Fig. 5. Shaft’s central track,
depth of the crack
t
= 0
,
2
r
,
eccentric
e
= 0
,
030
x
and
2
α
= 90
◦
and
1
.
010
x
. Conditioned to this point
shaft’s center has been moved for
z
1
(
t
)
and
z
2
(
t
)
. With the assumed degree of muffle
D
= 0
.
05
maximum movement is
0
.
0430
x
i
(Fig. 5).
In Fig. 6 maximum vertical movement
of the shaft is shown as the function
of the angular speed, where eccentric of
the gravity appeared first on the side of
the crack, and then on the opposite side.
Compared to the shaft without crack there
are following differences:
— near
ω
k
as its first frequency,
amplitude maximum is dependant on the
position of the eccentrics;
— there are additional resonant spots in frequency scope at
ω
k
/
2
and
ω
k
/
3
(ultraharmonical resonance).
Movement is similar in horizontal direction. At any angular speed the
movement, therefore, consists of harmonics with frequencies
Ω
,
2Ω
and
3Ω
:
— first harmonic at
Ω =
ω
k
,
— second harmonic at
Ω =
ω
k
/
2
,
— third harmonic at
Ω =
ω
k
/
3
.
The phase angle of harmonics changes fairly fast for
180
◦
inside the
frequency scope where the harmonics prevail (see Fig. 6).
Cracks expansion normally increases as well as the moving amplitude
of the first harmonics, but it is also possible the amplitude to be decreased,
when eccentricity appears in a definite scope on the side opposite to the
crack (
α
≈
270
◦
±
45
◦
). As soon as the crack appears, or it increases, the
phase angles of harmonics are changing.
After the cracks appeared on the exiciting side of the generator rotor, the
measured amplitude values of the shaft vertical vibrations were observed
near the bearing 7 (Fig. 7). Characteristically,
n
vibration only near the
first own frequency presents a little resonant place. Since the moments
of (mass) inertia of the generator rotor are not totally equal, so without
any cracks, there appears the vibration
2
n
with one resonant place at
n
1
/
2 = 340
min
−
1
and at
n
2
/
2 = 910
min
−
1
. There are no resonant places
at the nominal revolutions number of 3000 min
−
1
, and the amplitudes of
16
μ
m, i.e. 10
μ
m, are very low.
If the shaft had a crack, according to the theory it would follow that
— the amplitudes of the oscilations
n
and
2
n
had to be increased
respectively, i.e. to be reduced,
— the phase angle had to be changed, and
— the oscilation
3
n
had to appear especially at
n
1
/
3
(Fig. 7).
The measuring of cracks and vibrations.
After longer work in the
active part of the rotor, on the cogs different cracks appeared.
ISSN 0236-3941. Вестник МГТУ им. Н.Э. Баумана. Сер. “Машиностроение”. 2009. № 3 113
