MEASURING FORCES AND WEAR IN SWITCHING APPARATUS ^)()\ 



lliat 



Qu5,„ = 2.2 X 10"'; 



for pure l);ii'iuni litanate and 



Qn8,„ = 2.4 X 10 '; 



^^12530 = - .8 X 10 cgs units (25) 



r^i.,5;,,, = -.9 X 10"' cgs units (2()) 



for 4 jxn- cent lead titanate barium titanate ceramic. 



If a force F is applied uniformly over the whole siu-face of a small 

 barium titanate unit, then T3 = F/A, where .4 is the area, and all the 

 other stresses are zero. Under these circumstances when tho pcMinanent 

 l)()larization 83^ is along the Z axis (normal poling), tlu^ oi)en circuit 

 potential is 



E, = 



F3 2Qnd,,F 2 X 2.4 X 10 ' X F 



h 



u 



Itnl 



cgs units (27) 



where h is the thickness and /„. and / the cross-sectional dimensions. 

 To get the number of volts generated this factor is multiplied by 300 and 



V, = 



1.44 X 10~'F 



tint 



^olts 



(28) 



where force F is expressed m dynes. 



However for the data of Figs. 2 and 4, the voltage measured is that 

 for a load applied at the center of the ceramic and for this case the stresses 

 7\ and T2 of Equation (24) cannot be neglected. The solution'^ for the 

 stresses occurring Avhen a load F is applied at a point on the surface of a 

 semi infinite solid is used to evaluate the corrections caused by the non- 

 uniform load. In cylindrical coordinates the formulae for the three 

 stresses Tzz and Trr and Tee given by Timoshenko are 



Trr = 



Te 



T.. = 



F 



(1 - 2a) 



(1 



-3F 



r- 



1 , z 



-. {r + zy 



3r"2(;-" + z'Y 



1 I * / 2 I 2\— 1/2 I / 2 , 2\- 



r- r- 



(29) 



z'{r + z') 



-512 



where r is the radial distance from the point of contact, z the distance 

 below the surface and o- = Poisson's ratio. 



The response of a barium titanate unit in terms of cylindrical co- 

 ordinates has been shown to be for a unit polarized along the z axis 



E, = -2 [QuKT:. + Q125.3, {Trr + Tee)] 



(30) 



