ESTIMATION AND COXTHOL OF ()IM:k All': TIMI'; OF HKLAYS 1 io 



a more detailed and exact pi'ocedure than can l)e obtained enlii'eiy from 

 the application of these approximate relations. The information further- 

 more has to be (|uite versatile, to i)ermil all new tyjx^ \ariations to be 

 included, such as winding, number of contacts and armature travel. It 

 must, moreo\'er, be in a form that permits determination of the upper 

 and lower limits to the time observed in each specific type of I'elay as 

 actually used, as in applications, interest attaches not only to the 

 nominal conditions, but to all \'ariations that may arise in actual manu- 

 facture and use. 



Relay operation is complex, and in principle the nonlinear differential 

 equations which describe it can be solved exactly only by computers. 

 Even if this is done, the results are subject to any uncertainty that 

 exists as to the exact form of the relations that apply. The representation 

 of non-linear magnetic material properties, the discontinuous load-travel 

 characteristics, the eddy current effects, etc., do not make such an ap- 

 proach attractive. 



The relay, however, is a perfect analog of itself. With the magnetic 

 structure set, controlled models can be built to include dimensional and 

 magnetic material variations. With these, exact solutions to a variety 

 of conditions can be determined. With these data available, approximate 

 solutions can be used for interpolation and extrapolation, determining 

 the effect of small variations from the tested conditions. 



This part of the article will exhibit the form of data presentation in two 

 classes, mass and load controlled operation. It includes the theory used 

 in selection of the forms, and the correction methods used for estimation 

 of variations from the standards. The initial part will be concerned with 

 a single relay operating in a local circuit. The latter part will consider 

 series and series-parallel operation of similar structures but not neces- 

 sarilj' identical windings. This latter problem is solved by determination 

 of an equivalent relay in a local circuit for each of the several relays. The 

 earlier analysis then can be applied to each in turn. 



The order of analysis can be rcA'ersed. That is, given required operating 

 times, windings can be determined which will provide these times. 



In this article, a best winding is (1) that winding which, for the speci- 

 fied applied power, results in the minimum operate time or (2) that 

 winding ^vhich, for a specified operating time, requires the minimum 

 powder. A unique solution exists. 



Existence of Best Winding 



Fig. 1 shows measured operate time of a relay for two different do 

 power conditions, versus number of turns in the winding. That a best 



