Principles and Analysis of a Novel Switched Reluctance Motor with Radial Offset Angle

Abstract

Due to the double salient pole structure and the pulse discontinuous current excitation mode, the torque ripple of the traditional switched reluctance motor (SRM) is large in its commutation process and is easy to cause vibration and noise, which has become a bottleneck problem hindering its development. Based on the in-depth analysis of the influence of winding inductance and other factors on torque ripple, a novel switched reluctance motor with radial offset angle is proposed here. Its structural characteristics and operating principles are described, and winding excitation rules are designed. The motor has an inner stator and an outer stator which are radially staggered at a certain angle. Each inner stator pole is wound with an auxiliary winding, which is responsible for providing auxiliary torque to compensate for the torque drop during the commutation of main windings, so as to achieve the purpose of restraining torque ripple. The magnetic field characteristics are verified by finite element simulation. Based on the field-circuit joint simulation of Maxwell and Simplorer, the current chopping control system of the novel switched reluctance motor is constructed, and the simulation results show that after the auxiliary windings are put into use, the torque ripple coefficient of the motor can decrease from 1.326 to 0.494, and the torque ripple suppression effect is obvious.

Keywords

novel switched reluctance motor radial offset angle structural improvement torque ripple suppression finite element analysis joint simulation

Introduction

With the increasing shortage of traditional energy and the increasing global emphasis on environmental protection, new energy has developed rapidly, which makes research on energy storage technology crucial. Flywheel batteries have attracted widespread attention of scholars due to their advantages such as high-power density, no chemical pollution, and fast charging and discharging. Switched reluctance motors are suitable for use in flywheel energy storage systems due to their simple and robust structure, high efficiency, stability, and suitability to work under harsh environmental conditions (Song et al., 2013; Sun et al., 2018). However, the problem of large torque ripple has been affecting the further promotion and application of SRMs in this field.

Researchers mainly focus on the improvement of motor structure and the optimization of control strategy to suppress motor torque ripple. Among them, experts and scholars have successively proposed many schemes in terms of motor structure improvement. In reference (Li et al., 2012), a scheme of slotting on one side of the rotor poles is proposed, which can effectively suppress the torque ripple and noise during the unidirectional rotation of the rotor. In reference (Zhou et al., 2021), a scheme of simultaneous slotting on the stator and rotor is proposed, and the optimal slotting size is determined by multi-objective optimization, and the simulation results show that this scheme can effectively suppress torque ripple, but this scheme has certain effects on the mechanical strength and efficiency of the motor. In addition to suppressing torque ripple by slotting on the core, reference (Zhang et al., 2020) studies the effect of different rotor tooth shapes on the suppression of torque ripple, and finally conclude that the T-shaped rotor tooth with pole shoe can well reduce the radial force wave and increase the tangential force wave to achieve the purpose of suppressing torque ripple. Reference (He et al., 2021; Li et al., 2018; Liu et al., 2019) analyze the effects of different structural parameters on torque ripple, such as stator/rotor pole arc, stator/rotor yoke thickness and air gap width, then use different optimization algorithms to compute the optimal structural parameters of the motor.

In addition to motor structure improvement, control strategy optimization is also an effective way to suppress torque ripple. Currently, some advanced techniques have been applied to the control of SRMs, such as direct torque control, torque distribution control, and intelligent control. On the basis of direct torque control, reference (Yang et al., 2022) cancels the torque hysteresis control, and uses fuzzy controller to reduce the error between the instantaneous torque and the given torque, and obtain a good suppression effect on the torque ripple. In reference (Cai et al., 2022), a new DITC method is proposed, where the conduction period is divided into regions according to the inductance change rule of the motor winding, and proper hysteresis strategies are designed for each region based on the output torque capacity changes. Hence, the internal hysteresis loop of the motor phase with large output torque capacity is used to adjust the torque error in the whole conduction cycle, and the torque ripple of SRM is further reduced. Reference (Hu et al., 2023) proposes a torque distribution function based on interval segmentation, in which, the excitation capability of the incoming phase and the torque tracking capability of the outgoing phase are fully utilized in the first interval, and torque tracking ability of the incoming phase and demagnetization ability of the outgoing phase are fully taken advantage of in the second interval. In reference (Chen et al., 2022), with a proposed predictive fuzzy control method, which predicts the conduction current value in advance, not only the torque ripple falls, but also the efficiency of the motor can be improved.

