Performance Analysis of Axial-Flux Induction Motor with Skewed Rotor

: In recent years, with developing technology in the ﬁeld of electrical machines, more e ﬃ cient and high power density electric motors have been produced. The use of high energy e ﬃ ciency motors gains importance due to the increase in global energy demand. The main purpose of this study was to design an Axial Flux Induction Motor (AFIM) with the same e ﬃ ciency class as the Radial Flux Induction Motor (RFIM) in premium e ﬃ ciency (IE3) class which is used commonly in industrial applications. Various AFIMs are designed with di ﬀ erent rotor slot numbers and performance analyses as e ﬃ ciency and torque ripple changes are investigated. It is known that torque ripple is one of the key parameters in electrical machine design which should be kept as low as possible without decreasing e ﬃ ciency and torque. Accordingly, AFIMs’ rotor slots are skewed considering the stator and rotor slot numbers. The use of a Soft Magnetic Composites (SMC) material in design is also investigated. As a result of the analyses, many premium e ﬃ ciency classes for AFIMs are obtained. In addition, using SMC material and skewing the rotor slots provides that torque ripples be reduced.


Introduction
Today, more than 40% of the global energy consumption amount is consumed by induction motors and this rate exceeds 70% in the industry [1,2]. Additionally, these motors are key components of many industrial processes, with their reliability, and low cost of maintenance and construction [3,4]. Considering the amount of energy consumed by these motors, it is seen that even a small change in their efficiency will provide significant savings in worldwide energy consumption. The largest energy savings, particularly for medium and small power motors, arise for their higher efficiency classes [5,6]. Accordingly, the use of IE3 class motors has become mandatory due to the laws published in many countries. For instance, IE3 motors have been mandatory since 2011 in the United States and in Turkey, China, and the EU countries in 2015 [7][8][9]. Nowadays, energy consumption and environmental impacts are reduced with high efficiency motors. Additionally, motor reliability increases sustainable use and demand for investment [10]. In many countries around the world, many programs are encouraged to increase the use of high-efficiency motors. Among these programs, the Efficiency Increasing Project and the Efficient Motor Replacement programs are prominent in the world. Replacing existing low-efficiency motors with high-efficiency motors will result in significant energy savings even if same-sized motors are used [11,12]. Otherwise, if AFIMs are preferred over conventional RFIMs, more efficient and smaller volume motors can be designed [13,14].
With the developing technology, electric motors have a more compact structure and many studies are carried out to increase their efficiency. In many studies, instead of radial flux design of induction motors, axial flux design was found to have a more compact structure and it was concluded that their efficiency and torque density could be increased further [14,15]. induction motors, axial flux design was found to have a more compact structure and it was concluded that their efficiency and torque density could be increased further [14,15].
AFIMs have the same operating principle as RFIM. However, design of these motors is quite different. The main difference is the magnetic flux direction. In conventional radial flux machines, the flux is in radial direction relative to the machine axis. The magnetic flux produced in AFIMs is in axial direction with respect to the machine axis.
In recent decades, AFIMs have been a popular research topic for researchers. Many studies have been conducted in the literature on AFIM design and control [16][17][18]. Among these studies, the most notable ones are the design and implementation of different structures. Additionally, many AFIMs have been designed for various applications such as pumps, electric vehicles, wind turbine, etc. [19,20] For instance, in electric vehicles, which are among the popular topics of today, AFIMs have different uses such as wheel-directly coupled, on-wheel, or main motor [21]. In some studies, different materials have been used, such as iron, magneto dielectric, superconductors, etc. [22,23] In this study, AFIMs are designed to have the same efficiency class as RFIM in IE3 efficiency class used in industry. In addition, the rotor is skewed to minimize the torque ripple. In the literature, only stator slot numbers has been taken into consideration to determine the skew angles for the performance analysis of an induction motor [24][25][26][27]. In this study, and different from the literature, skew angles are selected considering both the ratio of stator and rotor slot numbers. Additionally, analyses are carried out using SMC material for stator, rotor, and both stator and rotor of the motor, which provides the best results in terms of efficiency and torque ripple. However, in the analysis results obtained, a considerable decrease in torque ripple over 11% is observed.
Following the introduction, Section 2 presents the topologies of AFMs and design parameters of AFIM. Section 3 introduces model properties, results, and discussion of all various types of AFIM models. Finally, the concluding remarks are presented in Section 4.

Methodology
In this section, considering the geometrical properties of the stator/rotor core, radial and axial flux machine equations are presented after the topologies of AFMs are introduced.

