**1. Introduction**

Eccentricity and demagnetization are two critical mechanical faults that can both occur in electrical machines, creating vital problems in the industry. Eccentricity appears when the stator is not placed correctly in relation to the rotor, a phenomenon that can occur during assembly or during machine operation. In other words, eccentricity is the result of manufacturing imperfections like unbalanced mass, poor alignment and excessive tolerances. 60% of the faults that appear in electrical machines are mechanical and 80% of them can create eccentricity [1]. This fault is responsible for unbalanced magnetic forces, vibration, and acoustic noise, creating problems in the machine operation and reducing its lifetime. If the level of eccentricity severity is quite high, stator and rotor can both be scraped, leading to the damage of the generator. Especially, the Axial Flux Permanent Magnet (AFPM) synchronous machines are prone to eccentricity fault because their overall axial length is short and as consequence, the ratio of machine diameter to length is high [2]. In addition, this type of machine contains permanent magnets that can ge<sup>t</sup> demagnetized or crack easily. The high temperatures, the structural defects, and the degradation of the coercive force are responsible for this fault. The demagnetization can be partial or total irreversible. The early diagnosis of both faults is a vital need for the interrupted operation of the systems in the industry.

In the international literature, several methods are proposed for demagnetization [3–6] and eccentricity detection [5–7]. The most commonly used methods are the Time Domain, the Frequency Analysis, and the Time Scale Analysis Methods, like Discrete or Continuous Wavelet Transform. The Motor Current Signature Analysis (MCSA) and the Motor Voltage Current Analysis (MVCA) are the most frequently used online methods for fault detection, since there is no need for any additional connections or hardware.

The majority of existing studies investigates these faults in Radial Flux Permanent Magnet (RFPM) synchronous machines. During recent years, the demagnetization and the eccentricity fault have also been studied in the AFPM synchronous machine. More specifically [2,8–21] study the eccentricity fault, while [21–30] investigate the demagnetization fault in AFPM synchronous machines. In [31] a combined eccentricity and demagnetization fault in a double-sided AFPM synchronous machine using a time analytical model is presented.

This study investigates the partial demagnetization fault, the static eccentricity (angular and axis) faults and the combined partial demagnetization and static eccentricity (angular and axis) faults. The Electromotive Force (EMF) spectrum will be used for fault diagnosis purposes and the fault signatures harmonics will be extracted. The machine simulation is performed while using the three-dimensional (3D)-Finite Element Analysis (FEA) that gives more accurate results for this machine type. In all demagnetized cases, one magne<sup>t</sup> of the generator is partially demagnetized in di fferent percentages, while the generator speed in constant, 375 rpm. Section 2 portrays the basic characteristics of the AFPM synchronous generator, in which the faults are studied. Section 3 provides a validation of the Finite Element Method (FEM) model of the machine, while Section 4 explains the two di fferent types of eccentricity. Section 5 presents the fault signature analysis and Section 6 investigates the partial demagnetization fault in the AFPM synchronous generator without the coexistence of the static eccentricity. Two percentages of partial demagnetization (50% and 80%) are examined. Section 7 studies the static angular and the static axis eccentricity faults. An additional spectrum, the spectrum of the phase EMF sum, has been used for fault diagnosis cases in this specific section. Subsequently, Section 8 studies the combined fault of partial demagnetization in combination with static angular and static axis eccentricity. The fault related harmonics in the EMF spectra are exported and comparisons are made when the level of partial demagnetization changes and the severity of eccentricities remains constant and when the level of partial demagnetization does not change, but the severity of eccentricities increases. Finally, Section 9 is the conclusion section which summarizes the basic assumptions. The novelty of the paper is that these combined faults have not been previously studied in the international literature as well as the phase EMF sum waveform has not been previously used for fault detection in this type of generator under these specific faults.

