Torque characteristic improvement of dual-PM modular doubly salient permanent magnet machine using machine ratio adaptation

Abstract

Machine ratio adaptation of a dual-PM modular doubly salient permanent magnet machine (DPM-DSPM) was proposed to improve the torque characteristics. An optimization design process was examined. Essential machine indicators were investigated to obtain an optimal machine ratio. It was found that p = 4 and a 0.8 rotor pole width ratio of the DPM-DSPM produced the best essential machine indicator that provided the appropriate magnetic flux path and high flux regulation quality. Then, the DPM-DSPM with an optimal machine ratio was investigated based on open-circuit and on-load tests and then compared to a reviewed DPM-DSPM. The results, based on 2-D finite element analysis, verified that the optimal proposed DPM-DSPM had better torque characteristics. In particular, the optimal proposed structure produced 35.04% higher electromagnetic torque with 61.75% lower ripple torque than the review structure. Therefore, an optimal machine ratio for a DPM-DSPM can be beneficial in solving industrial machine problems, especially noise reduction from vibration.

Keywords

Machine ratio split ratio rotor pole width ratio dual-PM modular doubly salient permanent magnet machine

1. Introduction

Electrical machine used by industry has problems associated with high maintenance, high rotor weight and excessive noise caused by vibration [1]. These problems result from poor torque characteristics [2,3].

A permanent magnet (PM) machine has been extensively used to address torque characteristics. Its structural design eliminates coil excitation and copper losses to enhance the torque density and ripple torque [4,5]. However, the rotor part of this machine is heavy and is subject to inertia because of the installed PM.

A stator-PM machine with the PM located at the stator yoke has been of considerable interest due to its lightweight rotor [6]. A doubly salient PM machine (DSPM) is one popular type of stator-PM machine because of its many outstanding merits, such as high back-electromotive force (back-EMF), high torque density and high reliability [7–9]. Its structure consists of the stator yoke with PM, stator teeth with a concentrated winding and a lightweight rotor pole. [10,11]. However, the torque characteristics of a DSPM have been shown to be lower than for other stator-PM machine types because of the low quality of magnetic flux regulation and asymmetrical magnetic flux path [12,13].

In 2019, Shen et al. introduced a dual-PM modular (DPM) in the linear machine to solve the magnetic flux path and flux regulation [14]. Its principal component includes the stator yoke PM and opening slot PM. Several researchers used a DPM to enhance these magnetic flux properties, such as the DPM utilized in the DSPM (DPM-DSPM) that was proposed by Wang et al. in 2020 [15]. Its structure was optimized to achieve an effective magnetic flux path. Recently, optimization of the PM dimension in a DPM-DSPM was presented by Meng et al. [16]. Their results showed an increase in flux regulation quality, resulting in an improvement in torque characteristics. From the literature review of a DPM-DSPM, its structure has been extensively studied to develop its torque characteristics due to its outstanding merits, such as no coil excitation, lightweight rotor, good magnetic flux path, high magnetic flux regulation quality and low manufacturing cost.

To further improve the torque characteristic, adjustment of the machine ratio, including split ratio and rotor pole wide ratio, has been studied to regulate the magnet flux in the machine structure due to its significant effect on torque production [17,18]. Many studies reported on machine ratio optimization in the machine structure aiming to improve the torque characteristics, such as split ratio optimization to obtain high torque in a PM motor that was introduced by Reichert et al. in 2013 [19]. Xiang et al. in 2018 investigated the optimal split ratio in flux-switching PM machines for studying the torque production [20]. Rotor-pole adaptation by considering the rotor pole width ratio in a PM machine was demonstrated to verify electromagnetic performance by Shao et al. in 2017 [21].

Nevertheless, the machine ratio has no consideration in a structural DPM-DSPM in any of the previous studies.

