Document 14407278

Experimental Study of Transverse Crack Fault Diagnosis in Rotating
Jian-zhong Lou 1,2 Xing Li1
Department of Bio-systems Engineering, Zhejiang University, Hangzhou, China
Department of Mechanical Engineering, Zhejiang Institute of Mechanical & Electrical Engineering, Hangzhou, China
([email protected] )
Abstract - The rotor transverse crack fault is one of the
most typical faults of rotating machinery. The transverse
crack fault mold was established to simulate the bearing
fault state of transverse crack in the rotor test table of
Bently in the laboratory. The main vibration characteristics
were stated through the analysis of laboratory data when the
bearing box was in the state of transverse crack fault. And it
has been applied in practice.
Where:  i --displace the node along the y-axis direction
Keywords - transverse crack; bearing box; rotating
machinery; fault diagnosis
mass matrix, damping matrix, stiffness matrix and
generalized force.
wi --displace the node along the x-axis direction
i --the angle around the x-axis
 i --the angle around the y-axis
M 、 C  、  K  and Q respectively displace
The large rotating machinery is one of the most
important equipment in petroleum, chemical, petrochemical, and other industries. It is also particularly
important for us to diagnosis machine fault of large
rotating machinery because it will cause serious economic
losses and casualties. And it is very useful for people to
monitor the fault diagnosis of large rotating machinery in
order to avoid vicious equipment damage accidents,
reduce corporate economic losses. The fundamental
purpose of fault diagnosis is to ensure the large rotating
machinery to run in safety, stable, long-period, full load
statement. Transverse crack is the most common faults of
rotating machinery and it is very important for us to get a
research [1-4].
The rotor system mechanics model is the premise of
obtains the rotor vibration characteristics and analysis
fault mechanism of rotating machinery. Figure 1 shows
the typical rotor system and its cell division. The vibration
differential equation was given as follows:
Mq  C q   K q  Q
Where the
is the generalized displacement
vector, the form of the vector
q :
Fig1. Typical rotor system and unit dividing
The rotor with transverse crack is to reduce the
overall stiffness of the rotor. There will have the effect on
the system with the crack opened and closed when the
rotor rotates. We looked it as a rotor with no crack when it
closed. And when it fully opened, we looked it as a rotor
with a slot. To establish the unit stiffness matrix of crack
in the fixed coordinate system (including two parts which
were the constant  Kc*  and variable  K c*  ), and
 f
 m
assemble with stiffness matrix without crack unit. The
stiffness matrix of transverse crack rotor system and the
vibration differential equation was given as follow:
Mq  C q   K   Kc*  q  Q   Kc*  qm  (3)
qm  is the static deformation caused by its
own weight of the rotor.
Cracked rotor system vibration differential equation
model of the rotor crack unit was established to simplify
the impact of crack on the vibration of the rotor to an
external force on the rotor which was given in equation:
 Kc*    Kc e  / 2   Kc e    Kc e    Kc e  ) cos t / 2 (4)
 
m 
 Kc  and  Kc  are the constant does not change
with rotation,
Author: Jian-zhong Lou (1973 -), male, lecturer in Zhejiang Institute of
Mechanical & Electrical Engineering, Ph.D., Zhejiang University.
 Kc e  changes periodically with the
Where E is the modulus of elasticity, l is the length
of unit, Ix and Iy are the moment of inertia for x and y
located on the right end (L = 100mm), the crack depth is
about 50% of the diameter.
h  sin 2t , C  cos 2t
From equation (3) we can be seen to contain only
sin 2t and cos 2t , that means it only contains the
second harmonic component.
Order:  Kce  cos t / 2  ( Kc3e    Kc1e  ) / 2
 t
t 
Where:  c t only contain cos3t and sin3t ,
that means it only contains the third harmonic component.
 Kc1e 
t only contain cos  t and sin t , that means it
 K 1e 
only contains base harmonic component.  c t has the
same matrix form. That is:
 K 3e 
q   V 0 0 
,V2 0 0  2 ,V3 0 0 3
We can see from above that the additional force
 Kc e  qc m 
which was caused by the transverse crack
rotor system is same in the rotor horizontal as in the
vertical directions.
