Quantitative comparison of low-cost electrical machines with soft magnetic composite and ferrite magnet materials

Abstract

Because of its special structure and manufacturing process, the soft magnetic composite (SMC) material has shown its advantages over silicon sheets, including magnetic and thermal isotropy, low high-frequency core loss, low material wastes during its manufacturing process, etc.. Considering the price of SMC raw material can be very cheap in the future, it is an ideal material for developing the low-cost electrical machine. Combined with SMC cores and low-cost ferrite magnets, some electrical machines with SMC and ferrite magnets for low-cost applications were developed in the past decades, which include the transverse flux flux switched permanent magnet motor (TFFSPMM), axial flux claw pole permanent magnet motor (AFCPM), axial flux vernier motor (AFVM), dual rotor axial flux permanent magnet motor (DRAFM) and axial radial flux permanent magnet motor (RAFM). To better utilize SMC material, all these machines are designed following the design guidelines of SMC machines. Though both of them with good performance for low-cost applications, it is necessary to know the main advantages of each machine. The main target of this paper is to compare these machines quantitatively. For obtaining the comparison results fairly all these machines are optimized by using the sequential robust Taguchi method. Finally, it can be seen that the AFVM and TFFSPMM are with relatively high torque ability and the DRAFM is with high efficiency and power factor ability.

Keywords

Soft magnetic composite quantitative comparison flux switching claw pole motor vernier machine axial flux machine

1. Introduction

Soft magnetic composite (SMC) material is a relatively new soft magnetic material manufactured by iron powders surrounded by the insulation layer. For forming the cores for an electromagnetic device, the SMC powders will be compacted to have the shape of cores, and then heat treated to have a good mechanical and electromagnetic characteristics. Compared with silicon sheets, the SMC has the merits of low eddy current loss and magnetic isotropy characteristics [1–3]. However, its hysteresis loss is very high, therefore, SMC is a good soft magnetic material for developing high-frequency electrical machines, e.g., high-speed electrical machines or electrical machines with high pole pair numbers. Meanwhile, for full utilization of the magnetic isotropy characteristic of SMC material, the electrical machine with SMC cores is always designed with a 3D magnetic flux path, e.g., the transverse flux machine, axial flux machine, or radial flux machine with extended stator teeth in the axial and radial direction. Compared with the radial flux and axial flux machine with silicon sheet, the extended stator teeth in the axial or radial direction will bring more magnetic fluxes for the windings, therefore the power density can be improved greatly. On the other hand, its permeability is much lower than that of silicon sheets and its hysteresis loss is much higher than that of silicon sheets. The electrical machine with SMC cores needs to be designed with permanent magnet excitation and a rated operation frequency higher than 300 Hz or more since the permanent magnet machine is not sensitive to the permeability of its employed soft magnetic material and low-frequency operation will bring the SMC machine with much higher core loss than that with silicon sheets [4].

In the past two decades, many electrical machines with SMC cores have been proposed, developed, and optimized for many driving applications. Among these machines, the transverse flux machine and axial flux machine show their better electromagnetic performance [5,6]. In the axial flux machine with SMC cores, a double stator axial flux machine using SMC cores with an emphasis on the cogging torque reduction is proposed in [7], and an axial flux machine developed for high-speed operation with an emphasis on cooling design improvement is proposed in [8], moreover, an axial flux permanent magnet machine with SMC cores is developed for the high power density driving applications in [9]. For the transverse flux machine with SMC cores, combined with the claw pole machine structure, flux switching operation principle and flux reversal operation principle, a flux reversal claw pole machine is proposed in [10], and a flux switching claw pole machine is proposed in [11], for improving the performance of claw pole machine, the new claw pole machine with S shape winding is proposed in [12]. Considering the SMC has the disadvantage of low permeability, the combined silicon sheets, and SMC cores are employed for fabricating the claw pole machine [13].

Furthermore, as electrical machines can be designed with flux concentrating structure, and based on this kind of structure, they can be designed with low-cost ferrite magnets for achieving high magnetic load and thus good performance [14]. Meanwhile, as SMC has the advantages of magnetic isotropy characteristics, it can provide the electrical machine with an additional flux concentrating path. Therefore, based on the low cost ferrite magnet, several electrical machines with SMC cores were proposed for low-cost applications in the past years, and each of them meets the design guidelines of the SMC machine and has relatively good performance [15,16]. However, from the machine topology viewpoint, it is difficult to know which of them is the best one, as each of them has its characteristic and it is a lack of a comparative study between these machines.

