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Vol.99(4) December 2008 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 97
VOL 99 No 4
December 2008
SAIEE Africa Research Journal
SAIEE AFRICA RESEARCH JOURNAL EDITORIAL STAFF ...................... IFC
Watermarking for JPEG images using error correction coding
by H. Zhu, W. A. Clarke and H. C. Ferreira ...............................................98
On the prevention of pole-zero cancellation in H
power system
controller design: a comparison
by K.A. Folly .............................................................................................103
Multiple frequency fault detection, correction and identication of vibration forces
on the rotor of a rotational active magnetic bearing system
by R. Gouws and G. van Schoor ...............................................................114
NOTES FOR AUTHORS ...................................................................................IBC
Vol.99(4) December 2008SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS98
Copyright © 2004 IEEE: An earlier version of this paper was rst published in AFRICON ‘04, 15-17 September 2004,
Gaborone, Botswana
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1. INTRODUCTION
Rotating machinery is commonly used in mechanical systems,
industrial turbomachinery, machining tools, turbine engines
and active magnetic bearing (AMB) pumps. An AMB is not
a classical technical system, it is a mechatronical system and
contains information processing components, software and
feedback loops [1].
AMBs provide the advantage of no additional equipment for
diagnosis and permanent monitoring tasks, during machine
operation. Stiffness, damping and force characteristics of the
bearing can be adapted to actual machine operating condi-
tions by adaptive control strategies, easily implemented into
the feedback control device [2]. As the area of industrial ap-
plications of AMB systems grows, there is a growing demand
of highly reliable systems at any operating conditions.
By inducing a rotating magnetic eld, vibrations can be re-
duced for either minimizing transmitted force, minimizing
rotor vibration, or reducing control efforts [3]. This project
uses the available sensors and actuators to perform multiple
frequency fault detection and correction of vibration forces
on the rotor of a rotational AMB. In this paper an on-line
detection, diagnosis, correction and identication system was
developed that induced correctional forces on the rotor of a
rotating AMB system.
The detection system constitutes displacement masking and
feature extraction performed by the Wigner-Ville distribution
(WVD).
The diagnosis and correction system constitutes pattern rec-
ognition and fuzzy logic.
Two AMB systems were required to complete this project. The
rst was a fully suspended 250 kW water cooling AMB pump
on which condition monitoring was performed over a period
of three years to obtain historical fault data. The water cool-
ing AMB pump is a fully working system and it was not pos-
sible to make any changes to the system.
MULTIPLE FREQUENCY FAULT DETECTION, CORRECTION AND
IDENTIFICATION OF VIBRATION FORCES ON THE ROTOR OF A
ROTATIONAL ACTIVE MAGNETIC BEARING SYSTEM
R. Gouws and G. van Schoor
School of Electrical, Electronic and Computer Engineering, North-West University, Private Bag X6001,
Potchefstroom, 2520, South Africa E-mail: Rupert.Gouws@nwu.ac.za / George.VanSchoor@nwu.ac.za
Abstract: In this paper, the authors propose a real-time multiple frequency fault detection, correction
and identication system for vibration forces on the rotor of a rotational active magnetic bearing (AMB)
system. Condition monitoring was performed on the displacement signals of a fully suspended 250 kW
water cooling AMB pump, to obtain historical fault data. A pattern recognition system compared the real-
time displacement error patterns with the displacement error patterns from the historical fault database.
A fuzzy logic system used the patterns from the pattern recognition system to perform error correction.
The Wigner-Ville distribution extracted the vibratory amplitudes and frequencies, which was used as input
features to the pattern construction and pattern recognition systems. Experiments were performed on a
double radial AMB test rack to demonstrate the effectiveness of the proposed system in the detection,
correction and identication of vibration forces on the rotor of an AMB system. The detection and cor-
rection system was able to correct and minimize multiple frequency vibration forces to a stable working
condition. The identication system calculated the type, parameters, vibratory level and zone of the vi-
bration forces. The main advantage of this system is its capability to detect, correct and identify multiple
frequency vibration forces.
Key words: Active magnetic bearing, control, on-line fault detection and diagnosis, vibration monitoring.
Figure 1: Double radial AMB test rack.
Therefore a second AMB system, the double radial AMB test
rack (diagram shown in gure 1) was used for verication
purposes. This system constitutes a driven unit with magnetic
bearings and position sensors on both sides. The controllers
use the position of the shaft to provide actuating signals to the
power ampliers, which in turn provide the magnetic bearings
with the correct current to suspend the shaft. The specica-
tions of this system are provided in table 3.
