Biomedical Engineering Reference
In-Depth Information
necessary to use the stationary drill natural frequency. Therefore, the
relationship between the chatter frequency and natural frequency of the
stationary drill has been defined:
2
2
r
n
r
n
4
N
2
2
where: r - ratio, N - integer number of full waves, θ - phase difference.
Figure 7. Regeneration effect in bending vibration [20].
3D laser scans in combination with Patran and Nastran models have been
used to obtain the drill surface and acquire mode shapes, natural frequencies,
and stiffness of drills. After all the modeling and analysis, stability lobes were
developed, showing results for both the short and the long drill. It has been
shown that the higher frequencies can be ignored since they are less critical. It
has also been shown that the bottom of the lobes which defines the minimum
stability of the process gets lower as the rotational speed increases due to the
gyroscopic force, which causes the chatter frequency to change with the speed.
Apart from lowering the stability minimum, the lobes get wider with the
gyroscopic effect. Owing to the fact that the gyroscopic effect will both widen
and lower the lobes, it is necessary to take this effect into consideration when
using high drilling speeds since this would extremely change the stability
boundaries for those cases, reducing the stable area to a minimum.
