Eccentric Reluctance and Permanent Magnet Synchronous Machines Comparison

This paper deals with a comparative study between reluctance (REL), permanent magnet assisted reluctance (PMAREL), and surface mounted permanent magnet (PM) synchronous machines with rotor eccentricity. Static, dynamic, and combined eccentricity cases are considered. For the sake of generality, this comparison is carried out at different levels of air-gap flux density, as different current angles, different PM materials, and different number of magnetic poles. Additionally, different stator windings arrangements, i.e, distributed and fractional slot concentrated windings are taken into account. Besides, different rotor geometries of REL and PMAREL machines are included. As a case of study, 36-slot machine is analyzed, considering three flux barriers per pole; however, the study can be applied to any machine geometry. Due to the structural criticality of the rotor iron ribs of the REL machines, the impact of the eccentricity on the mechanical stress acting on those ribs and the deformation of the rotor is studied.


I. INTRODUCTION
Manufacturing imprecisions of electrical machines, such as shaft bow, mass unbalance, bearing tolerance, and lamination tolerance are common during the manufacturing process. These imprecisions could result in several types of rotor eccentricity, in which magnetic, dynamic and structural problems can occur in the electrical machine [1]- [3].
In the literature, the impact of eccentricity on the induction machine performance is reported in [2], [4], [5], besides, the eccentric surface mounted permanent magnet (SPM) machines are studied in [6]- [10]. However, the literature is showing that the magnetic performance of the eccentric reluctance (REL) and permanent magnet assisted reluctance (PMAREL) synchronous machines are only marginally investigated in [11]- [13]. Although there are several comparisons between the performance of REL, PMAREL, and SPM synchronous machines, with cylindrical rotor [14], [15], a detailed and wider  comparison among these machines at different eccentricity cases is missing. In [16]- [18], comparisons between eccentric PMAREL and SPM synchronous motor are reported, however, those comparisons had not consider all possible eccentricity cases, lacking of generality. In addition, the REL motor has not been included in those comparisons. The mechanical/structural analysis of the eccentric REL and PMAREL synchronous machines is not reported in the literature. These analyses are necessary to study the impact of different eccentricity scenarios on mechanical stresses acting on the rotor iron ribs, i.e., the rotor iron parts bordered by the flux-barriers, as shown in Fig. 1. Hence, the design safety factor of the iron ribs thicknesses can be checked if it covers the eccentricity impact or not [19]- [21].
To fill these gaps, this paper deals with the comparison between the three machines, in different eccentricity cases, aiming to draw useful design consideration and highlighting what are the eccentricity effects. For a fair comparison, the main geometry, number of poles, stator winding arrangement, and operating conditions are set to be the same for the three machines. For the sake of a generality, the comparison are repeated for other machines with different number of poles, stator windings (distributed and concentrated windings), and different types of PMs (Ferrite and NdFeB), particularly for PMAREL and SPM motors, as well as with different rotor geometries, in particular, REL and PMAREL synchronous machines. Besides, the comparison is carried out for wide range of the operating current angles.
Finally, structural analysis of cylindrical and eccentric REL machine is conducted. The stress acting on the iron ribs due to both centrifugal and radial magnetic force are computed separately. This helps to understand the eccentricity impact on both forces components. Furthermore, the rotor deformation is studied for both cylindrical and eccentric rotors structures.
In static eccentricity case, the rotor axis is shifted from the stator axis and it rotates around its own center, as shown in Fig. 2 (a). In dynamic eccentricity case, the rotor axis is shifted from the stator axis and it rotates around the stator center, as shown in Fig. 2 (b). Whereas, in the combined eccentricity case, the rotor rotates around another different point. In this paper, as in Fig. 2 (c), it is considered in the middle of the stator and rotor axes.   The paper is organized as follows: • due to the common specific geometric features between the REL, and PMREL machines, as the existing of the flux-barriers, different rotor geometries (symmetric and asymmetric rotors), they will be compared together at the beginning without considering the SPM machine. Skipping the SPM in this comparison helps to apply a general comparison among the REL, and PMREL machines considering different flux-barriers dimensions, different rotor geometries, and different PMs (Ferrite and NdFeB) excitations inside the flux-barriers of the PMAREL, at different eccentricity cases. These comparisons are presented in section. III. • The SPM machine is compared with the REL, Ferrite PMREL, and NdFeB PMAREL machines in terms of different stator windings arrangements and different number of poles. These comparisons are reported in section. IV. • Finally, structural and deformation analyses are applied on the REL and PMAREL machines in eccentricity case, as discussed in section. V. The impact of the eccentricity on the stresses acting on the critical mechanical parts of the REL machine is studied.

