ESTIMATION AND CONTROL OF OPKUATH TLME OF KELAYS 



141 



4.5 

 4.0 



3,5 

 3.0 



0.5 0.6 0.7 0.8 1.0 



2.0 2.5 3.0 3.5 



Fig. 10 — Release motion time relations. 



doubled and the mass halved, Im would be hah'ed. These values of Im 

 are of the same order but smaller than the values of Ie generally apply- 

 ing, corresponding to the range in tultE covered by the figures. Similarly, 

 the total travel usually lies in the range covered by the values of ;<, 

 corresponding to travels up to 48 mils for the above value of A(Ro . 



The curves of Fig. 11 show that the fraction W jV of the spring load 

 energy absorbed by magnetic drag varies from 15 to 80 per cent over 

 the range covered, and consequently that the kinetic energy at the end 

 of the stroke, which determines the rebound amplitude, varies from 85 

 per cent to 20 per cent of T^, or by a factor of 4 to 1. 



The way in which ^Y jV varies wdth u and with iMJtE is readily under- 

 stood from physical considerations. Referring to Fig. 9, it is apparent 

 that for a given time rate of field decay, the faster the rate of armature 

 motion, the higher is the restraining pull and the less the kinetic energy 

 T . For a short travel, or low value of u, the restraining pull will h^ 

 larger than for a high value of u: hence W jV decreases as u is increased. 

 As 1^1 measures the time for a travel of ylcRo , or ii ^ 1, for a force Fo , 

 t mIIe is a measure of the motion time relative to the time of field decay. 

 1 lence a large value of ^a///b coti'esponds to a condition wheie the motion 

 is slow relative to the field decay, giving little restraining ])ull. Thus 

 W jY decreases as /az/Zb increases. 



