MAGNKTIC DKSIC.N OF UKLAYS 



63 



7 PULL EQUATIONS 



Pull in Tcrnis of Gap Flux 



With llu> magnetization relations i<nown, the pull can be determined 

 from (^(luations (7) or (8). Ovvv the low density range, in which the 

 magnetic circuit constants are independent of the flux, the field energy 

 r is gi\-en by (')). Sul)stitution of this in (7) gi\-(>s the following expression 

 for the pull F: 





(20) 



In terms of the e(iui\'alent circuit constants of Fig. 23, the reluctance 

 (R is given by equation (24). Substituting this expression in (26) gives 

 the equation: 



F = 



6h 



(iio + (Rl + 



By comparison with (24), it can be seen that the bracketed term is the 

 ratio ai/^cRo + x/A), which equals the ratio of the gap flux to the total 

 flux if. Hence the preceding expression may be written in the form: 



F = 



8^ 



(27) 



By a parallel treatment it can be similarly shown that the application of 

 equation (26) to the magnetic circuits of Fig. 3 and 21 gives expressions 

 identical with (27) except that A is replaced by A3 in the former case 

 and by A2 in the latter. Equation (27) is the famihar expression for 



,-b— -»K 



t 



-b-^ 



M{ 



t 



b+hx b-hx 



I — Vv\ ^l| 



d cr^ 



Fig. 25 — Magnetic circuit of a polar relay. 



