MACiNK'riC DKSIC.N OF RELAYS 29 



( )\('r the linear portion of a magnetization curve, rtl is a function of x 

 only, or a constant for a pailicular cur\'e. In this case, inte}>;ralion of 

 (Miuation (3) gives the followinji; alternatixc expiessions for the liekl 

 energy U: 



Over the upper curved portions of a magnetization curve, (R is a func- 

 tion of v? as well as of x, and equations (5) do not apply. 



Decreasing Magnetization 



In relay terminology, "operation," following closure of the coil circuit, 

 is distinguished from "release," which follows opening of the circuit. 

 The preceding discussion applies directly to the relations for increasing 

 magnetization, as in operation. In release, the field energy and the cur- 

 rent decrease together, giving a decrease in Ntp measured by a voltage 

 time integral similar to the right-hand side of ecjuation (2), but of op- 

 posite sign. The resulting decreasing magnetization curve is obtained by 

 subtracting the decrease in AV from its initial ^'alue. The decreasing mag- 

 netization curve is higher than the magnetization curve, and the field 

 energy recovered electrically is correspondingly less than that stored in 

 magnetization; the difference corresponds to the loss of energy through 

 hj'steresis in the magnetic material. 



Mechanical Output 



Referring to Fig. 2, let the current have the steady value /i , with the 

 armature at rest at Xj . If the current increases to lo while the armature 

 moves from .ri to .r2 , the flux (p varies with Ni along some curve such as 

 1-2 corresponding to the values of x and Ni concurrently attained. The 

 electrical energy drawn by the coil in this process (aside from th(^ heating 

 loss) is given by the integral of i d(N(p), or Ni dip, taken along the curve 

 1-2. Part of this energy appears in the increase in the field energy from 

 Ui to Uo as given by eciuation (3) for the points 1 and 2 respecti\-ely. 

 The V>alance represents the mechanical work done, the integral of Fdx 

 from Xi to x-2 where F is the pull. Hence: 



f ' Fdx = f ' Nidif - (Ta - Ti). 



J Xl '''Pi 



(6) 



The first right-hand teim is represented in Fig. 2 by the area 5-1-2-6 

 while Ui and U- are represented respecti\-ely by the areas 0-1-5 and 



