An Engineering Model of Magnetic Flux Density and Electromagnetic Force Density at the Structural Discontinuity within Transformer Cores

The structural discontinuities in the form of air gaps in transformer cores cause the concentration of electromagnetic force, which is an important source of transformer vibration and noise. In this paper, an engineering model of magnetic flux density and electromagnetic force density on transformer core discontinuities is analytically developed. Based on a reasonable structural simplification and assumptions, magnetic flux density and electromagnetic force density are deduced as explicit functions of the geometric, material, and electrical excitation characteristics of the gap region and the transformer core. The accuracy of the established model is validated by the finite element method (FEM) combined with a magnetic measurement experiment. According to this engineering model, the electromagnetic force density can be reduced by decreasing the gap ratio and increasing the gap thickness to a reasonable level. The outcome of this paper can help to understand the physical mechanism of the electromagnetic force generated by core air gap discontinuities, which is meaningful for noise control and the condition monitoring of transformers.