76 THE BELL SYSTEM TECHNICAL JOURNAL, JANUAin l'J.34 



cases minor compared with that of the gaps and joints. The latter are 

 equivalent to an air gap of 0.005 cm (2 mil-in) over the area of the joint, 

 giving a marked advantage to one-piece construction of core and return 

 members. The heel and main gaps necessarily introduce reluctances of 

 similar magnitudes, further increased at the main gap by the height of 

 the stop pins required to reduce the residual flux to the release level. It 

 is therefore advantageous to use large areas for both heel and main gaps. 

 When a small value of (Ro is thus obtained, providing high sensitivity, its 

 value is the more sensitive to variations in fit and alignment at the heel 

 and main gaps, and high sensitivity therefore requires close tolerances 

 on the dimensions controlling the fit of the armature to the pole pieces. 

 Heavy section magnets tend to high sensitivity, partly because of the 

 reduced reluctance of the magnetic members, but principally because 

 heavy sections facilitate the provision of large areas at the gaps and 

 joints. 



As shown above, the effective pole face area is the reciprocal of the 

 coefficient of x in the expression for the variable reluctance term. It 

 therefore depends upon both the heel and main gaps, though the con- 

 tribution from the heel gao is small when the armature is hinged there. 

 For optimum sensitivity, or optimum work capacity, there are optimum 

 values of the gap reluctance Xi/A as shown above, which can be obtained 

 either by a choice of leverage to the load or by a choice of pole face area. 

 It is preferable to attain these optima by varying the leverage, using as 

 large a pole face area as possible, in order to make (Ro small. 



10 SUMMARY 



The material given in this article provides a basis for relaj^ design 

 through the relationships between mechanical output and electrical 

 input. From the indicated relations, one ma^^ find the mechanical work 

 from a given magnet design, or find the magnetic design needed to 

 provide a required mechanical output. Relationships for gaining opti- 

 mum performance are also given. 



The first step was to show that the mechanical work depends upon the 

 field energy of the magnet, which is a consequence of the magnetomotive 

 force pro\-ided. The magnetomotive force in turn is furnished by the 

 electrical circuit, being determined jointly by the number of turns in the 

 coil and the circuit resistance. The electrical output and the magnetic 

 input were thus equated as 



fR = -^ 

 IQw'Gc ' 



