30 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1954 



0-3-2-6. Thus the mechanical ^vork, the left-hand term of eciuation (6), 

 is represented by 0-1-2-3-0, the area bounded by the two magnetiza- 

 tion curves and the path follo\ved by (p, x and Ni in the concurrent 

 change from 7i at Xi to h at X2 . 



If armature motion occurs at constant flux, the first right-hand term 

 in equation (6) is zero, and the mechanical work ec^uals the change in 

 the field energy U.lf cp = (pz in Fig. 2 for example, the work done as the 

 armature moves from xi to X2 is U4 — Uz , represented by the area 

 0-4-3-0. From equation (6), the pull F is then given bj^: 



f) TJ 



F = — — {(p constant). (7) 



dx 



If armature motion occurs at constant current, the first right-hand 

 term in eciuation (6) becomes the change in NI(p. If / = /i , for example, 

 motion of the armature from Xi to X2 increases Nltp from NInpi to A"/i^3 . 

 Hence the mechanical work done is the difference between NIi(pi — Uz , 

 represented by the area 0-3-8 and A^/1^1 — L\ , represented by the 

 area 0-1-8. The work done at constant current is therefore the change in 

 the quantity W defined by the equation: 



W = f <pd{NI), 



which is represented by the area between the magnetization curve and 

 the NI axis. From equation (6), the pull F is given by: 



F = ^^ (I constant). (8) 



dx 



The pull F can therefore be determined either from equation (7) or from 

 equation (8), pro\'ided the magnetization curves are known. These ec[ua- 

 tions may be applied graphically or numerically to compute the pull in 

 specific cases. They may also be used, as shown in Section 7, to obtain 

 expressions for the pull from expressions for the magnetization relations. 

 In addition, they afford the following graphical interpretation of the 

 dependence of the mechanical output upon the magnetization relations, 

 the current, and the armature travel. 



If Xi in Fig. 2 represents the unoperated position of the armature, and 

 Xo its operated position, the work that can be done at constant current 

 is Wi — Wi , which varies with the value of I applying. For small ^'alues 

 of I, for which both magnetization curves are linear, the work capacity' 

 TT2 — IFi varies approximately as (iV/)'. At higher values of XI, the 

 two magnetization curves approach each other as the}" approach the 



