Explain how the magnitude and direction of displacement can be measured with the help of an inductive sensor? [2075 Bharda 6 Mark]

  

Ans: We can measure the magnitude and direction of displacement with the help of linear variable differential transformer (LVDT) which is described below:-

Working Principle: 

when a sinusoidal input V_i =V_msinѠt is applied to the primary winding, a sinusoidal flux will link with primary winding(p), as well as two secondary windings S₁ and S₂ due to high permeability of the core the reluctance of the path will be very low . As S₁, S₂ are stationary and the flux is rotating, the flux will cut both S₁ and S₂. So, there will be induced emf e₀₁ and e₀₂ in S₁ and S₂ respectively. As S₁ and S₂ are connected in series opposition, the differential output, Δe₀ = e₀₁ - e₀₂. The differential output Δe₀ will be either in phase with input voltage (V_i) or it will be 180 out of phase with input voltage (V_i)

 

					Figure 2: variation of output voltage with linear displacement
		Figure 1: linear variable differential transformer

 

Case I: core at the midpoint between S₁ and S₂ 

Suppose no displacement is applied then the iron core will be in the middle of the S₁ and S₂ in that case the flux linking with both S₁ and S₂ will be same ideally. So, the induced emf e₀₁ and e₀₂ will be equal. Hence ideally the differential output Δe₀ = e₀₁ - e₀₂=0. But in actual practice, there will be some differential output due to the harmonics. This differential output is known as residual voltage as shown in figure 2 

 

Case II: core moving left side 

 

 let’s us suppose a moving object is connected to the shaft and the object is moving in the left-hand side  then the flux linking with S₁ increases and that of S₂ decreases. So e₀₁ increases and e₀₂ decreases and the differential output, Δe₀ = e₀₁ - e₀₂ increases. So, there exists a linear relation between the differential output and the displacement up to the saturation point as shown in figure 2.and the differential output in this case is in phase with input voltage (V_i). 

 

 

 

 

Case III: Core moving right side:

 Again, let’s suppose the core is at the mid-point and a moving object is connected to shaft and now it is moving in right hand side flux linking with S₂ increases and that of S₁ decreases. So, e₀₂ increases and e₀₁ decreases and the differential output, Δe₀ = e₀₂ - e₀₁ increases  again there exists a linear relation between differential output and the displacement up to the saturation point as shown in the figure 2  and beyond saturation point that relation is no more linear. and the differential output in this case is 180⁰out of  phase with input voltage (V_i). 

 

So, we conclude that magnitude of differential output gives the magnitude of displacement and phase angle of differential output gives the direction of displacement in this way, we can measure both direction and magnitude of the displacement by using LVDT .