The unsymmetrical hysteresis loop

The paper gives results and analyses of tests to determine losses in hysteresis loops wherein the magnetism is carried through cycles in which limiting values of flux are different in amount or the mean values of flux differ from zero. Such variations of magnetism occur in inductor generators, in teeth of induction machines and in materials magnetized from rectifier circuits, etc. The author finds that: 1. The losses in unsymmetrical loops are greater than in symmetrical loops of the same difference of limiting values of flux. 2. For loops of the same difference of limiting values of flux, the losses increase as a definite power of the mean flux density. 3. The increased loss as a power of the mean density is the same for any range of loops or difference of limiting flux values. 4. With any given value of mean density, the increased losses with increased range increases as definite power of the range irrespective of the mean value of density selected. The author covers these points in an equation to express the loss in any loop. The general equation is:
$h=(\eta + \alpha B_{m^{y}}) B^{x}$
wherein η and x are the constants of the Steinmetz law, α is a coefficient depending upon the material, and y a power of the mean density. The present tests satisfied the equation in the form:
$h=(\eta + \alpha B_{m^{1.9}}) B^{1.6}$
.