Fig. 1.

(a) Topology of TFFSPMM, (b) stator core, coil and PM, (c) rotor core, (d) rotor core with its teeth shifts.

In this paper, five electrical machines with SMC cores and low-cost ferrite magnets are compared quantitatively, including the transverse flux flux switched permanent magnet machine (TFFSPMM), axial flux claw pole permanent magnet machine (AFCPM), axial flux vernier machine (AFVM), dual rotor axial flux permanent magnet machine (DRAFM) and axial radial flux permanent magnet machine (RAFM), all of them are employed for low-cost home applications [17–21]. In this paper, the main topology of these machines is presented, and for achieving fair comparison results, the main design parameters of these machines are optimized by using the sequential robust Taguchi method with the same objective. Finally, the comparison results show that the AFVM and TFFSPMM are with relatively high torque ability and the DRAFM is with high efficiency and power factor ability.

Fig. 2.

(a) Topology of AFCPM, (b) rotor core and PM, (c) claw poles, coil and stator yoke, (d) complete stator.

2. Topology and operation principle of SMC machines

2.1. Transverse flux flux switched permanent magnet machine

Figure 1 shows the main topology of one phase of TFFSPMM, the whole machine is composed of three phases where the adjacent phases have to be shifted by 120 electric degrees with each other. As shown, both the permanent magnet (PM) and winding are located on the stator, and the rotor is only made by using the SMC. The PMs and the stator cores are arranged alternatively to form a ring shape, the PMs are magnetized along the circumferential direction and the magnetization direction of the adjacent PMs are opposite. Moreover, the rotor teeth shifting technique method is employed for reducing the torque ripple, as the torque ripple of initial TFFSPMM is very high which will bring the machine with vibration and noise [22–24]. Figure 1(c) shows the initial rotor structure and Fig. 1(d) shows the rotor structure with the rotor teeth shifted at a determined angle for reducing its cogging torque, where A _original is 22.5° and A _shift is 27.2°.

Fig. 3.

(a) Overall topology of AFVM with part windings, (b) air gap, (c) rotor, (d) stator core.

2.2. Axial flux claw pole permanent magnet machine

Figure 2 shows the main topology of one phase of AFCPM. Similar to the transverse flux machines, the whole machine is composed of three phases where the adjacent phases have to be shifted 120 electric degrees from each other. The AFCPM combined the merits of the axial flux machine and PMCPM, its stator core is composed of a disk shape stator yoke, some claw pole teeth, and a ring winding. The PMs are magnetized along the circumferential direction and the magnetization direction of the adjacent PMs is opposite. The operation principle of the AFCPM is quite similar to the traditional PMCPM, the main difference is its air gap flux density is along the axial direction.

Fig. 4.

(a) Topology of DRAFM, (b) stator winding, (c) stator core, (d) rotor and PM.

2.3. Axial flux vernier machine

Figure 3 shows the main topology of AFVM. As shown, it has one spoke PM rotor in between two stators. Compared with conventional AFVM made by silicon sheet cores, the stator teeth of analyzed AFVM are extended in the radial direction as its rotor cores and stator cores are made by using SMC materials. Similar to AFCPM and TFFSPMM, the PMs are magnetized along the circumferential direction, and the magnetization direction of adjacent PMs is opposite. The windings are wounded on the stator yoke. As shown, the outer radius of the winding is the same as that of the stator core, and the stator teeth have the same plane as the winding in the axial air gap surface. Therefore, more magnetic flux can be linked by each winding.

Fig. 5.

(a) Topology of RAFM, (b) stator core and PM, (c) stator core.

2.4. Dual rotor axial flux permanent magnet machine

Figure 4 shows the main topology of DRAFM. As shown, the DRAFM is with 6 stator slots and 4 rotor poles, its stator is in between two external rotors. For reducing the imbalanced force between the stator and rotor, the double rotor structure is employed. Figure 4(c) shows the specific structure of the stator. As shown, the rectangular slot shape is employed for achieving more slot space to put the winding. Similar to AFCPM and TFFSPMM, the PMs are magnetized along the circumferential direction, and the magnetization direction of the adjacent PMs is opposite.

