MAGNETIC DESIGN OF RELAYS 59 



The effective pole face area, Ao , is determined by equation (18), follow- 

 ing the procedure described in the discussion of Fig. 12. 



The leakage reluctance, (Rlo , is determined in the case of Fig. 22(a) by 

 the procedure discussed in Section 5 and indicated in Fig. 17. In using 

 this, A is the length 1-2, while 4 is the length 2-3 in Fig. 22(b) and 

 ^2 = in Fig. 22(a). The reluctance terms C/2 and C2d correspond to the 

 armature leakage reluctance (Rl.4 of Fig. 3, here taken as in parall(>l with 

 the core leakage reluctance in determining (Rl2 . 



It should be noted that this procedure provides foi two flux paths 

 across each gap: the flux through the reluctance x/Ai , varying linearly 

 with gap, and the parallel leakage flux through a reluctance calculated 

 as though the armature were absent. This representation allows for the 

 effect of fringing, taking the total field across the gap as the sum of these 

 two fields. It carries the implication that experimentally the two fields 

 cannot be separated by search coil measurements. 



For the magnetic circuit of Fig. 21, the low density reluctance is given 

 i)y eciuation (23). The reluctance terms are calculated for maximum 

 permeability m', corresponding to density B', and hence for a total core 

 flux <p' = B'a. As discussed in Section 4, these values are approximately 

 applicable through the low density region, or for <p less than (p'. For ^ 

 greater than (p', (Re is taken as given by equation (13). Thus in the high 

 density region, the total reluctance may be written as: 



(R = (Re + (^E, 

 where. 



(R 

 (Re = — 



<^» + j) 



(Ro + (Rl + J 



(Re = (Rc-TT ' 



(P — (p 



in which, 



// _ ^ (p — (p 

 [x a tp 



and ip" = B"a, where ( and a are the length and cross-section of the 

 core, respectively. The values of B m in Table 1 may be taken as esti- 

 mates of the effective value of the saturation density B" . 



