Reduction of Torque Ripple and Axial Force in a Fully Pitched Axial Flux Switched Reluctance Motor Using a Double Stator Structure

Abstract

Switched reluctance motors (SRMs) are highly advantageous electric motors for various industrial applications, particularly in electric vehicles (EVs), due to their winding-free rotor, magnet-free design, simplicity, and ease of manufacturing. The growing interest in axial flux SRMs (AFSRMs) is particularly noticeable, as axial flux electric motors with a flat shape and high aspect ratio have become commonly used in various industrial applications, including in-wheel motors for EVs. Structurally, AFSRMs significantly differ from radial flux SRMs (RFSRMs), but share the same electromagnetic operating principles. When compared to RFSRMs, AFSRMs generate higher torque per unit volume due to their more effective utilization of their air gap. In this study, the axial force on the rotor and torque ripple of a 6/4 pole fully pitched axial flux SRM (FP-AFSRM) were minimized by combining the advantages of “single-stator and single-rotor AFSRM” and “double-stator and single-rotor AFSRM” models. The proposed FP-AFSRM model, which has a “double-stator and single-rotor AFSRM” design and has the operating logic of a “single-stator and single-rotor AFSRM”, was analyzed using 3D finite element analysis. The results show that the torque ripple decreased (Δ % T_rip) between (−30.42) and (−41.14), and the axial force on the rotor decreased between 17.61% and 25.4%.

1. Introduction

In recent years, climate change and the energy crisis caused by the excessive consumption of fossil fuels has been an important issue that has attracted worldwide attention [1]. Due to climate change, air pollution, and the need to reduce dependence on limited fossil fuels, there has been a significant increase in the demand for sustainable and environmentally friendly transportation systems [2]. The adoption of electric vehicles (EVs) instead of conventional internal combustion engine (ICE) vehicles can contribute to the solution of climate change and the energy crisis by greatly reducing both fossil energy consumption and carbon dioxide emissions [1]. This situation has accelerated the technological development trend of EVs and has facilitated the growth of the EV industry. The fact that motor systems, which are the key components of EVs, have a direct impact on vehicle performance has highlighted the importance of electric motors [3]. At this point, the most critical expectations of electric motors are that they should be cost-effective, simple, and robust in design. Among electric machines, switched reluctance motors (SRMs) stand out as a significant option for various applications due to their simple and robust structure, as well as cost advantages. The absence of windings or magnets in the rotor allows SRMs to operate efficiently at high speeds and temperatures [4]. Extensive research has also focused on eliminating or reducing the use of rare-earth permanent magnets (PMs) in motor designs due to their continuously rising prices [5]. Interior permanent magnet motors (IPMSMs), which have a high starting torque and high efficiency, especially at low and medium speeds, are widely used in most modern commercial vehicles. However, the rare-earth permanent magnets used in their structure pose significant and concerning issues for motor manufacturers and users in terms of price volatility and supply chain challenges [6]. Therefore, SRMs, which do not contain permanent magnets (PMs) in their structure, are an important option for manufacturers and users. Since SRMs are produced without PMs, they can be manufactured at a lower cost, and the absence of conductors in their rotating parts ensures robust and reliable operation. All these factors make SRMs particularly well-suited for a wide range of industrial applications, including electric vehicles (EVs) [7]. There are a wide range of studies in the literature where EVs and SRMs are combined. For instance, Belhadi et al. compared AFSRMs and RFSRMs for EVs in equal volumes and evaluated the advantages and disadvantages of both structures [8]. In another study conducted by Andrada et al., a novel in-wheel double rotor AFSRM structure for electric traction was presented. Soft magnetic composites were used for the stator and rotor materials, and electromagnetic analyses were performed using 3D finite element analysis (FEA) [9]. Padmanaban et al. designed and compared configurations, such as C-core stators with dual rotor SRMs and C-core stators with disk-type segmented rotor SRMs and dual gap inner segmented rotor SRMs, for in-wheel applications [10]. Cheng et al. also conducted a study on the design of SRM drives for EVs [11]. Zhu et al. presented an SRM with a wide speed range for EVs, featuring an in-wheel structure for direct drive and a design with multiple teeth per stator pole to increase the torque [12]. Consequently, SRMs have the potential to replace IPMSMs in many applications, including drive systems. Their modular winding structure and simple rotor design provide superior fault tolerance. Additionally, SRMs, which are also well-suited for sensorless operation, can use active phases or passive phases for position estimation. The absence of a position sensor also positively enhances system reliability [13].