Axial Flux Machine Topologies
A machine with one air gap is the oldest and simplest structure of AFM, has a single-sided motor, and a single stator-single rotor (SSSR). The structure of this machine is easier due to a single air gap [28]. Generally, this machine is the best choice for low torque applications such as fans, pumps, food processors, etc. [29] Also, it can be said that single-sided AFIMs are more resistant to static eccentricity than conventional motors [30,31]. The disadvantage of this type of machine is that bearing life depends on their load. Active material utilization of the SSSR machine is higher [32]. In Figure 1, single-sided AFIM components are shown.   There are two air gaps in this type of machine. Both of these air gaps can be axially (double-sided motor), or one axially and the other radially. Such motors consist of a double stator-single rotor, with the rotor sandwiched between the stators, or single stator-double rotor with the stator sandwiched between the rotors. The advantages of double-sided motors include high torque density and balanced axial forces.
In this context, and in terms of economy, the production of two stators is more costly, especially in small powerful machines compared to the single-sided structure. However, the difference in production cost between single-sided motor and double-sided motor for high torque machines is decreasing. In double-sided motors, the moment of inertia is lower and the rotor is lighter [33].
Although the double-sided motor structure has better performance, for high-powered motors, the multi-air-gap disc structure is a better choice [34]. Multi air gap machines have two topologies that are determined by the number of stators and rotors. If the number of stators is more than the number of rotors, these machines are called external stator and internal rotor machines. If the number of rotors is more than the number of stators, these machines are called internal stator external rotor type machines. Internal stator external rotor type machines are preferred due to their high efficiency [35]. This topology can be defined as a concept rather than a machine type. The aim is to place the stators and rotors alternately to meet the requirements of the application. An advantage of this configuration is that it offers modularity [36].
In this study, single air-gap motor topology-which is also prominent in terms of ease of design and analysis-is chosen. It is an advantage that the volume of this structure is smaller. A conventional radial flux induction motor used industrially in the premium efficiency class is taken as a reference to the designed AFIMs.

Design Parameters of AFIM
The rotating magnetic field can be solved analytically by integrating the basic flux with respect to all radius (r) and pole form factor (α). The rotating magnetic field is within a pole range and electrical angle values are accepted. Axial rotating magnetic field is obtained as in Equation (1).
where φ ax is axial rotating magnetic field in disk-like air gap; B max is maximum induction in the air gap; p is number of poles; r 2 is outer radius of the core of axial induction motor and r 1 is inner radius of the core of axial induction motor. Basically, the output power of electrical machines (P 2 ) is a function of flux per pole as in Equation (2).
Therefore, both types of induction motors can be compared using the flux equations of the rotating magnetic field. In 1986, Varga compared both types of motors using the flux equations of the rotating magnetic field in his study [37]. Thus, the flux equation of AFIM (Equation (1)) has been compared with the similar equation of RFIM (Equation (3)).
where φ rad is radial rotating magnetic field in cylindrical air gap; L r is length of the radial induction motor, r r is rotor radius of the radial induction motor; r o is radius of shaft opening. Flux values for two types of motors are equalized for predictive comparison (φ ax = φ rad ), so Equation (4) where i S is apparent internal power; ax C is axial induction motor constant; 2 D is core outside diameter with no slots; 1 D is core inside diameter; 1 n is synchronous speed.
In Equation (6), ax C is calculated as; where α is deflection, pole form factor; w k is winding factor; and 1 F is distributed MMF; w k and α values are taken 0.9 and 0.7, respectively, as the average values usually used [38].
In Equation (7), a D refers to the average diameter of the core; In Equation (8), L refers to the radial width of the core; While establishing equations for diameter dimensions of AFIM, slots are neglected. The motor air gap is assumed to be constant when the slots are neglected. In these conditions, the outer diameter of the core 2 D can be found as in Equation (9).
Core volume of the entire stator and rotor (V ) is calculated in Equation (10). The shaft opening increases the rotor radius r r by r o . The equations given AFIM have a single air gap and no volumetric assumptions are made. In Equation (5), apparent internal power is solved; r 1 and r 2 are halves of D 1 and D 2 , respectively.
where S i is apparent internal power; C ax is axial induction motor constant; D 2 is core outside diameter with no slots; D 1 is core inside diameter; n 1 is synchronous speed. In Equation (6), C ax is calculated as; where α is deflection, pole form factor; k w is winding factor; and F 1 is distributed MMF; k w and α values are taken 0.9 and 0.7, respectively, as the average values usually used [38]. In Equation (7), D a refers to the average diameter of the core; In Equation (8), L refers to the radial width of the core; While establishing equations for diameter dimensions of AFIM, slots are neglected. The motor air gap is assumed to be constant when the slots are neglected. In these conditions, the outer diameter of the core D 2 can be found as in Equation (9).