Vol.99(4) December 2008 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 115
There are two ways to perform diagnosis on AMB systems.
The rst is a signal-based approach, which relies on the analy-
sis of the displacement and current signals and the last is a
model-based approach which utilizes a mathematical model
of the system [4]-[6]. A combination of signal-based analysis
and model-based analysis was performed during the develop-
ment process of the on-line diagnosis and correction system.
2. VIBRATION FORCES ON THE AMB ROTOR
The following section provides an overview of the vibration
forces on the rotor of the 250 kW water cooling AMB pump.
Historical fault data have been captured by performing con-
dition monitoring on the displacement signals of the water
cooling AMB pump over a period of 3 years. Error signals
were then calculated for each of the historical data sets and
the signals were used as input to the simulation and practical
AMB models (see section 3.1) to induce the same faults that
occurred on the water cooling AMB pump on the double ra-
dial AMB test rack.
It became evident from the historical fault data of the 250
kW water cooling AMB pump that vibration forces can be
categorised into the following three vibration force catego-
ries: 1) subsynchronous, 2) rotor synchronous and 3) super-
synchronous. Subsynchronous refers to vibration forces with
frequencies lower than the rotational speed frequency of the
rotor, rotor synchronous refers to frequencies very close to
the rotational speed frequency and supersynchronous refers
to frequencies higher than the rotational speed frequency (ω)
of the rotor. Normal vibration level refers to a vibration level
where the vibration forces are within the safety specications
of the AMB system.
Multiple frequency vibration forces occurred where a combi-
nation of faults (with different frequencies) caused vibration
forces on the rotor.
2.1 Historical fault dataset 1: Subsynchronous vibration
Vibration forces causing subsynchronous vibrations on the ro-
tor of the 250 kW water cooling AMB pump occurred due to
external vibrations from machines running at low rotational
speeds in the vicinity.
2.2 Historical fault dataset 2: Rotor synchronous vibration
Rotor synchronous vibration forces on the rotor of the 250
kW water cooling AMB pump occurred due to temperature
growth of the machine structure, shifting of the relative posi-
tion of components after assembly and the coupling face not
being perpendicular to the shaft axis. Further vibrations in this
dataset occurred due to excessive force of the water against the
pump blades, during extreme valve opening and closing. The
faults (vibration forces) in this dataset were either character-
ised as coupling misalignments or as rotor unbalances [7].
2.3Historical fault dataset 3: Supersynchronous vibration
Supersynchronous vibration forces on the rotor of the 250 kW
water cooling AMB pump occurred due to loose bolts on the
motor side, which caused vibration forces in the motor that
were carried onto the shaft of the AMB pump. Further vibra-
tions on the rotor occurred due to external vibrations from
machines running at high rotational speeds in the vicinity. The
faults in this dataset were characterised as foundation loose-
ness faults. Foundation looseness or motion of the system
base can occur in various applications and environments. Ex-
ternal vibration sources (e.g. other machines) and accidental
impacts or explosions may cause base motion [8].
3. SYSTEM DEVELOPMENT
The following section explains the system development pro-
cess of the on-line detection, diagnosis and correction system.
A process diagram of the vibration and correction forces is
shown in gure 2. At start up the AMB system is suspended
only with PID controllers and rotated at the desired speed of
1000 rpm. Displacement masking is performed during this
initial period when no vibration forces are occurring on the
system. The rotational speed of the rotor is used as input to
the displacement masking process. The masked displacement
is stored to memory.
When a vibration force occurs on the rotor (and when the PID
controller fails to correct the vibration), the system detects the
fault and calculates the vibration error, frequency and pattern.
The stored no fault displacement is used to calculate the vi-
bration error. Data tting is then performed on the vibration
error and masked displacement.
The fault identication system identies the fault according
the result obtained from the data tting, vibration error, fre-
quency and pattern. The frequency and pattern are sent to the
fault diagnosis and error correction systems, which calculate
the correction currents needed to stabilize the rotor.
Correction forces are applied on the rotor by increasing or de-
creasing the reference currents
i
ref_1
and i
ref_2
according to the
direction of the vibration force.
Figure 2: Process diagram: vibration and correction forces.
