166 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



Maximum and Minimum Values 



The next to last part of this phase of the article concerns estimates 

 of the range of the mass controlled maximum operate time of a particu- 

 lar relay code. This involves determining the range of each of the vari- 

 ables from the manufacturing specifications. Then with the variation 

 chart the range in the time, due to each component, is evaluated, as a 

 ratio. The actual range of course is not the product of these, as all vari- 

 ables never will be adverse simultaneously, but it is greater than the 

 largest single individual contribution. For general purposes, a root 

 sum square addition is used. For the wire spring relay this amounts to a 

 range of about ±30 per cent. 



Preliminary Estimate of Type of Operation 



Earlier, a rule of thumb expression for an estimate of whether an 

 electromagnet is in the mass or load controlled class was given. It is 

 easily derived by use of the F concept, and the observation from com- 

 puting the variation charts, that the waiting time generally is about 

 one-half of the motion time when the electromagnet is mass controlled. 



When the motion time begins, the force starts to build up according 

 to equation (19). However, multiplying this initial rate by the motion 

 time need not result in a force value equal to the load for operation to be 

 complete. Four factors act to this end: (1) during the waiting time the 

 back tension Fi already has been overcome; (2) when the armature gap 

 closes, the armature takes a greater portion of the winding flux; (3) as 

 the armature moves in the winding flux builds up more rapidly ; and (4) 

 the kinetic energy can cause the armature to crash through a small 

 distance where the load projects through the rising dynamic pull curve. 



Calling I'm the longest average motion time which is mass controlled, 

 and arbitrarily setting 



Fit M = -^ 



in view of the foregoing, an estimation of the limiting average Fi is deter- 

 mined. Substituting this in (20), the maximum average mass controlled 

 motion time is : 



t\r = //^ 



I- = w 12m(a:3 — .Ti) 



F, 

 w^hich, when multiplied by ^2 to allow for waiting time, and dropping 