This paper aims to adapt the machine ratio, consisting of the split ratio and rotor pole width ratio, of a DPM-DSPM for torque characteristic improvement. An explanation of the optimization design process was developed for achieving an effective machine ratio. Essential machine indicators were investigated, consisting of back-EMF, cogging torque, average torque and ripple torque. In addition, the DPM-DSPM with a suitable machine ratio was verified and compared individually to a review of DPM-DSPM in the same condition. The results were based on 2-D finite element analysis (2-D FEA). The open-circuit test was used to examine the magnetic flux distribution, flux linkage, back-EMF, total harmonic distortion (THD), and cogging torque. The electromagnetic torque and ripple torque were further verified under on-load conditions.

2. Machine ratio adaptation

As indicated in Fig. 1(a), an initial DPM-DSPM with 12s/10r-poles (stator/rotor-poles) is presented in this work, based on the concept of Wu et al. in 2015 and Meng et al. in 2021 [13,16]. Its components consist of the PM mounted at the yoke and the opening slot of the stator and T-shape modular stator teeth. Both positions of the PM provide additional magnetic flux for improving the quality of the magnetic flux regulation. Its stator teeth are modulated as a T-shape to reduce manufacturing costs. The double-layer concentrated winding is installed at the stator teeth. Lightweight rotor poles are used because the PM and winding move to address the stator. These structural properties provide advantages over the other structures of the DSPM type.

Many literature reviews proposed DPM-DSPM development aiming to enhance torque characteristics. However, the machine ratio adaptations, including the split ratio and rotor pole width ratio, of the DPM-DSPM were unverified in previous research.

To adapt the split ratio and rotor pole width ratio in the DPM-DSPM structure, the process of optimization design is explained. Initially, the initial design specification, such as the number of stators and rotors, was determined due to its main machine scale. Typically, the outer stator radius is fixed since it is the initial indicator of machine scale. The winding coil area and PM volume were set as the constant parameters for a fair comparison. A 39.03 A/mm² of current density was applied in the on-load investigation to maintain the same copper loss. According to the literature review of the structural DSPM category, this machine can normally run at 100–1000 rpm because it is suitable for low-speed applications [9]. For this analysis, the rotating speed was defined as 400 rpm for intermediate operation. The other design specifications of an initial DPM-DSPM are given in Table 1. The descriptions of the machine ratio and machine analysis are illustrated below.

Table 1
Design parameters of proposed DPM-DSPM

Structural parameter Unit Initial DPM-DSPM, p = 1 Optimal proposed DPM-DSPM, p = 4

Stator teeth number, N _s Teeth 12

Rotor teeth number, N _r Poles 10

Number of PMs Pieces 24

Stack length mm 25

PM type — Nd-F-B

Magnetic flux remanent T 1.2

Outer stator radius, R _os mm 45

Inner stator radius, R _is mm 29 27

Split ratio — 0.64 0.61

Thickness of stator yoke PM, T _sy mm 4.5 3

Thickness of slot opening PM, T _so mm 0.5 2

Rotor pole width ratio — 0.8 0.8

Rotor pole arc, θ_rpa Degree, ° 12 12

Stator tooth arc Degree, ° 12

Stator yoke radius mm 36.5

Air gap length mm 0.5

Outer rotor radius mm 16

Inner rotor radius mm 10.4

Number of coil turns per pole Turns 60

Winding coil radius mm 3.58

Rotating speed rpm 400

Current density, J _z A/mm² 39.03

Structural parameter	Unit	Initial DPM-DSPM, p = 1		Optimal proposed DPM-DSPM, p = 4
Stator teeth number, N _s	Teeth		12
Rotor teeth number, N _r	Poles		10
Number of PMs	Pieces		24
Stack length	mm		25
PM type	—		Nd-F-B
Magnetic flux remanent	T		1.2
Outer stator radius, R _os	mm		45
Inner stator radius, R _is	mm	29		27
Split ratio	—	0.64		0.61
Thickness of stator yoke PM, T _sy	mm	4.5		3
Thickness of slot opening PM, T _so	mm	0.5		2
Rotor pole width ratio	—	0.8		0.8
Rotor pole arc, θ_rpa	Degree, °	12		12
Stator tooth arc	Degree, °		12
Stator yoke radius	mm		36.5
Air gap length	mm		0.5
Outer rotor radius	mm		16
Inner rotor radius	mm		10.4
Number of coil turns per pole	Turns		60
Winding coil radius	mm		3.58
Rotating speed	rpm		400
Current density, J _z	A/mm²		39.03

