Zahra Shabahang, Mostafa Shahnazari, Alireza Sedighi* *Department of Electrical and Computer Engineering, Yazd University Yazd, Iran

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1 No. E-5-ELM-8 Analysis of Dynamic Eccentricity in a Coreless Axial Flux Permanent Magnet machine Zahra Shabahang*, Mostafa Shahnazari*, Alireza Sedighi* *Department of Electrical and Computer Engineering, Yazd University Yazd, Iran Abstract This paper studies about the effects of dynamic eccentricity fault on double rotor-one stator axial flux threephase coreless permanent-magnet machine using threedimensional finite-element analysis. To the best awareness of the authors, effects of dynamic eccentricity in this type of machine have not been studied before. Hence, the definition of dynamic eccentricity fault (F) and air gap length in F in axial flux machine is presented. Then, definition of voltage variations with F is presented. A machine with different degrees of dynamic eccentricity is simulated and the flux distribution in the air gap and coil voltages is obtained. In addition, spectrum of induced voltages is investigated and indicates that dynamic eccentricity has noticeable effects on machine parameters that can be used in fault detection. Keywords Dynamic eccentricity, Fault, Axial flux permanent magnet machine, Three-dimensional finite element method I. INTRODUCTION The history of electrical machines reveals that the earliest machines were axial flux machines (AFM). The AFMs, also called the disc-type machine, is an attractive alternative to the cylindrical RFMs due to their "pancake" shape, compact construction and high power density, which made them suitable for electrical vehicles, pumps, fans, valve control, centrifuges, machine tools, flywheel, robots and industrial equipment and They can be directly coupled to low-speed turbines such as wind and hydro turbines [-]. Stator of Axial flux machines have different types, such as slotless stator type, that may have ferromagnetic cores or be completely coreless. Coreless stator configurations eliminate any ferromagnetic material from the stator (armature) system, thus making the associated eddy current and hysteresis core losses nonexisting. AFPM machines with coreless stators are regarded as highefficiency machines for distributed power generation systems []. It is interesting that slotless AFM machines are often classified according to their winding arrangements and coil shapes, namely, toroidal, trapezoidal and rhomboidal forms. In axial flux permanent magnet machines (AFPMM), In order to maintain a reasonable level of flux density in the air gap, a much larger volume of PMs in comparison with laminated stator core AFPM machine is required []. Manufacturing dissymmetry have important effects on the operation of electrical machines, particularly in AFMs, where the pancake geometry implies that even a little positioning error of rotor (or stator) disks causes high errors in the air gap width [5]. As a consequence, during the rotation, an air gap modulation arises, and additional strengths and unbalance in the electrical quantities are expected [6]. A classical design approach for analyze electrical machines is based on the sizing equations, whereas a more refined review of the design choices is demanded to the check evaluations. Of course, this procedure may prevent an effective device optimization. Differently, the modern design algorithms tend to implement more accurate models during the same sizing stage, frequently using FEM codes, in order to obtain a more reliable achievement of the design objective functions. Finite element method (FEM) is widely applied because of its high reliability in general [7-8]. In this paper, We're going to investigate dynamic eccentricity fault (F) effects in a double rotor-one stator AFPPM with coreless stator structure. the AFPMM, that presented in [], is modeled and develop different fault degree condition. The model is validated by comparing D FEM results with reference. Next, define the air gap length, voltages and their variation by F. then to find the F effects and detect methods for fault diagnosis, coil voltages and their harmonic spectrum is investigated. The paper is structured as follows. Section II illustrates dynamic eccentricity in AFPMMs, section III illustrates machine specification, section IV shows how the machine is simulated and validation of primary results. Section V illustrates fault effects on machine parameters, and section VI investigates FEM results. II. DYNAMIC ECCENTRICITY IN AFPMMS Mechanical faults are common in electric machines and represent up to 6% of the faults. Eccentricity fault as a mechanical fault is categorized to static eccentricity (SE), dynamic eccentricity (), and mixed eccentricity (ME) [9]. A cause of dynamic eccentricity can be a bent shaft, bearing wear and movement, or mechanical resonances at critical speeds []. In axial flux machines the ratio of diameter to length (D/L) is more than, hence a small deviation in rotor axis considering the high diameter, causes high variations in air gap length. In the dynamic eccentricity, the rotor axis is not unify with shaft and have a small deviation angle. In this type of fault the rotor shaft and stator axis are unify and the rotor

th Power System Conference - 5 Tehran, Iran axis is deviate with β (Fig. ). In such case, the air gap is not uniform throughout rotor circumference and is timedependent.

. Prototype designed and made in []. TABLE II. SPECIFICATIONS OF THE AFPMM Fig.. Shematic representation of dynamic airgap eccentricity in AFPMM [].

Hence deviation angle shown in table I. this table is related to the investigated generator that will be presented in the next section. F (%) TABLE I....6.8 VIATION ANGLE FOR SELECTED MOTOR r.

It's consist of a 8 coil stator that has no iron core as shown in fig.. The surface winding of the stator is perpendicular to the machine shaft.

