Laminated cores simulation

Laminated cores or laminations are used in the electrotechnical devices of almost any type. The goal of lamination is to decrease the eddy current and losses by splitting the ferromagnetic material into smaller sections, insulated from each other electrically. Due to lamination the amount of the flux conductive media (pure steel) is somewhat less then total width of laminated core. It is taken into account by use of lamination factor k_st, which is equal to the ratio of the sum of steel part widths to the total width of the laminated core:
k_st = l_st / l_total

Electromagnetic simulations of the device or equipment, which has laminated parts, may be performed using special approach, allowing replacement of the layered materials in the laminations by homogenous media with specially adjusted magnetic properties. Finite element mesh density in the laminations may be decreased, which leads to decrease of the computer resource requirements, and considerably increases the speed of simulation of the device with laminations.

In the linear problem involving laminated core you can simply reduce the magnetic permeability of the core by k_st factor:
μ1 = μ * k_st.
In non-linear case it is necessary to define the magnetization curve. Instead of material original curve B(H) the modified curve B1(H) should be used.

Input data:
units: H B
columns order:
Stacking factor k_st =

Output data: B1(T) H(A/m)

In the strong fields the difference between B and B₁ becomes significant. For example, the flux density B = 1.3 T corresponds to magnetizing force H = 1080 A/m. Considering lamination the actual flux density is B1 = 1.3/0.93 = 1.4 T. This flux density value corresponds to the magnetizing force of H₁ = 1490 A/m, i.e. flux density difference 7% leads to magnetization force difference of about 38%.

More about laminated cores simulation and design:
Saturable reactor.
Laminated cores simulation and design in the recorded webinar:
QuickField Analysis for Electric machines design.
Additional links on this subject: Stacking factor from Wikipedia, the free encyclopedia.

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