2.1. Split ratio

The split ratio is key to altering the stator shapes, resulting in an improvement of the magnetic flux path. Based on the structural DPM-DSPM, the split ratio adjustment provides a modification of the PM thicknesses at the stator yoke and opening slot to keep the PM volume and winding area constant. Then, a variable positive integer, p, is determined to describe the split ratio and PM thickness adaptation of this machine. The boundary condition of p is limited to 1–10 (p = 1,2,3, … ,10) as any higher value would result in structural machine distortion and unsatisfactory performance. Thus, the split ratio is defined as: $\begin{eqnarray}\displaystyle \text{Split ratio}={\displaystyle \frac{\left(R_{is,pri}+\frac{1}{2}\right)-\frac{p}{2}}{R_{os}}} & & \displaystyle\end{eqnarray}$ (1) where R _{is, pri} is the inner stator radius based on the initial DPM-DSPM and R _os is the outer stator radius.

The stator yoke and opening slot PM thickness of this DPM-DSPM can be defined as: $\begin{eqnarray}\displaystyle \left\{\begin{array}{@{}l@{}}T_{sy}=T_{sy,pri}-{\displaystyle \frac{(p-1)}{2}}\\ T_{so}=R_{is,pri}-\left[R_{is,pri}-{\displaystyle \frac{p}{2}}\right]\end{array}\right. & & \displaystyle\end{eqnarray}$ (2) where T _sy is the thickness of the stator yoke PM, T _so is the thickness of the opening slot PM and T _{sy, pri} is the stator yoke PM thickness based on the initial DPM-DSPM. For example, when p = 1, the calculated split ratio is 0.64. T _sy and T _so are calculated as 4.5 and 0.5, respectively, as shown in Fig. 1(a). In addition, the 0.61 split ratio, T _sy = 3 mm and T _so = 2 mm are assigned p = 4, as indicated in Fig. 1(b).

Fig. 1.

Cross-section perspective of (a) p = 1, initial DPM-DSPM, (b) p = 4, optimal proposed DPM-DSPM and (c) parametric models.

2.2. Rotor pole width ratio

The rotor pole width ratio is the ratio between the rotor pole and the slot width. Thus, when the rotor pole width ratio is 1, the opening slot width is equal to the rotor pole width. In this analysis, the rotor pole width ratio is concurrently calculated while the split ratio is varied since they have a mutual influence on the arrangement of the magnetic flux path at the air gap, resulting in the flux regulating capability afterwards. The rotor pole width ratio is calculated from the rotor pole arc multiplied by one-half of the pole pitch: $\begin{eqnarray}\displaystyle \text{Rotor pole width ratio}={\theta}_{rpa}\times {\displaystyle \frac{N_{s}}{360\left(\frac{1}{2}\right)}} & & \displaystyle\end{eqnarray}$ (3) where θ_rpa is the rotor pole arc and N _s is the stator teeth number. The initial rotor pole width ratio, based on an initial DPM-DSPM, is about 0.8 for a rotor pole arc of 12°. Calculating the rotor pole width ratio, the rotor pole arc is defined from 1° to 19° due to its possible boundary condition. The values p = 1 and p = 4 of the parametric models of the DPM-DSPM are based on Fig. 1(c).

2.3. Machine analysis

Essential machine indicators of the adapted DPM-DSPM were investigated for static evaluation using the 2-D FEA, which is a simple process, as studied in [11,22]. The essential machine indicators analysed in this work, consisted of root-mean-square back-EMF, peck-to-peck cogging torque, average torque and ripple torque.

