principle of operation of inductive sensors, and inumerate applications of inductive sensors. In the previous class, we discussed about what sensor classification, what is measurement system, potentiometric sensors, and so we'll continue from there, and in today's class we'll be discussing inductive transducers, which is again a very important family of transducers, which is extremely and very widely used in industry. Based on Faraday's laws of electromagnetic induction, these inductive transducers are based on Faraday's laws of electromagnetic induction, which states that the induced voltage or AMF is proportional to the rate at which magnetic flux for the circuit changes, and if a varying magnetic flux is applied to a coil and each turn has the same area, then the flux is given by the formula v is equal to n d phi by dt. Now continuing, flux is also given by b into a, where b is the magnetic field strength and a is the area of the coil. So the equation when rewritten is given as v is equal to n d phi by dt. This again gets written as n derivative of b into a, in which which finally we write as v equal to d is high by dt. The inductance L in turn is given by is high upon i, and hence this whole thing is rewritten as n phi upon i. Now flux is also given as n i by r, where i is the current and r is the reluctance of the flux bar. So finally the self-inductance can be rewritten by the following formula where L equals to n square mu A by L. Now the whole intention of this exercise is to see how different parameters can be varied in order to get a certain value of self-inductance. So this tells us that the inductions can be varied by changing either the length or the area of the coil by the effective permeability of the medium, which is mu, changing the reluctance of the magnetic path and by variation of the air gap. So the different ways by which one of these features can be altered in order to vary the inductance, so which we can measure it later. Now inductive transistors typically when constructing inductive transistors, they consist of two parts which are mounted on ion cores, one part being stationary and the other movable. The displacement changes the position of the moving part of the coil, which produces a change in the self-inductance of the coil. Transistors can be designed, which utilize variation in the number of turns as well. The output relation then in turn can be written as L equal to n square, proportional to n square, sorry, which is in turn proportional to displacement square. So inductance in turn is proportional to the square of the displacement, which is being measured. So coming to LVDTs, which are a special case of inductive transistors, these are based on the principle of mutual inductance, not self-inductance, and hence we'll be discussing mutual inductance in a minute. Now consider two coils which will be labeled 1 and 2 and turns n1 and n2, and the current i is going to foil one which produces a flux. If r is the reluctance of the magnetic flux, then the induced MF in coil 2 due to the current i will be given by the formula e2 is equal to n2 d phi by dt, which if you notice can be simplified and written as e2 is equal to Mdi by dt, where M is the coefficient of mutual inductance. So mutual inductance again is written as n1 and n2 upon r. Now if you account flux encages, coefficient of coupling, etc., etc., the final formula for M works out to be k under root L1 and L2. Now mutual inductance of the coil can be affected by this, changing in the self-inductance, either of the self-inductance or the coefficient of coupling. So this is what the LVDT will try to exploit when measuring displacement. So when the core is at the center, the LVDT core is at the center, the voltage induced in each secondary will be the same. When the core is displaced, there is a change in flux linkage which causes one of the secondary voltage to increase and the other to decrease. The voltage amplitude is linear with the core displacement over some range of the core and this is typically where the measurement will actually be done. If you intend to measure in the nonlinear ways, then corresponding circuitry, signal conditioning circuitry will be required. Now take a look at the LVDT construction. You have a primary core as discussed labeled as P1 and two secondaries S1 and S2. These are connected in phase opposition as shown in the circuit diagram next to it. The result is that when the core is in the central position, the voltage in the secondaries is zero. As the curve moves, the voltage will be developed in the secondaries and there is a linear range which is a good range when it comes to measurement. So basically the LVDT is a transformer with a mechanically actuated core. The primary coil is driven by a sine wave excitation signal having from a stabilized amplitude. It eliminates error related to harmonics and AC signal is induced in the secondary coils. The core is typically a ferromagnetic material inserted coaxial into the cylindrical opening without physically touching coils. So this is non-contact and there is no friction as such involved in this. That's one of the reasons it gives very accurate measurements. The two secondary coils are connected in an opposed phase. When the core is positioned in the magnetic center of the transformer, the secondary output signal cancels and there is no output voltage. Moving the core away from the central position unbalances the induced magnetic flux between the secondary coils and develops an output. As the core moves, the reluctance of the flux path changes and the degree of flux happening depends upon the axial position of the core which in turn is the displacement being measured. At a steady state the linear operating region, the amplitude of the induced voltage is proportional to the course voltage and hence voltage is used as the measure of the space. So here the output is voltage and the input is displacement. The LVDT provides direction as well as magnitude displacement. The direction is determined by the phase angle between the primary reference voltage and the secondary voltage. Remember all sophisticated instrument will have additional signal conditioning circuitry to eliminate noise to account for non-linearities etc. So where can you find an application for elevators, let's say for our laboratory projects? Now if you actually do a survey, some manufacturers, elevators, manufacturers advertise as DTDC inductive sensors as well. So what are DC-DC inductive sensors? Because basically from what we know transformer action is basically an easy phenomenon. So try to find out what it means, what is unique about these particular sensors? Now coming back to LVDT, what are some of the unique features of LVDT? And we'll see why these features make it so important in certain applications. LVDTs can resolve very small displacements. They have very high resolution accuracy and very good stability. And hence they are ideal for applications involving short displacement measurements, especially where precision is required. The sensor is a non-contact device with very little friction with very small resistive force. There are certain applications where it can be used for dynamic measurement, but not as extensively as a capacitive transducer. Hysteresis are negligible and output impedance is low. So these are very unique and desirable features of LVDT. It has lower susceptibility to noise and interference. It has a very solid and robust construction. In fact, if you go to websites of different manufacturers, you'll notice that they have advertised the LVDT with infinite symbol resolution. So this indicates how accurate these devices are available today in the market. And they are available in very wide measurement ranges from nano measurement to measurement involving up to several millimeters as well. So what are the other issues with the LVDT? So some of the negative features are, the heavy core limits its application for dynamic measurement. So since the magnetic core is heavy, for transient motions, frequency of the momentum has been at least 10 times the highest significant frequency which may be involved in the measurement. Now, when it comes to misalignment and nonlinear motion, to be very honest, textbooks typically tend to mention the fact that LVDTs are susceptible to misalignment and nonlinear motion. And hence it must be avoided in these cases. I have seen manufacturers advertise their LVDT products as being tolerant to misalignment and being highly linear. So I'll leave it to you when it comes to this. Textbooks tend to say a certain thing, whereas manufacturers tend to advertise the LVDT as extremely tolerant to misalignment and nonlinearities. Now what are the other features of LVDTs? Inductive transducers typically are used in proximity sensing, position detection, motion control, process control, and the applications can be generalized as measurement of precision gap between well-touched work surfaces, thicknesses of plate in rolling mills, detection of surface irregularity, which are very typical applications of LVDTs. Other applications typically, and very specific applications, are engage heads, especially in inspection and gauging. LVDTs may also be used as secondary transducers involving pressure and force measurement, and as primary transducers also in other cases. A small survey which I have done for applications on different websites of LVDT manufacturers, and I have summarized the applications as typically as follows. Extensively used in server position systems. One application which came up was currency thickness measurement in ATM machines, suspension field-bound travel in automatic control systems or suspensions, height thickness inspection in assembly, level monitoring, which is a very generic application, and inspection machines. So as you see there are a wide range of applications for LVDTs in industry. Now the books that I have referred to this is Mechatronics Handbook by Bishop, and Introduction to Mechatronics by Bolton, along with Mechatronics System designed by Shetty. Thank you very much, and we'll be continuing with other senses in the next class.