II. THEORETICAL ANALYSES LITERATURE REVIEW
A wide investigation of the theoretical models of both REL and PMAREL machines is presented in [11], [12], [23], and [13]. Those models are general and valid for different stator winding arrangements, number of poles, and number of slots. Besides, they can be applied for a rotor with general number of the flux-barriers, not only three barriers, as shown in [11], [12] and [23]. It has been proven that the analysis presented in [11] and [23] works for any end angles of the rotor flux-barriers. As it can be noted in [13], the machine non-linearity, as the stator slotting effect and the magnetic saturation of the motor iron are considered analytically. Then, the FE and the experimental validation of the theoretical analyses is reported in [13]. In addition, this non-linear analytical model is extended to the eccentricity case and again it is validated by the FE analyses and the experimental measurements.
Analogously, the SPM machine theoretical analyses are carried out in the literature, as reported in [10], [8], [23], and [24], considering both cylindrical and eccentricity cases. Additionally, the 3D FE and experimental validation of these analytical models is reported in [24] and [10], respectively.

III. COMPARISON BETWEEN REL AND PMAREL MOTORS
The radial force acting on the whole rotor and the rotor islands of both REL, Ferrite and NdFeB PMAREL motors have been computed. Fig. 3 shows the computations of the radial magnetic force acting on each rotor island by integrating the Maxwell stress tensor over an arc in the middle of the airgap in front of each rotor island. The computation of these magnetic forces have been applied at the rotor position when the radial force is maximum. The geometrical data of both REL or PMAREL, shown in Fig. 1, are reported in Table I.
Two different rotor geometries of REL and PMAREL motors are considered. They are: (a) symmetric rotor (SR) and (b) asymmetric (Machaon) rotor (ASR). Both REL and PMAREL motors are characterized by three flux barriers per pole. In case of SR geometry, the flux-barriers have the same dimensions for all poles. Two symmetric rotors are considered to highlight the flux barrier dimensions in this study. They     Table I. The third rotor geometry is an ASR with flux barrier dimensions of the first and third poles as those of SR−A, besides, the flux-barriers of the second and the fourth poles are as those of SR−B. This asymmetry is adopted to minimize one or more torque ripple harmonics, as can be noted from Fig. 4.