Based on the 2-D FEA methodology, magnetic flux distribution was initially examined to descript the behaviour of the magnetic flux density and path in the machine structure. It can be calculated using a 2-D Poisson nonlinear differential equation, as defined in: $\begin{eqnarray}\displaystyle {\displaystyle \frac{\partial }{\partial x}}\left({\upsilon}{\displaystyle \frac{\partial A_{z}}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left({\upsilon}{\displaystyle \frac{\partial A_{z}}{\partial y}}\right)=-(J_{z}+J_{pm}) & & \displaystyle\end{eqnarray}$ (4) where A _z is the z-axis magnetic vector potential, J _z is the z-axis current density, J _pm is the current density from the PM source, and 𝜐 is reluctivity.

Root-mean-square back-EMF is the first essential indicator to explain an open-circuit voltage. It is utilized to evaluate the quality of flux regulation and the waveform characteristic of other indicators in this work and is defined as: $\begin{eqnarray}\displaystyle e=N{\displaystyle \frac{\partial {\psi}}{\partial t}} & & \displaystyle\end{eqnarray}$ (5) where e is the back-EMF, 𝜓 is the flux linkage, and N is the number of turns per coil.

Cogging torque is an open-circuit torque that represents the starting torque described by the relation of magnetic flux tension between the PM and rotor pole at the air gap. It is defined by the position derivative of the energy at the air gap as: $\begin{eqnarray}\displaystyle T_{\text{cog}}({\theta}_{m})={\displaystyle \frac{\partial W_{\text{airgap}}}{\partial {\theta}_{m}}} & & \displaystyle\end{eqnarray}$ (6) where T _cog is the cogging torque, W _airgap is the energy at the air gap and θ_m is the mechanical degree.

Electromagnetic torque is equal to the on-load torque used in the performance analysis of an electrical machine. Its behavior can be explained by the features of back-EMF and cogging torque and can be defined as: $\begin{eqnarray}\displaystyle T_{e}={\displaystyle \frac{\displaystyle \mathop{\sum }_{i=1}^{n_{\text{phase}}}e_{n}i_{n}}{{\omega}_{r}}} & & \displaystyle\end{eqnarray}$ (7) where T _e is the electromagnetic torque, n _phase is the number of phases, e _n is the root-mean-square back-EMF of each phase, i _n is the root-mean-square current of each phase and ω_r is the angular velocity of the rotor.

Ripple torque indicates the vibration of the machine structure causing acoustic noise in an industrial application. It is calculated by the characteristic of electromagnetic torque [13] as: $\begin{eqnarray}\displaystyle T_{\text{ripple}}={\displaystyle \frac{T_{\max }-T_{\min }}{T_{\text{avg}}}}\times 100 & & \displaystyle\end{eqnarray}$ (8) where T _ripple is the ripple torque, and T _max, T _min and T _avg are the maximum, minimum and average values, respectively, based on the electromagnetic torque.

The overall optimization design process is summarized in the flowchart, shown in Fig. 2. Based on the 2-FEA, the simulation results were evaluated for suitable machine ratio selection for a DPM-DSPM. The proposed machine with an optimal machine ratio was verified and then compared to a review of a DPM-DSPM in fair structural condition. The machine indicators, consisting of the magnetic flux distribution, flux linkage, back-EMF, THD, and cogging torque, were investigated in an open-circuit test. For the on-load condition, the torque characteristics were examined, consisting of the electromagnetic torque and ripple torque.

Fig. 2.

Flowchart of the optimization design process.

3. Influence of machine ratio adaptation on essential indicators

The machine ratios of the DPM-DSPM were optimized by studying essential machine indicators, consisting of back-EMF, cogging torque, average torque and ripple torque. Investigation of these machine indicators was dependent on the optimization design process, as explained above.