2 th Power System Conference - 5 Tehran, Iran axis is deviate with β (Fig. ). In such case, the air gap is not uniform throughout rotor circumference and is timedependent. In other words, in the case of dynamic eccentricity the position of minimum air gap length is rotate in rotor circumference with time periodicity equal to the mechanical time period of rotor. Fig.. Prototype designed and made in []. TABLE II. SPECIFICATIONS OF THE AFPMM Fig.. Shematic representation of dynamic airgap eccentricity in AFPMM []. It assumed that eccentricity happens by deviation of rotor around X axis at point O. The dynamic eccentricity factor (F) in electrical machines is defined as static eccentricity described in []. Hence deviation angle shown in table I. this table is related to the investigated generator that will be presented in the next section. F (%) TABLE I VIATION ANGLE FOR SELECTED MOTOR r.... parameters III. MACHINE SPECIFICATIONS Fig. shows the study case generator, three-phase, V, 9W, rpm, coreless, low cost AFPMM that was designed in []. It's consist of a 8 coil stator that has no iron core as shown in fig.. The surface winding of the stator is perpendicular to the machine shaft. In this case, the single layer trapezoidal three-phase winding is used. The rotor disc has magnet, that opposite poles of rotors are in front of each other (NS structure []). The machine parameters are given in table II. Dimensions of magnets (mm) 5** Stator Outer radius (mm) 6 Stator Onner radius (mm) 5 Diameter of bare wire (mm). Thickness of rotor disk (mm) Air gap distance of one side (mm) Current density (A/mm).8 Number of turn per coil 5 Thikness of statore (mm) 8 Br (Tesla). Frequency (Hz) IV. FINITE-ELEMENT SIMULATION In order to study fault in each case, the first step is accurate modeling of machine. Analytical methods are very complex when accurate evaluation are needed. AFPMMs are intrinsically D machines []. Therefore, a D finite element model by MAXWELLD is a simple and good model in order to study dynamic eccentricity for selected AFPMM. the Flux is a very important parameter in machines, and the voltage it's results, To validate the simulation, fig. shows the phase voltage and three phase voltages of generator from [] and MAXWELLD results. That clearly shows the accuracy of simulation.

....9.8.7 Air gap (deg).6 5 6 7 8 9....9.8.7 Air gap (9deg).6 5 6 7 8 9....9.8.7 Air gap (8deg).

5 5 voltage of one phase y vs. x untitled fit (a) Vb(volt) Va(volt) - three phase voltages - 5 6 7 8 9 V. AIR GAP AND INDUCED VOLTAGE VARIATION WITH DYNAMIC ECCENTRICITY FAULT A.

3 Air gap (deg) Air gap (9deg) Air gap (8deg) Analysis of Dynamic Eccentricity in a Coreless Axial Flux Permanent Magnet machine th Power System Conference - 5 Tehran, Iran Fig. 5. Simulation of dynamic eccentricity fault in AFPMM. 5 5 voltage of one phase y vs. x untitled fit (a) Vb(volt) Va(volt) - three phase voltages V. AIR GAP AND INDUCED VOLTAGE VARIATION WITH DYNAMIC ECCENTRICITY FAULT A. Air gap variation with F As mentioned in previous section, at F conditions the variation of air gap length is a function of time and angle of rotation φ, that can be expressed as follows: Vc(volt) (b) Fig.. Phase voltages waveforms for one phase and three phases (a) [] results (b) simulation results at 6rpm and ohm load. Where is the air gap length at healthy condition, is the arbitrary position of minimum air gap and is the mechanical period of machine, that is ms for 6rpm. So the variation of air gap length for angle in rotor circumference,, 9 and 8 degree as follows: () Fig. shows mesh diagram of the generator and as it would be, density of meshes increases near the edges and air gap. Fig. 6. Air gap variation at fault condition, in order from left to right for, 9 and 8 degree in rotor circumference Considering that airgap length variation causes changes in airgap flux density, hence variation of coil voltages is the next effect. Fig. 7 shows the variation of this main parameter of generator..5 Fig.. Mesh diagram of simulated generator -.5 To formation the dynamic eccentricity, the stator and motion axis fixed at the global coordinate system and the rotor axis (upper rotor with it's PMs) rotate with β angle around X axis. As shown in Fig. 5, if the rotor is deviated around X axis at point O, at t=, the maximum air gap happens at φ= (φ is the angle of rotation that measured from a reference point at Y axis), and then rotate around rotor circumference with time periodicity equal to: T=6/ω () That ω is rotor speed in rps and p is the pole number. Then T is ms when rotor speed is equal to 6rpm Fig. 7. Air gap flux densiyt at Rmid=7.5mm