A. Comparison in healthy case (no eccentricity)
The REL, Ferrite PMAREL, and NdFeB PMAREL motors with cylindrical rotors (no eccentricity) are compared together in terms of the radial forces acting on the overall rotor and the rotor islands. The three different rotor geometries are considered in this comparison, which are SR−A, SR−B, and ASR. From Table II, it can be noted that, the radial forces are distributed evenly over the poles, offsetting to each other for both SR−A and SR−B. Besides, in case of ASR, the forces acting on the rotor islands of the second and fourth pole are different than those acting on the rotor islands of the first and third pole, due to the diversity of flux barriers. Since the forces are two by two equal and in opposite direction, the resultant forces acting on the overall rotors of the three machines are always very low. Therefore, it can be concluded that the magnetic radial force acting on the overall rotors of the three machines can be approximated to be zero for three rotor geometries.
As can be noted from Table II, there are no significant difference between the radial forces acting on the rotor islands of both REL and Ferrite PMAREL machines. This because the Ferrite PM is a low energy PM and is used only for saturating the rotor ribs to improve the power factor and is not used to increase the machine magnetic loading. Thus, it has no significant impact on the air-gap flux density in front to the rotor islands, and hence it has no significant impact on the radial magnetic forces acting on those islands. This conclusion has been achieved for the SR−A, SR−B, and the ASR.
Furthermore, comparing the radial forces acting on the rotor islands of both REL and NdFeB PMAREL machines, it can be noted that the magnetic force acting on first rotor island of SR − A, SR−B, and ASR is increased by 180 %, 210 %, and 240 %, respectively. Referring to the second rotor island, the force is increased by 12 %, 3 %, and 43 %, respectively. Besides, the force acting on the third island is increased by 6 %, -0.5 %, and 13 %, respectively. From the previous numbers, it can be concluded that the most affected rotor island by inserting the NdFeB is the first/outer island, because the air-gap flux density in front of this island is increased significantly with respect to the other two island, due to the high percentage of NdFeB PM affecting the first barrier than the other two barriers.

B. Comparison in static eccentricity case
This section deals with the static eccentricity shown in Fig. 2 (a). Both REL and PMAREL machines have the same eccentricity distance, electric loading, and current angle. The latter is equal to 60 • for both motors, where the maximum torque per ampere (MTPA) occurs.
The radial force acting on the whole rotor of REL and PMAREL (Ferrite and NdFeB) machines is shown in Fig. 5, Fig. 6, and Fig. 7, respectively. As expected, there is high force in x-axis direction where there is minimum air-gap length. From these figures, it can be noted that the radial force acting on the SR − B is slightly lower than that acting on SR − A highlighting the effect of the flux-barrier dimensions on the radial force. It is also worth noticing the small difference between the SR − B and the ASR.  In addition, the inserted Ferrite and NdFeB PMs have no significant impact on the overall radial force acting on rotor and the bearings. Besides, the PM type has negligible effect   on this overall radial force. Thanks to the symmetric effect of the added PMs on all rotor poles, whereas the PMs increases the flux density not only in front of the two poles close to the minimum air-gap length, but also in front of the other two poles.  island. On the other side, the magnetic force acting on the corresponding island of SR − A is increased by 14%, when NdFeB PMs are inset in the flux-barriers. Besides, there is no significant difference (only 4%) is noted in case of SR − B and ASR. The third rotor island is refereed because it is the most affected island by the static eccentricity force as shown in Table III), due to the wide integration range of the air-gap region in front to it during the magnetic pressure computation, and hence the force computation.

C. Comparison in dynamic eccentricity case
Referring to the dynamic rotor eccentricity described in Fig. 2 (b), the radial force acting on the overall rotor of REL and PMAREL (Ferrite and NdFeB) machines are shown in Fig. 8. The different rotor geometries are considered for both machines at the same eccentricity, current angle, and the same electric loading.
Once again, the radial force acting on the SR − B is lower than that acting on the SR − A and close to that acting on the ASR. Furthermore, the introduction of the Ferrite PMs within the flux-barriers yields a slight reduction of the radial force acting on overall the rotor. In case of introduction of NdFeB PMs, the radial force on overall the rotor is comparable with that in case of REL motor, as well.
The maximum radial forces acting on the different rotor islands of REL, Ferrite PMAREL, and NdFeB PMAREL motor are reported in Table IV. Similar to the previous subsection, referring to the rotor island 3 (from the underlined red values in Table IV), the same conclusion of the comparison in static eccentricity case is found in the dynamic eccentricity case.