2.5. Axial radial flux permanent magnet machine

Figure 5 shows the main magnetic topology of RAFM, it can be seen that both the radial flux and axial flux have been employed for producing the magnetic flux, and the winding is enclosed by the stator teeth. The PMs located on the axial rotor are magnetized along the axial direction while those located on the radial rotor are magnetized along the radial direction, meanwhile, the magnetization direction of the adjacent PMs is the opposite.

3. Design optimization based on Taguchi method

For comparing the main performance of these five electrical machines fairly, all these machines are optimized under the same conditions in this paper. During the optimization process, the air gap length of these machines is kept to equal 1 mm, and they are all designed with the same volume. As these machines are with 3D magnetic flux structures, the 3D finite element method (FEM) is employed for the parameter calculation and performance analysis.

The sequential robust Taguchi method is adopted for achieving the optimization results quickly. Figure 6 illustrates the flowchart of the robust Taguchi method [25].

Fig. 6.

Flowchart of the robust Taguchi method.

Step 1: Define the objective function, design parameters, and their ranges (or the initial design space) for the motor.

Step 2: For the initial design space, select a level number for each control factor, and implement the conventional Taguchi parameter design to identify the best combination of the control factor values.

Step 3: Compute the motor performance with the obtained design and compare it with the last objective. If the relative error between them is less than ϵ (a positive value like 0.5%), finish the optimization process and output the obtained optimal design. Otherwise, go to the next step and reimplement the Taguchi parameter design process.

Taking the TFFSPMM as an example. According to the derivation of the machine power equation in reference [17], the following five parameters determine the main performance of TFFSPMM, the angle of rotor teeth (A_rt ), stator yoke thickness (H _sy), stator teeth length (L _st), stator teeth thickness (H _st), and rotor teeth length (L _rt), which are employed as the main optimization parameters. To implement the robust Taguchi method, an orthogonal array consisting of an inner array (designed for control factors) and an outer array (designed for noise factors that are hard or expensive to control) will be required to implement the simulation of machine performance. Table 1 lists the initial values and ranges of the design parameters.

Table 1

Design parameters and ranges

Par	Unit	Initial	Min	Max
A _rt	deg	15	14	18
H _sy	mm	6	3	8
L _st	mm	15	14	20
H _st	mm	5	3	8
L _rt	mm	5	3	8

During the manufacturing process of the electrical machines, some design parameters cannot be controlled precisely, therefore the performance of the obtained electrical machine will be changed. In robust design optimization, these manufacturing errors can be represented as the noise factor. Tables 2 and 3 list the five control factors and four noise factors as well as their design levels. As shown, there are four levels for each control factor and 2 levels for each noise factor.

Table 2

Levels of control factors

Control factor	Unit	Levels
		1	2	3	4
A _rt	deg	15	15.5	16	16.5
H _sy	mm	4.5	5.5	6.5	7.5
L _st	mm	15	16	17	18
H _st	mm	3.5	4.5	5.5	6.5
L _rt	mm	3	4	5	6

Table 3

Levels of noise factors

Noise factor	Unit	Levels
		1	2
ΔH _sy	mm	+0.1	−0.1
ΔL _st	mm	+0.1	−0.1
ΔH _st	mm	+0.1	−0.1
ΔL _rt	mm	+0.1	−0.1

