How Core Laminations Reduces Eddy Current Loss?

We are well aware of the fact that electrical machine core is made up of laminated sheets. This is done to reduce the eddy current loss. But how laminated core reduces the eddy current loss and what is the relation between the Eddy Current Loss and thickness of lamination?

Let us consider an electrical machine as shown in figure below.

Let the rotor of the machine is made of solid iron core. Suppose the cross-sectional area perpendicular to the magnetic field is A. Therefore, the total flux linkage of rotor with the magnetic field will be Ø = BA. As the rotor of machine rotates, the magnetic flux linking with the solid rotor body will change with time. Therefore according to Faraday’s Law of Electromagnetic Induction, an emf will be induced on the body of rotor core. This current is called the Eddy Current.

The resistance offered to this Eddy Current by the solid rotor core will be inversely proportional to the cross sectional area of the core. Thus,

R_solid = Resistance offered by solid rotor core = k/A

where k is some constant.

Therefore,

Eddy Current Loss = (emf induced in solid rotor core)² / Rsolid 

Let the emf induced in the solid rotor core = E

Hence,

Eddy Current Loss = AE² / k  ……………………..(1)

Now suppose the same rotor core of machine is made of 4 laminated sheet stacked together as shown in figure below.

As 4 laminations are stacked together, hence the cross-sectional area of each lamination perpendicular to the magnetic field will become (A/4). Thus, the flux linking through each lamination will be Ø = BA/4. Therefore emf induced in each lamination will be (1/4)^th of the emf induced in the solid iron core.

So, emf induced in each lamination = E/4

Let us now calculate the resistance offered by the lamination to the eddy current.

R_lamination= Resistance offered by each lamination = 4k/A

Therefore,

Eddy Current Loss in each Lamination = (emf induced)² / Rlamination

                                                                = A(E/4)² / 4k

                                                                 = AE²/64k

As there are 4 laminations, hence total eddy current loss

= 4 x AE²/64k

= AE²/16k  …………………………..(2)

Thence,

(Eddy Current Loss in Laminated Rotor / Eddy Current Loss in Solid Rotor)

= 1/16    ……………………[from equation (1) and (2)]

=(1/4)²

If the axial length of rotor is assumed to be unity then the thickness of each lamination will be ¼. Therefore, we can say that Eddy Current Loss is directly proportional to the square of lamination thickness. If more lamination are used for a given rotor axial length, the thickness of lamination decreases which result in decrease in Eddy current loss. Thus the use of thin lamination reduces the Eddy Current Loss. Normally the thickness of lamination is in between 0.4-0.5 mm. Further reduction in the thickness results into reduction of loss but at an increased cost.