Structural Multi-Tooth Modification of Hybrid-Excited Doubly Salient Dual-PM Machine for Torque Production Improvement

Abstract

A hybrid-excited doubly salient dual-PM machine (HE-DSDPM) was presented by using the structural multi-tooth modification for an improvement of torque production. The multi-tooth structure modification of HE-DSDPM was clearly described. The PM and stator arcs were further examined for structural optimization. The electromagnetic performance including magnetic flux distribution, flux linkage, back-electromotive force (back-EMF), total harmonic distortion (THD), cogging torque and electromagnetic torque, was investigated with various field current under the same structural constraint. The simulation based on 2-D finite element analysis was used to validate all electromagnetic performance. The results showed that the proposed multi-tooth HE-DSDPM provides the best stator/rotor combination, the appropriate PM characteristics and the enlarged winding slot area. This proposed structure produces better overall electromagnetic performance because of its improved symmetrical magnetic flux path and greater flux regulation quality. In particular, it can generate a larger average torque of 26.18% with the lower ripple torque of about 4% compared to the conventional structure at no field current since the good back-EMF profile and low cogging torque. The largest variance of the torque percentage is occurred when excited by different field currents for the proposed multi-tooth HE-DSDPM. Hence, modification of multi-tooth structure could be beneficial in the electrical machine design of other types of doubly salient structures.

1. Introduction

Permanent magnet (PM) machines produce high magnetic field, torque density and efficiency due mainly to their structures without coil excitation [1,2]. Several studies of these machines have investigated developing their performance for many years [3,4]. In particular, the PM machines, in which the magnet is placed in the stator region, are called stator-PM machines and these have been proposed to be beneficial for efficient wide-speed-range operation because of the lightweight rotor with no winding coil and brushes [5,6]. Based on this advantage, the stator-PM machines have been developed for many applications, such as renewable energy generators, electric vehicle motors, maglev trains and electrical aircraft [7,8,9,10].

Such machines have been categorized into three popular types according to different PM positions, namely the flux reversal PM machine (FRPM), flux switching PM machine (FSPM), and doubly salient PM machine (DSPM).

The FRPM type has the PM addressed at the stator tooth tip [11]. Its research studies have discovered that the structure of the FRPM helps cogging torque reduction due to an improved working airgap flux density harmonic and is appropriate to operate over a high-speed range due to the high number of rotor poles [12]. The FSPM includes the PM installed at the stator tooth. This structure exhibits a bipolar magnetic flux path, resulting in high torque density [13]. Most reviews related to the FSPM operation have identified torque capability improvement for several applications [14].

In addition, the DSPM with the PM mounted in the stator yoke has been of considerable interest because it has many notable merits over other stator-PM machines, such as an uncomplicated structure, effective cooling and a direct drive [15,16,17]. Especially, several literature reviews of the DSPM structure have noted that it is suitable for low-speed operation because of its wide-diameter configuration [18,19]. These properties result in high back-electromotive force (back-EMF), reliability and torque production [20]. However, the DSPM has suffered the trapezoidal waveform of the back-EMF due to asymmetrical magnetic flux path in the machine structure, which severely impacts on torque production [21,22].

The magnetic field excitation combined between the PM and field coil has been contained in the hybrid-excited (HE) machine. Its structure is helpful in reducing the risk of demagnetization for PM pieces because of the dc current excitation in the field coil [23]. Good flux control is achieved in this machine to improve the flux regulation quality and magnetic flux path [24]. Thus, the HE functions can be an important choice in order to fix the aforementioned non-sinusoidal back-EMF of the DSPM [25,26].

Recently, a hybrid-excited dual-PM has been utilised in the DSPM structure (HE-DSDPM) to receive a sinusoidal back-EMF with a symmetrical magnetic flux path and better torque production than traditional DSPM [27]. Figure 1a shows the main structural components of the HE-DSDPM, including the stator part with dual-PM and armature winding and the rotor part with the salient lightweight poles. The magnetic field in this machine can be excited by the dual-PM and the armature winding using an innovative dc-biased sinusoidal current [28]. The dual-PM contains the PM at the slot opening and another one at the stator yoke to produce a strong supplemental magnetic flux, as inspired by the combination of a slot-PM machine and a biased-flux PM machine [29,30]. The innovative dc-biased sinusoidal current injected in the armature winding can be divided into ac-armature current and dc-excited current. The ac-armature current is used to produce the rotating armature field, while the dc-excited current is used for magnetic flux regulation [31]. The dc-biased sinusoidal current utilizes only one winding coil set for copper loss reduction, as introduced by [32].

