Novel Design of Six-Phase Spoke-Type Ferrite Permanent Magnet Motor for Electric Truck Application

Abstract

This paper proposes a 300 kW 24-slot/10-pole 6-phase stator-shifted fractional-slot concentrated winding spoke-type ferrite permanent magnet machine for electric truck applications. The proposed motor consists of a stator with dual three-phase windings positioned 75 degrees apart to reduce higher-order MMF harmonic order, and a rotor with an inexpensive and high-resistance ferrite permanent magnet in the spoke configuration. The simulated result of the stator-shifted machine is compared with a fabricated stator-shifted machine, and the results show good agreement with each other. To further reduce the torque ripple from 2.5 to 0.9% while maintaining a high maximum torque of 2980 Nm, circular voids with a diameter of 11 mm are embedded in the rotor. The proposed motor is evaluated for irreversible demagnetization, mechanical and thermal stability, and fault tolerant ability. To assess the proposed motor performance, the electric truck simulation model is constructed using MATLAB/Simulink and used to compare with the reported 12-slot/10-pole rare-earth permanent magnet-based machine. Compared to a previously reported six-phase rare-earth permanent magnet based flat-type machine, the proposed motor can save 4.3 kWh of energy with a USD 2512 lower cost while retaining a similar motor performance.

1. Introduction

Throughout the world, many municipal governments have announced the replacement of diesel transit buses with electric buses to reduce the air pollution in cities [1,2,3]. Eliminating diesel exhaust emissions from the diesel transit buses by replacing them with electric buses not only improves the air quality by eliminating 2 million tons of greenhouse gas emissions each year, but also delivers financial benefits, including reduced maintenance and fuel cost by USD 200,000 over the lifetime of the bus, and societal benefits, including reduced health care expenses caused by air pollutants [1,2,3]. It is reported that air pollutants can cause heart attacks, premature deaths, asthma, and other severe health issues. The transit bus is classified as class-7 heavy-duty truck (HDT), which also covers most of the city vehicles, such as street sweepers, garbage, beverage, and furniture trucks. Accordingly, electrifying the class-7 HDTs is essential to substantially reduce air pollution in the city.

Among the reported electric motors used for HDTs, multi-phase rare-earth permanent magnet (RE-PM)-based synchronous machines are widely utilized due to their high torque and power density, maximum speed, and efficiency [1]. For multi-phase machines, fractional-slot concentrated winding (FSCW) is generally utilized because the FSCW provides the inherent fault-tolerant capability, higher winding factor, and lower cogging torque than distributed winding [4,5,6]. However, the FSCW produces unwanted space harmonics in the stator magnetomotive force (MMF), resulting in high eddy current losses in permanent magnet (PM), localized core saturation, and difficulty to produce high reluctance torque from interior-mounted rotor topology [7,8].

To suppress the stator MMF harmonics, various methods, including PM segmentation [4,5], multilayer winding design [9], coils with a different number of turns per coil side [10], and stator-shifting [11], have been reported. Among these MMF harmonic suppression methods, the stator-shifting concept reduces both sub- and high-order stator MMF harmonics effectively without increasing manufacturing costs and material usage [4,5,6,11]. This concept has been validated with various rotor topologies, including surface-mounted and interior-mounted single- and multi-layer V-type rotor topologies [4,5,6]. However, this concept has not been validated for interior-mounted spoke-type rotor topology yet.

For HDTs, rare-earth NdFeB magnets are widely used for permanent magnet synchronous machines (PMSMs) to achieve high torque density, efficiency, and maximum speed by exploiting its high maximum energy product (BH)_max. However, NdFeB RE-PM suffers from high and volatile cost, unstable supply, complicated manufacturing processes, and low electrical resistivity [12,13]. The traction motors of HDTs need PMs with a lower price and more stable supply than the motors used in light-duty vehicles because a high peak power rating in the range from 300 to 360 kW is required for HDTs [1]. The motor must be large enough to produce such a high peak power, requiring a large PM volume. Further, the high electrical resistivity of PM is essential for the motor employing the FSCW winding to minimize the temperature of the PM. The PM temperature rises by the eddy current loss caused by higher-order space harmonics. Thereby, a cost-effective and high electrical resistive PM is demanded to address the above issues.