Like other electrical machines, SRMs have certain disadvantages in addition to their advantages. Specifically, due to their double salient structure, SRMs exhibit non-linear magnetic characteristics, high acoustic noise, high vibration, and a significant torque ripple [5,7]. Electromagnetic studies in the literature emphasize that reducing the torque ripple in SRMs is extremely important. In the studies where the torque ripple is attributed to the tangential and radial components of electromagnetic forces, understanding and eliminating these factors are considered crucial for effectively addressing the torque ripple problem in SRMs [2] since acoustic noise in electrical machines can originate from both mechanical and electromagnetic sources. Mechanical noise is often caused by production asymmetries, bearing vibrations, rotor alignment issues, and similar factors, while electromagnetic noise results from the temporal and spatial variations of the air gap forces in the radial and tangential directions [14]. In particular, SRMs tend to produce high levels of acoustic noise and vibration due to the vibratory nature of the radial forces. This poses a significant disadvantage in applications where quiet operation is required [15].

When examining the geometric structure of SRMs, it can be seen that, like other electrical machines, SRMs are classified into “radial flux” and “axial flux” based on the direction of magnetization. Radial flux SRMs (RFSRMs) have magnetic flux lines in their air gap that are perpendicular to the machine axis, and their air gap depends on their motor length. In axial flux SRMs (AFSRMs), the motor’s air gap is dependent on the motor’s diameter, and the magnetic flux lines in their air gap are parallel to the machine’s rotation axis. The increased air gap area in axial machines compared to radial machines allows for the effective utilization of the magnetic flux produced by the winding current. Additionally, the flat shape and high aspect ratio of AFSRMs make them highly suitable for wheel hub motor applications [8,9,16]. In electric vehicles, a multi-motor drive system created by placing motors within the wheels eliminates transmission losses. This is because transmission losses in electric vehicles lead to reduced range, lower efficiency, higher operating costs, and increased weight [10]. Axial flux motors are also a critical parameter for electric vehicles in this context. Additionally, AFSRMs, despite having significant structural differences from RFSRMs, operate based on the same electromagnetic principles. AFSRMs are driven by the reluctance torque generated between the stator and rotor. Additionally, although AFSRMs share the same operating principles as RFSRMs, they produce a higher torque per unit volume compared to an RFSRM of the same volume and weight [17,18,19,20]. The phase inductances of AFSRMs can be expressed using the Fourier series, as shown in Equations (1)–(4) [21,22].

$$L\left(i,\theta \right)=L_0(i)+L_1(i)cos\left(P_r\theta \right)+L_2(i)cos(2P_r\theta )$$

(1)

$$L_0(i)={\displaystyle \frac{1}{2}}\left[{\displaystyle \frac{1}{2}}\left(L_a+L_u\right)+L_m\right]$$

(2)

$$L_1(i)={\displaystyle \frac{1}{2}}(L_a-L_u)$$

(3)

$$L_2\left(i\right)={\displaystyle \frac{1}{2}}\left[{\displaystyle \frac{1}{2}}\left(L_a+L_u)-L_m\right)\right]$$

(4)

where $\theta$ represents the rotor position, $i$ represents phase current, $P_r$ refers to the number of rotor poles, $L_a$ and $L_u$ represent the inductance values in the aligned and unaligned positions, and $L_m$ is the inductance value obtained at the midpoint between the aligned and unaligned positions.

In this study, the axial flux SRM design, which combines the fully pitched structure, which has more difficult control algorithms compared to the short-pitched structure, but has made great progress with the developments in recent years, and the axial flux structure, which is increasingly used, with a low torque ripple and minimized axial forces, is presented. Fully pitched SRMs produce a higher torque than conventional SRMs at equivalent copper losses. In fact, in a typical industrial context, this situation can reach levels of 20–30% [23,24,25,26]. It is thought that the fully pitched axial flux SRM structure, which minimizes the torque ripple and axial forces, proposed in this study will contribute to researchers in many areas where SRMs are preferred, especially in EVs. In addition, FEA analyses performed for the proposed motor can be considered as a powerful method for making accurate analyses of electrical machines due to the advanced high-capacity and high-speed microprocessors of today [27]. There is various software, such as Ansys Maxwell, COMSOL, and MagNET, in the literature to make motor analyses. Ansys Maxwell software was used in this study.

