500 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1952 



the force is supported bj^ a single point at a time, then for 



8^ = ±3 X 10"' inches = ±7.5 x 10"' cm; 



A^ = 30 grams = 2.94 x lO' dynes; 



IJL = 2 X 10 dynes/cm ; 



(7 = 0.45 



and the coefficient of friction/ = 0.25, the value of r becomes 0.008 cm. 

 If the weight were supported equally by n points the radius would be 

 divided by n . Since the sidewise displacement would result in a strain 

 of 0.009 for a single point and 0.036 for two points, the latter strain 

 would be beyond the yield strain for the material. Hence the evidence 

 seems to indicate that a single point supports the major part of the weight 

 at any particular time. 



While it is difficult to reduce the gross tangential slide of a relay to 

 the values required for the low wear (no gross slide) region, the existence 

 of such a region has considerable importance for other sources of wear 

 in relays, namely long continued vibrations of component parts such as 

 undamped wu'es. The tangential motions caused by such vibrations are 

 small, but since they are repeated many times for each operation, the 

 total integrated wear is considerable. By introducing damping so that 

 the vibrations are quickly brought down to the low wear, no gross slide 

 region, a considerable reduction in wear has been found for relays. 



Appendix 



VOLTAGE generated BY COMPRESSIONAL AND TANGENTIAL CERAMICS 

 BY FORCES APPLIED UNIFORMLY OR AT CONCENTRATED POINTS 



When a stress is applied to a prepolarized barium titanate ceramic it 

 has been shown that the open circuit field generated along the Z axis 

 is given by the equation 



E, = -2[Qn[8^J^ + 8,J, + 8,J\] + Qvl8,,iTr + T-^ 



- {8,J, + 8,J,)]] ^^^^ 



where Si^ , 52„ , 8s^ are the remanent values of polarization introduced 

 along the three axes by the poling process, Ti , T^ , Ts , Ti , T^ , T^ the 

 three extensional stresses and the three shearing stresses, and Qn and 

 Qi2 are the two electrostrictive constants for the ceramic. From the 

 "effective" piezoelectric constants measured for these ceramics we find 