Nevertheless, the torque characteristics produced by the HE-DSDPM are still unsatisfactory compared to those produced by other stator-PM machines due to its limitation issue of the configuration such as for the stator and rotor topologies, PM characteristics and slot area of the winding coil [33].

To solve this problem and further improve torque production, structural modification by using the multi-tooth technique seem a good candidate. The structural multi-tooth modification is a helpful solution in adjusting the stator/rotor combination, adapting the PM characteristics and enlarging the slot winding area in the electrical machine. This modification of structure also results in an increase in torque density and the reduction of the ripple torque [34]. Many literature reports presented the simulation design of the stator-PM machines using the structural multi-tooth modification for effective torque production, such as the multi-tooth technique utilised in FSPM for torque capability improvement, the analytical structure of an alternative multi-tooth FSPM for high torque density, the structural simulation of several FSPM types to study electromagnetic performance, and a theoretical study between multi-tooth and V-shaped FSPM to improve torque production [35,36,37,38]. Furthermore, multiple research reviews related to utilising the multi-tooth technique in HE machines, such as the design of the multi-tooth HE-FSPM for EV propulsion, the innovation of multi-tooth HE motors for torque enhancement and the investigation of the influence of stator/rotor and PM combinations in a HE-FRPM on electromagnetic performance [39,40,41].

This paper aims to modify the structure of the HE-DSDPM using the multi-tooth technique to improve torque production. The structural modification using the multi-tooth technique of HE-DSDPM is explained in the detail. The influence of PM and stator arcs on torque production, including slot opening PM arc, θ_sp, stator yoke PM arc, θ_yp, stator tip arc, θ_st, and stator teeth arc, θ_t, is considered by optimization to obtain the optimal structure of the multi-tooth HE-DSDPM. Electromagnetic performance is examined based on magnetic flux distribution, flux linkage, back-EMF, total harmonic distortion (THD), cogging torque and electromagnetic torque with different current excitation and then compared to a conventional HE-DSDPM. All electromagnetic results are studied using the 2-D finite element analysis (FEA).

2. Structural Multi-Tooth Modification of HE-DSDPM

As shown in Figure 1a, the conventional HE-DSDPM with 12/10 (stator teeth/rotor pole) was initially proposed by Y. Meng [33]. Regarding the outstanding properties of this conventional structure as mentioned in the introduction, the structural modification of HE-DSDPM using a multi-tooth technique for torque production enhancement is presented, as inspired by F. R. Wei [41].

Based on the HE with dual-PM properties, even with the structural modification, its appearance resembles the HE-DSDPM. The dual-PM comprises the slot opening PM and the stator yoke PM as the source of the magnetic field in the machine. The slot opening PM acts as the main source, while the stator yoke PM regulates the magnetic flux production. The armature winding is utilized for excitation by a dc-biased sinusoidal current, divided into the ac-armature current for the production of the rotating armature field and the dc-excited current for regulation of the magnetic flux. The three-phase dc-biased sinusoidal current is expressed by

$$\begin{array}{l}{I}_{A1}=\sqrt{2}{I}_{ac}sin(2\pi ft)+I_{dc}\\ I_{A2}=\sqrt{2}{I}_{ac}sin(2\pi ft)-I_{dc}\\ I_{B1}=\sqrt{2}{I}_{ac}sin(2\pi ft-2\pi /3)+I_{dc}\\ I_{B2}=\sqrt{2}{I}_{ac}sin(2\pi ft-2\pi /3)-I_{dc}\\ I_{C1}=\sqrt{2}{I}_{ac}sin(2\pi ft-4\pi /3)+I_{dc}\\ I_{C2}=\sqrt{2}{I}_{ac}sin(2\pi ft-4\pi /3)-I_{dc}\end{array}$$

(1)

where I_ac is the root-mean-square, rms, of the ac-armature current, I_dc is the dc-excited current, f is the electrical frequency.