Among such PMs, hard ferrite shows the most viable solution. Ferrite has USD 86–93 lower cost and 6667-times higher electrical resistivity than NdFeB PM [14]. However, the ferrite-based PM motors suffer from low torque density due to the relatively low magnetization. One of the ways to address this drawback is to employ spoke-type interior-mounted rotor topology. This topology arranges the ferrite PMs in oriented planes to increase the air-gap flux by focusing the PM flux and increasing the reluctance torque [15]. However, this design results in significant flux density distortion in the air gap, causing a high torque ripple. Although many methods, from design-based to control-based, have been reported to minimize the torque ripple, they either decrease the maximum torque or increase an unbalanced axial electromagnetic force [16].

In the previous paper [17], we reported a novel 24-slot/10-pole 6-phase stator-shifted FSCW spoke-type ferrite interior PMSM (6Φ-SS-FSCW-Fer-SIPMSM), exhibiting a peak power of 250 kW, peak torque of 2150 Nm, and torque ripple of 4.1%. The circular-notch torque ripple reduction method and the stator-shift concept were introduced and explained.

In this paper, the proposed 6Φ-SS-FSCW-Fer-SIPMSM is scaled up to produce a peak power of 300 kW, peak torque of 2980 Nm, and torque ripple of 0.9% for quantitative comparison with the reported 300 kW 12-slot/10-pole 6-phase FSCW NdFeB-based flat-type IPMSM (6Φ-FSCW-Nd-FIPMSM) [3]. The circular-notch torque ripple reduction method and stator-shift concepts are further advanced and quantitatively analyzed via winding-function theory, harmonic spectrum analysis, and flux distributions in the motor. In addition, the proposed 6Φ-SS-FSCW-Fer-SIPMSM performance is compared with the conventional 12-slot/10-pole 6-phase FSCW spoke-type ferrite interior PMSM. Lastly, the electric truck model, constructed with MATLAB/Simulink, is used to evaluate the proposed motor performance and efficiency, and for comparison with the reported 6Φ-FSCW-Nd-FIPMSM.

2. Initial Motor Design and Validation

Recently, Morozov et al. evaluated the performance of five 12-slot/10-pole 6Φ-FSCW-Nd-FIPMSM, having various power ratings of 150, 200, 250, 300, and 350 kW, with 4 gearboxes from 3- to 6-speed [3]. Class-7 HDT simulation was performed under various drive cycles. The simulation result show that a 300 kW 12-slot/10-pole 6Φ-FSCW-Nd-FIPMSM with a 3-speed gearbox satisfies the required performance goals of 27 s acceleration time from 0 to 60 mph, 30% starting grade, and 113 km/h top speed with good energy efficiency [3]. Thus, the reported 300 kW 12-slot/10-pole 6Φ-FSCW-Nd-FIPMSM was chosen as a benchmark motor in this paper and investigated more thoroughly.

Table 1. Specifications of benchmark motor. Data from [3].

Parameter	Value
Stator outer/inner diameter [mm]	550/366
Rotor outer/inner diameter [mm]	362/196
Stack length [mm]	300
Number of slots/poles	12/10
Number of turns	64
Number of parallel paths	8
Rated/peak current density [A/m2]	6.3/16.4
Rated/peak current [Arms]	250/636
Copper mass [kg]	135
Maximum torque [Nm]	3110
Soft iron core material	M19–29G

shows the specification of the benchmark motor [3], while Figure 1a shows the schematic of the reported benchmark motor. With the given specification in Table 1, the reported 6Φ-FSCW-Nd-FIPMSM was designed and simulated using ANSYS Maxwell 2D finite-element-analysis (FEA) v.18.1 to validate the reported motor performance. Because the reported literature did not provide a specific grade of Nd-Fe-B PM, the reported 6Φ-FSCW-Nd-FIPMSM with various grades of the Nd-Fe-B PM was first simulated to determine the grade of Nd-Fe-B PM used in the literature. The simulation results show that N42UH grade Nd-Fe-B PM, which has remanent flux density of 1.28 T and coercivity of 955 kA/m at room temperature [18], produces same maximum torque of 3110 Nm as reported by the authors of [3].

