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WOLFRAM|DEMONSTRATIONS PROJECT

Chatter Stability with Orthogonal Rotation

​
natural frequency f (Hz)
100.
overlap factor μ
1.
structural damping ratio ζ (%)
1.
diameter d (mm)
25.
process damping coefficient (μm)
300.
R
max
(RPM)
20000
κ
max
0.5
chatter freq.
f
c
(Hz)
no. of lobes
N = 40
The classical model of regenerative chatter is a simple harmonic oscillator excited by a vibration-dependent force with constant delay. This results in a delay-differential equation whose stability analysis gives rise to a chart demarcating the nondimensionalized depth-of-cut
κ
and the rotational speed
R
. The well-developed theory available in [1, 2] is adapted for a general overlap factor
0≤μ≤1
and process damping
>0
. This Demonstration studies the effect of natural frequency
f
and structural damping ratio
ζ
on the
κ
-
R
space and chatter frequency
f
c
at the threshold of stability. Process damping is important at low rotational speeds and high lobe numbers, where the lobed borderline of stability is completely separated from the asymptotic borderline.
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