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Core volume of the entire stator and rotor (V) is calculated in Equation (10).
where V s is core volume of stator; V r is core volume of rotor; i h i is total height of the machine.
where η is efficiency in percent; P output is output power; P input is inner output [39]. P losses is total losses and presented as in Equation (12); P losses = P core + P cu + P FW + P STR (12) where P core is stator and rotor core losses; P cu is stator and rotor copper losses; P FW is mechanical losses as frictional and windage losses and P STR is stray-load losses. The biggest cause of stray-load losses is harmonic energies when the motor is operating under load. If the load current consists of harmonic components, flux magnitude and waveform were distorted, which results in harmonic torques, vibrations and the noise [40,41]. In the IEEE Standard 112-2017, the assumed values for stray-load losses are shown in Table 1. According to the table, in the study, stray-load losses percent of rated load are taken as 1.8% for designed AFIMs [39]. In this study, transient analyses are carried out and torque values are calculated with the help of ANSYS Maxwell program. Torque ripple (τ ripple ) in percent is defined as the ratio of difference between maximum (τ max ) and minimum torque (τ min ) values to average torque (τ avg ) as in Equation (13).
AFIM results based on different rotor slot numbers are examined in the next section. In this study, the rotor slots are skewed to achieve better efficiency and fewer torque ripple. Skew angles are given for all slot numbers of the non-skew models, and analyses have been made by taking into account the stator and rotor slot numbers. Skew angle analyses adjusted according to stator slot number are given in Equations (14)- (16).
Energies 2020, 13, 4991 where β s is skew angle according to stator slot number in degrees, N s is stator slot number. By using Equations (14)-(16); 10 • , 15 • and 20 • are selected. These values are the same for all design and analyzed for all of them. Skew angle analyses adjusted according to rotor slot number are given in Equations (17) and (18).
where β s is skew angle according to rotor slot number in degrees, N r is rotor slot number. In this context, geometries with three additional skew angles, β s , 1.5 · β s , 2 · β s , β r and 2 · β r are applied in the rotor slots of the 28, 30, 32, 34, 38, 40 and 42 slotted models, and analyses results are presented.

Results and Discussion
In this section, general design parameters of analyzed AFIMs with reference RFIM are presented. In addition, many AFIMs are designed to be in the same energy efficiency class as the RFIM referenced. While making these designs, no changes are made on the stator. When using the same stator, rotor slot numbers and skew angles are changed.

RFIM Model Details
This section provides information about the reference RFIM, which is widely used in the industrial applications. The analysis results of this motor, which is IE3 efficiency class with 93.2% efficiency and 7.49% torque ripple, was made by using the ANSYS Maxwell program. Analyses in which the motor model is suitable for 2D analysis are done in two dimensions. The ANSYS model of the model is shown in Figure 3. In addition, general design parameters of RFIM are shown in Table 2.

AFIM Model Details
In this section, Finite Element Analysis (FEA) is needed to perform electromagnetic analysis of AFIM. Unlike other types of machines, 3D analysis is mandatory because 2D analysis of such machines does not give detailed results. For this reason, analyses are performed in 3D Cartesian coordinate system and these analyses take a considerable amount of time due to high meshing. Also, for detailed analysis, the number of meshes is kept as high as the processor allowed. In this study, ANSYS Maxwell software is preferred to the FEA analysis, since it is suitable for magnetic field analysis of machines and has a wide usage area.
Firstly, an AFIM designed with the same number of stator and rotor slots. AFIM model and the magnetic field density of AFIM is shown in Figure 4. This model is designed with a non-skewed rotor. According to the analysis results, the efficiency of AFIM is 82.83%, while the torque ripple is 7.4%. Thereafter, in the next section, AFIMs are designed with different rotor slot numbers and various

AFIM Model Details
In this section, Finite Element Analysis (FEA) is needed to perform electromagnetic analysis of AFIM. Unlike other types of machines, 3D analysis is mandatory because 2D analysis of such machines does not give detailed results. For this reason, analyses are performed in 3D Cartesian coordinate system and these analyses take a considerable amount of time due to high meshing. Also, for detailed analysis, the number of meshes is kept as high as the processor allowed. In this study, ANSYS Maxwell software is preferred to the FEA analysis, since it is suitable for magnetic field analysis of machines and has a wide usage area.
Firstly, an AFIM designed with the same number of stator and rotor slots. AFIM model and the magnetic field density of AFIM is shown in Figure 4. This model is designed with a non-skewed rotor. According to the analysis results, the efficiency of AFIM is 82.83%, while the torque ripple is 7.4%. Thereafter, in the next section, AFIMs are designed with different rotor slot numbers and various skewed rotors to increase the efficiency to IE3 efficiency class. Table 3 shows the general design parameters of the analyzed AFIMs. Firstly, an AFIM designed with the same number of stator and rotor slots. AFIM model and the magnetic field density of AFIM is shown in Figure 4. This model is designed with a non-skewed rotor. According to the analysis results, the efficiency of AFIM is 82.83%, while the torque ripple is 7.4%. Thereafter, in the next section, AFIMs are designed with different rotor slot numbers and various skewed rotors to increase the efficiency to IE3 efficiency class. Table 3 shows the general design parameters of the analyzed AFIMs.

