KSTIMATIOX AXD COXTHOL OF Ol'lllJ ATI: I'lMl'; OF UlsLA^S 125 



the curves of Fig. 5, it can be seen that if Ie is not negligible, the optimum 

 value of V is less than 0.715, and will be smaller the larger the ratio of the 

 first term in (15), that in Ie , to the other two terms. From (12), a reduc- 

 tion in V corresponds to an increase in NI, and hence in the coil constant 

 Go U^R being given) . Thus the optimum coil constant for fast operation 

 is larger for electromagnets with long cores of low resistivity material, 

 for which Ge and ts are large, than for those with short cores of high 

 resistivit}^ material, for which these quantities are small. 



The physical significance of the optimum coil constant can be deduced 

 from the relations shown graphically in Fig. 4. For a given value of the 

 power input PR, an increase in Gc increases both the steady state mmf 

 IFs and the time constant of flux development 47rGc/(Ri , increasing the 

 upper limit to the attainable pull while reducing the rate at which this 

 limit is approached. If the coil constant were so small that the area 

 under the dynamic pull curve equalled the static work load T^, the operate 

 time would be infinite. On the other hand, an infinitely large coil con- 

 stant would correspond to infinite inductance and an infinite operate 

 time. Between these extremes lies the optimum value of the coil con- 

 stant, giving minimum operate time. This is a broad optimum, near 

 which a change in i^s is compensated by a corresponding change in the 

 rate of flux development, so that the realized dynamic pull curve is not 

 affected by a small change in Gc . 



In addition to the operate time, the value of Gc affects the final 

 velocity of the armature, and thus its kinetic energy in impact with the 

 core at the end of the stroke. This energy is dissipated in the relay and 

 spring \abration associated with contact chatter. For values of Gc above 

 the optimum, the higher inductance reduces the pull in the early travel, 

 while the higher value of iFg increases it in the later travel. The net effect 

 is to increase both the operate time and the final velocity. Values of Gc 

 ii\)ove the optimum are therefore disadvantageous not only in slower op- 

 eration, })ut in increased impact energy tending to cause contact chatter. 



FACTORS CONTROLLING SPEED 



Aside from the term in Ie , equation (15) shows that the minimum 

 operate time, corresponding to the optimum A'alue of v, is determined by 

 the static load V, the inertia load measured by 7n(xi — X2)', the steady 

 state power /-/?, and the constant Cn-. The latter is given by (13), and 

 is the only quantity in (15), aside from ts , which depends upon the mag- 

 netic design. In the range of values applying in practice, Cw is deter- 

 mined ])rimarily by the leakage factor Cl , measuring the ratio of leak- 

 age to useful flux. In most practical cases, X2 is small (zero for complete 