The aforementioned conventional methods for enhancing the structure of SRMs primarily focus on refining the stator and rotor structures. While these approaches are effective in minimizing torque ripple, they may compromise the mechanical robustness of the motor due to factors like slotting and opening. In contrast, the novel motor structure introduced in this article offers a solution that mitigates torque ripple without encountering the aforementioned issues related to mechanical strength. In this paper, the causes of torque ripple in SRMs are analyzed and a new type of SRM with radially offset angle is proposed from the aspect of motor structure improvement. The motor has two stator cores with radial offset angle. The auxiliary windings on the inner stator poles are responsible for providing auxiliary torque to compensate for the torque drop during the commutation of main windings, thus suppress the torque ripple. Based on the field-circuit coupling joint simulation of Maxwell and Simplorer, the current chopping control system of this novel switched reluctance motor is constructed, and the simulation results confirm that the double-stator with radial offset angle structure can effectively suppress the torque ripple.

Torque Characteristic Analysis of Traditional SRM

In traditional SRM, the magnetic flux is closed along the path with minimum magnetic reluctance. When rotor pole is not aligned with stator pole, the magnetic field will be distorted, which can generate the tangential magnetic tension that drives the rotor to rotate. The magnitude of the electromagnetic torque generated in the rotating process is not constant under the excitation current of a fixed value. The mathematical model of traditional SRM can be divided into three parts, that is, circuit equation, mechanical equation and electromechanical linkage equation.

When the winding resistance is ignored, the winding voltage equation can be expressed as:

U_{k} = \frac{d ψ_{k} (i, θ)}{d t}

(2.1)

Where, U_k represents the terminal voltage of phase k; ψ_k(i,θ) represents the flux linkage of phase k; i and θ are the current and rotor position angle respectively. The magnitude of winding flux linkage is related to the value of the current flowing through the winding and the rotor position θ.

According to the laws of mechanics, the mechanical equation of motion can be expressed as:

T_{e} = J \frac{d^{2} θ}{d t^{2}} + D \frac{d θ}{d t} + T_{L}

(2.2)

Where T_e represents electromagnetic torque; T_L represents load torque; J represents rotational inertia; and D represents friction coefficient.

In the electromechanical linkage equation, according to the principle of energy conservation, the electrical energy input to the motor is equal to the sum of magnetic storage energy and magnetic co-energy. Where, the magnetic co-energy W_c can be expressed as:

W_{c} = \int_{0}^{i} ψ (i, θ) d i

(2.3)

According to the circuit theory, the flux linkage ψ=Li. When the mutual inductances are considered, the flux linkage matric can be written as:

[\begin{matrix} ψ_{a} \\ ψ_{b} \\ ψ_{c} \end{matrix}] = [\begin{matrix} L_{aa} & M_{ab} & M_{ac} \\ M_{ba} & L_{bb} & M_{bc} \\ M_{ca} & M_{cb} & L_{cc} \end{matrix}] [\begin{matrix} i_{a} \\ i_{b} \\ i_{c} \end{matrix}]

(2.4)

Where ψ_a, ψ_b, ψ_c are the winding flux linkage of phase A, B and C respectively; L_aa, L_bb, L_cc are the winding self-inductance of phase A, B and C respectively; M_ab, M_ac, M_ba, M_bc, M_ca, M_cb are the winding mutual inductance between phase A, B and C.

