In this paper, the magnetic flux density distribution on the cross-sections of a transformer core is studied. The core for this study consists of two identical U-shaped cores joint at their open surfaces with known air gaps. The magnetic flux density at one of their joint boundary surfaces was measured for different air gaps. A finite element model (FEM) was built to simulate the magnetic flux density and compared with experiment data. Using the validated FEM, the distributed magnetic flux density on the cross-section of the core structure can be obtained when the air gap approaches zero. An engineering model of the density based on the Ampere’s circuit law was also developed and used to explain the relationship between air gap and mean magnetic flux density on the cross-section. The magnetic flux density on the cross-section was found to have a convex-shaped distribution and could be described by an empirical formula. Using this approach, the magnetic flux density distribution in cores with different interlayer insulation was obtained and discussed. This method could also examine the leakage of magnetic flux density in the air gap region when the distance is non-zero, and the relationship between the leakage field and the field in the core structure. The proposed method and model can provide a more detailed understanding for the magnetic field of transformer cores and potential application in designing quiet transformers and condition monitoring.
Comparison between measured and computed magnetic flux density distribution of simulated transformer core joints assembled from grain-oriented and non-oriented electrical steel