Phase difference is 90 degrees which is similar with
the unbalanced force, but it excites the rotor with second
harmonic vibration components.
 K c e  q c m     K c3e  / 4   K c e  / 2   K 1e  / 4   K c e    K c e  cos  t / 2 q c m 
The above analysis only considers the bending
stiffness of the crack unit. The shear stiffness of the crack
unit also has the same conclusion. The linear increase
naturally has the same features.
Through the analysis of the vibration differential
equation of the cracked rotor system, you can see the rotor
with transverse crack has the typical characteristics of the
vibration and diagnostic information: The rotor with a
transverse crack vibrate with high multiplier of the second
harmonic, third harmonic components and cause the rotor
power frequency component amplitude and phase
Figure 2 crack shaft used in test bench
Through the above experiments, the result shows
that: With an opening crack on the rotor, it appeared the
rotation frequency of 2 times, 3 times and high-harmonic
components. When crack propagation, stiffness further
reduces, amplitude of 1 time, 2 times frequency also
When the operating speed passed half of the critical
speed, the amplitude will appear the resonance peak.
In order to find the phenomenon of frequency
modulation cause by the phase modulation and reducing
signal frequency modulation caused by the changing of
rotational speed. We collected a group of data when the
rotor speeds up in the same phase. Figure 3 shows the
vibration signal time-domain waveform and the Fourier
spectrum under the speed of 1900RPM with rotor
transverse crack. From the figures we can find the two
times frequency clearly.
Figure 2 shows the shaft with the transverse crack
which was customized for this experiment. The shaft
machined through the following processing. First, cut the
notch in given depth in the specified location of the shaft
and the notch width is about 0.12mm, then cut the slot
and embedded in piece of metal with the thickness of
0.10mm and fixed it in the notch with No.502 glue which
is similar to opening and closing of the crack. The
location of the crack was shown in Fig.2 which was
Fig3 Time-domain waveform and spectrum of vibration signal with rotor
transverse crack
One of air pressure machines in Fujian
Petrochemical catalytic company was shut down in
June12, 2009 because of the fault. The monitoring system
recorded the data in the black box in details. From the
analysis of data, we found that some time before the
machine shutdown, the speed of air pressure machine
fluctuations. Then the security protection system worked,
and the power system of air pressure machine shut down
automatically and the air compressor stopped too.
Figure 4 shows the vibration waveform under normal
operation, it is clear that there are 8 cycle sine waves. Its
spectrum is shown in Figure 5 which has only the
fundamental frequency of the vibration amplitude. The
amplitude of high frequency components is very small.
Figure 6 shows the vibration waveform under fault states,
it is clear that the vibration waveform is different from it
in normal conditions. Spectrum also contains high
frequency components which were shown in Figure 7.
8. From figure 9, the vibration amplitude of the high
frequency spectrum of the vibration signal increased
significantly, and speed soaring at the same moment, so it
can prove that the result of the malfunction of the air
pressure machine is load lost, which caused by transverse
crack. After technical personnel adjust the control system,
reboot, and the pressure resume to normal operation.
Fig.8 pressure machine speed trend in fault state
Fig4 waveform in normal conditions
Fig. 5 Spectrum in normal conditions
Fig. 6 waveform in fault conditions
Figure 9 pressure machine base frequency trend in fault state
Fig. 7 Spectrum in fault conditions
Normal speed of air pressure machine is 8300 r/min.
Due to the failure of pressure control system, the speed of
air pressure machine fluctuations. The protective
measures of control system began to work. The air
pressure machine shut down. In this process, loads begin
to lose. So speed instantly rose to 10,000 rpm, and
instantly went back to normal speed, as shown in Figure
Through building the model to add the transverse
crack in the rotor test table of Bently in the laboratory to
simulate the bearing fault state of rotor transverse crack
fault, through experimental results and theoretical
analysis. The main vibration characteristics were stated
through the analysis of laboratory data when the bearing
box was in the state of transverse crack fault. This is a
great help for fault diagnosis and research.
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