ESTIMATION" AND CONTHOL OF OI'KUATK TIMK OF KKT.AYS 11/ 



induced in the coil and imposed on the contact opening the coil circuit. 

 Because of the changing field pattern, the gap field which determines the 

 pull has a ditVerent, though similar, decay rate. 



These considerations, as supported by Wwcdensky's relations and 

 Logan's results, indicate that the rate of pull decay in normal release is 

 faster, and only roughly of the same order of magnitude, as that esti- 

 mated on the assumption that (2) applies, with \-alues of Ge similar to 

 those applying in operation. 



LIMITATIONS OF THE ANALYSIS 



The validity of equations (2) through (5) rests on the assumption that 

 the pattern of the dynamic field is essentially that of the static field to 

 which the magnetization relations apply. The above discussion of the 

 eddy currents indicates that this assumption is valid when Ge is a minor 

 term in G. This condition is approximately satisfied in normal operation. 

 In open circuit release, howe\'er, the condition is not satisfied, and equa- 

 tion (2) is only a crude first approximation to the controlling relation. 



The use of (-i) as an expression for the reluctance (R rests on the fur- 

 ther assumption that the magnetization is linear, a condition only satis- 

 fied in the low density region. The initial and controlling stages of opera- 

 tion are usually complete before the field passes out of the lo^v density 

 region, and (4) is therefore applicable to the operate case. A different 

 expression for (R is required in the release case, as discussed in Section 7. 



2 Character of the Operate Solution 



GRAPHICAL representation 



Some understanding of the relations applying to operation rciiiy be 

 obtained from their graphical representation in Figs. 3 and 4. In these 

 two figures the path followed by the \ariables in dyamic operation is 

 indicated by the dotted lines, with the dots spaced to indicate equal 

 time intervals between them. Fig. 3 shows the ip versus 3^ relation, referred 

 to the steady state magnetization curves for various values of x, with 

 .T = corresponding to the operated position, and x = Xi to the initial 

 unoperated position. Fig. 4 shows the d.ynamic F \^ersus x relation, to- 

 gether with the load curve (bounding the cross hatched area Y) and the 

 steady state pull curve for the applied mmf iFs . 



The flux and pull increase together with the armature at rest at .Vi 

 until the pull equals the back tension at the point 1. In the earlier mo- 

 tion, 1-2, the velocity is small, and the reluctance (from (4)) changes 

 slowly with x so the motion has little effect on the rate of flux develop- 