To observe the effect of the ferrite PM on motor performance, the reported 6Φ-FSCW-Nd-FIPMSM was simulated with Hitachi’s NMF-12G ferrite PM, which has a remanent flux density of 0.45 T and coercivity of 334 kA/m at room temperature. Due to lower magnetic properties of the ferrite PM than Nd-Fe-B PM, the torque at peak current was significantly reduced from 3110 to 1550 Nm (50% reduction), as shown in Figure 2. In order to improve the torque, four different rotor topologies, including PM-assisted synchronous reluctance machine (PMASynRM), V-type PMSM, surface-mounted PMSM (SPM), and spoke-type PMSM, were simulated and investigated under the same motor specifications, operating conditions, and NMF-12G ferrite PM as in our previous studies [17]. The simulation results show that among the above topologies, the spoke-type topology, which is shown in Figure 1b, delivered the highest torque of 2320 Nm and relatively low back EMF at 3000 rpm, but suffered from high torque ripple. Compared to the reported flat-type topology, the spoke-type topology increased the maximum torque from 1550 to 2320 Nm (49.7% improvement), as shown in Figure 2. This is mainly attributed to the flux concentration effect of the spoke type topology [19] and increased PM volume. The motor, having this spoke-type rotor topology, and the FSCW winding were simulated and verified experimentally by the authors of [19], who showed that the rotor sustained its operation up to 14,000 rpm without mechanical breakdown.

2.1. Winding Configuration

A typical dual 3Φ 12-slot/10-pole configuration with a double layer winding is shown in Figure 3a. According to the authors of [4], the most detrimental MMF harmonics are those close to the torque-producing harmonic. For the five pole-pair motor, the detrimental MMF harmonics are the first and seventh harmonic, whereas the torque-producing harmonic is the fifth harmonic. It was reported that when the phases of the two three-phase windings are shifted by 30°, all harmonics below the torque-producing harmonic can be canceled [20]. However, the harmonics above the torque-producing harmonic, which is the seventh harmonic, remain.

Thus, the concept of stator-shifting was employed to minimize the seventh harmonic by shifting one of the dual three-phase windings with a specific mechanical angle (α) against another three-phase winding, as illustrated in Figure 4. The number of slots and coil pitches must be doubled from 12 to 24 and from 1 to 2, respectively, to accommodate the shifted 3-phase winding. The number of turns was halved from 64 to 32 to maintain the same total copper volume. An optimal α that minimizes the seventh harmonic can be calculated using a winding function theory [16]. Based on the winding function theory, the MMF of the unshifted and α-shifted three-phase winding are:

$$F_1\left(\theta ,t\right)={{\displaystyle \sum }}_{k=1,-5,7}^{\infty }\frac{12N_c{I}_m}{k\pi }\sin \left(\frac{k\pi }{12}\right)·\sin \left(\frac{\left(k-1\right)\pi }{12}\right)·\sin \left(k\theta -\omega t-\frac{\left(k-1\right)\pi }{12}\right)$$

(1)

$$F_2\left(\theta ,t\right)={{\displaystyle \sum }}_{k=1,-5,7}^{\infty }\frac{12N_c{I}_m}{k\pi }\sin \left(\frac{k\pi }{12}\right)·\sin \left(\frac{\left(k-1\right)\pi }{12}\right)·\sin \left(k\theta -\omega t-k\alpha -\frac{\left(k-1\right)\pi }{12}\right)$$

(2)

where N_c is the number of turns, I_m is the peak phase current, and k is the harmonic order. The negative k for the fifth harmonic is required to account for the harmonic sequence direction. Since N_c and I_m were the same for both windings, the total MMF (F_t) was calculated by adding F₁ and F₂, resulting in Equation (3).

$$F_t\left(\theta ,t\right)=F_1\left(\theta ,t\right)+F_2\left(\theta ,t\right)={{\displaystyle \sum }}_{k=1,-5,7}^{\infty }\frac{24N_c{I}_m}{k\pi }\sin \left(\frac{k\pi }{12}\right)·\sin \left(\frac{\left(k-1\right)\pi }{12}\right)·\cos \left(\frac{k\alpha }{2}\right)·\sin \left(k\theta -\omega t-\frac{k\alpha }{2}-\frac{\left(k-1\right)\pi }{12}\right)$$

