IGO 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



these factors, the differential equation of motion can be solved, and the 

 time for a given travel determined. 



Thus there is now needed an expression for the armature force de- 

 veloped by the pole face gap flux as a function of time. Briefly, the basis 

 for the method to be described is the assumption developed in Part I, 

 that the winding flux continues to rise during the initial motion interval 

 in the same way it would have risen if the armature had not moved. With 

 this assumption, an expression for the motion can easily be derived. 

 With this expression it then can be shown that the armature does spend 

 most of its time in the close vicinity of the backstop, justifying the 

 initial assumption. 



The present approach differs from the more general one of Part I. 

 It uses the results there de\'eloped regarding the l:)ehavior of mass con- 

 trolled operation, to simplify the initial motion equation and obtain 

 an expression for motion time in a form better suited for the present 

 purpose. 



Armature Force Rise and the F Concept 



As an introduction to the method which will be used, consider the 

 general character of flux l)uild-up in a relay. It will have a shape some- 

 what similar to an exponential cur\'e. Now with the armature at the 

 backstop, from the first approximation magnetic network of Fig. 7, a 

 fixed portion of this winding flux will pass through the pole face gap, 

 with the result that the pole face gap flux curve will also have the same 

 general character. Such a measured curve is shown in Fig. 8, as well as 

 the curve when the armature is free to move. 



Now the armature force developed is proportional to the square of 



X3 X2 



ARMATURE TRAVEL 



Fig. 7 — Schematics of nomenclature applying to operate time. 



