Errors in the magnetic testing of ring specimens

It is the usual practice to make the ratio of the radial thickness to the mean diameter of a ring about 1/10 to 1/15, so as to limit the error due to non-uniform flux distribution. The adoption of a ratio of this order is apparently based upon the work of M. G. Lloyd, who calculated the errors involved in the determination of the magnetization curve and of the hysteresis loss for various ratios of radial thickness to mean diameter. His calculations, however, were based on the assumption of constant permeability. It is shown in this paper that, when the variation of permeability is taken into account, the errors involved in the determination of the above-mentioned quantities are almost invariably either smaller or larger than those calculated by Lloyd. The paper discusses the influence of the ratio of radial thickness to mean diameter, and of reluctivity, upon:- (a) The relationship between the average flux density in the ring and the flux density corresponding to the average magnetizing force. (b) The relationship between the actual hysteresis loss in the ring and the hysteresis loss in the same volume of iron owing to the flux density corresponding to the average magnetizing force. The influence of the exponent of B upon this relationship is also considered. (c) The relationship between the true hysteresis coefficient and that determined from a test performed with (1) an alternating-current supply, (2) a ballistic galvanometer. Reference is made to the desirability¿under certain conditions¿of using a higher ratio of radial thickness to mean diameter than is customary, in order that any error due to mechanical strain produced by punching, etc., may be reduced.