Critical stresses of radial stability of flexible circular ring with initial plastic bending strains

Purpose. With regard to plastic bending strains originating during fabrication, there has earlier been studied stability of the flexible circular ring with rectangular cross section without fillets as applied to analysis of transformer winding conductors. Real conductors have fillets in cross section corners. Conductors with round cross section are widely utilised. It is necessary to determine critical stresses of radial stability of flexible circular rings with round and filleted rectangular cross sections with initial plastic bending strains originating during fabrication. Methodology. With regard to initial plastic bending strains, there were determined critical stresses of radial stability of the ring with round cross section. There was developed a numerical method for determining critical stresses of radial stability of the ring with filleted rectangular cross section with initial plastic bending strains. This method covers all conductor cross section types utilised in transformers. Findings. The methods developed were applied to calculation of critical stresses of radial stability of windings with round and rectangular conductors. The obtained results demonstrated that due to the initial plastic bending strains the examined rings (conductors) do not follow Hooke's law. Therefore, the deformable solid body mechanics formulae based upon it are not applicable to such rings. The initial plastic bending strains cause significant reduction of critical stresses of radial stability, thus the methods that do not take these strains into account cannot be used for analysis of the rings under consideration. Comparison of calculation results and windings test data confirmed validity of the methods developed. Originality. There was developed a generalised numerical method for determining critical stresses of radial stability with regard to initial plastic bending strains that covers the rings with round and filleted rectangular cross section. Practical value. The developed methods for calculation of critical stresses of radial stability of flexible rings with round and filleted rectangular cross section are widely used for stability analysis of transformer winding conductors under the action of radial compressive short circuit forces.