### **2. The AFPM Synchronous Generator**

The machine, in which the faults are investigated, is a three phase, star connected with neutral, double-sided rotor AFPM synchronous generator [32]. Figure 1 depicts the axial representation of the generator. The generator has 375 rpm nominal speed, 50 Hz nominal frequency, 80 V nominal voltage, 250 W nominal power, 16 poles in each rotor, 12 coils, and 210 turns per coil. The rotor, the magnet, the airgap, and the stator have 12 mm, 10 mm, 3 mm, and 18 mm axial thicknesses, respectively, while the stator external radius is 158mm and internal 60 mm.

**Figure 1.** The axial representation of the generator.

Beside the two rotors, there is a coreless stator with concentrated, non-overlapping, and trapezoidal, windings embedded in resin. Figure 2 depicts its layout, where bco is 34.3 mm, bci is 9 mm, bsc is 16.52 mm, lc is 63.2 mm, Ri is 58.35 mm, Ro is 121.55 mm, and r is 89.95 mm. Each rotor has 16 permanent magnets of trapezoidal shape made by NdFeB and their layout is presented in Figure 3, where bmo is 47 mm, bmi is 6 mm, Ri is 77.57 mm, Ro is 138.2 mm, and R is 107.885 mm.

**Figure 2.** The basic dimension parameters of the generator winding.

**Figure 3.** The basic dimension parameters of the permanent magnets of the generator.

In the axial flux permanent magne<sup>t</sup> synchronous generator, the axial component of the magnetic flux density is divided to the axial component of the magnetic flux density due to the winding Magnetomotive Force (MMF) and the axial component of the magnetic flux density due to the permanent magnets that can be given by (1):

$$\mathbf{B}\_{\mathbf{z}} = \mathbf{B}\_{\mathbf{z}\\_\text{MMF}} + \mathbf{B}\_{\mathbf{z}\\_\text{PM}} \tag{1}$$

where Bz is the axial component of the magnetic flux density in the AFPM, Bz\_MMF is the axial component of the magnetic flux density due to the winding MMF, and Bz\_PM is the axial component of the magnetic flux density due to the permanent magnets.

In an AFPM machine with three phases, the axial component of the magnetic flux density due to the MMF can be given by (2):

$$\mathbf{B\_{z\\_MMF}} = \sum\_{\mathbf{a}=1}^{3} \frac{\mu\_0}{1 + 2\mathbf{h\_m}} \mathbf{F\_a} \tag{2}$$

where

$$\mathbf{F}\_{\mathbf{a}} = \sum\_{\mathbf{v} \in \mathcal{P}} \mathbf{i}\_{\mathbf{a}} \frac{1}{\pi} \frac{\mathbf{w}\_{\mathbf{s}}}{|\mathbf{v}|} \sin(|\mathbf{v}| \frac{\varepsilon\_{\mathbf{r}}}{2}) \frac{\sin\left(|\mathbf{v}| \frac{\mathbf{a}\_{\mathbf{s}\mathbf{c}}(\mathbf{r})}{2}\right)}{|\mathbf{v}| \frac{\mathbf{a}\_{\mathbf{s}\mathbf{c}}(\mathbf{r})}{2}} \mathbf{e}^{|\mathbf{v}|(\mathbf{x} - \mathbf{x}\_{\mathbf{a}})} \tag{3}$$

and

$$\mathbf{x}\_{\mathbf{a}} = (\mathbf{a} - 1) \frac{2\pi}{3\mathbf{p}\_s} \tag{4}$$

where Fα is the MMF of the phase α winding, ws the number of phase winding turns, ps the number of phase coils, x the location according to the stator, ε(r) = bcr , bc ≈ bc0+bci 2 , asc(r) = bscr , and P = { ... −3ps, −2ps, −ps, ps, 2ps, 3ps ... } [33].