Substitute equation (2.4) into equation (2.3) to obtain:

W_{c} = \frac{1}{2} L_{aa} i_{a}^{2} + \frac{1}{2} L_{bb} i_{b}^{2} + \frac{1}{2} L_{cc} i_{c}^{2} + i_{a} i_{b} M_{ab} + i_{b} i_{c} M_{bc} + i_{c} i_{a} M_{ca}

(2.5)

It is known from the electromechanical energy conversion law that ΔW_m= T_eΔθ, where ΔW_m represents the change of mechanical energy, whose value is equal to the change of magnetic co-energy ΔW_c. When the change of rotor position angle Δθ is small, the current can be considered constant, and the electromagnetic torque T_e can be expressed as:

T_{e} = \frac{\partial W_{c}}{\partial θ}

(2.6)

Substitute equation (2.5) into equation (2.6) to obtain:

T_{e} = \frac{1}{2} i_{a}^{2} \frac{d L_{aa}}{d θ} + \frac{1}{2} i_{b}^{2} \frac{d L_{bb}}{d θ} + \frac{1}{2} i_{c}^{2} \frac{d L_{cc}}{d θ} + i_{a} i_{b} \frac{d M_{ab}}{d θ} + i_{b} i_{c} \frac{d M_{bc}}{d θ} + i_{c} i_{a} \frac{d M_{ca}}{d θ}

(2.7)

Neglect the coupling among different phases. If the windings of a certain phase are energized with a constant current, the electromagnetic torque will be proportional to the slope of the inductance relative to θ. The smaller the change of inductance slope, the smaller the torque ripple.

Under ideal condition, the relationship between the inductance of the winding and θ is linear, but after considering the magnetic flux edge effect and magnetic saturation effect, this relationship is not ideal linear. Figure 1 shows the L-i-θ curves and the T_e-i-θ curves of phase A for a traditional three-phase 12 / 8 pole SRM, in which, 0^o represents the position where the stator poles of phase A are completely aligned with the rotor poles. It can be seen from Figure 1(a) that the phase inductance L starts to rise at the position where the stator poles of phase A and the rotor poles are completely out of alignment, and the slope of the inductance curve changes from positive value to negative value before and after the position where θ is 0^o. It can be seen from Figure 1(b) that there exists obvious ripple phenomenon of phase A torque T_a within a complete rotor pole pitch angle. Especially before and after the positon where θ is 0^o, the torque changes from positive to negative.

Figure 1.

Static characteristic curves of three-phase 12/8 SRM.

Topology and Operating Principle of the Novel SRM

Topology of the Novel SRM

The basic structure of the novel SRM is shown in Figure 2. The outer stator, the inner stator and the rotor are concentrically nested. The main poles and the auxiliary poles are radially offset by a certain angle. The main poles are wound with main windings and the auxiliary poles are wound with auxiliary windings. There is no winding on the salient poles of the rotor.

Figure 2.

Topology of the novel SRM.

The core structure of the novel SRM is shown in Figure 3. For rotor core, the centerline 1 of the outer salient pole and the centerline 1′ of the inner salient pole are not aligned, and are radially offset by an angle which is defined as “rotor pole offset angle” and is recorded as α. The centerline 2 of the main pole A1 and the centerline 2′ of the auxiliary pole a1 are also not radially aligned, and there exists a radial offset angle between them which is defined as “stator pole offset angle” and is recorded as β.

Figure 3.

The structure of rotor core and stator core.

The windings are distributed as shown in Figure 4(a) and 4(b). On the outer stator, there are twelve main poles in total, which are separately recorded as A1∼A4, B1∼B4, C1∼C4. The main windings on A1∼A4 are connected in series to form phase A. The distribution of Phase B and phase C are similar to phase A. On the inner stator, there are twelve auxiliary poles in total, which are separately recorded as a1∼a4, b1∼b4, c1∼c4. The auxiliary windings on a1∼a4 are connected in series to form phase a. The distribution of Phase b and phase c are similar to phase a. (Except for phase A and phase a, the connecting wirings of other phases are omitted in the figures).