Figure 3 provides an overview of the detection, diagnosis, cor-
rection and identication system that was implemented on the
double radial AMB test rack. The fault detection subsystem
uses the displacement (x
p
) to detect the vibration forces on the
AMB system and calculates the displacement error (e) and
frequencies (B
1
, B
2
and B
3
), through a process of displacement
masking. The parameters B
1
, B
2
and B
3
represent three dif-
Vol.99(4) December 2008SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS116
ferent frequencies obtained from the displacement error. This
project focus on the analysis of only three frequencies, since a
maximum of three frequencies was obtained simultaneously
in the historical fault data of the water cooling AMB pump.
The fault detection system is explained in section 3.2.
After a fault has been detected, the error (e) and frequencies
(B
1
, B
2
and B
3
) are sent to the fault diagnosis system, where
feature extraction is performed. The fault diagnosis system is
explained in section 3.3.
The error correction system uses the diagnosis output error
(e
d
) and the workforce relation current (i
ref_1R
) as features to
stabilize the rotor by inducing correction forces on the rotor.
The error correction system is explained in section 3.3.
The parameters
i
ref_1_
add
and i
ref_2_
add
represents the correction
reference currents for the top and bottom magnetic bearings,
respectively.
The fault identication system uses the displacement error (e),
historical database errors (e
1_ref
, e
2_ref
and
e3_ref
) and the fre-
quencies (B
1
, B
2
and B
3
) to identify the vibration force. The
fault identication system is explained in section 3.4.
controller, which together with the bias current (i
0
) provides
the reference currents (
i
ref_1
and i
ref_2
) for the power ampli-
ers. The forces (f
1
and f
2
) are calculated with (K
m
i
1
2
)/X
p
2
and
(K
m
i
2
2
))/(X
pref
- X
p
)
2
, where Km is the constant of the magnetic
bearing. The position (X
p
) is obtained by double integrating
the forces and dividing the answer with the mass of the rotor
(m).
For the simulation model, the vibration force (f
4
) on the ro-
tor was induced by subtracting the position error (e
p
) from
the reference error index (e
ref
sin(ω
2
t)) and feeding this to a
controller. The reference error (e
ref
) represents the error calcu-
lated from the historical fault data of the water cooling AMB
pump and the index (sin(ω
2
t)) represents the carrier of the
AMB pump.
The output of the controller is then added as a reference force
(f
4
) and the connection to add a reference current fault (i
f
) to
the reference current (
i
ref
) is disconnected. The carrier force
(f
3
(ω
2
t)) of the double radial AMB was kept constant and the
vibration force (f
4
) was stored to le. The stored le now con-
tains both the carriers of the water cooling AMB pump and
the double radial AMB test rack.
The le was then demodulated to subtract the carrier of the
water cooling AMB pump and the remainder was used to sim-
ulate vibration forces on the rotor. These vibration forces (f
4
)
are synchronously placed on the carrier of the double radial
AMB test rack.
For the practical AMB system the connection to add a refer-
ence current fault (i
f
) to the reference current (i
ref
) is restored
and the vibration force (f
4
) is disconnected.
The reference current fault (i
f
) is then stored to le, during the
controlling process of the rotating double radial AMB test
rack. The le is demodulated to subtract the carrier of the wa-
ter cooling AMB pump and the remainder is used as reference
current faults to induce vibration forces on the rotor. These
reference current faults (i
f
) are synchronously placed on the
carrier of the double radial AMB test rack.
3.2 Fault detection system
The fault detection system (shown in gure 5) constitutes
displacement masking, error calculation and parameter cal-
culation. Displacement masking is performed by capturing
one cycle of the displacement (X
p
) during a no fault condi-
Figure 4: Simulation (dashed and solid lines) and practical (solid lines) AMB models with rotational rotor faults.
Figure 3: Detection, diagnosis, correction and identication.
3.1 Simulation and practical AMB models
A simulation model of the AMB system was necessary to ob-
serve how the practical system will respond to faults, when the
diagnosis and correction system is implemented. The simula-
tion (dashed and solid lines) and practical (solid lines) mod-
els of the rotating double radial AMB system with vibration
forces are shown in gure 4.
The actual position (X
p
) is subtracted from the reference posi-
tion to provide the position error (e
p
). This is fed to a PID
Vol.99(4) December 2008 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 117
tion of the AMB system. A sine wave representation of the
no fault displacement (X
mp
) is obtained and stored to memory.
This process is done only once and when no vibration force is
occurring on the system. When a fault occurs in the system,
the displacement (X
p
) is called the fault displacement (X
p_fault
).