The axial component of the magnetic flux density due to the permanent magnets can be given by (5):

$$\mathbf{B}\_{\rm z\\_PM} = \sum\_{\boldsymbol{\varsigma} \in \mathbf{Q}} \frac{4}{\pi} \frac{\mathbf{B}\_{\rm r}}{\boldsymbol{\varsigma}} \frac{\mathbf{h}\_{\rm m}}{2\mathbf{h}\_{\rm m} + \mathbf{l}} \mathbf{p} \sin(\boldsymbol{\varsigma} \boldsymbol{\beta}(\mathbf{r})) \mathbf{e}^{\mathbf{j}\boldsymbol{\varsigma}(\mathbf{x} - \boldsymbol{\varphi})} \tag{5}$$

where

$$\beta(\mathbf{r}) = \frac{\mathbf{b}\_{\mathbf{m}}}{2\mathbf{r}} \tag{6}$$

where b m ≈ bmo+bmi 2 , ϕ the angle of a rotor position and Q = { ... −5p, −3p, −p, p, 3p, 5p ... } [33].

The harmonics that will be created in the magnetic flux density spectrum are responsible for the harmonics that will appear in the EMF spectrum.

### **3. Model Validation**

For the validation of the model in the healthy condition, we present the waveforms of the stator current, derived from the simulation and experiment, respectively, when the machine has nominal speed 375 rpm and supplies the nominal resistive load 70 Ohm, as Figure 4 shows. It can be observed that the two waveforms are qualitatively and quantitatively similar and they validate the accuracy of our FEM model. In addition, Figure 5 depicts the waveforms of the stator current when one magne<sup>t</sup> is totally demagnetized derived from simulation and experimental procedure when the generator has nominal speed and supplies a load 70 Ohm. It can be seen that the FEM waveform also agrees with the experimental waveform. More specifically, we have used the 3D-Opera mesher while our model contains 5128737 elements. The transient electromagnetic analysis with motion has been used. On a PC (Intel i7-4770 with 8 GB RAM) the finite element analysis requires 12 h in order to reach the steady state condition.

**Figure 4.** The stator current waveform in the healthy condition when the generator has nominal speed 375 rpm and supplies the nominal load of 70 Ohm (blue line-simulation results, red line-experimental results).

**Figure 5.** The stator current waveform when one magne<sup>t</sup> is totally demagnetized, the generator has nominal speed 375 rpm and supplies the nominal load of 70 Ohm (blue line-simulation results, red line-experimental results).

### **4. Types of Eccentricity**

Two types of static eccentricity appear in the literature [15,16]: the static angular and the static axis eccentricity. The first type occurs when the rotor axis coincides with the rotation axis but does not coincide with the stator axis. In this case, the air gap is not uniform, but, during the rotation, the maximum and minimum air gap positions are constant. In other words, the air gap does not change in time. The second type occurs when the stator and rotor are offset from each other in the axis direction. Figure 6 depicts the axial representation of the machine when the two different types of static eccentricity exist in the generator.

**Figure 6.** The axial representation of the machine when the generator is: (**a**) static angular eccentric and (**b**) static axis eccentric. Axial representation of the generator.

### **5. Fault Signature Analysis**

From the literature [7,34–36], it is known that the stator current spectrum of a RFPM synchronous machine with demagnetization or eccentricity fault contains new harmonics that are given by Equation (7):

$$\mathbf{f\_{demag}} = \mathbf{f\_s} \begin{pmatrix} 1 \pm \frac{\mathbf{k}}{\mathbf{P}} \end{pmatrix} \tag{7}$$

where fdemag are the frequencies of the fault related harmonics, fs is the fundamental frequency, p the number of machine poles pairs, and k an integer number. Previous studies [29,30] prove that this Equation can predict also the fault related harmonics in the EMF and stator current spectra of an AFPM synchronous machine with totally demagnetized magnets. In this article, it is examined whether this Equation is applicable in the case of the combined fault, in order to interpret the fault related harmonics.