2. General Structure of Fully Pitched SRMs

In SRMs, phase control is conducted independently. Since each phase is controlled independently, a fault in one phase does not affect the others. In other words, SRM continues to operate even in the event of a phase fault. However, this situation also causes major losses in motor performance [7]. In SRMs, their air gap power or electro-mechanical power $P_m$ can be expressed as given in Equation (5), neglecting friction and windage losses [28].

$$P_m={\displaystyle \frac{1}{2}}{i}^2{\displaystyle \frac{dL(\theta )}{d\theta }}{\omega }_m$$

(5)

where $i$ is the active phase current, $L$ is the active phase inductance, $\theta$ is the rotor position angle, and $\omega$ is the angular velocity. In this case, the electromagnetic torque $T_e$ is given as in Equation (6) [28].

$$T_e={\displaystyle \frac{P}{{\omega }_m}}={\displaystyle \frac{1}{2}}{i}^2{\displaystyle \frac{dL(\theta )}{d\theta }}$$

(6)

In conventional SRMs, only one phase is active at a time. However, in fully pitched SRMs (FPSRMs), also known as mutually coupled SRMs (MCSRMs), two phases are active depending on the selected position [13]. This is because the torque production in FPSRMs relies on the mutual inductance between the phases [23]. Additionally, when two phases are active simultaneously in FPSRMs, they effectively function as a single tooth winding with twice the magnetomotive force (MMF). This configuration enables FPSRMs to achieve a higher torque output compared to conventional SRMs [13]. Additionally, in torque production, while conventional SRMs, also known as short-pitched SRMs, neglect mutual inductance between phases, FPSRMs disregard self-inductance [23,24]. The generalized electromagnetic torque equation for SRMs is given in Equation (7) [23,24,29].

$$T={\displaystyle \frac{1}{2}}{i}_a^2{\displaystyle \frac{{\partial L}_a}{\partial \theta }}+{\displaystyle \frac{1}{2}}{i}_b^2{\displaystyle \frac{{\partial L}_b}{\partial \theta }}+{\displaystyle \frac{1}{2}}{i}_c^2{\displaystyle \frac{{\partial L}_c}{\partial \theta }}+i_a{i}_b{\displaystyle \frac{{\partial M}_{ab}}{\partial \theta }}+i_b{i}_c{\displaystyle \frac{{\partial M}_{bc}}{\partial \theta }}+i_c{i}_a{\displaystyle \frac{{\partial M}_{ca}}{\partial \theta }}$$

(7)

where $i_a$, $i_b$, $i_c$ represent phase currents, $M_{ab}$, $M_{bc}$, $M_{ca}$ represent mutual inductance between phases, $L_a,L_b$, $L_c$ represent the self-inductance of the phases, $ϴ$ represents the rotor position angles, $T$ represents the torque. Since self-inductances are neglected in FPSRMs, the torque expression is expressed as in the Equation (8). Figure 1 shows the 2D image of a 3-phase 6/4 pole FPSRM with a radial structure, and Equation (8) shows the FPSRM torque expression.

$$T=i_a{i}_b{\displaystyle \frac{{\partial M}_{ab}}{\partial \theta }}+i_b{i}_c{\displaystyle \frac{{\partial M}_{bc}}{\partial \theta }}+i_c{i}_a{\displaystyle \frac{{\partial M}_{ca}}{\partial \theta }}$$

(8)

Fully Pitched AFSRMs

AFSRMs, which have flux flowing in the axial direction, feature a larger and more effective air gap compared to radial machines. The flat structure of AFSRMs allows for the easy adjustment of their air gap, making them well-suited for various applications, including electric powertrains, wind turbines, microelectromechanical systems (MEMS), simple devices such as fans, and in-wheel motors (IWMs) in electric vehicles [30]. AFSRMs are generally categorized into three main types: (1) the “single-stator and single-rotor AFSRM”, which is the most basic structure with one stator and one rotor; (2) the “double-stator and single-rotor AFSRM”, which includes two stators and one rotor; and (3) the “single-stator and double-rotor AFSRM”, featuring one stator and two rotors [8].

The “single-stator and single-rotor AFSRMs”, also known as “single-sided (SS) rotor and stator AFSRMs”, have only one air gap. One major drawback of this design is the non-uniform distribution of the forces between the stator and rotor. This leads to axial force issues, which can cause high noise levels, the deformation of windings, collisions between rotor and stator pole heads, and bearing damage. Additionally, because the forces disrupt the symmetry of the air gaps, they can increase motor vibrations and torque ripples. For these reasons, it is crucial to ensure that the rotor is properly aligned [8,30].