3.1. Back-EMF

The values of root-mean-square back-EMF of the various machine ratios in the DPM-DSPM were investigated. As shown in Fig. 3, a high range back-EMF is exhibited by the small p of 3–5 and a rotor pole width ratio of 0.7–1. Since the flux path permeability at the stator and rotor increases, the flux regulating quality in the structural DPM-DSPM is enhanced by the additional magnetic flux of both the stator yoke PM and the opening slot PM. Typically, the stator yoke PM of DPM-DSPM generates the majority of the magnetic flux in the machine structure. However, the large p value with the very small split ratio in this machine results relatively in low back-EMF because of the small PM thickness at the stator yoke. Thus, there is insufficient strength of the magnetic flux to induce the voltage at the armature winding, even though the thickness of the opening slot PM increases. In addition, the small rotor pole width ratio shown by the narrow rotor pole arc provides a thin magnetic flux path with high leakage flux. In contrast, the rotor pole arc is over-wide, increasing the rotor weight and producing high inertia.

Fig. 3.

Influence of machine ratios on back EMF.

3.2. Cogging torque

The peck-to-peck cogging torque of the proposed DPM-DSPM structure was examined by varying the machine ratios, as indicated in Fig. 4. The magnetic flux tension at the air gap is used to describe its characteristics. A large tension at the air gap between the narrow stator yoke PM thickness and the rotor is represented as a large p value in this DPM-DSPM while all rotor pole width ratios have a similar waveform pattern. The 0.4 and 0.8 rotor pole width ratios at all p values are less than for the other rotor pole width ratios because the magnetic flux path at the stator teeth and rotor pole provides a small amount of leakage flux, resulting in the decreased tension at the air gap. Thus, the cogging torque, obtained from the 0.4 and 0.8 rotor pole width ratios at p values between 2 and 5, has a low value with a reduced tension due to its suitable magnetic flux path.

Fig. 4.

Influence of machine ratios on cogging torque.

3.3. Average torque

Figure 5 shows the average electromagnetic torque of the structural DPM-DSPM with various machine ratios for the same 39.03 A/mm² current density. It is observed that the high average torque has a large p value and rotor pole width ratio for the DPM-DSPM due to the large magnetic flux permeability at the stator teeth and rotor poles, and the good flux regulation of both PMs at the stator yoke and slot opening. However, with a rotor pole width ratio greater than 1 at all p value, there is the average torque reduction because of the occurrence of the leakage flux. Notably, a p value between 3 and 5 and a rotor pole width ratio between 0.7 and 0.9 produce the large average torque since it has suitable permeability of the magnetic flux path and the best flux regulation.

Fig. 5.

Influence of machine ratios on average torque at J _z = 39.03 A/mm².

3.4. Ripple torque

As shown in Fig. 6, the ripple torque of each machine ratio was obtained based on the electromagnetic torque characteristics of each structure. The high ripple torque indicates high vibration and a noisy machine structure. Since large flux leakage causes an imbalanced magnetic flux with a narrow rotor pole arc, the 0.2 rotor pole width ratio with all p value has the highest ripple torque, whereas the other rotor pole width ratios have low ripple torque values. All p value exhibits the same feature because of the negligible effect on this indicator. Thus, the suitable ripple torque with a high average torque occurs for a p value between 3 and 5 and a rotor pole width ratio between 0.7 and 0.9, with the same torque characteristics. This machine ratio range provides low vibration with almost no noise.

Fig. 6.

Influence of machine ratios on ripple torque.

From these results, the optimal machine ratio is chosen by consideration of the overall machine indicators. It can be concluded that a machine ratio, consisting of p = 4 and a 0.8 rotor pole width ratio, of the DPM-DSPM, shows a better essential machine indicator than the other proposed machine ratios in this work. This can be explained by its advantages of a high root-mean-square back-EMF of 5.10 V _rms and a low cogging torque of 0.049 Nm_p−p. In particular, this proposed machine ratio produces appropriate torque characteristics of about 6.62 Nm of average torque with 4.49% of ripple torque and its structure indicates the suitable permeability of the magnetic flux path and high flux regulation quality obtained by the additional machine flux from both PMs. Therefore, the DPM-DSPM with p = 4 and a 0.8 rotor pole width ratio is selected as the optimal structure for comparison in a review DPM-DSPM, as explained below.