The no fault displacement (X
mp
) is subtracted from the fault
displacement (X
p_fault
) to provide the displacement error (e).
When there is a sudden change in the rotational speed (Ω)
of the rotor, the frequency of the no fault displacement (X
mp
)
is changed to compensate for the change. The displacement
masking process during the practical implementation process
is discussed in section 4.
The WVD is very often used in practical applications, since it
avoids interference between positive and negative frequencies
[10]. The properties of the WVD have been studied extensively
over the past 15 years [13]. It has been shown that the WVD
fulls the greatest number of theoretical and practical proper-
ties within the class of time-frequency distributions [14]. The
WVD always goes to zero at the beginning and end of nite-
duration signals [15]. The discrete representation for (2) is:
The phase of the displacement error (e) was calculated by
using trigonometrical functions and a phase calculator algo-
rithm and dividing the phase equally between C
1
, C
2
and C
3
.
The offset was calculated from the maximum and minimum
values of the displacement error (e) and an offset calculator
algorithm and dividing the offset equally between D
1
, D
2
and
D
3
. The same process was used to calculate the phases and
offsets of the reference displacement errors in the historical
fault database.
The Wigner-Ville distribution (WVD) was developed to
overcome a limitation of the Short-Time Fourier Transform
(STFT), where high-resolution cannot be obtained simulta-
neously in both time and frequency domains [9]. The WVD
was developed to utilize the Fourier transform in a similar way
and due to this similarity the WVD has been interpreted as a
modied version of the STFT [10].
Data point number reduction is not necessary during the time-
shifting operation of the WVD process. The process is started
with the Fourier transform of the ensemble-average instanta-
neous correlation product as shown in the following equation:
Figure 5: Fault detection system.
Figure 6: Multiple frequency fault calculation with the WVD.
where χ* is the conjugate of x for complex signals or Hilbert
transform of χ for real signals which, in theory, is a measure
of the frequency content of a non-stationary random process
χ(t) [11]-[12].
It is not possible to compute the ensemble-average function
accurately in practice, because of the innite number of data
required. One solution to deal with the non-stationary case is
to omit the ensemble-average in (1):
where T
s
is the sampling period and must be chosen so that
Ts (π/2ωmax) and ωmax is the highest frequency in a ran-
dom signal.
The WVD was calculated by using (3) and the frequencies (B
1
,
B
2
and B
3
) were calculated from the WVD and a frequency
calculator algorithm. The accuracy of the frequency was im-
proved by increasing the sampling time of the WVD to two
times the cycle time (t
c
) of the error signal (e).
Figure 6 provides the WVD spectrum of a multiple frequency
fault. The WVD was calculated from the displacement error
(e) and the peaks P
1
to P
9
was obtained from the positive
peaks of the WVD as shown in gure 6. Table 1 provides the
values of the peaks shown in gure 6.
The amplitudes (A
1
, A
2
and A
3
) are calculated from peaks P
1
,
P
2
and P
3
at 0.098 mm, 0.055 mm and 0.049 mm, respectively.
The amplitude values were calculated by multiplying the cor-
responding peak with the amplitude of the multiple frequency
displacement error (e). From peak P
1
the frequency B
1
was
calculated at 83.3 Hz.
Vol.99(4) December 2008SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS118
From peaks P
2
, P
5
and P
7
the frequency B
2
was calculated at
17.2 Hz. The frequency B3 was calculated from peaks P
3
, P
5
and P
7
at 2.4 Hz.
From table 1 it can be seen that P
4
and P
8
are multiples of the
second peak (P
2
) and P
2
and P
9
are multiples of the third peak
(P
3
). These peaks provide an estimate of the error on peaks
P
2
and P
3
, respectively. The accuracy of frequencies B
2
and B
3
was calculated at 99.9 % and 99.3 %, respectively.
3.3 Fault diagnosis and correction systems
This section discusses the fault diagnosis and correction sys-
tem, shown in gure 7. An error pattern component calculator
subsystem uses the parameters (A, B, C and D) obtained from
the fault detection system to construct displacement error pat-
terns e
r1_pat
, e
r2_pat
and e
r3_pat
.