In this work, the stator/rotor combination of the HE-DSDPM is modified for the addition of a multi-tooth technique. The possibility of a stator/rotor combination can be expressed by

$$N_r=\left(n\times N_s\right)+1$$

(2)

where N_r is the number of rotor poles, N_s is the number of stator poles, and n is the number of stator teeth.

Figure 1b shows the cross-section perspective of the HE-DSDPM with the multi-tooth structure. Its structure consists of the 6 big stator poles, N_s = 6, with 2 stator teeth, n = 2 and there are 13 salient rotor poles, N_r = 13. This stator/rotor combination has been claimed to produce strong electromagnetic performance because it shows a suitable magnetic flux path and high-frequency operation [41]. The PM number is reduced by half while the PM size is changed for the suitability of the structure. The three-phase concentrated armature winding is wound at the big stator pole. It can be seen that the slot winding area of the multi-tooth HE-DSDPM structure is enlarger than the conventional HE-DSDPM structure for better excitation by the dc-biased sinusoidal current. Consequently, the number of turns of the winding can be doubled compared to the conventional one.

Therefore, the HE-DSDPM with the structural multi-tooth modification can illustrate a magnetic flux path improved by the proposed stator/rotor combination, magnetic resource improved by the adapted PM characteristics and flux regulation improved by the enlarged winding slot area. Then, the influence of PM and stator arcs, including θ_sp, θ_yp, θ_st and θ_t, on torque production will be further studied since they relate to the multi-tooth modification in the HE-DSDPM.

3. Influence of PM and Stator Arcs on Torque Production

The θ_sp, θ_yp, θ_st, and θ_t are important factors to impact the achievement of a better magnetic flux path and influence torque production. So, the influence of PM and stator arcs is investigated to objectively achieve a high average torque with low ripple torque in optimal multi-tooth HE-DSDPM. The optimization procedure can be explained by the flowchart, as indicated in Figure 2. Firstly, the initial design specifications and electrical constraints are parameterized to be constant values for structural optimization based on

Table 1. Initial design specifications and electrical constraints of the multi-tooth HE-DSDPM.

Initial Parameters	Units	Values
Outer stator radius, Rso	mm	50
Inner stator radius, Rsi	mm	30
Stator teeth radius, Rst	mm	34
Outer rotor radius, Rro	mm	29.5
Inner rotor radius, Rri	mm	10
Rotor pole arcs, θr	degrees	12
Stack length	mm	50
Steel type	-	Silicon steel 1010
PM type	-	NdFeB—N35
Magnetic flux remanent	T	1.23
Armature current, Iac	A	8
Current density	A/mm2	2
Slot opening PM arc, θsp	degrees	3–32
Stator yoke PM arc, θyp	degrees	1–12
Stator tip arc, θst	degrees	28–57
Stator teeth arc, θt	degrees	13–30

. Secondly, the θ_sp, θ_yp and θ_t are defined as possible variables and the θ_st is calculated by the determined θ_sp and N_s because they are interrelated. This optimization is based on a genetic algorithm (GA) to reach the objective of this investigation. Then, the boundary condition of these variable parameters is limited to reduce the structural distortion of the machine design. If the variable parameters are not appeared in the limited condition, they return the loop until the possible variable parameters are done. Finally, the 2-D FEA is utilised to calculate the torque production and then, investigate for optimal machine structure. The parametric model of multi-tooth HE-DSDPM is supportive of this consideration as indicated in Figure 3.