Table 4 lists the orthogonal array generated from these factors. As shown, it has 16 rows to form the inner array. These rows are defined by those control factors. The outer array has 8 columns, and they are listed as 1111, 1112, 1221, 1222, 2121, 2122, 2211, and 2212 in the table. 1 or 2 represents the level of the noise factor. For example, the first 1 in 1221 means the stator yoke thickness (H _sy) of TFFSPMM is 4.6 mm. It is calculated by 4.5 + 0.1, where 4.5 mm is the initial design value. Therefore, 128 (16 × 8) combinations (FEM samples) need to be calculated. Based on FEM, the average torque and torque ripple of these samples can be obtained. To determine the best values of control factors, an objective function is defined as follows $\begin{eqnarray}y(i,j)=1.5\frac{T_{\text{av}e_{\text{initial}}}}{T_{\text{ave}(i,j)}}+0.5\frac{T_{\text{rip}(i,j)}}{T_{\text{rip}_{\text{initial}}}}\end{eqnarray}$ (1) where T _ave and T _rip are the average torque and torque ripple, respectively, subscript initial means the corresponding performance parameters of the initial design as listed in Table 1, i (1,2, …,16) and j (1,2, …,8) are the experiment numbers of the control and noise factors, respectively. Table 4 lists the calculated objective values for these 128 simulations.

Table 4

The orthogonal array and objective values for TFFSPMM

	Control factors					Noise factors
No	1	2	3	4	5	1111	1112	1221	1222	2121	2122	2211	2222
1	1	1	1	1	1	1.984	1.991	1.987	2.043	2.004	2.040	1.932	2.045
2	1	2	2	2	2	1.880	1.936	1.865	1.899	1.873	1.899	1.827	1.873
3	1	3	3	3	3	1.813	1.885	1.867	1.894	1.842	1.880	1.829	1.866
4	1	4	4	4	4	1.884	1.963	1.855	1.854	1.849	1.853	1.890	1.892
5	2	1	2	3	4	1.688	1.751	1.728	1.777	1.737	1.750	1.767	1.724
6	2	2	1	4	3	1.663	1.709	1.728	1.761	1.730	1.766	1.727	1.794
7	2	3	4	1	2	2.115	2.222	2.094	2.183	2.081	2.191	2.098	2.169
8	2	4	3	2	1	1.993	2.082	2.008	2.031	1.995	2.016	1.920	2.076
9	3	1	3	4	2	1.705	1.755	1.730	1.718	1.732	1.771	1.765	1.770
10	3	2	4	3	1	1.905	1.918	1.829	1.920	1.827	1.898	1.760	1.922
11	3	3	1	2	4	1.828	1.882	1.755	1.801	1.775	1.772	1.813	1.859
12	3	4	2	1	3	1.946	1.999	2.094	2.200	2.135	2.202	2.005	2.109
13	4	1	4	2	3	1.760	1.757	1.837	1.842	1.834	1.835	1.995	1.884
14	4	2	3	1	4	1.833	2.080	1.890	2.071	1.905	2.074	2.029	2.067
15	4	3	2	4	1	1.796	1.782	1.869	1.908	1.866	1.906	1.742	1.796
16	4	4	1	3	2	1.801	1.817	1.760	1.744	1.758	1.722	1.704	1.830

According to the Taguchi parameter design, the signal/noise (S/N) ratio is employed to identify the best combination of control factor values.

There are two main steps for the calculation of the S/N ratio. First, compute the S/N ratio (dB) for each row of the inner array. As the design target is smaller the better, the calculation equation is $\begin{eqnarray}SN(i)=-10\times \lg \left[\frac{1}{8}\times \mathop{\sum }_{j=1}^{8}y^{2}(i,j)\right].\end{eqnarray}$ (2) Table 5 lists the calculated S/N ratio for each row of the inner array or the number of the simulation for the control factors. Second, calculate the average S/N ratio for all levels of control factors based on the obtained S/N ratios given in Table 5. $\begin{eqnarray}\displaystyle R(H_{st},3) & = & \displaystyle \frac{SN(3)+SN(5)+SN(10)+SN(16)}{4}\nonumber\\ \displaystyle & = & \displaystyle -5.15∼\text{dB}\end{eqnarray}$ (3) For example, the average S/N ratio for the third level of the control the numbers 3, 5, 10, and 16 can be found in the orthogonal array Table 5. Table 6 tabulates the calculated average S/N ratios for all factors.

