Design Considerations of Switched Flux Memory Machine with Partitioned Stators

Abstract

This paper presents general design considerations of a partitioned stator switched flux hybrid magnet memory machine (PS-SF-HMMM). The armature windings and permanent magnets (PMs) are placed on two separate stators, respectively, in the PS-SF-HMMM, and thus both high torque density and wide flux regulation capability can be obtained. The topology and working principle of the machine are introduced briefly first, and then different magnet arrangements and stator/rotor pole combinations are investigated. In addition, various design parameters are optimized based on finite element (FE) methods. Finally, a prototype is fabricated to experimentally validate the FE results.

1. Introduction

Variable flux permanent magnet (VFPM) machines [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] have been studied extensively in recent years for their potentials in wide-speed range applications. Based on the flux adjusting patterns, the VFPM machine can be generally categorized into hybrid excited [2,3], mechanical adjusted [4], and memory machines [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. Hybrid excited machines are widely reported, which can be considered as a combination of permanent magnet (PM) and wound field machines [2,3]. However, the continuous currents in the wound field windings will degrade the overall operating efficiency, particularly at light load operation. Meanwhile, mechanical adjusted machines [4] utilize extra actuators to change the flux linkage. Nevertheless, the complicated mechanical systems are the major concerns.

Memory machine (MM) equipped with low-coercive-force (LCF) PMs have been reported as a competitive candidate for traction applications in recent years [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. A magnetizing or demagnetizing current pulse can be employed to regulate the magnetization states (MS) of the LCF PMs, and hence the associated copper loss is ignorable during the flux adjustment. Hence, high efficiency can be achieved over a wide operation range. Basically, MMs are categorized into AC- and DC-magnetized types according to the magnetizing current types used in the machine. The MM concept is first proposed in an interior PM machine with a sandwiched rotor structure [5]. Since then, various MMs with LCF PMs on the rotor have been proposed (commercialized as the TOSHIBA laundry machine [6,7]). Most of AC-magnetized MMs have a positive saliency ratio, under the so-called flux-intensifying design [8,9,10,11,12,13]. The positive reluctance torque can be obtained to keep the MS of LCF PMs stable at on-load operation. However, the AC-magnetized MMs generally suffer from relatively complicated MS manipulation control. Besides, LCF PMs are subject to high risk of unintentional demagnetization under on-load operation. On the other hand, all the stator PM machines, e.g., doubly salient [15,16,17], and switched flux (SF) [18,19,20,21,22,23] topologies can be converted into DC-magnetized type MMs. Compared with conventional stator PM machines, DC magnetizing coils are added in the stator PM MMs to generate a transient current pulse to change the intensity of magnetization level of the LCF PM materials. Besides, the merits of good rotor mechanical robustness and easy heat dissipation are maintained from those conventional stator PM machines simultaneously. Nevertheless, for all of the previously reported DC-magnetized MMs having a single stator, there is a severe geometric conflict between magnetic and electrical loadings in the stator, and consequently the reduced slot areas result in the decreased torque density. Very recently, the concept of “partitioned stator (PS)” is extended to stator PM machines [24,25,26]. By moving the PMs located in the outer stator in the conventional single-stator design to the inner one, the copper slot areas in the outer stator can be enlarged significantly, which can lead to an improvement in the torque density of the machine.

Based on the PS design concept, a partitioned stator switched flux hybrid magnet memory machine (PS-SF-HMMM) [21,22,23] is developed in order to resolve the compromised torque density of the single-stator counterpart. The PS-SF-HMMM combines the advantages of the torque improvement in PS machines, and excellent flux regulation capability in MMs. The design possibilities of various PM configurations for the PS-HMMMs are investigated in reference [21], which shows the spoke-type PM design is preferable for the torque enhancement. In reference [22], the performance comparison of SF-HMMMs with single- or dual-stator structures is conducted, which confirms the benefits of the PS design in terms of torque improvement and wider flux regulation range. Triple magnets are employed in reference [23] to further improve the unintentional demagnetization withstand capability. In reference [22], comparison between the PS-HMMMs and the commercialized EV machine has been made regarding the back-EMFs (electromotive force), torque characteristics, and efficiency maps. It shows that the PS-HMMMs have comparable torque density, better efficiency maps, and higher torque at light load. Yet, the previous studies on the PS-SF-HMMM mainly pay attention to the features of the new topology or the electromagnetic performance of the specific machines, a comprehensive general design guideline and optimization process are still unreported.