(3)

where the sum to product trigonometric identifies for sine is used to simplify the equation. As Equation (3) suggests, one of the simple and effective ways to cancel the seventh harmonic is to find the α that can make the term cos(k(α/2)) equal to zero for k = 7. The optimal α is 77.14°. However, realizing such α requires an uneven tooth width. Instead, the α closest to the optimal α and in multiples of tooth pitch, i.e., multiplication of 360°/24 = 15°, meet the requirement. The closest value to the optimal angle of 77.14° and yielding an integer multiple to tooth pitch is 75°, which corresponds to five slots apart from each winding. Figure 3b illustrates the proposed 24-slot/10-pole 6Φ-SS-FSCW-Fer-SIPMSM with an α of 75°.

The MMF distribution and corresponding harmonic spectrum of the conventional 12-slot/10-pole unshifted and the proposed 24-slot/10-pole shifted 6-phase PM machine are shown in Figure 5. As Figure 5b indicates, the stator-shifting design significantly decreased not only the 7th harmonic from 0.79 to 0.1 (87.3% reduction), but also other higher-order harmonics, such as the 17th harmonic, from 0.375 to 0.03 (92% reduction), the 19th harmonic from 0.36 to 0.26 (27.8% reduction), and the 29th harmonic from 0.2 to 0.16 (20% reduction). Hence, the corresponding winding layout with a 75° shift was selected and employed throughout this paper.

To validate the simulation results of the proposed 24-slot/10-pole 6Φ-SS-FSCW-Fer-SIPMSM, the reported 6-phase 18-slot/8-pole V-type IPMSM with a 20° electrical phase shift between two three-phase windings [4] was designed and simulated using ANSYS Maxwell 2D FEA v.18.1. Figure 6 shows the designed motor with a winding layout and prototype. The simulated back electromotive force (EMF) waveforms of the A-B-C windings at 2800 rpm using an in-house FEA tool were investigated and compared with the back EMF waveforms of the A-B-C windings that were measured and reported by the authors of [4]. Figure 7 shows the corresponding performance comparison. As shown, the simulated back EMF shows good agreement with the measured back EMF.

2.2. Electromechanical Performance Comparison

The maximum torque, torque ripple (T_rip), cogging torque (T_cog), and back-EMF harmonic spectrum of the conventional 12-slot/10-pole unshifted and the proposed 24-slot/10-pole shifted 6-phase spoke-type ferrite IPMSM were simulated and compared. The specifications of the conventional and proposed motors are summarized in

Table 2. Specifications of the conventional and proposed motor.

Parameter	Conventional	Proposed
Stator outer/inner diameter [mm]	550/366
Rotor outer/inner diameter [mm]	362/196
Stack length [mm]	300
Number of slots/poles	12/10	24/10
Number of turns	64	32
Number of parallel paths	8	8
Coil pitch	1	2
Rated/peak current density [A/m2]	6.3/16.4
Rated/peak current [Arms]	250/636

. The simulated maximum torque, T_rip, T_cog, and total harmonic distortion (THD) of the back-EMF of the conventional and proposed motors are presented in

Table 3. Performance comparison between the conventional and proposed motor.

Parameter	Conventional	Proposed
Maximum torque [Nm]	2320	2970
Torque ripple (Trip) [%]	10.9	2.5
Cogging torque (Tcog) [Nm]	3.3	3.3
Total harmonic distortion (THD) of back-EMF at 2000 rpm [%]	37.3	33.1

. The T_rip was calculated by Equation (4).

$$T_{rip}=\frac{T_{max}-T_{min}}{\left(T_{max}+T_{min}\right)/2}$$

(4)

where T_max and T_min are the maximum and minimum torque magnitude, respectively. It is noted that the proposed stator-shifted machine increased the maximum torque from 2320 to 2970 Nm (28% improvement), and decreased the T_rip from 10.9 to 2.5% (77.1% reduction) without affecting the T_cog compared to the conventional unshifted machine. The significant increase in the maximum torque is mainly attributed to the increased air gap flux density. Figure 8 shows the air gap flux density at maximum current. Further, the T_rip reduction of 77.1% may be attributed to the suppression of the 8th, 9th, 11th, 13th, 15th, and 17th harmonics in back-EMF, as shown in Figure 9. The suppression led to 11.3% less THD compared to the conventional unshifted motors.