Table 5

S/N ratio for the inner array

No	S/N ratio	No	S/N ratio
1	−6.04	9	−4.83
2	−5.49	10	−5.45
3	−5.39	11	−5.16
4	−5.48	12	−6.39
5	−4.81	13	−5.32
6	−4.79	14	−6.00
7	−6.63	15	−5.27
8	−6.09	16	−4.95

Table 6

Average S/N ratio for each level of control factors

Factor	Level	S/N ratio	Factor	Level	S/N ratio
A _rt	1	−5.60	L _st	3	−5.58
	2	−5.58		4	−5.72
	3	−5.46	H _st	1	−6.27
	4	−5.38		2	−5.51
H _sy	1	−5.25		3	−5.15
	2	−5.43		4	−5.09
	3	−5.61	L _rt	1	−5.71
	4	−5.73		2	−5.47
L _st	1	−5.23		3	−5.47
	2	−5.49		4	−5.36

Figure 7 shows the average S/N ratios for all levels of each control factor. As the design target is smaller the better, the best level of each factor is the one that has the highest S/N ratio. Therefore, levels 4, 1, 1, 4, and 4 are the best for the five control factors, respectively. Under the optimal level, the optimal performance of the motor in this iteration can be obtained. For TFFSPMM with this optimal design, the average torque is 2.92 N m, which is better than the initial design (2.23 N m).

Fig. 7.

Illustration of S/N ratios for all factors.

Fig. 8.

Optimization processes of TFFSPMM.

As the design target is smaller the better, the best level of each factor is the one that has the highest S/N ratio.

Therefore, levels 4, 1, 1, 4, and 4 are the best for the five control factors, respectively. For TFFSPMM with this optimal design, the average torque is 2.92 N m, which is better than the initial design (2.23 N m).

By using the Taguchi method, the optimal design can be found, and the optimized objectives can be obtained for this round. For obtaining the best design, the sequential optimization design is employed, then the levels for each control factor will be updated with new levels, and the new optimal design can be obtained. Comparing two optimal objectives when their difference is lower than 0.5%, the optimization process will end. Otherwise, the levels will be updated furthermore, and the Taguchi method will be adopted again.

Figure 8 shows the value of the objective function under the optimal level selected by each iteration in the optimization process. As shown, for the TFFSPMM three times iterative are required for obtaining the final optimization results. The difference between the objective values obtained in the second and third iterations is less than 0.5%, which satisfies the convergence condition and ends the optimization.

Table 7 tabulates the parameter values obtained in each iteration. After the design optimization, it can be seen that the torque ripple of TFSPMM is 6.8%, and the average torque is about 3.03 N m, compared with the initial design the average torque has been improved by about 36%.

Table 7

Optimization results of every iteration

Par	A _rt/deg	H _sy /mm	L _st /mm	H _st /mm	L _rt /mm
Initial	15.00	6.000	15.00	5.000	5.000
1	16.50	4.500	15.00	6.500	6.000
Level	15.00	4.500	15.00	3.500	3.000
	15.50	5.500	16.00	4.500	4.000
	16.00	6.500	17.00	5.500	5.000
	16.50	7.500	18.00	6.500	6.000
2	17.00	3.500	15.00	7.000	6.500
Level	16.50	3.000	14.00	6.500	6.000
	17.00	3.500	14.50	7.000	6.500
	17.50	4.000	15.00	7.500	7.000
	18.00	4.500	15.50	8.000	7.500
3	17.00	3.525	14.95	7.050	6.575
Level	16.75	3.450	14.90	7.000	6.500
	17.00	3.475	14.95	7.025	6.525
	17.25	3.500	15.00	7.050	6.550
	17.50	3.525	15.05	7.075	6.575

By using the same optimization method, the other four SMC machines have been optimized. Figure 9 shows their optimization process. The main dimensions for these five SMC machines are tabulated in Table 8. The material type of ferrite permanent magnet is Y30, the residual magnetic flux density is 0.38 T, the maximum magnetic energy product is 27 KJ/m³, and the coercive force is 188 KA/m.

Fig. 9.

Optimization processes.