AFIM Analyze Results with Different Rotor Slot Numbers
In this section, analyses are made according to seven different slot numbers for the rotor slots without skewing, 28, 30, 32, 34, 38, 40 and 42 slots, respectively. While determining these numbers, rotor slot widths are taken into account according to the machine size. Therefore, the maximum slot number is specified as 42 and the minimum as 28 for the number of rotor slots. Since the stator slot number is 36, 36-slot rotor design is not feasible, and because the stator slot and rotor slot areas are overlapped, the magnetic flux production is not possible.
It is known that torque ripple is one of the most challenging parameters in electrical machine designs. While making designs, decreasing this value is an aim. Therefore, torque ripples are taken into consideration while making comparisons. Figure 5 shows the efficiency and torque ripples of the analysis results according to 7 different slot numbers from 28 to 42. In Figure 5, torque ripple in 30 and 42 slotted AFIMs varies a lot compared to others. As the reason for this, it can be said that the number of these two slots is a multiple of 6; that is, the pole number. Thus, they are forced more in magnetic field transition. From the other five AFIMs, the torque ripples of only 28 and 34 slotted rotor designs are over 10%, while the other three designs' torque ripples at 9%. In this way, AFIM models with the best performance in terms of torque ripples are 32, 38 and 40 slotted models. There are six models in the same energy efficiency class (IE3) as RFIM. Only 34 slotted model is in a lower efficiency class (IE2).

AFIM Analyze Results with Different Rotor Slot Numbers
In this section, analyses are made according to seven different slot numbers for the rotor slots without skewing, 28, 30, 32, 34, 38, 40 and 42 slots, respectively. While determining these numbers, rotor slot widths are taken into account according to the machine size. Therefore, the maximum slot number is specified as 42 and the minimum as 28 for the number of rotor slots. Since the stator slot number is 36, 36-slot rotor design is not feasible, and because the stator slot and rotor slot areas are overlapped, the magnetic flux production is not possible.
It is known that torque ripple is one of the most challenging parameters in electrical machine designs. While making designs, decreasing this value is an aim. Therefore, torque ripples are taken into consideration while making comparisons. Figure 5 shows the efficiency and torque ripples of the analysis results according to 7 different slot numbers from 28 to 42. In Figure 5, torque ripple in 30 and 42 slotted AFIMs varies a lot compared to others. As the reason for this, it can be said that the number of these two slots is a multiple of 6; that is, the pole number. Thus, they are forced more in magnetic field transition. From the other five AFIMs, the torque ripples of only 28 and 34 slotted rotor designs are over 10%, while the other three designs' torque ripples at 9%. In this way, AFIM models with the best performance in terms of torque ripples are 32, 38 and 40 slotted models. There are six models in the same energy efficiency class (IE3) as RFIM. Only 34 slotted model is in a lower efficiency class (IE2). As a result of the analyses made according to different rotor slot numbers, although it does not have the highest efficiency, it can be said that the 40 slotted model, which is in the same energy efficiency class and has little difference between its efficiency, is the best model among them since the torque ripple is much less.

Results of AFIM with Skewed Rotor
In the analysis of the rotor with 28 slot non-skew model, torque ripple 13.9%, efficiency 92.6% are obtained. The efficiency class of this model is in IE3 class. As the first analysis, skew angles are As a result of the analyses made according to different rotor slot numbers, although it does not have the highest efficiency, it can be said that the 40 slotted model, which is in the same energy efficiency class and has little difference between its efficiency, is the best model among them since the torque ripple is much less.