3. Optimal Motor Design and Specification

In this section, the T_rip reducing circular notch method is discussed. The efficiency map with torque versus speed characteristics of the proposed 6Φ-SS-FSCW-Fer-SIPMSM was constructed and compared with the reported 6Φ-FSCW-Nd-FIPMSM. After the mechanical stress analysis at the maximum speed and the thermal analysis at the peak power, the irreversible demagnetization analysis was conducted to assess the reliability of the proposed motor at extremely low temperature of −40 °C and regular temperature at 80 °C.

3.1. Torque Ripple Reducing Circular Notch

Despite the small 2.5% T_rip of the proposed motor, the T_rip needs to be further decreased to reduce any stress affecting mechanical parts of the motor. One circular notch, having a diameter of 10 mm, was introduced on the edge of the rotor near the air gap to achieve T_rip reduction, as shown in Figure 10. A nonmagnetic shaft with a rectangular notch was also introduced to hold the rotor in one piece and rotate it. The performances of 6Φ-SS-FSCW-Fer-SIPMSM with and without the circular notch and a rectangular cavity-based nonmagnetic shaft are summarized in

Table 4. Performance comparison between conventional and proposed motor.

Parameter	No Notch	Circular Notch on Rotor	Notch with Shaft
Torque [Nm]	2970	2980	2980
Torque ripple [%]	2.5	1.2	1.2
Torque ripple difference from no circular void [%]	-	53	53

. A circular notch, having a diameter of 10 mm on the rotor, significantly decreased the T_rip from 2.5 to 1.2% (53% reduction) while retaining the maximum torque. This is mainly attributed to the 0.3–0.4 T increased flux density in the blue dashed rectangular region in Figure 11b compared to the flux density in the blue dashed rectangular area in Figure 11a. This high flux density results in a 10.8% reduction in THD of back-EMF, which may be the main reason for the 53% reduction in the T_rip.

A parametric study ws conducted to investigate the effects of circular notch diameter on the maximum torque and T_rip. Figure 12 shows the maximum torque, T_rip, and the T_cog of the proposed 6Φ-SS-FSCW-Fer-SIPMSM as a function of the circular notch diameter. The maximum torque was unaffected by the circular notch diameter, as shown in Figure 12a, while the T_rip showed a positive quadratic trend. The lowest T_rip of 0.9% (64% reduction compared to that of the motor without notch) was observed for the motor having a circular notch with a diameter of 11 mm, which was also equivalent to 3.04% of outer rotor diameter. This reduction was mainly due to the lowest cogging torque at 11 mm diameter, as shown in Figure 12b. In summary, although the introduction of the circular notch may increase the manufacturing process and cost, the significant T_rip of the motor can be reduced to 0.9%, which can decrease the cost of shock absorbing materials and components. Figure 13 shows the detailed schematic of the proposed 6Φ-SS-FSCW-Fer-SIPMSM, while

Table 5. Machine dimensions of the proposed 6Φ-SS-FSCW-Fer-SIPMSM.

Parameter	Symbol	Value [mm]
Stator
Yoke height	Hy	32
Upper slot width	Wsu	27.5
Bottom slot width	Wsb	15
Slot height	Hs	55
Tooth width	Wt	36
Slot opening height	Hso	3.3
Slot opening width	Wso	3.3
Outer stator radius	Rso	275
Inner stator radius	Rsi	183
Rotor
Rotor opening height	Hro	12.1
Rotor opening width	Wro	20.5
Rectangular cavity 1 height	Hw1	7.3
Rectangular cavity 2 height	Hw2	11.4
Rectangular cavity 3 height	Hw3	12.6
Rectangular cavity 1 width	Ww1	20.8
Rectangular cavity 2 width	Ww2	10.4
Circular notch rotor	Rcir	5.5
Outer rotor radius	Rro	181
Inner rotor radius	Rri	98
Permanent Magnet
Upper permanent magnet width	Wu_pm	31.7
Bottom permanent magnet width	Wb_pm	23.3
Upper permanent magnet height	Hu_pm	37.1
Bottom permanent magnet height	Hb_pm	23.8

shows the detailed machine dimensions.