D. Comparison in combined eccentricity case
The combined eccentricity occurs when the machine is subjected simultaneously to the static and dynamic eccentricity. The distance between the rotor and stator axes is constant in static and dynamic eccentricity cases. On the contrary, in combined eccentricity case, the relative position of the rotor axis is varied by varying the position of the rotor. This study assumes that the stator is shifted horizontally to the left hand side by 0.15 mm and the rotor axis is shifted horizontally to the right hand side by 0.15 mm at θ m = 0 • . Therefore, the maximum distance between the stator and rotor axis is e 0 = 0.3 mm at θ m = 0 • . By increasing θ m with the rotor rotation, this distance is reduced till to reach zero value at where θ m varies from 180 • to 360 • . Then, the maximum and minimum air-gap length are given by: From Fig. 9, it is noted that there is no significant change in the overall force acting on the rotor results from adding the Ferrite and NdFeB PMs within the flux-barriers.
Since, the rotor is horizontally shifted to the right hand side, the most stressed rotor islands are of poles 1 and 4, which agree with the results reported in Table V. From Table V, comparing REL and NdFeB PMAREL motors together, it can be concluded that, adopting NdFeB PMs within the fluxbarriers of SR − A, the radial forces acting on the rotor islands 1, 2 and 3 are increased by 245%, 25%, and 15%, respectively. Whereas the Ferrite PMs have no significant effect of the forces acting on the corresponding rotor islands. Analogously, for SR − B, the forces are increased by 430%, 38%, and 7% for the rotor islands, respectively. Moreover, in case of ASR, the forces are increased by 440%, 30%, and 8%, respectively. Again, the Ferrite PMs impact on the SR − B and ASR is negligible.
From Tables V and II    of the mixed eccentricity on the radial forces acting on the rotor islands can be studied. Referring to the third island of SR − A, SR − B, and ASR, the magnetic force is increased by 48%, 43%, and 45%, respectively. The REL motor results are compared in the tables, as an example.

IV. COMPARISON OF SPM, PMAREL AND REL MOTOR
Similarly, the radial force acting on the overall rotor of the SPM machines for all rotor position (from 0 to 360 • ) is computed in this section, as well as the maximum radial forces acting on the PMs. Fig. 10 shows a cross section of the SPM motor considered in this study. As mentioned before, for the purpose of fair comparison between the three motors, the analyzed SPM motor has the same main geometrical dimensions of the other two motors, as reported in Table I. Besides, the same distributed windings are fixed for the stator (36 slots 4 pole windings) for having the same stator MMF harmonic contents, as in case of REL and PMAREL motors.

A. Comparison in healthy case (no eccentricity)
Referring to SPM motor with cylindrical rotor, the radial force acting on each pole is computed. The results are reported in Table VI. It is noted that the force acting on the third pole compensates that acting on the first pole. Similarly, the force on the second pole almost cancels the force acting on the fourth pole. Therefore, the overall force on the rotor is equal to a few Newtons (can be approximated to zero). By comparing this motor with the REL and PMAREL motors, it is noted that, the three motors exhibit the same zero force on the whole rotor in no eccentricity case.