Results of AFIM with Skewed Rotor
In the analysis of the rotor with 28 slot non-skew model, torque ripple 13.9%, efficiency 92.6% are obtained. The efficiency class of this model is in IE3 class. As the first analysis, skew angles are given to 28-slot AFIM. Accordingly, the skew angles in analyses are 10 • , 12.86 • , 15 • and 20 • . Torque ripple and efficiency results of the analyses are presented in Figure 6. Modeling of 25.72 • skew is not feasible due to the overlay occurring between stator and rotor. In Figure 6, it is observed that there is no increase in efficiency when the rotor is skewed. However, when the models with skewed according to the number of stator slots are examined, it is seen that the efficiency decreases as the skew angle increases. On the other hand, when the skew is given according to the number of rotor slots, the efficiency keeps the same value.
Energies 2020, 13, x FOR PEER REVIEW 9 of 15 given to 28-slot AFIM. Accordingly, the skew angles in analyses are 10°, 12.86°, 15° and 20°. Torque ripple and efficiency results of the analyses are presented in Figure 6. Modeling of 25.72° skew is not feasible due to the overlay occurring between stator and rotor. In Figure 6, it is observed that there is no increase in efficiency when the rotor is skewed. However, when the models with skewed according to the number of stator slots are examined, it is seen that the efficiency decreases as the skew angle increases. On the other hand, when the skew is given according to the number of rotor slots, the efficiency keeps the same value. As a result of the non-skew model analyses, 30-slot AFIM model has the highest torque ripple value and the best efficiency. In the second analysis, this model is skewed. In addition to the nonskew model; in Figure 7 the torque ripple and the efficiency results of 10°, 12°, 15° and 20° skewed AFIM models are presented. In Figure 7, the torque ripple has decreased as the skew angle degree increases in analyses made only considering the number of stator slots. When analyses made according to the number of rotor slots are compared among themselves, it is seen that as the skew angle increases, the torque ripple decreases. In Figure 7, an increment in efficiency was not observed when the rotor is skewed. However, according to the skewed models, efficiency is increasing with the increment in the skew angle. Considering the number of stators and rotor slots, the third analyses are done to 32-slot AFIM model with the skew angle of 10°, 11.25°, 15°, 20° and 22.5°. The non-skewed 32-slot AFIM model's torque ripple is 9.5% and the efficiency is 92.2%, which is in the IE3 class. Torque ripple and efficiency results of the analyses are shown in Figure 8. A comparison of the non-skew and 10° skew models shows that 10° skewed model has less torque ripple. On the other hand, a comparison of only skewed As a result of the non-skew model analyses, 30-slot AFIM model has the highest torque ripple value and the best efficiency. In the second analysis, this model is skewed. In addition to the non-skew model; in Figure 7 the torque ripple and the efficiency results of 10 • , 12 • , 15 • and 20 • skewed AFIM models are presented. In Figure 7, the torque ripple has decreased as the skew angle degree increases in analyses made only considering the number of stator slots. When analyses made according to the number of rotor slots are compared among themselves, it is seen that as the skew angle increases, the torque ripple decreases. In Figure 7, an increment in efficiency was not observed when the rotor is skewed. However, according to the skewed models, efficiency is increasing with the increment in the skew angle.
Energies 2020, 13, x FOR PEER REVIEW 9 of 15 given to 28-slot AFIM. Accordingly, the skew angles in analyses are 10°, 12.86°, 15° and 20°. Torque ripple and efficiency results of the analyses are presented in Figure 6. Modeling of 25.72° skew is not feasible due to the overlay occurring between stator and rotor. In Figure 6, it is observed that there is no increase in efficiency when the rotor is skewed. However, when the models with skewed according to the number of stator slots are examined, it is seen that the efficiency decreases as the skew angle increases. On the other hand, when the skew is given according to the number of rotor slots, the efficiency keeps the same value. As a result of the non-skew model analyses, 30-slot AFIM model has the highest torque ripple value and the best efficiency. In the second analysis, this model is skewed. In addition to the nonskew model; in Figure 7 the torque ripple and the efficiency results of 10°, 12°, 15° and 20° skewed AFIM models are presented. In Figure 7, the torque ripple has decreased as the skew angle degree increases in analyses made only considering the number of stator slots. When analyses made according to the number of rotor slots are compared among themselves, it is seen that as the skew angle increases, the torque ripple decreases. In Figure 7, an increment in efficiency was not observed when the rotor is skewed. However, according to the skewed models, efficiency is increasing with the increment in the skew angle. Considering the number of stators and rotor slots, the third analyses are done to 32-slot AFIM model with the skew angle of 10°, 11.25°, 15°, 20° and 22.5°. The non-skewed 32-slot AFIM model's torque ripple is 9.5% and the efficiency is 92.2%, which is in the IE3 class. Torque ripple and efficiency results of the analyses are shown in Figure 8. A comparison of the non-skew and 10° skew models shows that 10° skewed model has less torque ripple. On the other hand, a comparison of only skewed Considering the number of stators and rotor slots, the third analyses are done to 32-slot AFIM model with the skew angle of 10 • , 11.25 • , 15 • , 20 • and 22.5 • . The non-skewed 32-slot AFIM model's torque ripple is 9.5% and the efficiency is 92.2%, which is in the IE3 class. Torque ripple and efficiency results of the analyses are shown in Figure 8. A comparison of the non-skew and 10 • skew models shows that 10 • skewed model has less torque ripple. On the other hand, a comparison of only skewed models shows that the torque ripple is lowest at 10 • and highest at 15 • . Comparing the 32-slot skewed models and the non-skew model, it is seen that the torque ripple decreases when the skew angle is 10 • .
Energies 2020, 13, x FOR PEER REVIEW 10 of 15 models and the non-skew model, it is seen that the torque ripple decreases when the skew angle is 10°. In addition, efficiency increases and the efficiency class increases from IE2 to IE3. Only from skewed models according to the number of stator slots, the efficiency decreases while the skew angle increases. On the other hand, according to the skewed models skewed with rotor slots number, the torque ripple increases and the efficiency decreases while the skew angle increases.
The fourth analysis is performed to 34-slot AFIM and the skew angles are calculated as 10°, 10.58°, 15°, 20° and 21.17°. In the 34-slot non-skewed model, the torque ripple is 11%, the efficiency is 90.8%, while the efficiency class is in the IE2 class. Torque ripple and efficiency results of the 32slot AFIM analyses are shown in Figure 9. It is observed that the torque ripple does not fluctuate very much. Accordingly, it can be seen that the 15° skewed model is the most efficient model. In the 5th analysis step, the 38-slot AFIM, which has the least torque ripple, is analyzed by considering the stator and rotor slots numbers. Accordingly, skew angles are determined as 9.47°, 10°, 15°, 18.95° and 20°. When the skewed analysis results are compared to the non-skewed model, the analysis with the lowest torque ripple is obtained when the skew angle is 9.47. Torque ripple and efficiency results of the 38-slot AFIM analyses are shown in Figure 10. In addition, efficiency increases and the efficiency class increases from IE2 to IE3. Only from skewed models according to the number of stator slots, the efficiency decreases while the skew angle increases. On the other hand, according to the skewed models skewed with rotor slots number, the torque ripple increases and the efficiency decreases while the skew angle increases.
