RELAY ARMATURE REBOUND ANALYSIS 



175 



A. Free Interval 



The motion of the armature will be described by the displacement at 

 the stoji points: Xi , x^ , Xi * Let m be the mass and R the radius of 

 gyration of the armature about the center of gravity. The latter is 

 located by the dimensions l\R, loR, and fji relative to the stop points, 

 i.e., the points on the armature which contact the stops in the rest 

 position (Fig. 3). 



The equations of motion arc derived in Appendix I and are put into 

 dimensionless form: 



+ ijw 

 + ho 



+ 2/30 



+ 2/10 

 + 2/20 



+ 2/30 



(1) 



where: 



Vi = 



Xi_ 

 XaT 



XaTn 



Fi 



.2 Xi 



XaTn 



Xq 



f 



(2) 



Xa is the front velocity ii, just prior to the "zero" impact, and 



Cn = in + 1) Cn = C31 = fil3 

 C22 = (f2 + 1) C:2 = Cn = (1 



^23 — [^ ~\~ 1) C2Z = C32 = —12^3 



(3) 



2/10 , 2/20 , 2/30 , are the initial velocities and yw , 2/20 , 2/30 the initial dis- 

 placements for the free interval in question. 



The equations of motion for a two-degree-of-freedom system are 

 obtained, if F3 = 0. Then for the two coordinates of interest: 



2/1 



2/2 = 



+ 2/1 



+ 2/20 



(4) 



A summar}' of all notations used in this papar is given in Appendix IV. 