The pattern recognition subsystem calls (e
call1
) the reference
displacement errors from the database at specic frequen-
cies (B
1
, B
2
and B
3
). The pattern recognition subsystem then
compares the displacement error patterns (e
r1_pat
, e
r2_pat
and
er3_pat) of the on-line system with the reference displacement
error patterns (e
1_ref
, e
2_ref
and e
3_ref
) of the historical fault da-
tabase. The same process used to calculate the displacement
error patterns e
r1_pat
, e
r2_pat
and e
r3_pat
was used to calculate the
reference displacement error patterns e
1_ref
, e
2_ref
.
When a fault occurs without a recognizable pattern, the pat-
tern is band-pass ltered (centre frequency being the error fre-
quencies B
1
, B
2
and B
3
) and stored to the historical fault data-
base. The parameters e
1_c
, e
2_c
and e
3_c
refer to the constructed
patterns for frequencies B
1
, B
2
and B
3
, respectively.
available data is found, the system uses the on-line error to
correct the fault. A new pattern is constructed and stored to
the database and the pattern calculation process is repeated.
If the system nds a combination pattern, the system uses the
pattern and stores the pattern as a combination pattern.
Figure 8 shows the process diagram of the pattern recogni-
tion subsystem. The system tests the difference between the
on-line displacement error patterns (e
r1_pat
, e
r2_pat
and e
r3_pat
)
and the reference displacement error patterns (e
1_ref
, e
2_ref
and
e
3_ref
) from the historical fault database. If the error difference
is big, the error obtained from the on-line AMB system is used
for correctional purposes. At this stage no recognizable pat-
tern exists and the pattern construction system constructs and
stores a new pattern.
When the error difference is small (close to zero), the system
calculates the frequency and closest pattern to the available
on-line data. If the frequency stays constant, the system uses
the closest pattern to correct the fault. If the frequency chang-
es the system tests the data in the historical fault database for
a possible combination pattern. When no combination of the
Figure 7: Fault diagnosis and correction system.
Figure 8: Process diagram of the pattern recognition subsystem.
Figure 9: Orbital representation of the subsynchronous
vibration force correctional pattern errors.
Figure 10: Fuzzy membership functions for pattern error 1.
The construction subsystem constructs and stores new pat-
terns (e
1_c
, e
2_c
and e
3_c
) according to the displacement error
(e), when it receives a pattern fault (P
f
) from the pattern rec-
ognition subsystems.
The more faults occur in the system, the more new correc-
tional data becomes available. The system is able to switch be-
tween different patterns and train itself to react on faults that
are a combination of the available fault data.
A displacement orbital representation of three subsynchro-
nous vibration force correctional patterns is shown in gure 9.
Pattern subnew is a trained pattern which consists of pieces of
three sub-synchronous correctional patterns sub
1
, sub
2
and
sub
3
. The pattern sub
new
was stored as a combination pattern
and decreased the vibration forces on the rotor of the AMB
system. For each of the patterns in the historical fault data-
base there exist a frequency and description.
Vol.99(4) December 2008 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 119
Figure 10 provides the fuzzy membership functions for pat-
tern error 1 (e
1_pat
). Fuzzication is performed by using the
overlapping fuzzy sets bad negative (B-), good (G) and bad
positive (B+). The membership function for pattern error 2
(e
2_pat
) and pattern error 3 (e
3_pat
) is the same as for pattern
error 1 (e
1_pat
).
The basic rule for using the features (e
1_pat
and e
2_pat
) is: IF
e
1_pat
AND e
2_pat
THEN efuz1. The same rule applies for vari-
able
i
ref_1R1
. Table 2 provides the rule matrix for fuzzy1 error
efuz1 and relation current1
i
ref_1R1
.
The fuzzy surface plots for fuzzy1 error (e
fuz1
) and relation
current1 (
i
ref_1
) are shown in gure 11a and gure 11b, respec-
tively. Defuzzication of the fuzzy membership functions e
fuz1
and
i
ref_1
are performed by using overlapping fuzzy sets nega-
tive (N), middle (M) and positive (P) and bottom (B), middle
(M) and top (T), respectively.
Workforce relation current 2 was calculated as follow:
Figure 11: Fuzzy surface plot for fuzzy1 error (e
fuz1
) and
relation current1 (
i
ref_1
)
Diagnosis of the whole system results in a complex set of rule
bases, which was simplied by using a cascaded fuzzy logic
module [16]-[17]. The displacement pattern errors (e
1_pat
, e
2_
pat
t and e
3_pat
) are the inputs of the cascaded fuzzy logic mod-
ule and fuzzy error (efuz) and relation current (
i
ref_1
) are the
outputs. The fuzzy surface plots for fuzzy2 error (e
fuz2
) and
fuzzy3 error (e
fuz3
) are the same as shown in gure 11a and
the fuzzy surface plots for relation current2 (
i
ref_2
) and relation
current3 (
i
ref_3
) are the same as shown in gure 11b.