Figure 4.

Winding distribution of the novel SRM.

Compared to SRM, the novel SRM is more complex in structure and occupies more space due to the addition of internal stator and auxiliary windings, resulting in increased manufacturing costs.

Operating Principle of the Novel SRM

During the operation of this motor, the outer salient poles of the rotor interact with the main poles, and the inner salient poles of the rotor interact with the auxiliary poles, which both form periodically changing air gap reluctance. Take the counter clockwise rotation of the rotor as an example, assuming that its initial position is as shown in Figure 5(a), the leading edge of the outer salient pole 3 is exactly aligned with the trailing edge of the outer stator main pole A1, at this time the main windings of phase A start to conduct. When the outer salient pole 3 rotates to position 2, assuming its rotation angle is $λ \circ$ , as shown in Figure 5(b), at this position, the auxiliary windings of phase a start to conduct, which can generate auxiliary torque. Then the rotor continues to rotate, and when it rotates to position 3, assuming that its rotation angle is $γ \circ$ , as shown in Figure 5(c), at this time, the windings of phase A are turned off and the windings of phase B are turned on, so that the magnetic lines of phase B are distorted to produce electromagnetic torque. At position 3, the leading edge of the outer salient pole 5 is just aligned with the trailing edge of the main pole B1. Therefore, when the motor rotates for $λ \circ$ again, the auxiliary windings of phase a are switched off and the auxiliary windings of phase b are switched on. During the commutation of phase A to phase B, the auxiliary windings of phase a provide auxiliary torque to compensate for the torque drop. Therefore, at the current initial position, if the rotor is to rotate counterclockwise, it is necessary to ensure that the windings are energized in the sequence of A-a-B-b-C-c. On the contrary, if the motor is to rotate clockwise, it is necessary to ensure that the windings are energized in the sequence of A-c-C-b-B-a.

Figure 5.

Several special positions.

The power converter of the external driving circuit of the novel SRM adopts an asymmetric half-bridge structure, which is convenient to control the on/off of each phase windings. Since the main windings and the auxiliary windings of the novel SRM are independent of each other, and each of them contain three phase windings, thus a total of 12 IGBT switches are required, which are divided into six groups, and each group individually controls the on/off of one phase windings. As shown in Figure 6, taking phase A as an example, when both V1 and V2 are conductive, the DC power supply is applied to phase A windings through V1 and V2; When V1 and V2 are both turned off, the phase A windings feedback electric energy to the DC power supply through the freewheeling diodes D1 and D2. The control rules of the rest windings are similar to those of phase A.

Figure 6.

The Power converter for Phase A.

Due to the addition of auxiliary windings, the switching devices used in the power converter of this novel SRM will double, and the control strategy will also become more complex.

Figure 7.

Winding excitation rules.

Winding Excitation Rules

In order to reduce the ripple of the synthesis torque of the motor, the excitation rules of the windings are preliminarily formulated, as shown in Figure 7. Figure 7(a) and Figure 7(b) respectively show the excitation rules when the motor needs to generate positive torque and negative torque. The vertical axis represents the on/off state of each phase windings, where high level represents ‘on’ and 0 level represents ‘off’. Take the case that the motor generates positive torque as an example, the commutation process from phase A to phase B is described in detail as follows. Turn off phase A and turn on phase B at the position angle 0^o. In order to ensure that no large torque drop will occur when phase A is turned off, thus phase a is turned on at the position angle −3.75^o in advance and continues to conduct until the position angle reaches 3.75^o. At the position angle 3.75^o, since phase B has experienced the current rising period, so phase a can be turned off. The commutation process from phase B to phase C, and that from phase C to phase A are also similar, that is, phase b and phase c are respectively used to provide auxiliary torque. When the motor needs to generate negative torque, the turning-on angle of each phase is delayed by 15°

Figure 8.

