Biomedical Engineering Reference
In-Depth Information
1
b
lim
j
k G
(
j
)(1
e
)
sm
where, G
m
(jω) is the frequency response function of the machine tool
structure, ω(rad/s) is the chatter frequency, and ε = ωT is the phase shift
between the inner and outer modulation.
The relationship between the tooth passing frequency and chatter
frequency has been defined as:
f
c
N
f
2
t
where, f
t
=zn
s
(z - number of cutting edges, ns - spindle speed), N is the largest
integer to satisfy the equation and 0 < ε/2π ≤ 1 .
When the phase shift was chosen to be 2π, the stable spindle speed was
calculated to be:
f
c
.
n
ss
(
Nz
1)
In this case it can was shown that chatter frequency curve and the stable
spindle speed curve intersect close at the place close to the largest stability
limit of the width of cut b
lim
.
When the phase shift is chosen as π/2, the stable spindle speed is:
f
c
.
n
ss
(
N
1 / 4)
It has been shown that in this case, the chatter frequency curve and the
stable spindle speed curve don't intersect, therefore proving that it is
impossible to use this combination.
After defining the chatter frequencies and the optimal shifts, the authors
continued their research in the area of chatter detection working on neural
networks for reduction of chatter in drilling [7].
