FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

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where x8 is the maximum value of x. Solving for xm yields:
/ -VA
xm=l.A22l _ I
\ E 2 d /
We can approximate the equation of motion of the sphere by a sine:
x xm sin uit
and knowing that when t = 0, dx/dt = vo, we have: (o = vo/xo
The interaction time, T, corresponds to a half cycle of the sine wave:
Thus, finally:
T = TT/ÜJ
= IT Xm/Vo
In the case of 3" diameter balls, the numerical parameters are:
m = 1.8 kg
d = 76 ram
E = 2 x 10 5 MPa
vo= 1 m/s
width yields:
T = 280 us
This value is in good agreement with the experimental data and offers
and explanation to the absence of frequency components higher than 2-3 kHz
in the initial pulse.
Resonances of uncracked grinder balls
Sound measurements of uncracked grinder ball impacts were made using a
high pass filter to attenuate the low frequency noise associated with the
initial pulse (up to 3 kHz as mentionned above). The filtered signals show
the enhanced presence of a high frequency resonance in the acoustic waveform
ranging from 35 kHz for 3" dia balls to 65 kHz for H" dia balls. This
oscillation can be related to one of the lower modes of resonance of a solid
steel sphere. Fig. 4 is a plot of the inverse of the resonance frequency as
a function of ball diameter. The straight lines represent theoretical
curves for the first 3 modes of vibration of solid steel spheres as
calculated from relations given in (8), and with elastic constants given in
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