The “double-stator and single-rotor AFSRMs”, also known as “double-sided (DS) rotor(s) and stator(s)”, consist of a single rotor placed between two stators. This model, which features two easily cooled air gaps, has the significant advantage of balanced axial forces. The double-stator design aims to reduce the effects of electromagnetic forces without increasing the length of their air gap, because this model cancels the electromagnetic force in the axial direction due to its double stator. The axial force of each stator on the rotor is compensated by the force of the other stator. However, the twin air gap of this model reduces the maximum inductance and causes the output torque to decrease. This negativity causes a significant disadvantage for this model. In addition, although the torque ripple can be reduced by angularly shifting the stators, the angular shift can also cause unbalanced axial forces [8,31].

Another model of the “double-sided (DS) rotor(s) and stator(s)” structure is the “single-stator and double-rotor AFSRMs”. This model consists of a single stator in the middle and an external rotor on each side. The cooling situation is complicated; the windings are difficult to place and as a result, it is a high-cost model [8].

In addition to these three models, multi-layer/multi-stack AFSRM structures can be created using all three model structures. Depending on the model structures used in the multi-layer structure of AFSRM, the stator and rotor numbers can be equal, less or more [30]. Figure 2 shows (a) short-pitched AFSRM and (b) fully pitched AFSRM (FP-AFSRM). The stator and rotor geometric structures of both motors are the same, but the winding structure and, therefore, the control algorithms are different.

3. General Discussion

In an SRM, in addition to electromagnetic noise sources, various other noise sources such as mechanical and aerodynamic ones may also exist. Although all these sources can cause noise and vibration problems in the motor, the most prominent noise source in an SRM is structure-borne noise caused by radial electromagnetic forces [6]. In SRMs, the irregular and non-uniform distributions of flux and force densities in their air gap and near the stator/rotor lead to high levels of torque ripple and vibrations in the motor. In fact, the irregular and non-uniform force and flux distributions, which are already considered undesirable behaviors for the motor, are identified as the main causes of torque ripple and vibrations [32].

In SRMs, the attraction force is divided into two components, tangential and radial, based on the rotor structure. While the tangential force is converted into torque in the motor, the radial force causes unwanted vibrations and acoustic noise [33]. When the appropriate phase in an SRM is excited with direct voltage, the rotating rotor begins to turn in a direction that reduces the reluctance of the magnetic circuit. However, the sudden increase in torque at the point where the stator and rotor poles begin to overlap causes an abrupt tangential movement around the stator. This tangential movement combines with a strong centripetal motion when the stator phase is de-energized very quickly [32].

The radial force generated in RFSRMs contains various harmonic components that cause the vibration of the stator core and, consequently, acoustic noise. Over time, this leads to deformations in the stator core [34]. Similarly, in AFSRMs, an axial electromagnetic force is generated between the stator and rotor due to the axial magnetic flux. This force primarily causes rotor vibrations and negatively impacts the motor’s performance [35]. In other words, radial forces that occur in RFSRMs occur as axial forces in AFSRMs. However, due to their disk structure, AFSRMs are not as resilient to these forces as RFSRMs. This also leads to a risk of pole collisions in addition to high vibrations. Furthermore, while in AFSRMs, the bearings are expected to absorb these forces through balls; in RFSRMs, the radial forces are balanced by the rotor and stator structures. The axial force $(\mathrm{F})$ in a magnetic system with an air gap can be determined by the ratio of change of the coenergy $(W_c)$ with respect to the distance $\left(l_g\right)$, as expressed in Equation (9) [20]. Figure 3 illustrates the forces in RFSRM and AFSRM structures.

$$F={\displaystyle \frac{{dW}_c}{{dl}_g}}$$

(9)

When Figure 3a is examined, it can be seen that in electrical machines, the electromagnetic flux follows a path through the stator–air gap rotor to generate the electromagnetic torque. In SRMs, each phase is sequentially excited to align the rotor poles with the excited stator poles, minimizing the reluctance along the flux path. As a result of this alignment process, an electromagnetic force $F$ is generated, which consists of a tangential force $F_t$ and a radial force $F_r$. The torque obtained from the motor is derived from the tangential component of the electromagnetic force between the stator and rotor. While this situation can cause torsional vibrations in the stator poles and windings, most of the resulting vibrations are due to radial force fluctuations in the radial direction [14]. When examining Figure 3b, similar situations occur in the AFSRM structure. In AFSRMs, which operate on the same principle as RFSRMs, the phases are sequentially excited to minimize the reluctance along the flux path. As a result, the rotor poles move to achieve an aligned position with the stator poles. As a result of the alignment process, an electromagnetic force $F$ is generated, which consists of a tangential force $F_t$ and, an axial force $F_a$, which occur in the axial direction, unlike in RFSRMs. As a result, all the negative behaviors caused by the force, such as rotor vibrations, are also observed in AFSRMs.

