164 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



Substituting for T and rearranging: 



F = 



5(«, + G;)(,4«o + .r,)(l + | + 3|-J 



(26) 



Substituting (26) and (15) into (21), the final expression for motion 

 time becomes: 



h = 



^3^,„_.,(,,|,)(.«, + ,)(l+^^ + ^j. (27) 



This, with equation (18) for the waiting time, forms the basis for the 

 variation effects which now will be determined. Its region of accuracy 

 is for windings with turns exceeding the best, as it presupposes the relay 

 will always operate. It thus is applicable in the region where the time 

 curves are parallel. For studies of lower numbers of turns, the three 

 stage approximation of Part I does not have this limitation. 



Operate Time Variations 



For a particular electromagnetic structure the factors in equations 

 (18) and (27) can be measured. These measured factors can then be 

 compared to the manufacturing specification and estimates made of 

 average values for each. With these average values, the waiting time, 

 the motion time and then the sum, which is the operate time, can be 

 computed. This is the reference condition. 



Each factor is then varied over its appropriate range, one at a time, 

 and the computation repeated. The ratio of these variation times to the 

 reference condition can then be plotted. Fig. 9 shows the chart for the 

 wire spring type relay. For this chart, the range for each factor was 

 taken as 3 without regard to the actual range. Similar charts have been 

 prepared for other types of electromagnets, including quite a size dif- 

 ference. These ratio charts all agree remarkably well when plotted in 

 this way. For this reason, for early estimates of any structure in the mass 

 controlled class, this chart is entirely adequate for estimates of variations. 



The basic assumption made in this method of determination is that 

 for small variations, the interactions are negligible and a separated 

 solution of products, one for each factor, is applicable. Checks made 

 by varying two at a time confirm that essentially the presumption is 

 fulfilled. 



The Gc curve does not exhibit a minimum, as do the measured curves 

 of Fig. 6. This results from the simplifying stipulation made that the 



