284 



ELEMENTS OF ELECTRICAL ENGINEERING. 



Consider one of the polar regions of the stator, as shown in Fig. 245, in which 

 the stator and rotor surfaces are represented as being flat. The ordinates of the sine 

 curve represent the flux densities (mean flux densities, the flux being considered as 

 not concentrated in tufts under the stator teeth) in the gap space at various points in 

 the polar region. Let / be the breadth of the polar region as indicated in the figure, 

 and let A * be the length of stator and rotor iron parallel to the motor shaft. The 

 average flux density over the whole polar region is equal to two times the maximum 

 flux density (maximum mean flux density is here referred to, tufts assumed not to 

 exist) divided by TT, inasmuch as the distribution is harmonic ; but the average flux 

 density over the whole polar area is $/A/, therefore the maximum flux density (irre- 

 spective of concentration of lines of force as tufts under stator teeth) is 7r4>/2/t/. 



Fig. 246. 



Figure 246 represents a portion of an induction motor, N being the center of 

 a north polar region and 5 .the center of a south polar region at a given instant. 

 The mean flux density in the gap space at N or S is 7r4>/(2/l/), / being the dis- 

 tance from N to S measured along the gap space. The flux density in, or under, 

 a stator tooth at N or S is 7r<l>/(2A/) X (t + *)/*> where t is the width of a 

 stator tooth and s is the width of a stator slot. The flux density in the portion y 

 of the stator core is equal to \<b divided by "ky. 



(6) Calculation of power component of magnetizing current. The product of 

 the supply voltage by the power component of the magnetizing current per phase is 

 equal to (P e + P h )fy where P 6 -f P h is the total loss of power in the stator iron 

 due to eddy currents and to hysteresis, and q is the number of stator phases. Know- 

 ing the maximum flux density in the stator teeth, the volume of iron in the stator 

 teeth, the thickness of the laminations, and the primary frequency /, the eddy-cur- 

 rent and hysteresis losses in the stator teeth may be calculated as explained in Art. 

 103 ; and, knowing the maximum flux density in portion y of the stator iron, the 

 volume of this portion of iron, the thickness of the laminations, and the frequency, 

 the total loss in the portion y of the stator iron may be calculated. Then 



(c) Calculation of wattless component of the magnetizing current. The watt- 

 less component of the magnetizing current is assumed to supply the magnetomotive 



*A11 dimensions expressed in centimeters. 