In this study, a “double-sided rotor and stator FP-AFSRM” with the geometric structure of a “double-stator and single-rotor FP-AFSRM” and the operating logic of a “single-stator and single-rotor FP-AFSRM” was proposed. As a result of the magnetostatic analysis of the proposed model consisting of two stators and a single rotor, it has been observed that both the torque ripple is minimized and the average decreases in the generated force are observed. In addition, this proposed model has two air gaps since it has a twin stator structure. Moreover, one of the stators has a shift angle of $\alpha$ with respect to the other. However, since the operating principle is based on the “single-stator and single-rotor FP-AFSRM”, it does not have the disadvantages experienced in models with dual stators, such as reduced inductance leading to the decreased output torque, or the formation of unbalanced axial forces due to angular displacement in dual stators [8,31]. Although it shares the operating principle of the “single-stator and single-rotor FP-AFSRM”, the proposed models have minimized the common problem of the torque ripple and improved the forces on the rotor. In addition, the reason for preferring a double stator is that the winding structure is easy to place, and the cooling problem is simpler than double rotor structures. In traditional AFSRMs, the winding structure is wound as short-pitched on the pole head, as in RFSRMs. When a double rotor structure is preferred in AFSRMs, the placement and cooling of the windings is an important problem. In the proposed model, a fully pitched winding structure is used, which is scattered in the slots. In the case of using a double rotor, the placement and cooling of the fully pitched winding structure will create a more complicated situation. For this reason, a double stator was preferred instead of a double rotor structure. Figure 4 shows the trimetric and frontal general views of the proposed double-sided rotor and stator FP-AFSRM, while

Table 1. Geometric properties and nominal parameters of double-sided rotor and stator FP-AFSRM.

Geometric Properties and Nominal Parameters	Value
Stator/rotor outer diameter (mm)	220.00
Stator yoke thickness (mm)	17.50
Stator teeth axial length (mm)	50.00
Rotor yoke thickness (mm)	17.50
Rotor teeth axial length (mm)	16.50
Air gap length (mm)	1.0
Stator/rotor pole numbers	6/4
Number of phases	3
Rated current (Amps)	10
Rated power (W)	2750
Rated speed (rpm)	1500

provides the geometric and nominal parameters of the motor. The left stator is energized as the main stator, and the right stator serves as the auxiliary stator. All the geometric dimensions of both stators are identical. Both stators have a fully pitched winding structure. In summary, except for the phase energization timing, all the geometric features of the two stators are identical. Dimensions are given in Table 1 for one side.

There is a shift angle of $\alpha$ between the two stators of the proposed “double-sided rotor and stator FP-AFSRM” shown in Figure 4. Since both motors (left and right) operate separately during the operation process, the equation that determines the displacement angle between the layers in the multi-layer SRMs given in Equation (10) was used to determine the optimum $\alpha$ angle value [36].

$$\alpha ={\displaystyle \frac{{360}^0}{P_r{N}_{phase}{N}_{layer}}}$$

(10)

In Equation (10) $P_r$ indicates the number of rotor poles, $N_{phase}$ indicates the number of motor phases, and $N_{layer}$ indicates the number of layers. The $\alpha$ angle of the motor, which is considered as three phases, which has a rotor pole number of four and is considered as two layers, is found to be ${15}^0$. The slope angle between the two stators is seen in Figure 5.

The identical stators on both sides are energized at different times during the operating period. Both motors contribute maximally to torque production. The left stator, which serves as the main stator, provides the primary contribution to torque production, while the right stator, acting as the auxiliary stator, engages during intervals of torque reduction. This reduces the torque ripple and increases the average torque. In other words, when the appropriate phases in the left SRM are energized according to the rotor pole position, they reduce the reluctance in the common rotor air gap, thereby enabling torque production in the left SRM. During this time, as the rotor–stator poles of the left SRM move from an unaligned to an aligned state, the right SRM, with its stator having a 15⁰-shift angle, positions its rotor-stator poles in an unaligned state that contributes to a higher torque production. Consequently, the phase energy in the left SRM is cut off, and the appropriate phases in the right SRM are energized. This process is repeated, maximizing the torque production of both motors. Additionally, the proposed design results in a reduction in the average axial force on the rotor.