3.1. PM Arcs

Figure 4 shows the influence of θ_sp and θ_yp on torque production for the multi-tooth HE-DSDPM. Figure 4a can be observed that the average torque increases when increasing θ_sp between 3 and 25 degrees and gradually decreases when θ_sp of 26 degrees is too large because the magnetic flux density at the air gap is reduced with a decrease in magnetic permeance. Meanwhile, the small θ_yp between 1 and 3 degrees provides high average torque at large θ_sp due to the reduction of flux refutation at the stator teeth region. In addition, the ripple torque variation with varying θ_sp and θ_yp is indicated in Figure 4b. The large θ_sp between 20 and 32 degrees results in a lower ripple torque, while the θ_yp has little influence on the ripple torque. The results exhibit that the θ_sp has a higher significant effect on torque production than the θ_yp. In order to achieve high average torque and low ripple torque, the θ_sp of 23 degrees and θ_yp of 1.75 degrees are chosen as the best PM arcs because it produces good MMF and magnetic permeance around stator teeth and air gap of the proposed structure.

3.2. Stator Arcs

Figure 5 shows the influence of θ_st and θ_t on torque production for the multi-tooth HE-DSDPM. It is seen that the average torque increases with the θ_st reduction between 34 and 57 degrees as a consequence of the behaviour of θ_sp variation explained above, shown in Figure 5a. However, the θ_t variation indicates a minimal impact on the average torque since the big stator pole of the proposed machine structure has suitable magnetic permeance to sufficiently contain the magnetic flux produced by both PMs. Figure 5b presents that the low ripple torque is acquired by the small θ_st between 28 and 40 degrees, whereas the various θ_t results in the inconsistent magnitude of the ripple torque due to unstable magnetic flux density at the air gap. Thus, the optimal stator arc candidate is θ_st of 36 degrees and θ_t of 23 degrees because it exists a suitable magnetic permeance and provides high average torque with low ripple torque.

From the optimization results, it is concluded that the suitable PM and stator arcs are θ_sp of 23 degrees, θ_yp of 1.75 degrees, θ_st of 36 degrees and θ_t of 23 degrees. The multi-tooth HE-DSDPM using these suitable arcs can produce large average torque and low ripple torque because of its suitable symmetrical magnetic flux path with the best MMF and magnetic permeability. Thus, this proposed HE-DSDPM with the suitable PM and stator arcs is chosen as the optimal structure in this work. All design specifications of the optimal multi-tooth HE-DSDPM and the conventional HE-DSDPM are given in

Table 2. Design specifications of optimal multi-tooth HE-DSDPM and conventional HE-DSDPM.

Main Parameter	Unit	Conventional HE-DSDPM [29]	Optimal Multi-Tooth HE-DSDPM
Number of stator poles	pole	12	6
Number of stator tooth	teeth	-	2
Number of rotor poles	pole	10	13
Rate speed	rpm	1000
Outer stator radius, Rso	mm	50
Inner stator radius, Rsi	mm	30
Stator teeth radius, Rst	mm	34
Outer rotor radius, Rro	mm	29.5
Inner rotor radius, Rri	mm	10
Air gap length	mm	0.5
Stack length	mm	50
Stator yoke PM height	mm	5
Slot opening PM height	mm	4
Rotor pole arc, θr	degrees	12
Slot opening PM arc, θsp	degrees	11.5	23
Stator yoke PM arc, θyp	degrees	3	1.75
Stator tip arc, θst	degrees	-	36
Stator teeth arc, θt	degrees	18.5	23
Number of turns/coil	degrees	28	56
Slot area/coil	mm2	121	264
Steel type	-	Silicon steel 1010
PM type	-	NdFeB—N35
Magnetic flux remanent	T	1.23
Armature current	A	8
Current density	A/mm2	2

. Then, the electromagnetic performance of the optimal multi-tooth HE-DSDPM will be deeply analysed to compare it with conventional HE-DSDPM.

4. Electromagnetic Performance Analysis

The electromagnetic performance of the optimal multi-tooth HE-DSDPM was investigated by using the 2-D FEA. The I_dc excitations of +5 and −5 A were considered for the expansion of the flux-regulated behaviour in the machine. The magnetic field distribution, flux linkage, back-EMF, THD and cogging torque were investigated in the open-circuit condition, which is I_ac of 0 A. The production of electromagnetic torque and ripple torque were examined under load conditions, such as the I_ac of 8 A and current density of 2 A/mm². The analytical result is compared with the conventional HE-DSDPM based on the design specifications in Table 1.