The fourth analysis is performed to 34-slot AFIM and the skew angles are calculated as 10 • , 10.58 • , 15 • , 20 • and 21.17 • . In the 34-slot non-skewed model, the torque ripple is 11%, the efficiency is 90.8%, while the efficiency class is in the IE2 class. Torque ripple and efficiency results of the 32-slot AFIM analyses are shown in Figure 9. It is observed that the torque ripple does not fluctuate very much. Accordingly, it can be seen that the 15 • skewed model is the most efficient model.  In addition, efficiency increases and the efficiency class increases from IE2 to IE3. Only from skewed models according to the number of stator slots, the efficiency decreases while the skew angle increases. On the other hand, according to the skewed models skewed with rotor slots number, the torque ripple increases and the efficiency decreases while the skew angle increases.
The fourth analysis is performed to 34-slot AFIM and the skew angles are calculated as 10°, 10.58°, 15°, 20° and 21.17°. In the 34-slot non-skewed model, the torque ripple is 11%, the efficiency is 90.8%, while the efficiency class is in the IE2 class. Torque ripple and efficiency results of the 32slot AFIM analyses are shown in Figure 9. It is observed that the torque ripple does not fluctuate very much. Accordingly, it can be seen that the 15° skewed model is the most efficient model. In the 5th analysis step, the 38-slot AFIM, which has the least torque ripple, is analyzed by considering the stator and rotor slots numbers. Accordingly, skew angles are determined as 9.47°, 10°, 15°, 18.95° and 20°. When the skewed analysis results are compared to the non-skewed model, the analysis with the lowest torque ripple is obtained when the skew angle is 9.47. Torque ripple and efficiency results of the 38-slot AFIM analyses are shown in Figure 10. In the 5th analysis step, the 38-slot AFIM, which has the least torque ripple, is analyzed by considering the stator and rotor slots numbers. Accordingly, skew angles are determined as 9. When the results of the skewed models of the 38-slot AFIM model according to the number of stator and rotor slots are examined, we do not see a positive effect on efficiency. Although the results are close to each other, the non-skewed model gives better results than skewed models.
In the sixth analysis step, the skew applied to the rotor of the 40-slot AFIM, which has the second best efficiency among non-skewed models. This model is also in IE3 energy efficiency class and the only model with low torque fluctuation. Skew angles for this model are calculated as 9°, 10°, 15°, 18° and 20°. Figure 11 shows the torque and efficiency results of the non-skewed and skewed models. In Figure 11, the 18° skewed model has the best torque ripple percentage. It can be seen that giving a skew to the rotor of 40-slot AFIM affects the efficiency negatively. However, the non-skewed, 9°, 10°, 15° and 18° skewed models are in IE3 energy efficiency class, other 10° and 20° skewed models are in IE2 energy efficiency class. The last step of analyses among skewed models is done to 42-slot AFIM, which is another model with high torque ripple. Analyses results of non-skewed and skewed models of 42-slot AFIM are shown in Figure 12. The non-skewed model of 42-slot AFIM is in IE3 energy efficiency class. According to the analyses results, it is observed that there is a different situation between the efficiencies that are not encountered in the other slot numbers. Efficiency decreased in models with 10° and 20° skewed, whereas efficiency in skew angle 8.57° and 15° is significantly increased. In fact, it has been observed that three of these models are in the IE4 energy efficiency class. These are the highest efficient models achieved among analyses. When the results of the skewed models of the 38-slot AFIM model according to the number of stator and rotor slots are examined, we do not see a positive effect on efficiency. Although the results are close to each other, the non-skewed model gives better results than skewed models.
In the sixth analysis step, the skew applied to the rotor of the 40-slot AFIM, which has the second best efficiency among non-skewed models. This model is also in IE3 energy efficiency class and the only model with low torque fluctuation. Skew angles for this model are calculated as 9 • , 10 • , 15 • , 18 • and 20 • . Figure 11 shows the torque and efficiency results of the non-skewed and skewed models. In Figure 11, the 18 • skewed model has the best torque ripple percentage. It can be seen that giving a skew to the rotor of 40-slot AFIM affects the efficiency negatively. However, the non-skewed, 9 • , 10 • , 15 • and 18 • skewed models are in IE3 energy efficiency class, other 10 • and 20 • skewed models are in IE2 energy efficiency class. When the results of the skewed models of the 38-slot AFIM model according to the number of stator and rotor slots are examined, we do not see a positive effect on efficiency. Although the results are close to each other, the non-skewed model gives better results than skewed models.
In the sixth analysis step, the skew applied to the rotor of the 40-slot AFIM, which has the second best efficiency among non-skewed models. This model is also in IE3 energy efficiency class and the only model with low torque fluctuation. Skew angles for this model are calculated as 9°, 10°, 15°, 18° and 20°. Figure 11 shows the torque and efficiency results of the non-skewed and skewed models. In Figure 11, the 18° skewed model has the best torque ripple percentage. It can be seen that giving a skew to the rotor of 40-slot AFIM affects the efficiency negatively. However, the non-skewed, 9°, 10°, 15° and 18° skewed models are in IE3 energy efficiency class, other 10° and 20° skewed models are in IE2 energy efficiency class. The last step of analyses among skewed models is done to 42-slot AFIM, which is another model with high torque ripple. Analyses results of non-skewed and skewed models of 42-slot AFIM are shown in Figure 12. The non-skewed model of 42-slot AFIM is in IE3 energy efficiency class. According to the analyses results, it is observed that there is a different situation between the efficiencies that are not encountered in the other slot numbers. Efficiency decreased in models with 10° and 20° skewed, whereas efficiency in skew angle 8.57° and 15° is significantly increased. In fact, it has been observed that three of these models are in the IE4 energy efficiency class. These are the highest efficient models achieved among analyses. The last step of analyses among skewed models is done to 42-slot AFIM, which is another model with high torque ripple. Analyses results of non-skewed and skewed models of 42-slot AFIM are shown in Figure 12. The non-skewed model of 42-slot AFIM is in IE3 energy efficiency class. According to the analyses results, it is observed that there is a different situation between the efficiencies that are not encountered in the other slot numbers. Efficiency decreased in models with 10 • and 20 • skewed, whereas efficiency in skew angle 8.57 • and 15 • is significantly increased. In fact, it has been observed Energies 2020, 13, 4991 12 of 15 that three of these models are in the IE4 energy efficiency class. These are the highest efficient models achieved among analyses. As a result of all analyses carried out, giving skews to the rotor of the motor affects the efficiency differently, and the torque ripple in different rotor slot numbers of AFIMs. In some AFIMs, skewing has a positive effect in terms of torque ripple and decreases the torque ripple, while in others it is observed that the torque ripple increases. In the same way, it has different effects in terms of efficiency. For example, the 8.57°, 15° and 17.14° skewed 42-slot AFIMs are given results in IE4 energy efficiency class. Also, the torque ripple of the same model decreases by 28% to 26.6%. Therefore, the best configuration among 42-slot models is obtained as 8.57° skew angle.
However, in the analyses performed both in terms of torque ripple and efficiency, the most optimum condition result is achieved in the design with a 10° skew given to the 32-slot AFIM. The torque ripple of this model is 8.93%, the effıciency is 93.1% and efficiency class of this motor is IE3. In the next section, the effect of the material on efficiency and torque ripple by using SMC material is examined.