4. Analysis of Proposed FP-AFSRM

The analyses of the study were conducted using the Ansys Maxwell software package. The analyses, carried out using the finite element analysis (FEA) method, which is widely accepted in theoretical studies, represent one of the primary and crucial stages in motor design.

4.1. Finite Element Analysis

Finite element analysis (FEA) is one of the most widely used numerical methods for examining the electromagnetic properties of electrical machines. This numerical method utilizes a technique called the finite element method (FEM) to perform engineering analyses through computer simulations [37,38]. For SRMs, FEM analyses are essential due to their bidirectional salient structure and the intense saturation effects that occur at partially aligned stator–rotor poles [37]. FEA allows for the calculation of profiles such as torque, magnetizing, self-inductance, and mutual inductance of the SRM by using Maxwell’s equations, which can be expressed in both the differential form (as given in Equations (11)–(14)) and integral forms [39,40].

$$\nabla xE=-{\displaystyle \frac{\partial B}{\partial t}}$$

(11)

$$\nabla •B=0$$

(12)

$$\nabla xH=J+{\displaystyle \frac{\partial D}{\partial t}}$$

(13)

$$\nabla •D=\rho$$

(14)

In Equations (11)–(14), $E$ represents the electric field intensity (V/m), $B$ represents the magnetic flux (Tesla or Wb/m²), $H$ represents the magnetic field intensity (A/m), $D$ represents the electric flux density (C/m²), $t$ represents the time (s), $\rho$ represents the electric charge density (C/m³), and $J$ represents the current density (A/m²). The magnetic field resulting from the transformation of the electromagnetic field for SRMs due to winding and eddy currents is described by Equation (15) [41,42].

$${\displaystyle \frac{\partial }{{\partial }_x}}\left({\displaystyle \frac{1}{\mu }}{\displaystyle \frac{{\partial A}_z}{{\partial }_x}}\right)+{\displaystyle \frac{\partial }{{\partial }_y}}\left({\displaystyle \frac{1}{\mu }}{\displaystyle \frac{{\partial A}_z}{{\partial }_y}}\right)-\sigma {\displaystyle \frac{{\partial A}_z}{{\partial }_t}}=J_z$$

(15)

where $\mu$ the permeability, $\sigma$ represents the conductivity, and $j_z$ represents the source current given to the windings from outside.

3D-FEM analyses are time-consuming and involve very heavy operations. Nevertheless, since the analysis of axial flux electric machines involves a three-dimensional electromagnetic problem, the most accurate solutions are obtained using 3D-FEM. However, in a literature study, 2D-FEM analyses were conducted by taking 2D slices of the axial machine geometry. This approach can be considered as reducing the axial flux electric machine to a linear electric machine [9,43].

The analyses of the proposed FP-AFSRM model were conducted in 3D. Figure 6 shows the variation in the torque and axial force on the rotor as a function of the rotor angle, based on a magnetostatic analysis performed at 10 amperes. The 15° skew angle mentioned in the graph title refers to the 15° skew angle of the auxiliary stator, as indicated in Figure 5.

When examining the torque graph in Figure 6a obtained at 10 amperes, each layer (right–left) engages at the times when it contributes maximally to the torque production. The left stator remains active in the range of ${(-45}^0)$–$({-12}^0)$, providing the starting torque, and then disengages as the torque curve begins to decline. The right stator then engages in the range of ${(-12}^0)$–$({6.5}^0)$, contributing to the torque production. This results in a smooth torque curve.

4.2. Comparison of Magnetostatic Analysis Results and Discussion

The magnetostatic analyses of the proposed FP-AFSRM model were conducted in the range of 5 to 15 amperes, with 2.5 ampere steps. Figure 7 presents the torque and axial force graphs obtained from the magnetostatic analyses of the proposed model at various current levels.

For the performance comparison of the proposed FP-AFSRM model, average torques, torque ripples, and average axial force values were calculated from magnetostatic analyses conducted at different current levels. All three parameters are significant factors affecting the performance of electric motors. The torque ripple and axial forces should be minimized, while the average torque should be maximized. The torque ripple ($T_{rip})$ is calculated using the equation given in Equation (16) where $T_{max}$, $T_{min}$, and $T_{avg}$ represent the maximum, minimum, and average torques, respectively [29]. Figure 8 shows the torque ripple and average axial force values of the proposed FP-AFSRM model at 10 amperes.

Table 2. $T_{avg}$, $T_{rip}$ and $F_{avg}$ values of the proposed FP-AFSRM model.