4 th Power System Conference - 5 Tehran, Iran As seen in the figure, the airgap flux density at t=., that rotor rotate one sycle and being in initially place, so the maximum airgap occure at φ= and minimum at φ=8, the airgap flux density at φ= is decreas and at φ=8 is increas. B. Induced voltage variation with As expected due to square PMs, the flux created in air gap is not pure sinusoidal and contains third harmonic order, so the induced voiltage in coils has third harmonic order too, therfore the equation of volage in healthy condition for each coil of stator is: As we know the amplitude of coil voltage in F condition variates sinusidal with a period equal to mechanical period of rotor, (ms for 6rpm,so =). So voltage of a coil is variat as follows: () The reason for choosing this three coils is the structure of AFMs. when eccentricity fault occure, three coils in same place without Appropriate mechanical location differences in rotor circumference can't detecting fault. So for fault diagnosis Suitable coils must be selected to clearly Detect the fault. When a % F occur voltage of three coils are changed. The of maximum Voltage of coils oscillated with f=hz. So the push of voltage waveforms is a Hz Sinusoidal waveform as shown if Fig Voltage of coil x Voltage of coil () According to the above relationships, in condition the voltage of a coil may contains four subharmonic with and frequancy, that are equal to 6± and 8± for 6rpm. But this harmonic disappears in phase voltages due to symmetry of coils for each phase. V(vols) Voltage of coil 5- deg VI. FINITE-ELEMENT RESULTS In order to see the effect of F in coil voltages we studied voltages in three coils in different locations as follows: Coil 5 Coil 6 (5) Fig. 9. Voltage waveforms of three coils and their push at F % As mentioned in previos section, we expect increas in subharmonic amplitudes. So as shown in next figures, the 7Hz subharmonic amplitude is increas as a function of F. Coil Fig. 8. Location of three coils in stator

5 th Power System Conference - 5 Tehran, Iran.9 7Hz subharmonic coil Hz subharmonic coil Hz subharmonic coil Fig.. Induced voltages versus F for coils 6, and 5 respectively Table III shows fundamental and 7Hz harmonic order of coil voltages to more clearly shows the subharmonic increas at F conditions. TABLE III. AMPLITU OF HARMONICS FOR DIFFERENT CONDITIONS condition 6Hz 7Hz subharmonic Coil 6 Coil Coil 5 Coil 6 Coil Coil 5 healthy %.%.% F %.%.% F %.%.55% F %.5%.8% F %.8.78%.9.68% VII. CONCLUSION. The effects of dynamic eccentricity on an coreless AFPMM has been investigated with D FEM. The model is validated by compare first result of healthy generator with reference. The result of D FEM has shown that detect of dynamic eccentricity can be done by checking out the 7Hz sub harmonic of coil voltages. It can be a useful approach to estimate the degree of eccentricity by use of the amplitude of 7Hz sub harmonic. REFERENCES [] J.F. Gieras, R.J. Wang, M.J. Kamper, Axial flux permanent magnet brushless machines, Springer Netherlands, Secend Edition, 8. [] S.M. Mirimani, A. Vahedi, F. Marignetti, Effect of inclines static eccentricity fault in single stator-single rotor axial flux permanent magnet machines, IEEE Transaction On Magnetics, Vol. 8, NO., January. [] L.N. Tutelea, S.I. Deaconu, I. Boldea, Design and FEM validation for an axial single stator dual rotor PMSM, IECON, pp ,. [] S.M. Hosseini, M. Agha-Mirsalim, M. Mirzaei, Design, prototyping, and analysis of a low cost axial-flux coreless permanent-magnet generatore,, IEEE Transaction on machines, Vol., NO., January 8. [5] A. Di Gerlando, G.M. Foglia, M.F. Lacchetti, R. Perini, Effects of manufacturing dissymmetry in axial flux machiens, ICEM, pp. 87-9,. [6] A. Di Gerlando, G.M. Foglia, M.Felice Iachetti, R. Perini, Effects of manufacturing imperfections in concentrated coil axial flux pm machiens: evaluation and tests, IEEE Transaction on industrail electronics, Vol. 6, NO. 9, September. [7] A. Di Gerlando, G.M. Foglia, M. Felice Iachetti, R. Perini, Evaluation of manufacturing dissymmetry effects in axial flux permanent-magnet machines: analysis methode based on field functions, IEEE Transaction on magnetics, Vol. 8, NO. 6, June. [8] S.Y. Sung, J.H. Jeong, Y.S. Park, J.Y. Choi, S.M. Jang, Improved analytical modeling of axial flux machine with a double-sided permanent magnet rotor and slotless statore based on an analytical method, IEEE Transaction on magnetics, Vol. 8, NO., November. [9] B.M. Ebrahimi, M.J. Roshtkhari, J. Faiz, S.V. Khatami, Advanced eccentricity fault recognition in permanent magnet synchronous motors using stator current signature analysis, IEEE Transaction on industrial electronics, Vol. 6, NO., April. [] P.S. Bhowmik, S. Pradhan, M. Prakash, Fault diagnostic and monitoring methods of induction motor: a review, IJACEEE, Vol., NO., May. [] Aydin, M., S. Huang, T.A. Lipo, Axial flux permanent magnet disc machines: a review, research report, -, Wisconsin Power Electronics Research Center,. 5

Analysis of Losses in High Speed Slotless PM Synchronous Motor Integrated the Added Leakage Inductance

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