Effect of Empirical Constant of Ramberg-Osgood Relation on the Buckling Strength of Transformer Inner Winding

The governing equation for determining the critical buckling stress of the inner winding of a transformer is nonlinear as well as non-polynomial. The non-polynomial nature of the equation is due to the non-integer value of an empirical constant denoted by ‘m’ which is present in the Ramberg-Osgood stress-strain relation. Therefore, the solution of the equation is to be determined by the numerical method like Newton-Raphson method for which an initial guess is required. In this letter, an investigation has been done to determine the effect of changing the existing non-integer value of ‘m’ to an integer value on the inner winding's critical buckling stress. With the integer value of the empirical constant, the equation becomes a polynomial, and then by determining the eigenvalues of polynomial's companion matrix, the roots of the polynomial have been determined. It is observed from the case studies that the result obtained with the integer value of the empirical constant is in close agreement with the non-integer value of the constant.