Table 8

Main dimensions of five machines

	TFFS	AFC	AF	DRA	RA
	PMM	PM	VM	FM	FM
Outer radius/mm	50.0	50.0	66.0	50.0	66.0
Axial length/mm	31.0 × 3	31.0 × 3	55.0	93.0	53.4
Air gap/mm	1.0	1.0	1.0	1.0	1.0
Slot fill factor	0.6	0.6	0.6	0.6	0.6
Number of turns	56	56	92	92	92
Angle of PM/deg		21	7	88	31
Angle of stator teeth/deg	17	19			26
PM length in axial/mm	7.1	15.0	17.7	22.3	3.5
Thickness of stator yoke/mm	16.9	3.4	14.2	19.3	31.0
Length of stator yoke/mm	3.5	39.5	25.5	10.9	26.4
Width of stator yoke/mm			10.9	26.9

4. Performance comparison

The main parameters and performance of these optimized SMC machines are compared in this section, based on 3D FEM.

4.1. No load flux density and air gap flux density distribution

By using the 3D FEM, the no load flux density distribution of these SMC machines can be obtained, as shown in Fig. 10. It can be seen that the maximum flux density on these SMC machines is much higher than the residual flux density of employed ferrite magnet Y30 of 0.38 T. The magnetic flux density on the stator teeth of TFSPMM is about 1.0 T. The flux density on the stator yoke of DRAFM is about 1.4 T as the flux is not only concentrated by the spoke PM rotor but also concentrated on the stator. Meanwhile, for the AFVM, the flux density on its stator yoke is lower than that on its stator teeth as many harmonics existed.

Fig. 10.

No load flux density distribution on these SMC machines, (a) TFFSPMM, (b) AFCPM, (c) AFVM, (d) DRAFM, (e) RAFM.

Fig. 11.

Air gap flux density distribution, (a) TFFSPMM, (b) AFCPM, (c) AFVM, (d) DRAFM, (e) radial air gap flux of RAFM, (f) axial air gap flux of RAFM.

Fig. 12.

PM flux linkage per turn comparison.

Fig. 13.

Self-inductance per turn comparison. (a) TFFSPMM, AFCPM, DRAFM and RAFM. (b) AFVM.

Fig. 14.

Loss and electromagnetic power.

Figure 11 shows the air gap flux density distribution of these machines. For the TFSPMM, its radial flux density distribution is calculated as shown in Fig. 11(a). For the RAFM both the radial flux and axial flux density are calculated as shown in Fig. 11(e), while for the other machines only the axial air gap flux density is calculated.

4.2. PM flux linkage and inductance

Figure 12 shows the PM flux linkage per turn comparison of these SMC machines. It can be seen that the PM flux linkage of AFVM is the highest one. The PM flux linkage of DRAFM is the second one. The other SMC machines are with similar PM flux linkage. For the AFVM, though its air gap flux density is quite low, its PM flux linkage is the highest one as the determined high order flux density harmonics are employed. Figure 13 shows the inductance comparison. Due to the high order harmonics employed, the self-inductance of AFVM is much higher than that of other SMC machines. As shown its average self-inductance per turn is about 16.45 mH. The self-inductance of TFFSPMM is not fluctuating versus the rotor position while the inductance of other SMC machines fluctuates versus the rotor position. The main reason is that the leakage inductance dominates the self-inductance of TFFSPMM.

4.3. Loss and electromagnetic power

Figure 14 shows the core loss, copper loss, and electromagnetic power of these machines under the rated current density of 6 A/mm² and the rotor speed of 1000 rpm. As shown the electromagnetic power of AFVM is the highest one, however, its core loss is the highest one as well, the main reason is its harmonics are very high.

4.4. Torque characteristics and power factor

Cogging torque results from the interaction between the rotor PM or stator PM to the stator teeth or rotor teeth, which can bring the machine high vibration and noise. The average value of cogging torque is zero, however, for the different positions, its value is not zero. Moreover, it can affect the start of the machine. Figure 15 shows the calculated cogging torque of these machines, it can be seen that the cogging torque of AFCPM is the highest one.

Figure 16 shows the torque waveform of these machines under the rated working state. As shown, the torque ability of AFVM is the highest one, the second one is the TFFSPMM, and the torque ability of RAFM is the lowest one. The relationship between the average torque and the current density is shown in Fig. 17. The torque ability of AFVM is the highest one, followed by TFFSPMM. the average torque of RAFM is the lowest one. When the current density is below 6 A/mm², the torque ability of AFCPM is greater than that of DRAFM.

Fig. 15.

Cogging torque comparison.

Fig. 16.

Torque waveform comparison.