Fuzzy error efuz was calculated from the sum of e
fuz1
, e
fuz2
and
e
fuz3
and relation current i
ref_1
was calculated from the sum of
i
ref_1
, i
ref_2
and i
ref_3
.
When a vibration force causes the rotor to move downward,
the reference current 1 (
i
ref_1
) needs to be more than reference
current 2 (
i
ref_2
) to stabilize the rotor to the centre position.
This relation between the amplitude of the vibration force
and amount of current required by each amplier are called
the workforce relation current and is dened by
i
ref_1
and i
ref_2
.
i
ref_3
refer to the workforce relation current for the top power
amplier and
i
ref_2
refer to the workforce relation current for
the bottom power amplier.
The workforce relation current serves as an amplier (boost-
er) and increases or decreases the amplitude of the correction
force according to the error made on the current. These in-
creases and decreases of the correct ampliers, causes faster
correction force response times.
System parameter change of phase shifting was performed on
the fuzzy current error (e
fuz
), before send to the error correc-
tion system. The fuzzy current error is then called the diagno-
sis output error (e
d
).
Correctional reference current 1 was calculated as follow:
The correctional reference current 1 is added to reference cur-
rent 1 (
i
ref_1
). Correctional reference current 2 was calculated
by (6) and added to reference current 2 (
i
ref_2
).
3.4 Fault identication system
A process diagram of the fault identication system is shown
in gure 12. When no fault is detected, the identication sys-
tem provides no output. When a fault is detected, the system
uses the frequency to determine to which frequency dataset
(subsynchronous, rotor synchronous or super-synchronous)
the fault belongs. This process was performed on all the dis-
placement error patterns received from the on-line AMB sys-
tem.
The system performs data tting to calculate the best possible
t of the historical fault data in the specic dataset with the
data obtained from the practical AMB system.
If the frequency rapidly changes from one dataset to another,
the system saves the output, predicts the closest type of fault
(unbalance, misalignment, foundation looseness or as other-
wise specied in the historical fault database) and recalculates
the fault in the new dataset.
When the frequency stays within a certain dataset, the system
is set to repeatedly calculate the average error over a time pe-
riod of 1 second. The time period was calculated at ve times
the period of the masked displacement at 1000 rpm. The type
of fault is given to the fault in the dataset with the smallest
error over the available time period.
Figure 12: Process diagram of the fault identication system.
Vol.99(4) December 2008SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS120
After the type of fault is stored, the system displays the pa-
rameters of the fault and determines the vibratory level and
zone of the fault. The system determines the side and axes
where the fault occurs from the displacement error signals.
Faults are pinpointed to the A-side and B-side and can occur
in the x, y and z axes. The identication system was limited to
the A-side and the y-axes, due to the installation of the roller
bearing on the B-side and the limitation in the sampling time
of the dSPACE® controller. The day and time when the fault
rst occurred is saved and displayed.
Figure 13 shows the parameter diagram of the fault identi-
cation system used to calculate the type of fault, parameters
of the fault, the vibratory level of the fault, zone of the fault,
where the fault occurs and the day and time when the fault
rst occurred.
The data tting system calculates and compares the best pos-
sible t of the displacement error patterns (e
1_pat
, e
2_pat
and
e
3_pat
) of the on-line AMB system with the reference displace-
ment error patterns (e
1_ref
, e
2_ref
and e
3_ref
) of the historical
fault database. The data tting system sends the number of
the dataset (N) with the closest t and the accuracy of the t
(A
t
) to the diagnostic system.
The historical fault database provides the diagnostic system
with the type of fault (F
data
). The output is displayed as a per-
centage t to a specic dataset and the corresponding fault in
the dataset. Each time the identication system recalculates
the fault the parameters A, B, C and D are saved as the output
parameters of the fault.
The minimum radial clearance (C
min
) is dened as the mini-
mum gap when statically moving the rotor in any radial direc-
tion. The retainer bearing gap is generally set to be C
min
by
design [20]-[21].
The side and axes with the largest displacement error indicates
where the fault causes the most damage. The exact time when
the fault rst occurred was saved and displayed and was calcu-
lated from the running time (tr).
