RELAY ARMATURE REBOUND ANALYSIS 



179 



where : 



/ = 



Fi 



A large value of ixjli will result in a series of heel impacts and the 

 heel will come to rest while the front is still displaced from the stop. 

 This will be called a complete heel series. A small value of txlh results in 

 a similar complete front series. If hlU is near unity, a limited number of 

 impacts on one end are followed by an impact on the other end, etc. 

 An analysis of front and heel series follows: 



B. Front Series 



If ti/t2 < 1 a series of front impacts occurs. The impact velocities at 

 the front are 



?/i„ = 1, k, k'\ ■ ■ ■ , k" 

 The corresponding time intervals are 



„ zki 2iki 2/c 



'" " T' "X' ■ ■ ■ ' X 



where 



A = (Cu + Cuf) 

 During this time, the heel velocity and displacement are given by 



'23 



(1-t) 



(15) 



2/20(n+l) — y-lOn + 

 i/20(n+l) = U'lOn + 



- Pud + A-i) 



IJiOn 



'2B 

 A 



ijm + ?/20« 



yion 



(16) 



where 



B = (7i2 + C22/ 



The velocity and displacement at the heel after a given number of front 

 impacts are obtained by a summation of Equations (16). For a com- 

 plete front series w — > co ^ and 



Vicoo = 



2ki 



A{l-\- k^r L A 



2/2.00 



1 



"25A-1 



1 - kii A 



(17) 