B. Comparison in static eccentricity case
As mentioned before, to reduce the torque ripple of the PMAREL or REL motor, the asymmetric rotor geometry is preferred [22]- [24]. Besides, from Fig. 5, Fig. 6, and Fig. 7, it is noted that there is no significant difference between the radial forces acting on the whole rotor of both REL and PMAREL motors in different eccentricity cases (from 5% to 10 % considering the different rotor geometries). Consequently, SPM motor is compared with PMAREL motor with asymmetric rotor geometry. Table VII shows the maximum radial forces on the rotor of SPM, Ferrite PMAREL, and NdFeB PMAREL motors. It is noted that the radial force on the whole rotor of Ferrite PMAREL and NdFeB PMAREL is equal to 450 % and 510% of that acting on whole rotor of SPM motor, respectively. This difference results from the specific geometrical features of studied motors topologies, as: (a) the magnetic air-gap length of the SPM motor is higher than that of the REL and PMAREL motors due to the sleeve or PMs cover thickness added to the mechanical air-gap length, as highlighted in Table I, (b) the sensitivity of both REL and PMAREL machines to the air-gap length, and hence, the eccentricity, with respect to the SPM machines because their dependency on the reluctance torque component. Considering the maximum radial force on the rotor, whereas the rotor position is at (θ m = 121 • ), the radial force acting on each pole is computed and reported in Table VIII. The fourth and the third poles are the most affected because they are close to the minimum air-gap length. However, the worst radial force is that acting on the fourth pole. By comparing Table VI (of  the healthy case) and Table VIII, it can be observed that the radial force acting on this pole is increased by 12% due to the static eccentricity. As mentioned in the introduction, for the sake of the generality of this comparison, it is carried out at: 1) different operating conditions, 2) different stator winding configurations, 3) different number of poles, and 4) different rotor geometries, as considered in the previous section.
1) Different operating conditions: Referring to the vector diagram shown in Fig. 11, it can be noted that the current angle (α e i = tan −1 (i q /i d )) has an impact on the air-gap flux density. Therefore, the comparison between the three machines is carried out at different values of current angles, as shown in Fig. 12. It can be deduced, the unbalanced forces in case of PMAREL and REL motor are higher than that in case of SPM motor for the possible range of current angle due to the different sensitivity to the air-gap variation and the specific geometrical features which affect the magnetic air-gap length of the compared machines. 2) Different stator winding configurations: The previous comparison is carried out considering the distributed windings in the stator. Nevertheless, this comparison is repeated when fractional slot concentrated windings (FSCW) is adopted to identify which winding configuration is the worst in case of eccentricity. Due to the high unbalanced radial force for single layer FSCW at healthy case, as concluded in [12], the comparison is carried out only for double layer FSCW. As an example, 6-slot four-pole three motors are used for this comparison, as shown in Fig. 13. Hence, the radial force acting on SPM and PMAREL motor is equal to 116 N and 223 N, respectively, as can be noted from Fig. 14. The same conclusion has been achieved as the distributed winding case.
3) Different number of poles: To ensure the generality of this comparison, the analysis is repeated for two different motors with six-pole. As an example, 36-slot 6-pole motors are analyzed, as shown in Fig. 15. The radial force on both SPM and PMAREL motor is 180 N and 1220 N, respectively, as shown in Fig. 16 (a) and Fig. 16 (b). Once again, the radial force acting on the rotor of PMAREL motor is higher.

C. Comparison in dynamic eccentricity case
Similarly, the radial force acting on the rotor of the PMAREL motor is about 430% and 480% of that acting on the rotor of the SPM motor, in case of using Ferrite and NdFeB   PMs, respectively. The maximum force acting on the rotor of the SPM motor is at θ m = 240 • . Table IX shows the radial force acting on each pole. The most affected PM is that of the first pole. From Table VI and Table IX, the force acting on that pole is increased by 10% due to the dynamic eccentricity. Once again, this comparison is carried out at the following conditions: 1) different current angles, 2) different stator  winding arrangement, and 3) different number of poles. As expected, the PMAREL motor is the worst for all current angles range, as in static eccentricity case. Considering the FSCW, the radial force on SPM and PMAREL motor is 113 N and 282 N, respectively. Comparing six pole motors, the radial force on SPM and PMAREL motor is 179 N and 1288 N, respectively. As a consequence, the PMAREL motor is the worst motor in case of dynamic eccentricity, as well.
Furthermore, Fig. 17 shows the impact of the static and dynamic eccentricity on the electromagnetic torque of both motors. It is noted that, there are negligible effect of eccentricity on the torque. The impact of eccentricity on the flux linkage in d and q axes is shown in Fig. 17 for both motors. It is noted that, There are slight reduction in d-axis in case of the PMAREL motor. There are negligible effect on the d and q axes flux linkage of the SPM motor. This conclusion is useful from the control point of view because it gives an indication of how much the d and q axes inductances lookup table of those machines is affected by the eccentricity.