Proposed Double-Sided Rotor and Stator FP-AFSRM
Current (Amps)	Trip (%)	Tavg (Nm)	Favg (N)
5	4.40	6.63	713.7
7.5	4.91	13.03	1025
10	9.63	18.42	1197.2
12.5	10.06	23.85	1355.6
15	10.34	28.52	1503.6

presents the values of $T_{avg}$, $T_{rip}$ and $F_{avg}$ obtained from the analyses of the proposed FP-AFSRM model at various current levels.

$$T_{rip}={\displaystyle \frac{({\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}})}{{\mathrm{T}}_{\mathrm{a}\mathrm{v}\mathrm{g}}}}.100\mathrm{\%}$$

(16)

Additionally, in SRMs, the duration for which each phase remains energized during a rotor pole step is determined by the rotor step angle (${\theta }_s$) given in Equation (17).

$${\theta }_s={\displaystyle \frac{2\mathsf{\pi }(N_s-N_r)}{N_s{N}_r}}$$

(17)

where $N_s$ represents the number of stator poles and $N_r$ represents the the number of rotor poles. Since the proposed motor has a motor 6/4 pole structure, it was found that ${\theta }_s$ = 30⁰. Additionally, the unaligned–aligned position between the rotor and stator poles is defined by the maximum angle. The maximum angle (45⁰) between the poles is determined as follows:

$$Maximumangle={\displaystyle \frac{360}{2N_r}}$$

(18)

In the operating principle of the proposed FP-AFSRM model, each layer operates independently within its designated angle range. During the motor’s operation, only one of the left or right stators is active at any given time according to the rotor position; both stator phases are not energized simultaneously. This condition does not introduce additional losses in the motor. In other words, the losses experienced with a single layer operating as a “single-stator and single-rotor FP-AFSRM” are equivalent to the losses in the proposed configuration. For this reason, the operating principle of the proposed FP-AFSRM model is entirely similar to that of the “single-stator and single-rotor FP-AFSRM”. Consequently, the results obtained from the analysis of the proposed FP-AFSRM model have been compared with the results from the analyses of the single-layer “single-stator and single-rotor FP-AFSRM”. Figure 9 shows the torque and axial force graphs obtained from magnetostatic analyses of the left stator as “single-stator and single-rotor FP-AFSRM” at various current levels.

In Figure 9, only the left stator is active. In other words, the left stator has been analyzed as a “single-stator and single-rotor FP-AFSRM”. The left and right stators are twin stators with identical characteristics. If the right stator is also analyzed as a “single-stator and single-rotor FP-AFSRM”, the same curves are obtained. Therefore, analyzing either the left or right stator as a “single-stator and single-rotor FP-AFSRM” does not result in any differences in the comparison results. Figure 10 shows the torque ripple and average axial force values obtained at 10 amperes from the analysis of the left stator as a “single-stator and single-rotor FP-AFSRM”.

Table 3. $T_{avg}$, $T_{rip}$, and $F_{avg}$ values of single-stator and single-rotor FP-AFSRM.

Single-Stator and Single-Rotor FP-AFSRM
Current (Amps)	Trip (%)	Tavg (Nm)	Favg (N)
5	34.82	5.13	956.8
7.5	43.17	9.56	1305
10	48.98	13.50	1501
12.5	51.14	17.36	1671.2
15	51.48	20.84	1825.2

presents the $T_{avg}$, $T_{rip}$, and $F_{avg}$ values obtained from analyses of the left stator as a “single-stator and single-rotor FP-AFSRM” at various current levels.

The comparison of the $T_{avg}$, $T_{rip}$, and $F_{avg}$ values of the proposed FP-AFSRM model with the $T_{avg}$, $T_{rip}$, and $F_{avg}$ values of the “single-stator and single-rotor FP-AFSRM” is presented in

Table 4. The comparison of the proposed double-sided rotor and stator FP-AFSRM model and single-stator and single-rotor FP-AFSRM.

Single-Stator and Single-Rotor FP-AFSRM				Proposed Double-Sided Rotor and Stator FP-AFSRM
Current (Amps)	Trip (%)	Tavg (Nm)	Favg (N)	Current (Amps)	Trip (%)	Tavg (Nm)	Favg (N)	Δ %Trip	ΔTavg (%)	ΔFavg (%)
5	34.82	5.13	956.8	5	4.40	6.63	713.7	−30.42	29.23	−25.4
7.5	43.17	9.56	1305	7.5	4.91	13.03	1025	−38.25	36.26	−21.45
10	48.98	13.50	1501	10	9.63	18.42	1197.2	−39.35	36.43	−20.23
12.5	51.14	17.36	1671.2	12.5	10.06	23.85	1355.6	−41.08	37.32	−18.88
15	51.48	20.84	1825.2	15	10.34	28.52	1503.6	−41.14	36.85	−17.61

.