Figure 18 compares the power factor versus the current density of these machines, it can be seen that the power factor decreases with the employed current density increase. Among these machines, the power factor ability of TFFSPMM and AFVM is not good, though their torque ability is higher than the other machines. The main reason is that the leakage fluxes are high for these two machines. The TFFSPMM-C is the machine with the cogging torque reduced, and compared with the TFFSPMM its power factor has been reduced as well.

4.5. Core loss and efficiency map

Efficiency map is an effective way to evaluate the performance of electrical machine, it can show the performance of electrical machine under different working states. For obtaining the efficiency map, the efficiency of electrical machine under various working states needs to be calculated first, which can be calculated by, $\begin{eqnarray}{\eta}=\frac{P_{\text{out}}}{P_{\text{in}}}=\frac{P_{\text{em}}-P_{\text{core}}-P_{\text{mech}}}{P_{\text{em}}+P_{\text{copper}}}\end{eqnarray}$ (4) where 𝜂, P _out, P _in, P _em, P _core, P _mech, and P _copper are efficiency, output power, input power, electromagnetic power, core loss, mechanical loss, and copper loss respectively. The mechanical loss is estimated to equal about 1.5% of the output power.

Fig. 17.

Torque versus current comparison.

Fig. 18.

Power factor comparison.

Fig. 19.

Core loss map comparison, (a) TFFSPMM. (b) AFCPM. (c) AFVM. (d) DRAFM. (e) RAFM.

Fig. 20.

Efficiency map comparison. (a) TFFSPMM. (b) AFCPM. (c) AFVM. (d) DRAFM. (e) RAFM.

Fig. 21.

Consumed material weight comparison.

Table 9

Performance comparison of five machines

	TFFS	AFC	AF	DRA	RA
	PMM	PM	VM	FM	FM
Power (W)	317	225	547	195	136
Torque (N m)	2.31	1.81	6.14	1.78	1.31
Torque per unit weight (N m/kg)	0.56	0.48	1.79	0.40	0.34
Efficiency	0.935	0.938	0.880	0.939	0.802
Mass (kg)	4.11	3.79	3.43	4.42	3.90

Figure 19 shows the calculated core loss map of these machines. As there is no reluctance torque can be adopted for these machines, the d-axis current equals zero is employed for the machine control. It can be seen that the core loss increases quickly as the rotor speed increases, and the core loss of AFVM is much higher than the other machines as its harmonics is very high. Meanwhile, as the operation frequency of DRAFM is the lowest one, its core loss is the lowest one as well.

Based on the calculated core loss map, the efficiency map of these machines is obtained as shown in Fig. 20. The maximum efficiency of DRAFM can reach 0.939. however, the maximum efficiency of RAFM is about 0.802, which is the lowest one among the five machines.

4.6. Material weight and overall comparison

Figure 21 shows the comparison of the material consumed in these machines. The total material consumed in DRAFM is the highest one, while that consumed in the AFVM is the lowest one. Among the SMC, ferrite magnet, and copper, copper is the most expensive material, as shown the copper consumed in the TFFSPMM is the highest one, therefore the cost of TFFSPMM is the highest one among these machines. As tabulated in Table 9, the torque/weight of AFVM is much high than the other machines, therefore it is an ideal machine for high performance low cost drive applications, though, its main disadvantage is the low power factor ability.

5. Conclusion

Five electrical machines with SMC cores and ferrite magnets are compared quantitatively in this paper, for obtaining the comparison results fairly, all these machines are optimized with the same outer volume. Among these machines, it can be seen that the AFVM is with very high torque ability, and its torque/weight ratio is much high than the other electrical machines, however, its power factor and efficiency are not high as the determined high order harmonics are employed for producing the torque in this machine. Meanwhile, the TFFSPMM is with the second highest torque ability and DRAFM is with the highest power factor ability and efficiency. Among these electrical machines, our future work is to improve the power factor and efficiency of AFVM.

Footnotes

Acknowledgement

This work was supported in part by the National Natural Science Foundation of China under Grant 52007047, and in part by the Outstanding Youth Innovation Project funded by State Key Laboratory of Reliability and Intelligence of Electrical Equipment EERI_OY2021005, and S&T Program of Hebei 21567605H.

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