Therefore, this paper presents the design considerations of PS-SF-HMMM in order to fill the aforementioned knowledge gap in the existing literatures [21,22,23]. In Section 2, the machine structure and its working principle are described in brief. In Section 3, the feasibility of different PM arrangements based on series or parallel magnetic circuits for the proposed PS-SF-HMMM is investigated. The stator/rotor pole number combinations and other major design parameters are then comprehensively optimized by finite-element (FE) method. A prototype is fabricated and tested to validate the FE results in Section 4, and a conclusion is given in Section 5.

2. Machine Configuration and Operating Principle

The configuration of the proposed PS-SF-HMMM is illustrated in Figure 1a. It can be observed that the outer stator accommodates the concentrated non-overlapping armature windings, while the inner stator consists of “U-shaped” PM excitations and magnetizing coils. A cupped rotor consists of segmented iron pieces, which are placed between the two stators. The inner stator reduces the conflict between the armature windings and the two types of PMs in traditional single stator MMs. In addition, the LCF magnets are free from the severe on-load magnetic saturation on the outer stator, and consequently the corresponding demagnetization risk caused by either NdFeB or armature fields can be alleviated.

The working principle of the PS-SF-HMMM can be illustrated by using the variable flux characteristics of the LCF PMs [5]. Due to the nonlinear hysteresis characteristics, the LCF PMs can be repetitively magnetized by a magnetizing current pulse fed by the magnetizing windings. In fact, the spoke-type NdFeB PMs are magnetized tangentially and perform the flux-concentrating effect so as to improve the torque capability, whereas the LCF PMs are magnetized radially and behave in the same way as the flux adjustors. When the LCF PMs are bidirectionally magnetized via the magnetizing current, the magnetic fields induced by the NdFeB PM fields are either enhanced or weakened by LCF PM fields. Consequently, as illustrated in the open-circuit field distributions in Figure 1b, the air-gap flux can be flexibly adjusted. Actually, the transient torque and voltage ripples will be inevitably induced during the magnetization or demagnetization process. However, some control countermeasure can deal with this ripple issue, which will be reported in the further papers.

In addition, the switched-flux principle of the PS-SF-HMMM is essentially similar to that of the single stator one, as illustrated in Figure 2. The PM pole number is identical to that of the outer stator teeth, which allows switched flux action via alignment/misalignment between rotor segments and two separate stator parts.

3. Design Considerations

3.1. Hybrid Magnet Arrangement

First, the feasibility of hybrid PM types on the proposed PS-SF-HMMM is investigated in advance. The configurations and no-load field distribution of the machines having hybrid PMs with parallel and series circuits are shown in Figure 3. In order to ensure the rationality of the comparison, both the machines are equipped with a “U-shaped” PM type with same magnet usages. The only difference lies in the position of the LCF PM, which is surface-mounted for the series type, and interior-embedded for the parallel type. The distinct difference between field distributions of the parallel machine at the two states indicates its higher flux adjustable capability.

The back-EMF and torque-current characteristics of the two PS-SF-HMMMs under different magnetization states are compared as shown in Figure 4 based on the same peripheral parameters. It shows that the torque capability and flux regulation range of the parallel type significantly exceed those of the series type. This is mainly due to the large magnetic reluctance for the flux loop of the NdFeB PM that acts as the main contributor of air-gap flux in the “series” case. Therefore, the feasibility of the parallel magnetic circuit design is identified, and hence selected for the following investigation.