Inductance and torque characteristics of the novel SRM.

Basic Electromagnetic Characteristics Analysis of the Novel SRM

A finite element model of the novel SRM is established based on Ansoft/Maxwell2D. The inductance, torque and magnetic flux distribution of this motor are analyzed at different position angles, and the main parameters of the motor are shown in Table 1.

Self-inductance Curves

The relationship between the torque and the slop of the inductance relative to the position angle has been introduced theoretically. In this part, to further simulate the torque during the actual operation of the motor, the relationship between the phase inductance and rotor position angle, and the relationship between the torque of each phase and rotor position are obtained through finite element simulation, as shown in Figure 8(a) and Figure 8(b), respectively. During the simulation, keep the current of the main windings and the auxiliary windings equal, and the rotor rotates counterclockwise.

Figure 9.

Distribution of magnetic lines of the novel SRM.

From Figure 8(a), it can be seen that the self-inductance curves of phases A, B and C differ by 15° in turn, and the self-inductance curves of phases a, b and c also differ by 15° in turn. Meanwhile, the self-inductances of the A-phase, B-phase, and C-phase main windings differ by 7.5° in turn from the self-inductances of the a-phase, b-phase, and c-phase auxiliary windings. These characteristics are determined by the core structure of the motor.

From Figure 8(b), it can be seen that the torque generated by the main windings is larger than the torque generated by the auxiliary windings. The main windings and the auxiliary windings of each phase generate positive torque in the period when the corresponding phase inductance rises with the variation of θ, and generate negative torque in the period when the corresponding phase inductance falls with the variation of θ.

Magnetic Lines Distribution

For the novel SRM, the magnetic circuit is changed compared to the normal SRM because the inner stator is added. Figure 9(a) and Figure 9(b) respectively show the distribution of magnetic lines when only the main windings of phase A are excited and only the auxiliary windings of phase a are excited.

Figure 10.

Self-inductance and mutual-inductance curves.

It can be seen from Figure 9 that when only the main windings are excited, the distribution of magnetic lines is similar to that of the traditional SRM. At this time, the magnetic lines pass through the outer stator, the air gap, the rotor, and then reach the adjacent windings of the energized phase. During this process, the magnetic lines generated by main windings do not pass through the inner stator. When only the auxiliary windings are excited, the distribution of the magnetic lines is similar to that of the SRM with inner stator and outer rotor. At this time, the magnetic lines pass through the inner stator, the air gap, the rotor, then reach the adjacent windings of the energized phase. The magnetic lines generated by auxiliary windings do not pass through the outer stator. Therefore, the distribution of the magnetic lines generated by the main windings are independent of that generated by the auxiliary windings.

Mutual-Inductance Curves

In order to better verify that the inner stator and the outer stator of the novel SRM are structurally decoupled, the mutual inductance between phase A and phase C, and the mutual inductance between phase A and phase a are calculated through finite element simulation, then compared with the self-inductance curves of phase A and phase a as shown in Figure 10.

Figure 11.

Starting position of the arc added.

As can be seen from Figure 10, M_AC is the mutual inductance between phase A and phase C on the outer stator. M_Aa is the mutual inductance between phase A on outer stator and phase a on inner stator. M_AC is close to zero, and M_Aa is smaller than M_AC. Therefore, M_Aa can be ignored, which indicates that the inner stator and the outer stator of the novel SRM are structurally decoupled.

Magnetic Density Analysis

When the magnetic lines pass through the air gap, the air gap magnetic density is generated, which can be decomposed into two components in radial and tangential directions. The radial component generates radial force, while the tangential component generates electromagnetic torque.

As analyzed in Section 3.3, the new SRM may operate under two-phase conduction conditions. In order to implement the control strategy in the following text, it is necessary to verify the decoupling between the main windings and auxiliary windings. In this section, the decoupling of the main windings and the auxiliary windings of the novel SRM will be further validated from the perspective of magnetic density analysis.

