44 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1951 



The reluctance, as given in the figure, is the reciprocal of this. 



For the gap of Fig. 11, it is more convenient to estimate reluctances, 

 summing the elementary series contributions to the entire gap. For this 

 case: 



A(R = 



Ar 

 brd' 



where 



as noted in the figure. 



(R 



be in r be ^ n' 



(0 — ^ 



WHERE A = AREA OF ONE POLE FACE 



IF THE TWO POLE FACE 



AREAS ARE UNEQUAL, 



USE THE SMALLER VALUE 



Reluctance between parallel plane surfaces. 



Effective Pole Face Area of ari Electromagnet 



As illustrated in Figs. 9, 10, and 11, an individual air gap has a re- 

 luctance represented approximately by an expression of the form: 



(R = 



A' 



where x is the separation measured at the centroid of the area A . Arma- 

 ture motion is usually rotary, and a convenient point for the measure- 

 ment of armature position may be at some distance from the axis other 

 than that of the centroid. If x is so measured, then the separation at the 

 centroid is kx, where k is the ratio of the lever arms, and hence the re- 

 luctance (R is kx/A, equivalent to that of a gap of separation x and pole 

 face area A/k. This area A/k is called the effective pole face area referred 

 to the point at which x is measured. 



In general, an armature has at least two gaps, as illustrated in Fig. 12. 

 The expression for the armature reluctance must include the terms for 

 both gaps which can conveniently be combined as follows. Let x be the 

 armature motion measiu'ed at some distance f from the axis of rotation, 

 as indicated in the figure. Let kix be the corresponding separation at the 

 centroid of ai , and k2X the separation at the centroid of a2 . Then the 



