Vol.99(4) December 2008SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS114

1. INTRODUCTIONRotating 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 field, 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 identification 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 first 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 SYSTEMR. 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 identification 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 identification 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 identification 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 figure 1) was used for verification 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 amplifiers, which in turn provide the magnetic bearings with the correct current to suspend the shaft. The specifica-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 first 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 specifications 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 figure 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 fitting is then performed on the vibration error and masked displacement.

The fault identification system identifies the fault according the result obtained from the data fitting, 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 iref_1 and iref_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 identification system that was implemented on the double radial AMB test rack. The fault detection subsystem uses the displacement (xp) to detect the vibration forces on the AMB system and calculates the displacement error (e) and frequencies (B1, B2 and B3), through a process of displacement masking. The parameters B1, B2 and B3 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 (B1, B2 and B3) 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 (ed) and the workforce relation current (iref_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 iref_1_add and iref_2_add represents the correction reference currents for the top and bottom magnetic bearings, respectively.

The fault identification system uses the displacement error (e), historical database errors (e1_ref, e2_ref and e3_ref) and the fre-quencies (B1, B2 and B3) to identify the vibration force. The fault identification system is explained in section 3.4.

controller, which together with the bias current (i0) provides the reference currents (iref_1 and iref_2) for the power amplifi-ers. The forces (f1 and f2) are calculated with (Km•i1

2)/Xp2 and

(Km•i22))/(Xpref - Xp)

2, where Km is the constant of the magnetic bearing. The position (Xp) 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 (f4) on the ro-tor was induced by subtracting the position error (ep) from the reference error index (eref•sin(ω2t)) and feeding this to a controller. The reference error (eref) represents the error calcu-lated from the historical fault data of the water cooling AMB pump and the index (sin(ω2t)) represents the carrier of the AMB pump.

The output of the controller is then added as a reference force (f4) and the connection to add a reference current fault (if) to the reference current (iref) is disconnected. The carrier force (f3(ω2t)) of the double radial AMB was kept constant and the vibration force (f4) was stored to file. The stored file now con-tains both the carriers of the water cooling AMB pump and the double radial AMB test rack.

The file 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 (f4) 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 (if) to the reference current (iref) is restored and the vibration force (f4) is disconnected.

The reference current fault (if) is then stored to file, during the controlling process of the rotating double radial AMB test rack. The file 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 (if) are synchronously placed on the carrier of the double radial AMB test rack.

3.2 Fault detection systemThe fault detection system (shown in figure 5) constitutes displacement masking, error calculation and parameter cal-culation. Displacement masking is performed by capturing one cycle of the displacement (Xp) 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 identification.

3.1 Simulation and practical AMB modelsA 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 figure 4.

The actual position (Xp) is subtracted from the reference posi-tion to provide the position error (ep). 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 (Xmp) 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 (Xp) is called the fault displacement (Xp_fault). The no fault displacement (Xmp) is subtracted from the fault displacement (Xp_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 (Xmp) 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 fulfils 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 finite-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 C1, C2 and C3. 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 D1, D2 and D3. 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 modified 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 infinite number of data required. One solution to deal with the non-stationary case is to omit the ensemble-average in (1):

where Ts 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 (B1, B2 and B3) 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 (tc) 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 P1 to P9 was obtained from the positive peaks of the WVD as shown in figure 6. Table 1 provides the values of the peaks shown in figure 6.

The amplitudes (A1, A2 and A3) are calculated from peaks P1, P2 and P3 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 P1 the frequency B1 was calculated at 83.3 Hz.

Vol.99(4) December 2008SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS118

From peaks P2, P5 and P7 the frequency B2 was calculated at 17.2 Hz. The frequency B3 was calculated from peaks P3, P5 and P7 at 2.4 Hz.

From table 1 it can be seen that P4 and P8 are multiples of the second peak (P2) and P2 and P9 are multiples of the third peak (P3). These peaks provide an estimate of the error on peaks P2 and P3, respectively. The accuracy of frequencies B2 and B3 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 figure 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 er1_pat, er2_pat and er3_pat.

The pattern recognition subsystem calls (ecall1) the reference displacement errors from the database at specific frequen-cies (B1, B2 and B3). The pattern recognition subsystem then compares the displacement error patterns (er1_pat, er2_pat and er3_pat) of the on-line system with the reference displacement error patterns (e1_ref, e2_ref and e3_ref) of the historical fault da-tabase. The same process used to calculate the displacement error patterns er1_pat, er2_pat and er3_pat was used to calculate the reference displacement error patterns e1_ref, e2_ref.

When a fault occurs without a recognizable pattern, the pat-tern is band-pass filtered (centre frequency being the error fre-quencies B1, B2 and B3) and stored to the historical fault data-base. The parameters e1_c, e2_c and e3_c refer to the constructed patterns for frequencies B1, B2 and B3, 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 finds 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 (er1_pat, er2_pat and er3_pat) and the reference displacement error patterns (e1_ref, e2_ref and e3_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 (e1_c, e2_c and e3_c) according to the displacement error (e), when it receives a pattern fault (Pf) 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 figure 9. Pattern subnew is a trained pattern which consists of pieces of three sub-synchronous correctional patterns sub1, sub2 and sub3. The pattern subnew 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 (e1_pat). Fuzzification is performed by using the overlapping fuzzy sets bad negative (B-), good (G) and bad positive (B+). The membership function for pattern error 2 (e2_pat) and pattern error 3 (e3_pat) is the same as for pattern error 1 (e1_pat).