4. Comparison of machine performance of DPM-DSPM

The DPM-DSPM, introduced by Meng et al. in 2021 [16], was reviewed to compare its torque characteristics with our selected DPM-DSPM. The simulation setup used the same geometric scale and constraint for a fair comparison, as based on Table 2. The open-circuit test investigated the magnetic flux density, flux linkage, back-EMF, THD and cogging torque. The torque characteristics, consisting of the electromagnetic and ripple torques, were further examined in the on-load test.

Table 2
Simulation setup of review and optimal proposed DPM-DSPM

Item Unit Review DPM-DSPM Optimal proposed DPM-DSPM

Outer stator radius mm 45

Stack length mm 25

Number of PM pieces 24

Rotating speed rpm 400

Number of coil turns per pole turns 60

PM volume, V _PM mm³ 8825 13100

Winding coil area per pole mm³ 46.17 40.29

AC current A 30.03 26.21

Current density, J _z A/mm² 39.03

Item	Unit	Review DPM-DSPM		Optimal proposed DPM-DSPM
Outer stator radius	mm		45
Stack length	mm		25
Number of PM	pieces		24
Rotating speed	rpm		400
Number of coil turns per pole	turns		60
PM volume, V _PM	mm³	8825		13100
Winding coil area per pole	mm³	46.17		40.29
AC current	A	30.03		26.21
Current density, J _z	A/mm²		39.03

4.1. Magnetic flux distribution and flux linkage

The open-circuit magnetic flux distributions of the review and optimal proposed DPM-DSPMs were investigated at 0 electrical degrees, as shown in Fig. 7. As noticed in the stator teeth, the review DPM-DSPM and the optimal proposed DPM-DSPM produce magnetic flux densities of 0.52 T and 1.13 T, respectively. This can be explained because the review structure has wide stator teeth causing an inefficient distribution of the magnetic flux. The machine flux density at this position is used to predict the significant flux linkage. In addition, the magnetic flux destiny at the d-axis A1 phase air gap is about 1.25 and 1.62 T for review DPM-DSPM and the optimal proposed DPM-DSPM, respectively. Review one has a lower magnetic flux density compared to the optimal proposed one because its narrow PM thickness at the stator yoke provides insufficient magnetic flux distribution through the air gap. The wide stator teeth of the review structure impact the large increase in tension at the air gap and cogging torque.

Figure 8(a) shows the flux linkage waveform of the review and the optimal proposed DPM-DSPM. Notably, the flux linkage generated by our proposed one is 42.91% higher than for the reviewed one due to the effect of the magnetic flux distribution at the width of the stator teeth, as explained above.

Fig. 7.

Magnetic flux distribution of (a) review and (b) optimal proposed DPM-DSPM.

4.2. Back-EMF analysis

The behaviour of magnetic flux distribution was used to influence the back-EMF. Figure 7(b) illustrates the back-EMF comparison between the review and the optimal proposed DPM-DSPM at 60 turns of winding and 400 rpm. It is seen that the optimal proposed DPM-DSPM provides a 41.31% higher back-EMF than the review one because its optimal machine ratio improves the magnetic flux path to exhibit a higher magnetic flux density at the stator teeth. In particular, the symmetrical and sinusoidal back-EMF waveforms are evident in both the review and optimal proposed structures due mainly to their very low spectral values and THD percentages, as exhibited in Fig. 8(c). Thus, the characteristics of magnetic flux distribution and back-EMF can be further utilized to describe the torque characteristics.

Fig. 8.

Open-circuit test of review and optimal proposed DPM-DSPM with (a) flux linkage, (b) back-EMF, and (c) harmonic spectra at 60 turns and 400 rpm.

4.3. Torque characteristics

Figure 9(a) shows the cogging torque of the review and optimal proposed DPM-DSPM with variation in the rotor position. As explained above, a large cogging torque is produced by the review structure since its wide stator teeth with weak magnetic flux increase the magnetic flux tension between the PM and rotor pole at the air gap. In contrast, an optimal proposed DPM-DSPM has lower cogging torque and magnetic flux tension with optimal machine ratios compared to the review one.

