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1
(
ω
2
L
C
−
1
−
j
ω
C
R
(4)
Z
(
ω
)
=
=
m
m
m
m
G
[
ω
(
t
)]
ω
2
C
C
R
+
j
[
ω
3
L
C
C
−
ω
(
C
+
C
)]
e
m
m
m
e
m
e
m
Ȧ
V
Ȧ
V
Ȧ
Ȧ
V
Ȧ
V
Ȧ
_
*
Ȧ
V
_
_
*
Ȧ
V
_
_
*
Ȧ
V
_
_
*
Ȧ
V
_
W
W
W
W
W
W
ω
ω
ω
ω
ω
ω
(a)
shifts from
to
(b)
shifts from
back to
s
s
s2
s
s2
s
Fig. 2.
varying with
and
t
ω
G
[
ω
(
t
)]
of a transducer with and without load are respectively shown in black and
blue in Fig.2, which is
G
[
ω
(
t
)]
dependent. Their corresponding maximum values,
ω
ω
t
,
and
, are obtained at
ω
and
ω
. When
shifts from
ω
to
ω
at
G
(
ω
)
G
(
ω
)
s
s
s2
s
s2
s1
s2
ω
follows the red curve in graph (a). Subsequently
shifts back from
G
[
ω
(
t
)]
s
follows the red curve in graph (b).
In order to stabilize the output vibration velocity, it is required to regulate the volt-
age
ω
to
ω
at
t
,
G
[
ω
(
t
)]
s2
s
when
being changed. This can be described in equation (5).
U
(
t
)
G
ω
[
(
t
)]
I
(
t
)
=
U
(
t
)
G
(
ω
)
(5)
ω
being locked. Due to the fact of
the voltage still not being regulated using the traditional method, the current
)
will increase at
t
when
In graph (b),
G
[
ω
(
t
)]
s
tU
might go beyond the limit. In light of the above, a novel method termed as
asymmetric automatic regulation of the vibration velocity was described in this work.
The voltage increase speed should be much slower than the frequency regulation
speed (
(
)
G
(
ω
)
when
decreases immediately at the beginning of the
dU
(
t
)
dt
<<
d
ω
dt
G
[
ω
(
t
)]
load being changed
. Subsequently,
monotonically increases during the process
of the frequency-tracing.
The voltage decrease speed should be much faster than
dt
G
[
ω
(
t
)]
d
ω
to ensure transducer's current not overshoot
.
4 Structure of the Ultrasonic Power Based on Asymmetric
Regulation of the Vibration Velocity
The ultrasonic power based on asymmetric regulation of the vibration velocity is con-
structed and evaluated in this paper, illustrated in Figure 3.
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