Select the middle point between the position shown in Figure 5(b) and Figure 5(c) as rotor position angle, as shown in Figure 11. Add a circle of circular arc in the air gap between the rotor and the outer stator, and use the position shown in Figure 11 as the starting point of this arc. Compare the tangential air gap magnetic density when only the A-phase windings are subjected to 5A excitation current with that when both the A-phase and a-phase windings are subjected to 5A excitation current simultaneously, as shown in Figure 12. The horizontal axis represents the relative angle between the added point on the arc and the initial position, called “arc position angle”, denoted as δ. It can be seen that the tangential air gap magnetic density under these two excitation modes almost coincides, indicating that the excitation of the a-phase auxiliary windings will not have an impact on the tangential air gap magnetic density generated by the A-phase main windings.

Figure 12.

Tangential magnetic density analysis.

The radial component of magnetic density generates radial forces. In traditional switched reluctance motors, windings are symmetrically excited, and the radial magnetic flux generated is symmetrical with each other, so the radial force is balanced. Still select the middle point between the position shown in Figure 5(b) and Figure 5(c) as rotor position angle, then compare the radial air gap magnetic density when only the A-phase windings are subjected to 5A excitation current with that when both the A-phase and a-phase windings are subjected to 5A excitation current simultaneously, as shown in Figure 13. It can be seen that the radial air gap magnetic density curves under the two excitation conditions almost coincide, so it can be concluded that the radial magnetic density of phase A and phase a do not affect each other.

Figure 13.

Radial magnetic density analysis.

Field-Circuit Joint Simulation of the Novel SRM

Control Principle

In order to better analyze the torque ripple during the dynamic operation of the motor, the joint simulation method of Simplorer and Maxwell are adopted to link the finite element model of the motor built in Maxwell with the external current chopping control (CCC) circuit built in Simplorer. The control principle block diagram is shown in Figure 14.

Figure 14.

Control principle block diagram.

It can be seen from Figure 14 that the control system is composed of several modules such as speed outer loop, current inner loop, position detection, current detection, power converter and the novel SRM. When the motor is working, the expected rotation speed n_ref is given and compared with the actual rotation speed n. The current reference signal i_ref are obtained by the PI controller, and compared with the current detected by the current detector, then the error is sent to the hysteresis comparator to limit the current amplitude within a certain range. In addition, the rotor position angle is detected by the position sensor, then which phase should be excited is determined according to the winding excitation rules formulated above. The output signals of the winding excitation rule module and the current hysteresis comparator are superimposed to control the gate signals of the IGBTs in power converters for main windings and auxiliary windings.

Simulation Results and Analysis

Set the total simulation time as 30 ms, the motor rotating speed as 1000 rpm, and the load torque as 6N·m. The speed waveform is shown in Figure 15, which shows that the speed can be maintained at 1000 rpm under the control modes introduced in Section 5.1.

Figure 15.

Speed waveform.

In order to compare the effect of the auxiliary windings on the main windings, the current and torque waveforms are further given under the state that only the main windings are excited and the auxiliary windings combined with the main windings are excited, as shown in Figure 16 and Figure 17 respectively. As can be seen from Figure 16(a), when the auxiliary windings are not put into use, only the main windings of phase A, B, and C are turned on in turn, and the chopping current value is 6A.

Figure 16.

Current waveforms.

Figure 17.

Torque waveforms.

As can be seen from Figure 16(b), when the main windings and the auxiliary windings are excited together, during each operating cycle, the main windings and auxiliary windings conduct in the order of A-a-B-b-C-c. The chopping current values of the main windings and the auxiliary windings are 6A and 3A respectively. These characteristics are consistent with the winding excitation rules introduced in Section 3.3.

It can be seen from Figure 17(a) that when the auxiliary windings are not used, the motor has a large torque drop in the commutation process of the main windings, during which the maximum torque is 7.96N·m, the minimum torque is −0.2N·m, and the average torque is 6.15N·m.

