FIFTH CANADIAN CONFERENCE ON NONDESTRUCTIVE ... - IAEA

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(9) for hardened steel. All other modes fall below the 2S1 mode and so were
not considered. The data points indicate that either the 1S2 mode or the
1T2 mode is the one that generates the high frequency acoustic waves.
However, for torsional or "T" modes in spheres there is no radial
displacement and therefore it is assumed that these modes do not radiate any
sound in air. Only spheroidal or "S" modes can therefore couple with air
and generate an acoustic wave so that the 1S2 mode is believed to be the one
responsible for the high frequency tone. A representation of the
displacement associated with the 1S2 mode is included in Fig. 4. It shows
that this mode is very likely to be strongly exited by an impact because
such a uniaxal force will ovally deform the sphere. Other modes are
probably exited as well, including higher S modes. Some inharmonic
distortion was indeed observed on several high frequency waveforms. This is
expected if other modes are exited since their frequencies are not exact
multiples of each other.
Resonances of cracked grinder balls
When similar acoustic measurements are made using cracked grinder
balls, the appearance of medium range frequencies (5 - 15 khz) in the
waveforms is observed. These oscillations look like damped resonances.
Disappearance of the high frequency 1S2 vibration is also observed,
especially for severely cracked balls for which the amplitude of the
mid-range resonances is often the highest. This amplitude also depends on
the point of impact i.e. the orientation of the cracked ball relative to the
anvil. This effect however varies from one cracked ball to another and no
repeatable pattern emerged.
The mid-range resonances, characteristic of cracked grinder balls, are
attributed to some sort of "tuning fork" mode of vibration as the ball is
partially divided by deep running cracks. Acoustic measurements made on
artificially flawed grinder balls (saw-cut) reveal the presence of at least
two modes of vibration at frequencies lower than the 1S2 mode of the solid
sphere. The data is presented in Fig. 5 where the frequencies of the
various resonances observed are plotted against the depth, a, of the
saw-cut. We see that mid-range frequencies similar to those produced by
naturally cracked balls appear for values of a in the range of 30% to 70% of
the diameter d of the ball. The 1S2 amplitude becomes unmeasurable when a
reaches about half the diameter of the ball. The assumed displacements
corresponding to the two "tuning fork" modes are also illustrated in
Fig. 5. This assumption is in agreement with the observed variations in the
relative amplitude of the two frequencies with the orientation of the
impact: when directed perpendicular to the plane of the saw-cut, the lower
frequency mode was preferably exited whereas when directed parallel to the
bottom of the saw-cut, the higher frequency "shear" mode was preferably
exited. The frequency of both modes understandably tends towards zero when
the value of a approaches the value d.