Figure 13: Fault identication system.
Figure 14: Supersynchronous vibration force data tting with
sudden change to subsynchronous vibration force.
The international standard for mechanical vibration of rotat-
ing machinery denes four zones [18]-[19]: A) vibratory dis-
placement of newly commissioned machines, B) where the vi-
bratory displacement is acceptable for unrestricted long-term
operation, C) where the vibratory displacement is unsatisfac-
tory for long-term continuous operation and D) the vibratory
displacement causes severe damage to the machine.
These zones (Z) were used to identify the vibratory level (V
1
)
of faults, during the identication process. The ratio between
the minimum radial clearance (C
min
) and the maximum peak
displacement (D
max
) as dened in accordance with ISO 14839-
2 was used to determine the vibratory zone [18].
The maximum peak displacement (D
max
) of the rotor from the
clearance centre of the radial AMB, is calculated as follows:
Figure 14 displays data tting where the frequency of the fault
changed from the supersynchronous vibration force area to
the subsynchronous vibration force area. The solid lines rep-
resent the reference displacement error pattern (e
1_ref
) from the
historical fault database of the water cooling AMB pump and
the dashed lines represent the real-time displacement error
pattern (e
1_pat
) from the double radial AMB test rack. Sam-
pling (shown by the markers) was decreased when the frequen-
cy entered the subsynchronous vibration force area.
4. HARDWARE SETUP
The dSPACE® 1104 controller board, equipped with a DSP
TMS320F240 from Texas Instruments was used for discrete
sampling of the displacement and current signals of the
physical AMB system. An user-interface was created in Con-
troldesk® to perform data acquisition on the physical system.
Due to the complexity of the control, detection and correction
system, the dSPACE® controller was not able to handle all
the instructions and real-time errors occurred. This problem
was solved by implementing two dSPACE® 1104 controller
boards, one for each axes of the magnetic bearing. A roller
bearing was installed on the right side of the rotor, which in-
creased the sampling time of the DSP, since only one side has
to be suspended.
The vibration force calculations, displacement masking pro-
cess and speed sensor calculations were performed by the
left dSPACE® controller and communicated to the other
dSPACE® controller via serial communication.
The inducement of the vibration forces and diagnosis and
correction system calculations were performed by the right
dSPACE® controller. Figure 15 shows the hardware setup
with the dSPACE® controllers.
During the investigation of the displacement signals of the
double radial AMB system, it became evident that synchro-
nous vibrations were introduced by the roller bearing when
the rotor was rotating. These vibrations were therefore inte-
grated into the displacement masking and correctional pat-
Vol.99(4) December 2008 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 121
terns calculation process of the fault detection and diagnosis
systems (discussed in sections 3.2 and 3.3).
Figure 16 shows the masked displacement (X
mp
) and the actual
displacement (X
p
) during the practical implementation phase.
The no fault displacement (xmp) was subtracted from the
fault displacement (X
p_fault
) to provide the displacement error
(e). The amplitude of the displacement (X
p
) and the frequency
(ω) obtained from the rotational speed of the rotor was used
as scaling factors for the masked displacement. When the am-
plitude and frequency increased, the amplitudes and frequen-
cies of the individual signals in the masked displacement were
also increased.
Figure 19 shows the actual displacement of the AMB system
with multiple frequency vibration forces and dominant super-
synchronous vibration force. The system was designed to sim-
ulate and capture the actual displacement of the simulation
and practical AMB models (shown in gure 4) without any
vibration force for the rst 10 seconds, thereafter to induce
the fault and activate the detection, diagnosis and correction
system after 20 seconds.
Figure 15: Hardware setup with the dSPACE® controllers.
Figure 16: Displacement masking during the practical
implementation phase.
5. SIMULATION VERIFICATION
This section provides the simulated and experimental results
of the double radial AMB test rack, with multiple frequency
vibration forces and dominant subsynchronous, rotor syn-
chronous and supersynchronous vibration forces. During the
simulation phase of this project the carrier frequency was cho-
sen at 104.7 rad/sec (1000 rpm) and faults were induced by ap-
plying the vibration force (f
4
) les onto the system to see how
the diagnosis and correction system reacts.
During the practical implementation phase of this project,
the rotor was held constant at 1000 rpm and vibration forces
were induced by implementing the reference current fault (i
f
)
les onto the system to see how the diagnosis and correction
system reacts.