The electromagnetic torque of both DPM-DSPM structures is examined under the same current density of 39.03 A/mm², as shown in Fig. 9(b). The DPM-DSPM with the optimal machine ratio shows enhancement of torque characteristics due to its suitable magnetic flux path and high flux regulation quality, as indicated in Table 3. The average torque using the optimal proposed DPM-DSPM is 35.04% higher than for the review DPM-DSPM. In contrast, the proposed structure has a similar average torque per PM volume (T _avg∕V _PM) compared to the review structure. Especially, the optimal machine ratio of the proposed DPM-DSPM produces a 61.75% lower ripple torque with the smallest vibration compared to the other DPM-DSPM in this literature review.

Table 3
Torque characteristics of review and optimal proposed DPM-DSPM

Item Unit Review DPM-DSPM Optimal proposed DPM-DSPM

Root mean square back-EMF V _rms 2.98 5.10

THD % 0.021 0.020

Peak to peak cogging torque mNm_p-p 133.45 49.00

Maximum torque, T _max Nm 4.57 6.77

Minimum torque, T _min Nm 4.01 6.44

Average torque, T _avg Nm 4.30 6.62

Ripple torque, T _ripple % 13.02 4.98

T _avg∕V _PM Nm/cm³ 0.49 0.50

Item	Unit	Review DPM-DSPM	Optimal proposed DPM-DSPM
Root mean square back-EMF	V _rms	2.98	5.10
THD	%	0.021	0.020
Peak to peak cogging torque	mNm_p-p	133.45	49.00
Maximum torque, T _max	Nm	4.57	6.77
Minimum torque, T _min	Nm	4.01	6.44
Average torque, T _avg	Nm	4.30	6.62
Ripple torque, T _ripple	%	13.02	4.98
T _avg∕V _PM	Nm/cm³	0.49	0.50

Fig. 9.

On-load test of review and optimal proposed DPM-DSPM with (a) cogging torque and (b) electromagnetic torque at J _z = 39.03 A/mm².

In summary, the DPM-DSPM with a machine ratio of p = 4 and a 0.8 rotor pole width ratio has better torque characteristics than the review DPM-DSPM and other mentioned DPM-DSPM in this work because its magnetic flux path and flux regulation quality are improved by machine ratio adaptation. Hence, the optimal machine ratio of a DPM-DSPM can be another parameter that can be modified to address industrial machine issues, such as acoustic noise reduction from machine vibration.

5. Conclusion

This paper proposed torque characteristics improvement in a DPM-DSPM by using machine ratio adaptation of the split ratio and rotor pole width ratio. An optimization design process was explained to obtain an effective machine ratio. The influence of the machine ratio on the essential indicators was investigated. It was shown that p = 4 and a 0.8 rotor pole width ratio for the DPM-DSPM produced a higher root-mean-square back-EMF of 5.10 V_rms, a lower cogging torque of 0.049 Nm_p−p, and especially higher average torque of 6.62 Nm than the other machine ratio in this work because of its suitable permeability of the magnetic flux path and high flux regulation quality. Furthermore, the DPM-DSPM with the optimal machine ratio was compared with a review DPM-DSPM using the same machine conditions. The torque characteristics were examined using open-circuit and on-load tests. The results, based on the 2-D FEA, verified that the optimal proposed DPM-DSPM had better torque characteristics than the review one. Especially, the optimal proposed structure had a 35.04% higher average electromagnetic torque with 63.50% lower cogging torque and 61.75% lower ripple torque compared to the review structure, since the optimal machine ratio showed an effective magnetic flux path and flux regulation. Therefore, a DPM-DSPN with an optimal machine ratio could be a solution to industrial machine problems related to noise reduction caused by vibration.

Footnotes

Acknowledgements

This work was financially supported by the Office of the Permanent Secretary, Ministry of Higher Education, Science, Research and Innovation (grant no. RGNS 64-032).

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