200 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



term, from (12), is the total air gap reluctance Oi^ . To obtain long delays, 

 therefore, (Re must be made small, and consequently sensitive to small 

 dimensional variations. These may be compensated in an initial adjust- 

 ment, but subsequent changes must be minimized if constancy of per- 

 formance is to be attained. 



Two expedients have been used to provide a small and stable gap 

 reluctance. The older one is the use of a "residual screw," an adjustable 

 non-magnetic member which serves as an armature stop and assures a 

 small air gap at the pole face. With this scheme, the residual screw is 

 used to adjust the relay. The alternative scheme, used in the flat type 

 relays of the Bell System, is to employ a domed pole face on the arma- 

 ture, providing a spherical surface in contact with a mating plane surface 

 on the core. The only effective air gap at the point of contact is that of 

 the chrome finish on the parts. With this scheme, the relay is adjusted by 

 varying the spring tension, and thus the operated load. 



General expressions for the pull of electromagnets are discussed in a 

 companion article,^ where it is shown that the pull F provided by a gap 

 flux (p is given by the equation: 



F=f^-p, (13) 



Htt ax 



where x is the dimension in the direction of the pull, and (Rg is the gap 

 reluctance. In the usual case, (Rg varies linearly with x, and dGia/dx has 

 the constant value 1/A, where A is the effective pole face area. This is 

 applicable to any case of plane mating surfaces having an appreciable 

 separation, including the configuration usually employed with a residual 

 screw as separator. 



Pull for a Domed Pole Face 



In the case of a domed pole face there is a concentration of the field 

 near the point of contact, which varies with the effective air gap at this 

 point. An expression for the reluctance can be developed for the idealized 

 configuration shown in Fig. 9. In this, R is the radius of a spherical 

 surface mating with a plane over the projected area A bounded by the 

 radius aR. The separation x is that measured at the center of .4. As 

 indicated in the figure, an expression can be obtained for the gap re- 

 luctance (Rg in terms of its reciprocal, or permeance. The latter is given 

 by the integration of the permeances of the differential rings within the 

 projected area. (Rg is conveniently expressed in terms of the ratio (R^/(Rg 