Results of AFIM with SMC Material
In this section, the effect of the SMC material on efficiency and torque is examined. By this purpose, three analyses are done with using SMC material for stator, rotor and both of them. Somaloy 700-3P is selected as a SMC material with a density 7.57 g/cm 3 [42].
According to the analyses results, by changing the material, the efficiencies stayed in the same efficiency class as IE3. However, only SMC stator has the best efficiency value, both SMC stator&rotor has the best torque value. Compared to the non-skewed based model to both SMC stator&rotor used model over 11% of reduction is observed in torque ripple. Additionally, changing the material has a positive impact on the efficiency. Figure 13 shows the efficiency and torque results of SMC used AFIM by different parts.  As a result of all analyses carried out, giving skews to the rotor of the motor affects the efficiency differently, and the torque ripple in different rotor slot numbers of AFIMs. In some AFIMs, skewing has a positive effect in terms of torque ripple and decreases the torque ripple, while in others it is observed that the torque ripple increases. In the same way, it has different effects in terms of efficiency. For example, the 8.57 • , 15 • and 17.14 • skewed 42-slot AFIMs are given results in IE4 energy efficiency class. Also, the torque ripple of the same model decreases by 28% to 26.6%. Therefore, the best configuration among 42-slot models is obtained as 8.57 • skew angle.
However, in the analyses performed both in terms of torque ripple and efficiency, the most optimum condition result is achieved in the design with a 10 • skew given to the 32-slot AFIM. The torque ripple of this model is 8.93%, the effıciency is 93.1% and efficiency class of this motor is IE3. In the next section, the effect of the material on efficiency and torque ripple by using SMC material is examined.