4.1. Magnetic Flux Distribution and Flux Linkage Analysis

The magnetic flux distribution is verified to study the flux behaviour in a multi-tooth HE-DSDPM. Figure 6 presents the open-circuit magnetic flux and field density of the proposed machine with different I_dc. As illustrated in the red dashed circle, the strong magnetic flux is crowned at the stator tooth tip, the rotor tip and the air gap at all I_dc. This is because the most magnetic flux is produced by slot opening PM. Typically, the magnetic field density at the air gap has more important due to the influence on the magnetic flux path between the stator teeth and rotor poles. It can be seen that the highest magnetic field density at the air gap is about 2.13 T excited by I_dc of +5 A, followed by 1.74 and 0.94 T excited by I_dc of 0 A and −5 A, respectively. As a result, the strengthening flux distribution is achieved by excited at I_dc of +5 A while the wakening flux distribution is achieved by excited at I_dc of −5 A.

The flux linkage was computed from the magnetic flux distribution for primary investigation. As shown in Figure 7, the open-circuit flux linkage of the proposed HE-DSDPM structures with different I_dc is presented by varying the rotor positions. The multi-tooth HE-DSDPM provides the highest flux linkage of 0.013 Wb, similar to conventional HE-DSPM at I_dc of 0 A. Although the geometry configuration of the multi-tooth HE-DSDPM is modified, the flux linkage keeps the same magnitude because the magnetic flux path is improved.

When both machines are excited by I_dc of −5 and +5 A, it is found that the highest flux linkage of the proposed structure at I_dc of −5 and I_dc of +5 A has 32.82% smaller and 35.80% larger than that at no field current, respectively. Especially, the multi-tooth HE-DSDPM exhibits a larger variance flux linkage percentage with better flux regulation quality when compared to the conventional one due to the slot area of the winding coil being enlarged by the structural modification of the multi-tooth technique. Then, the behaviour of the magnetic flux distribution and flux linkage will be further utilised to describe the back-EMF and torque production.

4.2. Back-EMF Analysis

The back-EMF is the induced voltage calculated by the time derivative of flux linkage. Figure 8 shows the open-circuit back-EMF waveforms and their harmonic spectra of the proposed HE-DSDPM structures with various I_dc. As indicated in Figure 8a, the sinusoidal waveforms of the back-EMF are found in both proposed and conventional structures because of containing a symmetrical magnetic flux path. When exciting by I_dc of 0 A, the highest back-EMF of the multi-tooth HE-DSDPM is about 18.76 V and also 24.54% more than the conventional one because its multi-tooth modification helpfully improves the magnetic flux path and flux regulation.

The variance back-EMF percentage with I_dc variations is indicated in Figure 8b. It is found that the back-EMF percentage of the multi-tooth HE-DSDPM is decreased by 34.24% when excited by I_dc of −5 A and improved by 33.32% when excited by I_dc of +5 A. Especially, the highest back-EMF of the multi-tooth HE-DSDPM has 21.38% smaller and 29.98% higher than that of the HE-DSDPM with I_dc of −5 and +5 A, respectively. This is because of the effects of flux linkage percentage and flux regulation quality, as described previously.

The harmonic spectra back-EMF of the proposed structures is presented at different I_dc. The THD percentage represents the harmonic spectra system of the back-EMF waveform. It can be seen that the THD percentage is reduced by more than 3% when using the structural multi-tooth modification in the HE-DSDPM. This is explained that the back-EMF of multi-tooth HE-DSDPM receives high smoothness waveform. Furthermore, the THD percentage of both machines is changed with varying I_dc, which significantly impacts the behaviour of ripple torque. From these results, the back-EMF and THD percentages will be applied for the explanation of the torque characteristics.

4.3. Torque Production Analysis

The torque production of both proposed structures, consisting of the cogging torque and electromagnetic torque, is investigated. The cogging torque of the proposed HE-DSDPM structures excited by different I_dc is shown in Figure 9. The low cogging torque represents low tension between the magnet and rotor at the air gap while the electrical machine is started. The multi-tooth HE-DSDPM with all field currents is observed to have lower cogging torque than the conventional HE-DSDPM. Their peck-to-peck cogging torques are about 0.081, 0.064, and 0.238 Nm found at I_dc of −5, 0, and 5 A, respectively. This behaviour is exhibited that the multi-tooth machine indicates a lower starting tension because of the suitable magnetic flux path at the air gap from the structural multi-tooth modification with PM and stator arcs optimization.

