In concentric arrangement, how is the distribution of leakage flux in the windings and the resulting electromagnetic forces explained?

For double-winding concentric arrangement, the leakage flux is generally smaller than in a single concentric arrangement, and it is even further reduced in multi-winding concentric arrangements. Let's take the example of a double-winding single concentric arrangement to illustrate how the leakage flux is distributed.

In a double-winding setup, the current directions are opposite. Assuming the low-voltage winding current flows outward (represented by ⊙) and the high-voltage winding current flows inward (represented by ×), according to the right-hand rule, the leakage flux between them (represented by dashed lines) must go upward.

For convenience, the leakage flux can be divided into two components: axial (vertical) leakage flux and radial (horizontal) leakage flux. The axial leakage flux is vertical, while the radial leakage flux results from the outward dispersion of leakage flux at the upper end of the winding and the inward convergence at the lower end, generating a horizontal component. According to the left-hand rule, axial leakage flux generates radial electromagnetic forces, and radial leakage flux generates axial electromagnetic forces.

Axial leakage flux causes an outward radial tension on the outer high-voltage winding, requiring an increase in the diameter of the high-voltage winding. In the circumferential direction, it undergoes tensile stress, and the winding conductors must withstand this force. Conversely, axial leakage flux causes an inward radial pressure on the inner low-voltage winding, compressing the circumferential direction. During design and manufacturing, precautions must be taken to prevent instability and deformation in this winding.

Radial leakage flux induces both high and low-voltage windings to experience inward axial pressures. This force acts as a compressive force on the winding, and the conductors at both ends bear the maximum force. The compressive force on the spacers is the resultant force of the forces acting on the conductors, making this force maximum in the middle of the winding. The stress generated by these forces in the conductors and spacers must be limited to an acceptable range. For spacers made of oil-immersed laminated paperboard, the allowable compressive stress should be below 39.2 MPa.

Additionally, due to variations in winding height, imbalance in turns, and the removal of tap segments, the axial pressures and tensions generated are similar to those in an interleaved arrangement.

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