### **6. Partial Demagnetization**

First, the partial demagnetization fault without the coexistence of the eccentricity fault is studied. In all of the investigated cases, one magne<sup>t</sup> is partially demagnetized in two different percentages (50% and 80% partial demagnetization). Figure 7 depicts the machine 3D-FEA model when one magne<sup>t</sup> is partially demagnetized, and Figure 8 shows the waveforms of the axial component of the magnetic flux density when the fault exists. The increment of the severity of the demagnetization leads to the decrement of the amplitude of the waveform in the location of the faulty magnet.

**Figure 7.** The three-dimensional (3D)-FEA model of the machine when one magne<sup>t</sup> is partially demagnetized.

**Figure 8.** The waveform of the axial component of the magnetic flux density when one magne<sup>t</sup> is partially demagnetized (blue line—50% partial demagnetization, red line—80% partial demagnetization).

The above waveform can be given by Equation (8) [37]:

$$\mathbf{B}\_{\mathbf{z}\\_core\\_dem} = \mathbf{B}\_{\mathbf{z}\\_tot} - \mathbf{y}(\mathbf{t}) \tag{8}$$

where Bz\_tot is the axial component of the total magnetic flux density in the healthy case and y(t) is the product between the Bz\_tot and the square wave x(t) divided by Vdem, which is the Bz\_tot amplitude immersion due to TDF, as it can be seen by (9):

$$\mathbf{y}(\mathbf{t}) = \frac{\mathbf{B}\_{\mathbf{z}\\_tot}}{\mathbf{V}\_{\text{dem}}} \mathbf{x}(\mathbf{t}) \tag{9}$$

while x(t) can be expressed in Fourier series using (10):

$$\mathbf{x}(\mathbf{t}) = \frac{1}{2\mathbf{p}} + \sum\_{\mathbf{k}=1}^{\infty} \frac{2}{\mathbf{k}\pi} \sin\left(\frac{\pi\mathbf{k}}{2\mathbf{p}}\right) \cos\left(\frac{2\mathbf{k}\pi\mathbf{f}\_{\mathbf{s}}\mathbf{t}}{\mathbf{p}}\right) \tag{10}$$

Substituting (9) and (10) in (8) implies (11):

$$\mathbf{B}\_{\rm z\\_one\\_dem} = \mathbf{B}\_{\rm z\\_tot} - \frac{\mathbf{B}\_{\rm z\\_tot}}{2\mathbf{p}\,\mathbf{V}\_{\rm dem}} - \sum\_{\mathbf{k}=1}^{\infty} \frac{2\mathbf{B}\_{\rm z\\_tot}}{\mathbf{k}\pi\mathbf{V}\_{\rm dem}} \sin\left(\frac{\mathbf{k}\pi}{2\mathbf{p}}\right) \cos\left(\frac{2\mathbf{k}\pi\mathbf{f}\_{\rm s}\mathbf{t}}{\mathbf{p}}\right) \tag{11}$$

The harmonics that appear in Equation (11) are responsible for the harmonics that will be created in the EMF spectrum in the faulty condition. Equation (11) is suitable to interpret every percentage of partial demagnetization, because, as can been seen below, when the fault severity changes the kind of the fault related harmonics does not change but their amplitude changes. In Equation (11), it will be modification in Vdem when the severity of the fault changes.

Figures 9 and 10 depict the EMF waveforms and the corresponding spectra when one magne<sup>t</sup> is 50% and 80% partially demagnetized. The increment of the fault severity reduces the amplitude of the EMF waveform. In addition, the fault creates new harmonics in the corresponding spectra, which Table 1 summarizes. The new harmonics are of frequencies 25 Hz, 75 Hz, 100 Hz, 125 Hz, 175 Hz, 200 Hz, and 225 Hz and their amplitudes increase when the severity of demagnetization increases. The fundamental harmonic decreases in amplitude when the level of demagnetization increases. The fault related harmonics are both even and fractional and of the same frequencies, like the case wjere one magne<sup>t</sup> is totally demagnetized [30].