Figure 17 and gure 18 shows the actual displacement (X
p
) of
the AMB system with multiple frequency vibration forces and
dominant subsynchronous and rotor synchronous vibration
forces, respectively.
Figure 17: Multiple frequency vibration forces with domi-
nant subsynchronous vibration force.
Figure 18: Multiple frequency vibration forces with domi-
nant rotor synchronous vibration force.
Figure 19: Multiple frequency vibration forces with
dominant supersynchronous vibration force.
From the above gures it can be seen that the practical AMB
system provides even better results than the simulation AMB
model.
6. CONCLUSION
The work presented in this paper concentrated on the real-
time detection, correction and identication of multiple fre-
quency vibration forces on the rotor of an AMB system.
The real-time system only stabilizes the rotor with respect to
the stator and do not remove the vibration force. When correc-
tion forces are applied to the AMB system to correct the effect
Vol.99(4) December 2008SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS122
of the vibration forces, it may increase the stresses in other
critical components e.g. the power ampliers and system base,
which may cause components to be damaged or break down.
These stressed components need to be identied by the user as
critical on non-critical and the necessary steps must be taken
to operate the AMB system under the fault condition or to
shut down the system and repair the fault.
The method of performing detection, diagnosis, and correc-
tion must be seen as a whole and the performance of the com-
plete system, rather than a single component must be evalu-
ated. The method of real-time frequency extraction with the
WVD and real-time feature extraction by means of the fuzzy
logic controller are the most crucial components in the design
of the detection, diagnosis and correction system.
The implementation of the cascaded fuzzy logic module sim-
plied the fault diagnosis and correction system and decreased
the calculation time.
The maximum current capacity and bandwidth of the power
ampliers, run-time of the DSP processors and bandwidth of
the sensors were the main factors limiting the applicability of
the real-time system.
The experimental results of the double radial AMB test rack
correlated with the simulated results and vibration forces were
corrected or minimized to a stable working condition.
7. ACKNOWLEDGMENTS
The authors wish to thank the Institute for Process Technol-
ogy, Automation and Measurement Technology (IPM) at the
University of Applied Sciences Zittau/Görlitz in Germany for
making it possible to work on the 250 kW water cooling AMB
pump.
8. APPENDIX
Figure 20 shows a screenshot of the fault identication pro-
gram written in MATLAB®. This program calculates and
displays the parameters of the fault identication system of
gure 13. Faults are calculated and displayed as a specic type
(misalignment, foundation looseness, unbalance or as oth-
erwise specied in the historical fault database), percentage
t to a specic dataset, vibratory level (normal, acceptable,
system critical or unsatisfactory), zone (A-D), side where the
fault occurs (A-side or B-side), axes where the fault occurs (x,
y or z-axes) and day and time when the fault rst occurred.
The parameters (amplitude, frequency, phase and offset) of
the different faults are also shown.
A diagram and picture of the fully suspended 250 kW water
cooling AMB pump can be seen in gure 21 and gure 22, re-
spectively. Condition monitoring was performed over a period
of 3 years to obtain historical fault data on the water cooling
AMB pump.
Figure 21: Water cooling AMB pump.
Figure 22: Water cooling AMB pump (physical system).
Figure 23: Double radial AMB test rack (physical system).
Due to technical aspects it was not possible to make any
changes to the water cooling AMB pump.
The specications of the water cooling AMB pump and dou-
ble radial AMB test rack can be seen in table 3. A picture of
the double radial AMB test rack can be seen in gure 23.
Vol.99(4) December 2008 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 123
9. REFERENCES
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[2] O. Lang, J. Wassermann and H. Springer: “Adaptive Vi-
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Adaptive Vibration Control of a Rigid Rotor supported by Active Magnetic Bearings
  • O Lang
  • J Wassermann
  • H Springer
O. Lang, J. Wassermann and H. Springer: "Adaptive Vibration Control of a Rigid Rotor supported by Active Magnetic Bearings", Proc. of Int. Gas Turbine and Aeroengine Congress and Exposition, Houston, Texas, 1995.
Adaptive Vibration Control of Industrial Turbomachinery
  • R W Hope
  • L P Tessier
  • C Knospe
  • T Miyaji
R.W. Hope, L.P. Tessier, C. Knospe and T. Miyaji: "Adaptive Vibration Control of Industrial Turbomachinery", International Gas Turbine & Aeroengine Congress & Exposition, 98-GT-405, 1998.