It can be seen from Figure 17(b) that when the auxiliary windings and the main windings are used together, the drop of the resultant torque in the commutation process of the main windings can be significantly reduced. Under this operation mode, the maximum output torque is 8.23N·m, the minimum torque is 5.11N·m, and the average torque is 6.32N·m.

In order to better describe the torque ripple, the torque ripple coefficient is defined as a reference indicator and its expression is:

K_{rip} = \frac{T_{max} - T_{min}}{T_{avg}}

(5.1)

Where,

T_{max}

is the maximum torque;

T_{min}

is the minimum torque;

T_{avg}

is the average torque.

The larger the value of K_rip, the more serious the torque ripple. Through calculation, it can be concluded that when only the main windings are used, K_rip is 1.326; when the main and auxiliary windings are jointly used, K_rip is 0.494. It can be seen from the comparison that the torque provided by the auxiliary windings can effectively compensate for the torque ripple during the commutation of the main windings.

As shown in Table 2, several structural optimization schemes for switched reluctance motors aimed at reducing torque ripple in recent years are listed. Specifically, these schemes include optimizing the overall structural dimensions of the motor, and improving the stator poles and/or rotor poles. It can be seen that the optimization of the structure has remarkable effects in suppressing torque ripple in switched reluctance motors.

Table 1.

Main Parameters of the Novel SRM.

Parameter	Value
Outer diameter of outer stator (mm)	106
Inner diameter of outer stator (mm)	76
Thickness of outer stator yoke (mm)	7.5
Outer diameter of inner stator (mm)	33.4
Inner diameter of inner stator (mm)	12
Thickness of inner stator yoke (mm)	5.7
Outer diameter of rotor (mm)	75.4
Inner diameter of rotor (mm)	34
Thickness of outer salient pole yoke of rotor (mm)	6.7
Thickness of inner salient pole yoke of rotor (mm)	4
Pitch angle of rotor (°)	45
Pitch angle of stator(°)	45

Table 2.

Comparison of Different Improvement Schemes.

Improvement Methods	Torque Ripple Coefficient Before Improvement	Torque Ripple Coefficient After Improvement
Stator with symmetric eccentric pole face (Liu et al., 2019)	0.835	0.8261
Rotor poles with bilateral grooves (Liu et al., 2019)		0.8260
A new SRM with symmetric eccentric pole face of the stator and bilateral grooves on the rotor pole (Liu et al., 2019)		0.107
Both the stator poles and rotor poles are equipped with pole shoes on one side, and slots are opened at the top of the rotor poles on the other side where no shoes are installed. (Li et al., 2018)	0.616	0.132
Comprehensive optimization of body structure parameters (Chen et al., 2020)	1.256	0.842
The stator poles are equipped with polar shoes on one side, and slots are opened on both sides of the rotor poles. (Zheng & Zhang, 2020)	2.740	1.250
A new type of stator pole surface (the air gap is designed as a two-section non-uniform structure) (Zhang et al., 2017)	1.021	0.693
Stator with pole shoes with 90°wedge angle on both sides Both sides of the stator poles are equipped with pole shoes, and the wedge angle is 90^o. (Kong et al., 2018)	1.366	1.2118
Stator with pole shoes with 90°wedge angle on both sides Both sides of the stator poles are equipped with pole shoes, and the wedge angle is 45^o. (Kong et al., 2018)	1.366	1.1126
The novel SRM introduced in this paper	1.326	0.494

In reference (Liu et al., 2019), a new SRM with symmetric eccentric pole face of the stator and bilateral grooves on the rotor pole is studied. When only the stator is improved, the torque ripple coefficient can decrease from 0.835 to 0.8260. When only the rotor is improved, the torque ripple coefficient can decrease from 0.835 to 0.8261, with similar effects. When these two kinds of optimization methods are utilized simultaneously, the torque ripple coefficient can decrease from 0.835 to 0.107, resulting in a better outcome.

