MAGNETIC DESIGN OF RELAYS 77 



u hero Gc = N'/R, and is shown to be dependent on the coil (hmensions 

 and the conductivity of the wire in the winding. 



The magnetic field energy is described by "magnetic flux" which, 

 ax'eraged for the entir(> magnet, is related to magnefonioti\'(> force 

 through 



where ni is an (»\])i-ession accounting for the dimensions and materials of 

 the magnet and its air gaps, called ''magnetic reluctance." The validity 

 of this magnetic circuit concept is discussed at some length, leading to 

 the proof that for many cases a very simplified "equivalent two-mesh 

 circuit" may be used to represent the more complicated actual cases. 

 As a result, performance may be expressed in terms of the equivalent 

 values: olo , "closed gap reluctance"; (Ri, , "leakage reluctance"; and A, 

 "pole face area." Values for these terms may be estimated for cases of 

 initial design (magnet synthesis), or be measured so as to characterize 

 completed modqls (magnet analysis). Evaluation of reluctances of vari- 

 ous magnetic circuit components is described, with numerous relations 

 given for gaps and for magnetic materials, including an approximate re- 

 lation covering the non-linear behavior of ferrous materials. 



In terms of the magnetic circuit variables, force and work may then 

 be expressed as 



,-2 



F= ^ ^ 



w = 



SttAcRo (1 + w) 

 J" u 



2 ' 



87r(Ro 1 + W ' 



where u = x/A6{q , the ratio of air gap to the product A(Ro ■ It is thus 

 found that greatest magnet output for force systems common in i-elays 

 is obtained when the critical load is picked up at a gap Xo = .ICRo , which 

 may be accomplished by choice of lever arm. The maximum work that 

 may thus be considered useful, F^ax , depends somewhat on the particu- 

 lar load characteristic, and for the typical constant-load case, Vc , is 

 related to ampere turns, and to power input as follows: 



Vc/(Nlf = 7r/2(Ro, 



Vc/f-R = irGc/'M 



Greatest useful magnet output is thus seen to depend diicctly on Gc , 

 the "coil constant," and in\'(M'sely on (W,, , the e(iui\alent closed gap i-e- 

 hictance. 



