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.