Results of AFIM with SMC Material
In this section, the effect of the SMC material on efficiency and torque is examined. By this purpose, three analyses are done with using SMC material for stator, rotor and both of them. Somaloy 700-3P is selected as a SMC material with a density 7.57 g/cm 3 [42].
According to the analyses results, by changing the material, the efficiencies stayed in the same efficiency class as IE3. However, only SMC stator has the best efficiency value, both SMC stator&rotor has the best torque value. Compared to the non-skewed based model to both SMC stator&rotor used model over 11% of reduction is observed in torque ripple. Additionally, changing the material has a positive impact on the efficiency. Figure 13 shows the efficiency and torque results of SMC used AFIM by different parts.
In the X-axis of Figure 13, skew status and material of AFIM are defined as follows: (a) Rotor is not skewed and both stator and rotor material are steel, (b) Rotor is skewed and both stator and rotor material are steel, (c) Rotor is skewed and stator material is SMC and rotor material is steel, (d) Rotor is skewed and stator material is steel and rotor material is SMC, (e) Rotor is skewed and both stator and rotor material are SMC.
According to the analyses results, by changing the material, the efficiencies stayed in the same efficiency class as IE3. However, only SMC stator has the best efficiency value, both SMC stator&rotor has the best torque value. Compared to the non-skewed based model to both SMC stator&rotor used model over 11% of reduction is observed in torque ripple. Additionally, changing the material has a positive impact on the efficiency. Figure 13 shows the efficiency and torque results of SMC used AFIM by different parts.

Conclusions
Since the aim in this study is to achieve an AFIM in the same energy efficiency class as RFIM, the efficiency of AFIMs with torque ripples are investigated. In this study, transient analyses are carried out and torque values are calculated with the help of ANSYS Maxwell program. Efficiency values of analysis results according to seven different slot numbers from 28 to 42 are presented. In addition to the efficiency values, the percentage torque ripples and energy efficiency class are also examined. To reduce the torque ripple values, rotor is skewed according to stator and rotor slot numbers. It was seen that the effects of skewing on efficiency and torque ripple are variable. Also, it was observed that to choose the skewing angle degrees, not only with stator slot number, but also rotor slot number could affect positive the performance of AFIMs. Using a SMC material on different parts of AFIM had a positive impact on performance analysis of a model, as reducing the torque ripple over 11% while the models are in premium efficiency class. For further studies, different materials could be used for various applications.