160 



MEASUREMENT OF PRESSURES 



with the understanding that this equation describes the motion only up 

 to the first maximum of deformation of the crusher, after which time 

 the ball retains the permanent plastic set. For an applied pressure of 

 very long duration {d, wd —> ^) this maximum occurs at a time 

 3/2 ^o) = tt/co = TT^^rn/k and the deformation S^o is given by 



(5.3) 



Saa — 



2APr, 



k 



which is twice the static value for a slowly applied pressure. The nat- 

 ural periods Too of 5/32 inch and 3/8 inch balls in the NOL gauge for 

 which the effective mass is about 15 grams come out to be 355 and 514 



w 1.0 



UJ 



(/) 



o 0.8 



^ DC 



liJ 0.6 

 > 



LlI 



cr 0.4 



I 2 4 6 8 10 20 



RESPONSE VARIABLE u>e 



Fig. 5.2 Relative response and time of action of a ball crusher gauge. 



40 



microseconds, and Eq. (5.3) provides an accurate estimate of peak pres- 

 sure Pm only if the time constant d is much longer than these values. 

 If this condition is not fulfilled, it is evident that the final deformation 

 will be smaller, because of the smaller average pressure acting during 

 the time of response of the gauge, and will be a function of the duration 

 parameter B. The actual deformation for a given Q can be found from 

 Eq. (5.2) by determining the time 1^ of maximum deformation for which 

 dSjdi = 0, and solving Fa\. (5.2) using this value of (,„. The time /,„ is 

 given by the condition 



(5.4) 



e-fm/e = cQg ^f^^^ _|_ (j^0 gin ^/^ 



and the deformation S,,, is then 

 (5.5) 



Srn = ^" {cod) sin CO/, 



k 



The time tm can be computed from the transcendental equation (5.4) 

 as a function of o)d and these values substituted in l^]q. (5.5) to deter- 