The basic rule for using the features (e1_pat and e2_pat) is: IF e1_pat AND e2_pat THEN efuz1. The same rule applies for vari-able iref_1R1. Table 2 provides the rule matrix for fuzzy1 error efuz1 and relation current1 iref_1R1. The fuzzy surface plots for fuzzy1 error (efuz1) and relation current1 (iref_1) are shown in figure 11a and figure 11b, respec-tively. Defuzzification of the fuzzy membership functions efuz1 and iref_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 (efuz1) and relation current1 (iref_1)

Diagnosis of the whole system results in a complex set of rule bases, which was simplified by using a cascaded fuzzy logic module [16]-[17]. The displacement pattern errors (e1_pat, e2_

patt and e3_pat) are the inputs of the cascaded fuzzy logic mod-ule and fuzzy error (efuz) and relation current (iref_1) are the outputs. The fuzzy surface plots for fuzzy2 error (efuz2) and fuzzy3 error (efuz3) are the same as shown in figure 11a and the fuzzy surface plots for relation current2 (iref_2) and relation current3 (iref_3) are the same as shown in figure 11b.

Fuzzy error efuz was calculated from the sum of efuz1, efuz2 and efuz3 and relation current iref_1 was calculated from the sum of iref_1, iref_2 and iref_3.

When a vibration force causes the rotor to move downward, the reference current 1 (iref_1) needs to be more than reference current 2 (iref_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 amplifier are called the workforce relation current and is defined by iref_1 and iref_2. iref_3 refer to the workforce relation current for the top power amplifier and iref_2 refer to the workforce relation current for the bottom power amplifier.

The workforce relation current serves as an amplifier (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 amplifiers, causes faster correction force response times.

System parameter change of phase shifting was performed on the fuzzy current error (efuz), before send to the error correc-tion system. The fuzzy current error is then called the diagno-sis output error (ed).

Correctional reference current 1 was calculated as follow:

The correctional reference current 1 is added to reference cur-rent 1 (iref_1). Correctional reference current 2 was calculated by (6) and added to reference current 2 (iref_2).

3.4 Fault identification systemA process diagram of the fault identification system is shown in figure 12. When no fault is detected, the identification 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 fitting to calculate the best possible fit of the historical fault data in the specific 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 specified 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 five 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 identification 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 identification 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 first occurred is saved and displayed.

Figure 13 shows the parameter diagram of the fault identifi-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 first occurred.

The data fitting system calculates and compares the best pos-sible fit of the displacement error patterns (e1_pat, e2_pat and e3_pat) of the on-line AMB system with the reference displace-ment error patterns (e1_ref, e2_ref and e3_ref) of the historical fault database. The data fitting system sends the number of the dataset (N) with the closest fit and the accuracy of the fit (Afit) to the diagnostic system.

The historical fault database provides the diagnostic system with the type of fault (Fdata). The output is displayed as a per-centage fit to a specific dataset and the corresponding fault in the dataset. Each time the identification system recalculates the fault the parameters A, B, C and D are saved as the output parameters of the fault.

The minimum radial clearance (Cmin) is defined as the mini-mum gap when statically moving the rotor in any radial direc-tion. The retainer bearing gap is generally set to be Cmin 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 first occurred was saved and displayed and was calcu-lated from the running time (tr).

Figure 13: Fault identification system.

Figure 14: Supersynchronous vibration force data fitting with sudden change to subsynchronous vibration force.

The international standard for mechanical vibration of rotat-ing machinery defines 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 (V1) of faults, during the identification process. The ratio between the minimum radial clearance (Cmin) and the maximum peak displacement (Dmax) as defined in accordance with ISO 14839-2 was used to determine the vibratory zone [18].

The maximum peak displacement (Dmax) of the rotor from the clearance centre of the radial AMB, is calculated as follows:

Figure 14 displays data fitting 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 (e1_ref) from the historical fault database of the water cooling AMB pump and the dashed lines represent the real-time displacement error pattern (e1_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 SETUPThe 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 (Xmp) and the actual displacement (Xp) during the practical implementation phase. The no fault displacement (xmp) was subtracted from the fault displacement (Xp_fault) to provide the displacement error (e). The amplitude of the displacement (Xp) 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 figure 4) without any vibration force for the first 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 VERIFICATIONThis 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 (f4) files 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 (if) files onto the system to see how the diagnosis and correction system reacts.

Figure 17 and figure 18 shows the actual displacement (Xp) 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 figures it can be seen that the practical AMB system provides even better results than the simulation AMB model.