3.2. Feasible Stator-Slot/Rotor-Pole Combinations

Similar to the conventional SF machines [27,28,29], the PM pole-pair number P_m, rotor iron segment number N_r and pole-pair number of stator windings N_s must satisfy

$$\left|N_r-P_m\right|=N_s$$

(1)

On the other hand, in order to obtain the symmetrical phase flux linkage, the number of the phases N_ph, N_r and N_s must satisfy [22]

$$N_r/GCD(N_r\&N_s)=2N_{ph}ii=1,2,3\dots$$

(2)

where GCD is the greatest common divisor. The winding factor can be calculated by multiplying the distribution factor k_d and pitch factor k_p, which can be represented by [22]

$$k_d=\sin \left(Qk\alpha /2\right)/\left[Q\sin \left(k\alpha /2\right)\right]$$

(3)

$$k_p=\cos \left[\pi k\left(N_r/N_s-1\right)\right]$$

(4)

where Q is the number of the least EMF phasors per phase, α is the electrical angle between two adjacent EMF phasors, and k is the number of harmonic order [22]. By way of example as a unit machine, the winding factors of the 6-stator-slot PS-SF-HMMM are tabulated in

Table 1. Winding Factors of 6-Stator-Slot PS-SF-HMMM with Different Rotor Pole Numbers.

Nr	4	5	7	8	10	11
kd	1	1	1	1	1	1
kp	0.5	0.87	0.87	0.87	0.5	0.87
kw	0.5	0.87	0.87	0.87	0.5	0.87
Nr	13	14	16	17	19	20
kd	1	1	1	1	1	1
kp	0.87	0.87	0.5	0.87	0.87	0.5
kw	0.5	0.87	0.87	0.87	0.5	0.87

. It demonstrates that the maximum winding factor can be obtained when the rotor pole number is close to the multiples of 6, namely 5, 7, 11, 13, 17, and 19. These combinations are chosen for the subsequent parametric optimization. Then, due to the negligible saliency ratio, the sizing equation of PS-SF-HMMMs under brushless AC operation and zero d-axis current control can be given as

$$D_{so}{}^2{l}_a=\frac{P_{out}}{\frac{\sqrt{2}{\pi }^3}{120}\frac{N_r}{N_s}n\eta B_{g\max }{\alpha }_s{k}_l{\lambda }^{2}A}$$

(5)

where D_so is the stator outer diameter (90 mm), l_a is the stack length (25 mm); P_out is the rated output power (~200 W), η is the efficiency, k_l is the flux leakage factor, A is the electric loading (~200 A/cm), n is the rated speed (~400 r/min), α_s is stator pole-arc coefficient, and B_gmax is the maximum air-gap flux density (~0.9 T) corresponding to the full magnetization level of Al-Ni-Co PMs. Once the basic performance requirement is given, the main design envelops D_so and l_a are predetermined.

3.3. Optimization of the Major Design Parameters

In this section, the geometric parameters of the 6-stator-slot PS-SF-HMMMs featuring “N_r = kN_s ± 1” (k = 1, 2, 3) are globally optimized. The cross-sections and corresponding field distributions characterized by “N_r = kN_s − 1” (k = 1, 2, 3) are shown Figure 5. It is apparent that the flux adjusting capabilities of machines with “N_r = N_s − 1” are the lowest owing to the localized magnetic saturation in the inner stator.

The design parameters are tabulated in Figure 6. JMAG 17.0 package is employed for FE simulation. It is worth noting that the copper loss is fixed to 30 W during the optimization approach. The global optimization [29] was performed to maximize average torque at the flux-enhanced state. Subsequently, the PM sizing was refined in order to satisfy the requirements of flux regulation range and unintentional demagnetization withstand capability. After the global optimization, the influences of individual parameters varying around the optimum ones on the torque were investigated in order to establish the general design guidelines for the PS-SF-HMMMs.

For simplicity, the optimization results for only parts of the leading design parameters are presented here. First, various design variables are defined as follows

$${\lambda }_s=D_{si}/D_{so}$$

(6)

$${\lambda }_{so}={\tau }_{so}/{\tau }_{os}$$

(7)

$${\lambda }_{ro}=l_{r1}/{\tau }_r$$

(8)

$${\lambda }_{ri}=l_{r2}/{\tau }_r$$

(9)

where the split ratio λ_s can be defined as the ratio of D_si to D_so; the slot-opening ratio λ_so is defined as the ratio of τ_so to τ_os; the outer/inner rotor pole ratios λ_ro and λ_ri are defined as the ratios of l_r1/l_r2 to τ_r. The globally optimized parameters of all the 6-stator-slot PS-SF-HMMMs with “Z_r = kN_s ± 1” (k = 1, 2, 3) are tabulated in

Table 2. Design Specifications of the 6-Stator-Slot PS-SF-HMMMs.