D. Comparison in combined eccentricity case
The combined eccentricity is applied to the SPM motor with the same axis of rotation used for both other motors, as shown in Fig. 2 (c). The radial force acting on the rotor of the PMAREL motor is about 430% (using Ferrite PM) and 480% (using NdFeB PM) of that acting on the rotor of the SPM motor, respectively. The radial forces acting on each pole is computed, as reported in Table X. The most affected pole is the first pole, as occurs in the dynamic eccentricity. Once again, the same comparison is repeated in case of adopting FSCW, wide range of current angles, and different number of pole. It can be deduced that, the PMAREL motor is the worst in case of combined eccentricity, as well.

V. STRUCTURAL ANALYSIS
To evaluate the mechanical integrity of the rotor structure in healthy condition and under eccentricity, the mechanical stress and deformation in the rotor are predicted. Using electromag-netic FE analysis, the surface magnetic force density on the rotor are extracted and imported to mechanical FE analysis to compute the mechanical stress and deformation generated by these forces. In addition to the stress generated by the magnetic forces, the rotor is subjected to mechanical stresses generated due to the rotation, i.e. centrifugal forces. The rotor structural analysis are conducted when the rotor is under rotational forces only, magnetic forces only and both rotational and magnetic forces. The mechanical properties are listed in Table XI. The structural analysis has been conducted using ANSYS mechanical APDL solver. The boundary condition of the model is a fixed support at the inner rotor surface to simulate the contact with the shaft, whereas the load conditions are surface force density applied at the outer surface of the rotor, the forces are exported from ANSYS electronic workbench (Maxwell) electromagnetic FEA model, and applied rotational velocity of 5000 rpm. Quad mesh is used with different intensities being very fine in and around the inner and outer ribs, the total mesh elements are 232716 and total mesh nodes are 654646.  The mechanical stress (von-Mises) generated due to magnetic forces are shown in case A and B of Fig. 19 (a) for healthy and eccentricity cases, respectively. Besides, the radial forces results from the rotational speed (5000 rpm) are shown in case C and D of Fig. 19, for both cases, respectively. Consequently, the combination of both magnetic and rotational forces acting on the cylindrical and eccentric REL machines are shown in Case E and F of Fig. 19 (a), respectively. It is deduced that, eccentric rotor has higher mechanical stresses in the half near the eccentricity due to the higher magnetic forces. The maximum stress in the iron ribs is increased by 60%.
In addition, the deformation generated due to magnetic forces for both healthy and eccentricity cases is presented in case A and B of Fig. 19 (b), respectively. In addition, the deformation results from the rotational speed force is presented in case C and D of Fig. 19 (b), for both healthy and eccentricity cases, respectively. Furthermore, case E and F of Fig. 19 (b) presents the deformation results from the combination of both magnetic and rotational forces acting on the cylindrical and eccentric REL machines rotors, respectively.
Since the maximum stress in the combined case of magnetic force and rotation in healthy and under eccentricity is significantly lower than the yield stress of the material, the deformations in the rotor due to these stress are elastic and therefore they are reversible once the stress are removed, i.e. the rotor operates safely at maximum speed and under extreme eccentricity. This is since the machine is well designed with high mechanical safety factor (from 2 to 3) taking in consideration the magnetic forces and the rotational stresses.
The mechanical stresses are calculated at the point of maximum net force, in both healthy and eccentric conditions. Nevertheless, the maximum mechanical stress might not occur at this point since the surface force density and consequently the mechanical stress are related to the magnetic flux paths and their alignment with the stator teeth. Similarly, the maximum stress when eccentricity occurs highly depends on the rotor angle where the eccentricity occurs. Additionally, rotor with small diameter and low speed will exhibit lower rotational stress and therefore the magnetic forces in healthy and eccentricity cases become the dominant and therefore need to be considered carefully in the designing stage.
Finally, a test bench has been designed in order to validate the prediction of the unbalanced magnetic forces [26], as shown in Fig. 20. The measured magnetic forces are compared with those of the FE analyses. Fig. 21 shows the comparison between the results of both analytical and FE models and the experimental test at different eccentricity values. As an example, eccentricity equal to 0.2 mm and 0.26 mm are considered. It is noted that there are a good agreement between the carried analyses and the experimental test.

