ESTIMATION AND COXTUt)L OF OPEHATE TIME OF RELAYS 1G3 



curve like Fig. 8 is established. The waiting; time is read directly, cor- 

 responding to Fi . The slope of the ensuing linear force range determines 

 Fi . This, with equation (21) completes the determination of mass con- 

 trolled motion time. Of course, the final pull de\-elopcd has to exceed 

 the operated load. This check is made from another i)ull curve taken at 

 tiie armature gap Xz , using the known final ampere turns and the load. 



Analytical — For oin* present purposes, an analytical relation, expressed 

 in the finidamental constants, similar to that for the waiting time is 

 needed. Its derivation follows: 



The solution which will be developed is based on linear circuit theory. 

 This necessarily implies exponential flux rise, which is not exactly true. 

 However, the relation is dimensionally correct and accurate to better 

 than first order. Then the use which will be made is to determine the 

 motion time of an electromagnet as the parameters are varied one at a 

 time. These are plotted as ratios to one of them, chosen as a reference. 

 By this means the ratio curves become accurate to better than second 

 order and provide excellent correction factors for actual measured data. 



For a linear circuit, the pole face gap flux will increase, after the wind- 

 ing circuit is closed to a battery, with the same time constant as the 

 A\inding : 



e-"^) 



(22) 



47riV7 ., 



(fa = (1 



(Ro + I 



where T = U {Gc + G'e) and / = E/R. Then the pull: 

 — F— V^Q _ 1 (47riV/)" . _ -tiTs2 



SttA' 8tA/ ^ xV^ ^ ^ ' (23) 



di - ^y./ , xy ^' ^' ' ^^- (24) 



{(Ro + ly 



The bracket term is of the form a(l — a), < o < 1, which has a 

 maximum value of 0.25, and from 0.2 <t/T < 1.5 is between 0.15 and 

 0.25. This range corresponds to the maximum slope of the armature 

 force versus time plot in Fig. 8. Arbitrarily 0.2 is chosen and the expres- 

 sion for the maximum rate of force rise becomes: 



5 AT 



MNiY 



(25) 



(mo + 1 J 