6. CONCLUSIONThe work presented in this paper concentrated on the real-time detection, correction and identification 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 amplifiers and system base, which may cause components to be damaged or break down. These stressed components need to be identified 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-plified the fault diagnosis and correction system and decreased the calculation time.

The maximum current capacity and bandwidth of the power amplifiers, 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. ACKNOWLEDGMENTSThe 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. APPENDIXFigure 20 shows a screenshot of the fault identification pro-gram written in MATLAB®. This program calculates and displays the parameters of the fault identification system of figure 13. Faults are calculated and displayed as a specific type (misalignment, foundation looseness, unbalance or as oth-erwise specified in the historical fault database), percentage fit to a specific 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 first 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 figure 21 and figure 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 specifications 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 figure 23.

Vol.99(4) December 2008 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 123

9. REFERENCES[1] G. Schweitzer, A. Traxler and H. Bleuler: Magnetlager,

Grundlagen, Eigenschaften und Anwendungen berührungs-freier, elektromagnetischer Lager, Berlin: Springer Ver-lag, 1993.

[2] O. Lang, J. Wassermann and H. Springer: “Adaptive Vi-bration Control of a Rigid Rotor supported by Active Magnetic Bearings”, Proc. of Int. Gas Turbine and Aero-engine Congress and Exposition, Houston, Texas, 1995.

[3] R.W. Hope, L.P. Tessier, C. Knospe and T. Miyaji: “Adaptive Vibration Control of Industrial Turboma-chinery”, International Gas Turbine & Aeroengine Con-gress & Exposition, 98-GT-405, 1998.

[4] A. Duyar, V. Eldem, W. Merrill and T.H. Guo: “Fault detection and diagnosis in propulsion system: A fault parameter estimation approach”, J. Guidance, Contr., Dynam., Vol. 17, No. 1, pp. 104-108, 1994.

[5] P.M. Frank: “Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy - A survey and some new results”, Automatica, Vol. 26, No. 3,

pp. 459-474, 1990.[6] R. Isermann: “Fault diagnosis of machine via parameter

estimation and knowledge processing-Tutorial paper”, Automatica, Vol. 29, No. 4, pp. 815-835, 1993.

[7] R. Herzog, P. Buhler, C. Gahler and R. Larsonneur: “Unbalance compensation using generalized notch fil-ters in the multivariable feedback of magnetic bearings”, IEEE Transactions on Control Systems Technology, Vol. 4, No. 5, pp. 580-586, Sep. 1996.

[8] J.T. Marshall: “A Multi-Point Measurement Technique for the Enhancement of Force Measurement with Ac-tive Magnetic Bearings (AMB)”, Faculty of the Virginia Polytechnic Institute and State University, Blacksburg, Virginia, May 2001.

[9] W.J. Staszewski: “Gearbox vibration diagnostics-an overview”, The 8th International Congress on Condition Monitoring and Diagnostic Engineering Management (COMADEM-96), Sheffield, England, July 1996.

[10] D.E. Newland: An Introduction to Random Vibrations, Spectral & Wavelet Analysis, Longman Scientific & Technical, 3rd ed., 1993.

[11] M. Chiollaz and B. Frave: “Engine Noise Characteriza-tion with Wigner-Ville Time-Frequency Analysis”, Me-chanical Systems and Signal Processing, Vol. 7, No. 5, pp. 375-400, 1993.

[12] J. Ville: “Theorie et Applications de la Notion de Signal Analytique”, Cables et Transmissions, Vol. 2, No. 1,

pp. 61-74, 1948.[13] R.N. Bracewell: The Fourier Transform and its Applica-

tions, 3rd ed., New York: McGraw-Hill, 1999.[14] L. Cohen: “Time-Frequency Distributions - A Review”,

Proceedings of the IEEE, Vol. 77, No. 7, pp. 941-981, 1989.

[15] B. Boashash: In Advances in Spectrum Analysis and Ar-ray Processing, Vol. 1, Englewood Cliffs, New Jersey: Prentice Hall, 1991.

[16] R. Hampel, M. Wagenknecht and N. Chaker: Fuzzy Control: Theory and Practice, Berlin: Springer Verlag, Sep. 2000.

[17] O. Castillo and P. Melin: Type-2 Fuzzy Logic: Theory and Applications (Studies in Fuzziness and Soft Computing), Berlin: Springer Verlag, 2008.

[18] ISO/FDIS 14839-2: Mechanical vibration – Vibration of rotating machinery equipped with active magnetic bear-ings – Part 2: Evaluation of vibration, 2004.

[19] ISO 10816-7: Mechanical vibration – Evaluation of ma-chine vibration by measurements on non-rotating parts - Part 7: Rotodynamic pumps for industrial applications, including measurements on rotating shafts, 2009.

[20] ISO 7919-3: Mechanical vibration – Evaluation of ma-chine vibration by measurements on rotating shafts – Part 3: Coupled industrial machines, 2009.

[21] ISO 7919-5: Mechanical vibration – Evaluation of ma-chine vibration on rotating shafts – Part 5: Machine sets in hydraulic power generating and pumping plants, 2005.