194 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



From (5), the term outside the integral sign is 4x/(Ri. On integration, 

 the following expression is obtained for the release time t: 



(Ki \(p — ipQ (p — (po 



In slow release relays, a "soak" or high ampere turn value is applied 

 in operation, and the initial ^•alue tpi is close to the satui'ation \^alue (p" . 

 It is therefore a satisfactory approximation to take ^i = if" in the pre- 

 ceding equation, which then reduces to: 



where, 



z = ■ — . (0 



(p — (po 



The time therefore varies as the bracketed term in (6), which is shown 

 plotted against z in Fig. 5. As z varies inversely as ^ — v'n , the difference 

 between the flux and its ultimate value, (6) gives the release time for 

 the value of (p at which the pull ec^uals the operated load. 



To obtain an expression for the release time in terms of the ampere 

 turn value at w^hich release occurs requires an expression for z in terms 

 of 9^, or 4:tNI. This may be obtained by substituting in (4) the expres- 

 sion for (R" given by (5). The resulting ecjuation reduces to: 



- (Po (.<P — (Po)<3ii 



g^ = ((/? - ^o)cR,- - 



ip — ip Z — I 



giving the equation: 



^ = 1 + (^tLlJf^. (8) 



If CF is the \'alue of 47r.V/ at which release occurs, the corresponding 

 A'alue of z given by (8) may be substituted in (6) to determine the release 

 time. In this way there ha^^e been determined the values of tS{i/{4:TrG) 

 plotted against 'S/{(S{i{(p" — <po)) in Fig. 6. This is a universal curve for 

 the relation between release time and the ampere turn value at which 

 release occurs. The observed relation for any specific case is given by 

 this curve, displaced vertically by the value of 47r(j/(Rv and horizontally 

 by the value of (R,(^" — (pa) for the case in question. This is illustrated 

 in Fig. 7, which shows the observed release time versus release ampere 

 turn curves for the Y type relay for two sleeve sizes, corresponding to 