Items	Parameters
Stator slot/rotor pole number	5/7	11/13	17/19
Outer stator diameter (mm), Dso	90
Inner diameter of outer stator (mm), Dsi	63	67	68
Outer stator tooth width (degree), bst	16	12.5	12.5
Outer stator opening width (degree), τos	43	46	48
Outer diameter of inner stator (mm), Dis	53.5	57	59
Air-gap length (mm), go/gi	0.5
Arc of outer rotor edge (deg.), lr1	30/26	16/18	11/10
Arc of inner rotor edge (deg.), lr2	30/25	16/18	12/11
Rotor thickness (mm), hr	5.5	5.0	4.5
Active stack length (mm), lef	25
LCF PM thickness×length (mm), hm1 × lm1	4/12	3/12	3/12
NdFeB thickness×length (mm), hm2 × lm2	1.7/8	1.5/8	1.5/8
Rated speed (r/min)	400
PM volume (cm3)	19.7	18.2	16.9
Number of phase armature windings	84
Number of magnetizing windings per coil	100

.

3.3.1. Split Ratio

The average torque variation with the split ratio is illustrated in Figure 7a with fixed rated copper loss (30 W). It shows that the torque rises first, and then drops steadily. The torque rose as the PM area enlarged with the increase of the split ratio. However, as the split ratio is higher than the optimal value, the reduced armature area with increasing split ratio results in the torque decrease in turn. It can also be seen that the torque capability of the 11-rotor machine ranks first.

3.3.2. Stator Slot-Opening

Figure 7b depicts the variation of average torque with the slot opening ratio. It can be seen that the optimum slot-opening ratio decreases with the rotor iron segment number. This is due to the fact that the lower stator tooth width for the high rotor iron number cases reduces flux leaked by the adjacent rotor iron segments and stator tooth-tips. That is to say, the torque decreases significantly with the increase of the stator tooth width since the majority of the PM fluxes will be short circuited within the stator tooth part. Besides, the torque decreases dramatically with the increase of slot opening ratio since less flux effectively circulates through the outer stator teeth in those cases.

3.3.3. Outer Stator Back-Iron Thickness

The external stator back-iron thickness h_bi was optimized as shown in Figure 7c. The fluctuation of torque indicates that the narrow h_bi gave rise to the large magnetic reluctance for the main air-gap flux, while the over-wide h_bi reduced the slot areas. It can be observed that the optimal h_bi equals to 3.5 mm, regardless of the rotor pole numbers.

3.3.4. Outer Stator Tooth-Tip Width

The variation of torque with the external stator tooth-tip width l_tip is shown in Figure 7d The slight fluctuation of torque profiles can be observed for all the cases. It demonstrates that the narrow l_tip leads to the reduction of the effective PM fluxes penetrating through the stator, while the PM flux leakage increases as l_tip exceeds the optimum value. It can be observed that the optimal l_tip is equal to 6.5 degrees for all the machines with different rotor pole numbers.

3.3.5. Rotor Pole Ratios

The influences of the inner or outer rotor pole ratios on the average torque are illustrated in Figure 8a,b respectively. The results indicate that the excessive rotor arches leads to the flux leakage, and consequently the torque capability is compromised. However, the effective flux linkage will descend as the rotor pole ratio drops to become lower than the optimum value.

3.3.6. Rotor Radial Thickness

The rotor radial thickness is optimized as shown in Figure 8c. The torque rises first radically within a certain range, and then drops gradually, which is due to the significant flux leakage within the rotor and inner stator parts when the rotor thickness exceeds the optimum values. Moreover, it can be visualized that the higher the rotor iron segment number, the lower the optimum rotor radial thickness, since a thicker rotor pole causes more flux leakage between two adjacent rotor iron segments for the high rotor number cases.