Figure 10a indicates the electromagnetic torque of the multi-tooth and conventional HE-DSDPM structures with I_dc variation. The I_ac of 8 A and current density of 2 A/mm² was fixed as electrical constraints in the load conditions. Based on no field current, the HE-DSDPM with a multi-tooth structure produces an electromagnetic torque of about 3.04 Nm and is especially 26.18% higher than the HE-DSDPM with a conventional structure because of the better back-EMF characteristic. The ripple torque of the multi-tooth HE-DSDPM has a minimum value of about 3.25% and is 4% less than that of the conventional one due to a lower THD percentage and cogging torque value.

As shown in Figure 10b, the investigation of the average torque in the HE-DSDPM structures is proposed. It is seen that the variance average torque percentage of a multi-tooth HE-DSDPM with I_dc of +5 A indicates a 16.43% improvement from that of conventional HE-DSDPM. For I_dc of −5 A excitation, the proposed structure shows a 20.73% lower variance average torque percentage when compared to the conventional structure. It is also represented that the multi-tooth HE-DSDPM has the smallest ripple torque with a minimum vibration of the machine structure. As described in the magnetic flux distribution section, it indicates that the strengthening flux distribution excited by I_dc of +5 A can produce the average torque improvement, while the wakening flux distribution excited by I_dc of −5 A can produce minimum ripple torque for the HE-DSDPM with a multi-tooth structure. Therefore, the structural multi-tooth modification in HE-DSDPM can generate better electromagnetic torque, the lowest ripple torque and the best variance average torque percentage at all I_dc.

From the results, it can be concluded that the HE-DSDPM can generate better overall electromagnetic performance by using a structural multi-tooth modification since it enhances the magnetic flux path and the flux regulation. When compared to the conventional HE-DSDPM at I_dc of 0 A, it is found that the multi-tooth HE-DSDPM structure indicates a 24.54% higher back-EMF with about 3% lower THD percentage. Especially, the average torque provided by the proposed structure is 26.18% larger and 4% smaller ripple torque than the conventional one because of better back-EMF characteristics and the low cogging torque magnitude. Moreover, the multi-tooth HE-DSDPM with excited by I_dc of −5 and +5 A exhibits the largest variance percentage of torque production than conventional HE-DSDPM because of the greater flux regulation quality. Hence, structural multi-tooth modification may be another important way to improve torque production in the other DSPM categories.

5. Conclusions

This paper presented a structural multi-tooth modification used in an HE-DSDPM for torque production improvement. The PM and stator arcs were examined by optimization to achieve the optimal structure for effective torque production. The electromagnetic performance was investigated based on the magnetic flux distribution, flux linkage, back-EMF, THD, cogging torque and electromagnetic torque with varying I_dc values and compared to the conventional HE-DSDPM under the same machine conditions. The results, based on the 2-D FEA, verified that the proposed multi-tooth HE-DSDPM shows the best stator/rotor combination, the suitable PM characteristics and the enlarged winding slot area. Better overall electromagnetic performance of this proposed structure is achieved by the improvement of the symmetrical magnetic flux path and flux regulation. This improved configuration resulted in the back-EMF that is 24.54% higher with the lowest THD percentage than the conventional structure with I_dc at 0 A. In particular, this proposed structure provides a 26.18% higher average torque with a 4% smaller ripple torque when compared to the conventional one at no field current because of its greater back-EMF characteristics and the low cogging torque value. The proposed structure also exhibits the largest variance torque percentage with greater flux regulation quality at different I_dc values. Therefore, in summary, the structural modification using the multi-tooth technique could be utilised to improve torque production for other DSPM categories and especially, be a significant trend for the development of the electrical machine design of other morphologies, such as linear-field PM machine and axial-field PM machine.