As seen in Table 4, when the proposed model with a double-stator and single-rotor structure operates as a single-stator and single-rotor, the torque ripple varies between 34.82% and 51.48%. The average torque ranges from 5.13 Nm to 20.84 Nm, while the axial force varies between 956.8 N and 1825.2 N. Although the proposed double-sided rotor and stator FP-AFSRM has twin stators and a single rotor in its design, the two stators are never energized simultaneously. One stator acts as the main stator, while the other functions as an auxiliary stator. When the torque curve produced by the main stator begins to decline, the auxiliary stator is positioned to generate high torque. In the range where the torque curve that is produced by the main stator starts to decline, the auxiliary stator is in a position to produce high torque. At this point, the main stator disengages, and the auxiliary stator, which will produce high torque, enters transmission. Although the proposed motor has a twin stator single rotor structure, it operates in the logic of a single stator and single rotor. Although the proposed model has a single-stator and single-rotor operating logic, it is seen that the torque ripple varies between 4.40% and 10.34%. The average torque value varies between 6.63 Nm and 28.52 Nm and the axial force varies between 713.7 and 1503.6 N. In the overall comparison, the proposed model achieved an increase in the average output torque ranging from 29.23% to 36.85%, and a smoother torque curve with reduced ripple was obtained. Additionally, the axial forces showed an improvement of 17.61% to 25.4%. The flux distribution variation with respect to the force curve for the proposed double-sided rotor and stator FP-AFSRM at 10 amperes is shown in Figure 11.

When examining the flux distributions of the proposed model shown in Figure 11, as also indicated in the graph provided in Figure 6, the flux distribution is only on the main stator and rotor when the left stator is in transmission. Similarly, when the right stator is in transmission, the flux distribution is only on the auxiliary stator and rotor.

5. Conclusions

In this study, the “double-sided rotor and stator FP-AFSRM” structure, which combines the advantages of both the axial structure and the full pitch winding structure, and minimizes the torque ripple and axial forces, is proposed. The proposed model has twin stators and a rotor. However, it has the “single-stator and single-rotor FP-AFSRM” operating logic. Each stator contributes to the output torque separately. Each stator contributes to the output torque at the points where it produces the maximum torque. Only one stator—in other words, one layer—remains in transmission at a time. Due to its operating logic, the twin stator does not have disadvantages, such as the formation of unbalanced axial forces, when angular shifting is performed in models with two air gaps. In addition, although it has the “single-stator and single-rotor FP-AFSRM” operating logic, it does not have a high torque ripple. Magnetostatic analyses of the proposed FP-AFSRM model were performed, and the average torque, torque ripple, and average axial force were investigated. Since the operating logic is “single-stator and single-rotor FP-AFSRM”, magnetostatic analyses were performed by energizing a single layer of the motor and the average torque, torque ripple, and average axial force were examined. Finally, the results from both analyses were compared. The analyses of the proposed FP-AFSRM model showed a reduction in torque ripple percentages by up to “−41.14 (∆%)” compared to the single stator/single rotor configuration, and an improvement in the average output torque by up to “+% 37.32” was obtained. Additionally, the axial force was reduced by up to “−25.4”. As a result, the proposed “double-sided rotor and stator FP-AFSRM” model demonstrated a smoother torque curve with a lower average axial force. The torque ripple ratio, which is a negative aspect of SRMs, is always desired to be minimized. For example, in a layered study conducted by Vahedi et al. on a radial SRM, it was observed that the torque ripple decreased from 155.34% to 43.1% [36]. In the double-sided axial flux SRM, which is similar to the motor proposed by Kermanipour and Ganji in terms of geometric structure, but has a short-pitched winding structure, the rotor poles are given slip angles at certain angles in different directions. In the analysis of the axial SRM with shift angles ranging from 0 to 2.5 degrees, it was observed that the torque ripple varied between 61% and 62% [21]. In an earlier study conducted by Özoğlu et al., the geometric effect of pole heads was investigated. In short-pitched SRMs, improvements of up to 24.1% were observed, while fully pitched SRMs also showed improvements of up to 24.1% [44].