VI. CONCLUSIONS
This paper analyzes the impact of static, dynamic, and combined eccentricity on the radial force acting on the rotor of the REL, PMAREL, and SPM machines. Referring to the REL and PMAREL machines, the radial forces acting on  rotor islands are computed. Different rotor geometries are considered. The impact of the dimension of the flux-barriers on the radial forces is highlighted. It is noted that the radial force acting on the asymmetric rotor is comparable to that acting on the symmetric rotor. There are no significant difference between the radial forces acting on both REL and PMAREL motors in different eccentricity cases, only (5 to 10% higher in case of NdFeB PMAREL motor, which means the forces are still comparable).
The Ferrite PMAREL and NdFeB PAMREL are compared with SPM machines, as shown in Table VII, in static eccentricity case. It is noted that, the radial force acting on PMAREL with Ferrite PMs machines is about 450%, 430%, and 430% with respect to SPM machine, in case of static, dynamic, and combined eccentricity cases, respectively. Besides, the radial force acting on NdFeB PMAREL machines is about 510%, 480%, and 480% with respect to SPM machine, in case of static, dynamic, and combined eccentricity cases, respectively. Therefore, the impact of the eccentricity on SPM machines is lower than that on REL, Ferrite, and NdFEB PMAREL machines, even if there are high radial forces acting on the rotor poles. This difference results from the specific geometrical features of both machines topologies, as: (a) the magnetic air-gap length of the SPM motor is higher than that of the REL and PMAREL motors due to the PMs sleeve and (b) based on the reluctance torque dependency of both REL and PMAREL machines, they are sensitive to the airgap length variation results from the eccentricity, with respect to the SPM machines.
Again, the comparison between PMAREL or REL with SPM motor is carried out at different current angles, stator windings arrangements, and different number of poles. It can be deduced that PMAREL or REL motor exhibit the highest forces for all previous conditions in different eccentricity scenarios.
Structural and deformation analyses of cylindrical and eccentric REL machine are applied. The mechanical stress due to the magnetic forces increases by 60% due to the eccentricity (0.3 mm). Although, the large rotor diameter and high rotational speed makes the stress generated by the centrifugal forces the dominant, however, the eccentricity still contributes a significant amount of mechanical stress and therefore needs to be considered in the designing stage.
Finally, this study helps the designers to define the tolerance of the selected laminations of those machines. Furthermore, the robust design of the rotor bearings against the vibration and noise for the three motors can be applied. Besides, the thickness of the rotor iron ribs of PMAREL and REL motor can be designed avoiding the over sizing of the safety factor. In 1998, he joined the Department of Electrical Engineering, University of Padova, as an Assistant Professor. Since 2005, he has been an Associate Professor of electrical machines, converters, and drives. His activity is conducted in the Electric Drive Laboratory, Department of Electrical Engineering, University of Padova.
His teaching activity deals with the design methods of electrical machines, where he introduced the finite-element analysis of machines. He is the author or coauthor of several scientific papers and international books on electrical machines and drives. He is recipient of five awards for best conference and journal papers His research activity is in the field of design of electrical machines, particularly for drive applications, in which he is responsible for various projects for local and foreign industries.
He is an IEEE Fellow member and a member of the Electric Machines Committee and the Electrical Drives Committee of the IEEE Industry Applications Society. He served as technical program chair for IEEE ECCE 2014 and is Associate Editor of IEEE Trans on IA and IET-EPA proceedings.