Relay Armature Rebound Analysis 



BY ERIC EDEN SUMNER 



(Manuscript received October 25, 1951) 



Rebound of mechanical structures subsequent to impinging on stops gen- 

 erally has deleterious effects on their performance and shoidd, therefore, be 

 minimized. A considerable reduction in rebound cayi often be obtained by 

 introducing additional degrees of freedom to the structure. 



A mathematical treatise of the dynamics of rebound motion of systems 

 representing idealized relay armatures is presented. Normalized differential 

 equations of motion and their solutions for the "free^' and "impact" inter- 

 vals are derived for systems having one, two, and three degrees of freedom, 

 allowing the rebound behavior of a specific system to be calculated. The equa- 

 tions of series of rebounds, and possible combinations of such series are con- 

 sidered next for systems having one and two degrees of freedom. The field of 

 possible rebound ma.vima is mapped for a practical range of mass distribu- 

 tion constants, coeficients of restitution, and force ratios. A sufficiently broad 

 optimum design region is indicated. 



The results of this analysis have been checked closely on a model and have 

 led to appreciable reduction of armature rebound in relay designs. 



I. INTRODUCTION 



In numerous types of mechanisms it is desirable to arrest the motion 

 of a member at a particular point and to maintain it in this position. 

 One of the simplest means of accomplishing this is to allow the moving 

 member to impinge on a fixed member (stop) and to provide forces to 

 tension it against this stop. Because the member to be arrested possesses 

 kinetic energy and because the stop cannot generally absorb all of this 

 energy, the moving member will rebound from the stop. The rebound 

 motion generally deteriorates the performance of the mechanism and 

 should be minimized. 



Investigation of this phenomenon has been stimulated by the armature 

 rebound problem in relay operation, where rebound from the front stop* 

 tends to reclose contacts and must therefore be compensated for by 

 additional (waste) travel, resulting in deleterious effects on speed and 



* Among relay designers the front stop has been generally referred to as "back- 

 stop". In this paper the terms front stop and heel stop have been used through- 

 out for easier identification. 



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