CHAP. Ill] HYSTERESIS AND EDDY CURRENTS 53 



of steel laminations other than those given in Fig. 10, or at a differ- 

 ent frequency. For this purpose, it is necessary to separate the 

 loss due to hysteresis from that due to eddy currents, because the 

 two losses follow different laws, expressed by eqs. (20) and (22) 

 respectively. 



In order to separate these losses at a certain flux density it is 

 necessary to know the value of the total core loss at this density, 

 and at two different frequencies. For a given sample of lamina- 

 tions, the total core loss P at a constant flux density and at a 

 variable frequency /, can be represented in the form 



(23a) 



where Hf represents the hysteresis loss, and Ff 2 the eddy or Fou- 

 cault current loss. H is the hysteresis loss per cycle, and F is the 

 eddy-current loss when / is equal to one cycle per second. Writing 

 this equation for two known frequencies, two simultaneous equa- 

 tions are obtained for H and F, from which H and F can be deter- 

 mined. 



In practice the preceding equation is usually divided by/, lo- 

 calise in the form 



....... (236) 



it represents the equation of a straight line between P/f and /. 

 This form is particularly convenient when the values of P are 

 known for more than two frequencies. In this case the values of 

 P/f are plotted against / as abscissae, and the most proliaMe 

 straight line is drawn through the points thus obtained. The 

 intersection of this straight line with the axis of ordinates gives 

 directly the value of H. After this, F is found from eq. (236). 



Knowing H and F at a certain flux density, the separate losses 

 ///and Ff 2 can be calculated for any desired frequency. For the 

 same material, but of a different thickness, the hysteresis loss per 

 :ht is the same, while the eddy-current constant F 

 varies as the square of the thickness, according t _'). Thus, 



knowing the eddy loss at one thickness it can be estimated for any 

 other thickness. 



It is sometimes required to estimate the iron loss at a flux den- 

 sity higher than the range of the available curves; in other words, 



the proMem is soim-times put to extrapolate a curve like one of 



those in liV. 10. There arc two cases to be considered. 