**Figure 9.** The EMF waveform when one magne<sup>t</sup> is partially demagnetized (blue line—50% partial demagnetization, red line—80% partial demagnetization).

**Figure 10.** The EMF spectrum when one magne<sup>t</sup> is partially demagnetized (blue line—50% partial demagnetization, red line-80% partial demagnetization).


**Table 1.** Fundamental Harmonic and Fault Related Harmonics in the Spectrum of the EMF When One Magnet is Partially Demagnetized.

### **7. Static Eccentricity Fault**

### *7.1. Static Angular Eccentricity Fault*

In this section, the static angular eccentricity fault will be studied. As it is already proven in [18], the static angular eccentricity fault does not create new harmonics in the EMF and the stator current spectra. This can be justified by the fact that during this fault the airgap in a double-sided machine increases from the one side and decreases from the other size resulting in a constant total airgap. For that reason, the EMF waveform, the stator current waveform, and the corresponding spectra remain approximately unaffected by the fault. However, the spectrum of the phase EMF sum presents variation when static angular eccentricity exists in the generator. Figure 11 depicts the phase EMF sum spectra for two different severities of static angular eccentricity (30% and 40%). Equation (12) describes the phase EMF sum waveform. This signal has a fundamental frequency of 150 Hz (3fs), three times the fundamental frequency of the EMF waveform of each generator phase (fs). In both cases, the harmonic component of frequency 50Hz is the fault related harmonic that, in the faulty case, its amplitude

increases more than the other amplitudes when compared to the corresponding healthy spectrum for spectra normalized to the 3fs frequency (150 Hz). When the level of eccentricity increases, the amplitude of this harmonic component also increases, as can be seen by Table 2. In other words, we can tell that the component of frequency fs Hz is the most dominant fault related harmonic component in the EMF sum spectrum and it indicates the existence of static angular eccentricity fault. Finally, from Table 2, it can be seen that the absolute value of the 3fs harmonic component (150 Hz) also increases when the eccentricity severity increases.

$$\text{PhaseEMF}\_{sum} = \text{EMF}\_{\text{phaseA}} + \text{EMF}\_{\text{phaseB}} + \text{EMF}\_{\text{phaseC}} \tag{12}$$

**Figure 11.** The phase EMF sum spectra of the double-sided rotor generator when a static angular eccentricity exists in the machine: (**a**) 30% fault severity, (**b**) 40% fault severity. (blue line-healthy case, red line-faulty case).

**Table 2.** The Harmonics of Frequencies 50 Hz and 150 Hz in the Spectrum of the phase EMF sum When Static Angular Eccentricity exists in the Generator.


### *7.2. Static Axis Eccentricity Fault*

In this section, the static axis eccentricity fault will be studied. Like with the previous case, the static axis eccentricity fault does not create new harmonics in the phase EMF and the stator current spectra. In [18], it is referred that, when the severity of eccentricity increases, the amplitude of the third harmonic of the phase EMF spectrum slightly increases, while the amplitudes of the fifth and seventh harmonics slightly decrease. However, in the phase EMF sum, new harmonic components appear as Figure 12 depicts. As it can be observed, the harmonic component of frequency fs Hz is a fault related harmonic, like to the case of static angular eccentricity. Consequently, the increment of the amplitude of the harmonic component of 50 Hz indicates static eccentricity fault but we cannot separate the two faults. Finally, Table 3 summarizes the amplitude in dB and in absolute value of the harmonic components of frequencies 50 Hz and 150 Hz.

**Figure 12.** The phase EMF sum spectra of the double-sided rotor generator when a static axis eccentricity exists in the machine: (**a**) 2mm fault severity, (**b**) 3mm fault severity (blue line—healthy case, red line—faulty case).

**Table 3.** The Harmonics of Frequencies 50 Hz and 150 Hz in the Spectrum of the phase EMF sum When Static Axis Eccentricity exists in the Generator.