3.3.7. PM Dimensions

The dual magnet dimensions are further refined with the restriction of the other optimized parameters, as previously mentioned. The variations of torque and flux adjusting ratio with the magnet thickness and length are shown in Figure 9. It is worth mentioning that the flux adjusting ratio is defined as the ratio of phase flux linkages under the flux-enhanced and weakened states. It is obvious that the torque capability is more sensitive to magnet thickness rather than the magnet width, while the flux adjusting ratio rarely fluctuates with the variation of magnet thickness, which matches well with the preceding analyses. In addition, the flux adjusting ratio increases at first, and then drops drastically with the increase of LCF magnet width, which is attributed to the demagnetization occurring in the low LCF PM with lower widths. Whereas, the over-wide LCF PM width will lead to the magnetic saturation in the inner stator iron, and hence limiting the flux adjusting ability. Besides, the on-load demagnetization withstand capability of LCF PMs should be examined to get rid of the unexpected performance degradation. The unintentional demagnetization ratio (DR) due to the load effect can be defined as [22]

$$DR=\frac{\left({\psi }_1-{\psi }_2\right)}{{\psi }_1}\times 100\%$$

(10)

where ψ₁ and ψ₂ are the phase flux linkages of the machine before and after q-axis current excitation (40A). Figure 9c shows the variation of DR with the PM dimensions. It can be seen that the LCF thickness and width (3 mm/15 degree) can achieve the satisfactory trade-off. As a result, the flowchart of the overall design procedure is shown in Figure 10, which mainly includes the parameter initialization, the magnet arrangement design, parameter optimization and LCF PM sizing refinement, etc. If the predicted performances and specifications do not match very well, the fixed value of the parameters at the start of this design should be refined until they match well with each other. This process may take several iterative loops to get satisfactory results. FEM was employed to check the analysis results of the preliminary design stage.

The torque capability of the optimized 6-stator-slot PS-SF-HMMMs with various rotor pole pieces is analyzed and compared in Figure 11. Although the operating frequency of the machines satisfying “N_r = 3N_s + 1” is higher, they still produce lower average torque than those satisfying “N_r = 2N_s + 1”, which can be attributed to the significant flux leakage, as evidenced in Figure 5. In addition, it demonstrates that the machines with “N_r = 11” have highest torque capability, which was selected for the prototype manufacturing.

4. Experimental Validation

An optimized 6-stator slot/11-rotor pole prototype is fabricated for experimental validations to verify the preceding analyses. The prototypes and test platform are shown in Figure 12. The open-circuit phase back-EMFs for the 6-stator slot/11-rotor pole machine subject to various MSs have been measured and compared with FE predictions as shown in Figure 13a. Meanwhile, the measured and FE-simulated torques versus rotor position and q-axis current characteristics are demonstrated in Figure 13b,c, respectively. It can be founded that a slight mismatch between 2-D FE predictions and measurements exists, because end-effect and mechanical tolerance are not considered in the 2-D FE simulation [30,31,32]. Hence, the three-dimensional (3-D) FE method is conducted, and the relative errors between FE and measured results are tabulated in

Table 3. Relative Errors between FE and Measured Results of PS-SF-HMMMs.

Items	2D FE	3D FE	Measured	Error (%, 2D/3D)
Fundamental EMF @ Flux-enhanced	3.24	2.98	2.82	14.89/5.67
Fundamental EMF @ Flux-weakened	0.93	0.84	0.79	17.72/6.33
Rated-load average torque @ Flux-enhanced	1.88	1.75	1.68	11.90/4.17
Rated-load average torque @ Flux-weakened	0.55	0.50	0.42	23.63/19.05

. It can be observed that the error increases with the reduction of magnetization state of LCF PMs, which is mainly attributed to more severe fraction and mechanical tolerances at the flux-weakened state [33,34,35,36]. Overall, good agreement can be obtained between 3D-FE predictions and experimental measurements. Thus, the validity of the theoretical analyses was verified.

5. Conclusions

In this paper, the general design considerations of the PS-SF-HMMM were analyzed. In the proposed PS-SF-HMMM, the design of PM and armature windings on the two separate stators allows the torque improvement over its single-stator counterpart. The feasibility of hybrid magnet arrangements was investigated in advance. The results show that the parallel magnetic circuit type is preferable due to its higher torque capability and flux adjusting performance. In addition, the stator slot/rotor pole number combination and various design parameters were optimized. It can be found that the machines with “N_r = 2N_s ± 1” exhibit the highest torque. The design guideline for PM sizing was also provided, which aims to achieve better balanced torque capability, flux adjusting range, as well as the unintentional demagnetization withstand ability. Finally, a 6-stator slot/11-rotor pole prototype was fabricated to experimentally validate the feasibility of the design approach.