The purpose of adding pole shoes to stator and rotor is to increase the pole arc, change the path of magnetic flux, alleviate the edge magnetic flux effect and the saturation degree, thus the torque drop during commutation can be fundamentally alleviated and the motor can operate smoothly. In reference (Li et al., 2018), both the stator poles and rotor poles are equipped with pole shoes on one side. In order to maintain the same winding commutation angle and effective rotor pole arc as the motor before the structural improvement, slots are opened on the top of the rotor pole without pole shoes. As a result, the torque ripple coefficient can decrease from 0.616 to 0.132. In reference (Zheng & Zhang, 2020), the stator poles are equipped with polar shoes on one side, and slots are opened on both sides of the rotor poles. As a result, the torque ripple coefficient can decrease from 2.740 to 1.250. In reference (Kong et al., 2018), pole shoes are added to both sides of the stator poles. When the wedge angle of the pole shoes is 90 degrees, the torque ripple coefficient can decrease from 1.3666 to 1.2118; when the wedge angle is 45 degrees, the torque ripple coefficient can decrease from 1.3666 to 1.1126.

In reference (Chen et al., 2020), it is stated that an increase in the rotor outer dimension leads to an increase in torque ripple, while an increase in the stator outer dimension can effectively reduce torque ripple. When the core length is too long or too short, torque ripple increases, so it must be kept within a reasonable range. Increasing the stator pole arc within a reasonable range can effectively reduce torque ripple when the rotor pole arc is also within a reasonable range. The number of turns in the winding and the thickness of the stator and rotor yokes have little effect on torque ripple. Different motor size parameters have different effects on torque ripple, and there are complex coupling relationships between them. Only through comprehensive optimization analysis of size parameters can the minimum torque ripple be ensured.

In order to suppress the torque ripple in SRM, a new stator pole shape is proposed in reference (Zhang et al., 2017). It changed the traditional uniform air gap into non-uniform air gap of two sections. By creating an uneven air gap, the torque ripple coefficient decreased from 1.021 to 0.693, and effective suppression of torque ripple can be achieved while ensuring that the motor efficiency remains basically unchanged.

The radial magnetic density has been analyzed in Section 4.4 of the previous text. In this section, the radial force of the motor during operation is further verified, as shown in Figure 18. Figure 18(a) shows the radial force in x-axis direction, with a fluctuation range of only ± 12 mN. Figure 18(b) shows the radial force in y-axis direction, which only fluctuates within the range of ±15 mN. It can be seen that the radial forces in both directions are very small, and the motor can operate stably in the radial direction.

Figure 18.

Radial force waveforms.

Conclusion

Aiming at the problem of large torque ripple of SRM, the motor structure is improved in this paper. By adding an inner stator on the basis of traditional SRM and setting a fixed radial offset angle between the inner stator and the outer stator, a novel SRM with radial offset angle is proposed. The basic electromagnetic characteristics of this motor are analyzed by applying finite element method, and the winding excitation rules are preliminarily designed. The current chopping control of the motor is carried out based on the field-circuit joint simulation of Simplorer and Maxwell. The simulation results confirm that the torque provided by the auxiliary windings can effectively compensate for the torque drop during the commutation of the main windings, and achieve the purpose of suppressing the torque ripple of the motor.

Due to the addition of internal stator and auxiliary windings, the motor structure, power converter, and control strategy will become more complex, and the cost will increase. However, in some cases where there are strict restrictions on torque pulsation and vibration noise, it has higher application value. In addition, the combination of six phase windings will facilitate the introduction of more advanced and flexible control methods, thereby further improve torque performance.

Footnotes

Acknowledgements

This work was sponsored in part by the Key Research and Development Program of Jiangsu Province under Grant BE2021094, National Natural Science Foundation of China under Grant 51877101 and 51977103, and Nanjing Institute of Technology Research Fund under Grant YKJ202208.

ORCID iD

Yunhong Zhou

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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