### **8. The Combined Fault**

#### *8.1. The Combined Partial Demagnetization and Static Angular Eccentricity Fault*

In this paragraph, the combined partial demagnetization and static angular eccentricity fault is studied. In all cases, one magne<sup>t</sup> is partially demagnetized. Figure 13 depicts the EMF spectra when the severity of static angular eccentricity remains constant and the level of demagnetization changes, while Figure 14 shows the EMF spectra when the level of demagnetization remains constant and the severity of static angular eccentricity changes. Although the static angular eccentricity does not create new harmonics in this spectrum [18], when it is combined with demagnetization, new harmonic components appear. The new harmonics due to the combined fault agree with Equation (7) for k <sup>=</sup>−5, −4, −3, −1, 1, 3, 4, 5, 8, 12, 20, 24, 28. The machine odd harmonics (third, fifth, and seventh) appear variation when the combined fault exists. More specifically, the amplitude of the third harmonic decreases when there is combined fault in the machine, while the amplitudes of the fifth and seventh harmonics increase, like the case that only static angular eccentricity exists in the generator [18]. In other words, the variation of the amplitude of these harmonic components is due to static angular eccentricity fault. Tables 4 and 5 summarize the amplitudes of the fault related harmonics derived from Figures 13 and 14 respectively. As it can be seen by Table 4, when the demagnetization level increases and the static angular eccentricity level remains constant, the amplitude of all combined fault related harmonics also increases. However, the absolute value of the fundamental frequency, 50 Hz, slightly decreases. Observing Table 5, we can see that when the severity of the partial demagnetization remains invariable and the level of static angular eccentricity increases the amplitude of all combined fault related harmonics increases too with exception the demagnetization fault related harmonics. In other words, the increment of the eccentricity also creates an increment of the amplitude of the harmonics with frequencies 18.75 Hz, 31.25 Hz, 43.75 Hz, 56.25 Hz, 68.75 Hz, 81.25 Hz. The amplitude of the demagnetization harmonic components (0.5th, 1.5th, 2nd, 2.5th, 3.5th, 4th, and 4.5th) remains approximately constant, as expected when taking

into consideration that the level of demagnetization does not change. In addition, the absolute value of the fundamental frequency presents slightly increment, as Table 5 depicts.

**Figure 13.** The EMF spectra when a combined fault of partial demagnetization and static angular eccentricity exists in the generator and the level of demagnetization changes: (**a**) 20% demagnetization and 30% static angular eccentricity, (**b**) 50% demagnetization and 30% static angular eccentricity, and (**c**) 80% demagnetization and 30% static angular eccentricity.

**Figure 14.** The EMF spectra when a combined fault of partial demagnetization and static angular eccentricity exists in the generator and the level of eccentricity changes: (**a**) 50% demagnetization and 20% static angular eccentricity, (**b**) 50% demagnetization and 30% static angular eccentricity, and (**c**) 50% demagnetization and 40% static angular eccentricity.


**Table 4.** Fundamental and Fault Related Harmonics in the Spectrum of the EMF for the Combined Partial Demagnetization and Static Angular Eccentricity Fault When Changes the Level of Demagnetization.

**Table 5.** Fundamental and Fault Related Harmonics in the Spectrum of the EMF for the Combined Partial Demagnetization and Static Angular Eccentricity Fault When Changes the Level of Eccentricity.


