162 THE BELL SYSTEM TECHNICAL JOURNAL, JAXl AKY 1954 



cause of the inflection of the curve. Two other factors, caused by the 

 ensuing motion, act to provide e\'en more force than the open gap curve 

 indicated by Fig. 8. The first is that a smaller gap takes a larger portion 

 of the winding flux than assumed in the diagram, and the second is that 

 the winding flux rises more rapidl}^ and to a higher value than the open 

 gap curve assumed. The operating force curve shown includes these 

 effects. The relay operates in about 7 millisec and for 6 of the 7 millisec, 

 the two force curves differ very little. 



Hence, for a relatively long interval after the start of the motion time, 

 a very simple force relationship holds, namely that the force is directly 

 proportional to time, and the proportionality factor is the slope of the 

 straight portion of the curve, designated as F. For the example given, 

 this amounts to about 48 grams per millisecond. By using Xewton's 

 Law, an expression for the motion time can be written. 



from which, with the initial A'elocity zero 



7^3 



Ft 

 mill - x) = — . (20) 



Rearranging, the expression for motion time becomes: 



The factor F will now be considered. 



Derivation of Expression for F 



Experimental — The factor F can be determined graphically. This 

 brings in the second order effects such as quality of iron, cross section, 

 residual magnetism, fit of parts, etc. For this purpose three working 

 curves characteristic of the structure, all at the open gap, are first pre- 

 pared for the particular winding: 



(a) The dynamic flux rise curve, 



(b) The static flux curve versus ampere turns, and 



(c) The static pull curve versus ampere turns. 



Choosing a time on curve (a), the corresponding instantaneous flux 

 transferred to curve (b), determines the equivalent magnetomotive force. 

 This transferred to curve (c) yields the instantaneous magnetic force. 

 Repeating this for other times in the range of interest, an armature force 