*8.2. The Combined Partial Demagnetization and Static Axis Eccentricity Fault*

This paragraph investigates the combined partial demagnetization with static axis eccentricity fault. Figure 15 presents the EMF spectra for the combined fault when the level of static axis eccentricity remains constant and the severity of demagnetization changes, while Figure 16 depicts the EMF spectra for the combined fault when the level of demagnetization remains constant and the level of static axis eccentricity changes. The corresponding amplitudes of the combined fault related harmonics are depicted in Tables 6 and 7, respectively. The combined fault creates new harmonic components in the EMF spectra, in contrast to the case that only static axis eccentricity exists in the generator and in the EMF spectrum do not appear new harmonic components that are related to the fault, as [18] proves. The combined fault related harmonics are of frequencies 18.75 Hz, 25 Hz, 31.25 Hz, 43.75 Hz, 56.25 Hz, 68.75 Hz, 75 Hz, 81.25 Hz, 100 Hz, 125 Hz, 175 Hz, 200Hz, and 225 Hz. These harmonics agree with Equation (7) for k = −5, −4, −3, −1, 1, 3, 4, 5, 8, 12, 20, 24, and 28, like in the previous section, Section 8.1. In other words, in two combined faults appear the same fault related harmonics. The machine odd harmonics (third, fifth, and seventh) remain approximately constant when the combined fault exists when compared to the healthy case, like to the case that only static axis eccentricity exists in the generator [18]. Observing Table 6, it can be seen that, when the severity of demagnetization increases while the level of static axis eccentricity remains constant, the amplitude of the combined fault related harmonics also increases, like the case where a combined partial demagnetization and static angular eccentricity fault exists in the generator. Although the absolute value of the fundamental frequency presents a small decrement, as Table 6 depicts. Table 7 shows that, when the level of demagnetization remains invariable and the severity of static axis eccentricity increases, the amplitude of all combined fault related harmonics slightly increases apart from the harmonic components with frequencies 25 Hz, 75 Hz, 100 Hz, 125 Hz, 175 Hz, 200 Hz, and 225 Hz. These components are related with demagnetization and for that reason do not change amplitude when the demagnetization level is constant, like Section 8.1. Finally the absolute value of the fundamental frequency slightly decreases when changes the level of the eccentricity and the demagnetization level remains constant. To conclude, it can be observed that when only partial demagnetization exists on the generator, fault related harmonics of frequencies of 25 Hz, 75 Hz, 100 Hz, 125 Hz, 175 Hz, 200 Hz, and 225 Hz appear in the EMF spectrum, when only static eccentricity, either angular or axis, exists do not appear new harmonics in the EMF spectrum, while, in the cases of combined faults, fault related harmonics of frequencies 18.75 Hz, 25 Hz, 31.25 Hz, 43.75 Hz, 56.25 Hz, 68.75 Hz, 75 Hz, 81.25 Hz, 100 Hz, 125 Hz, 175 Hz, 200Hz, and 225 Hz appear. In other words, in the last cases, the demagnetization fault related harmonics and some sideband harmonics appear. The phase EMF sum signal can also be used in the case of combined faults, but the reason that we did not investigate it is because the EMF signal is able to provide the fault related harmonics that are related to combined faults, in contrast to Section 7. The fault identification using the EMF signal and not the phase EMF sum signal makes the detection process simpler and more cost effective, as we should measure one signal every time and not three different signals. However, the study of the phase EMF sum signal in combined faults can be an object of investigation in a future article.

**Figure 15.** The EMF spectra when a combined fault: (**a**) 50% demagnetization and 2 mm static axis eccentricity, (**b**) 80% demagnetization and 2 mm static axis eccentricity exist in the generator.

**Figure 16.** The EMF spectra when a combined fault: (**a**) 50% demagnetization and 2 mm static axis eccentricity, (**b**) 50% demagnetization and 2.5 mm static axis eccentricity, and (**c**) 50% demagnetization and 3 mm static axis eccentricity exist in the generator.


**Table 6.** Fundamental and Fault Related Harmonics in the Spectrum of the EMF for the Combined Partial. Demagnetization and Static Axis Eccentricity Fault When Changes the Level of Demagnetization.

**Table 7.** Fundamental and Fault Related Harmonics in the Spectrum of the EMF for the Combined Partial Demagnetization and Static Axis Eccentricity Fault When Changes the Level of Eccentricity.