3.2. Efficiency Map

The efficiency map with the torque-speed characteristics was drawn to evaluate the proposed motor’s base (ω_base) and maximum speed (ω_max) and power efficiency (η). The η at the desired motor torque (T_m) and speed (ω_m) is calculated by Equation (5).

$$\eta =\frac{P_{out}}{P_{in}}=\frac{T_m{\omega }_m}{T_m{\omega }_m+P_{cu}+P_{iron}}$$

(5)

where P_in and P_out are the input and output power, respectively, and P_cu and P_iron are the copper and iron loss, respectively. These losses are given by Equations (6) and (7),

$$P_{cu}=6I_{rms}^2{R}_s$$

(6)

$$P_{iron}=K_{h}f{B}_m^2+K_e{f}^2{B}_m^2$$

(7)

where R_s is the stator winding resistance; f is the frequency in Hz; K_e and K_h are the coefficient of eddy-current and hysteresis loss, respectively; and B_m is the magnetic flux density. For K_e and K_h, 0.409 and 164.2 were used, respectively.

The maximum torque per ampere (MTPA) control was utilized to find the optimal current and current angle to produce the maximum torque until ω_m reaches ω_base. ω_base is a speed when the back-EMF of the motor reaches the maximum dc-link voltage (V_{dc_link}), which can be calculated by Equation (8),

$$V_{dc\_link}=V_{bat}/\sqrt{3},$$

(8)

where V_bat is the battery dc voltage. Dividing V_bat by a square root of 3 is needed because the space-vector pulse width modulation (SV-PWM) limits V_bat at the expense of modulating voltage-fed inverter [21]. Above the base speed, the flux weakening control was applied to extend the motor operation until ω_m reached ω_max. The motor reached its ω_max when both back-EMF and operating current reached a V_{dc_link} of 433 V and current limit of 636 A_rms.

By utilizing the above equations and control, the power efficiency map of the proposed 24-slot/10-pole 6Φ-SS-FSCW-Fer-SIPMSM was drawn, as shown in Figure 14a. The motor retained the constant maximum torque of 2980 Nm until the motor speed reached 1500 rpm, i.e., ω_base, and sustained its operation until the speed reached 3750 rpm, i.e., ω_max. The peak η was higher than 97% when the ω_m was between 250 to 2750 rpm, and the T_m was below 600 Nm.

For comparison, the efficiency map of the benchmark 300 kW 12-slot/10-pole RE-PM 6Φ-FSCW-Nd-FIPMSM was imported from [3] and plotted in Figure 14b. The motor exhibited a maximum torque of 3100 Nm, ω_base of 500 rpm, and ω_max of 3250 rpm, with a peak η above 97% region for ω_m between 0 and 1000 rpm and T_m between 500 and 1250 Nm. Compared to the benchmark RE-PM motor, the proposed ferrite motor exhibited 1000 rpm and 500 rpm higher ω_base and ω_max, respectively, and 80% larger η of 97% region with only 3.9% lower maximum torque.

3.3. Mechanical Analysis

Mechanical FEA analysis was conducted to validate the mechanical stability of the motor at the ω_max of 3750 rpm using ANSYS Mechanical. Figure 15 shows the Von Mises stress distribution in the rotor lamination, rotor shaft, and the bottom wedge of the proposed 6Φ-S-FSCW-Fer-SPMSM at 3750 rpm. As shown in Figure 15, the maximum stress occurred at the contact surface between the rotor lamination and the nonmagnetic shaft. The calculated Von Mises stresses in all these parts are well below the stress limit, which is 345 MPa for the M19 rotor lamination, 586 MPa for the CuBe alloy rotor shaft, and 138 MPa for the non-metallic composite rotor wedge.

3.4. Thermal Analysis

Thermal FEA analysis was conducted to validate the thermal stability of the motor at maximum power, where the current was at its peak of 690 A_rms and speed was at its base speed of 1750 rpm.

Table 6. Thermal conductivity of the components used in the simulation. Data from [19,22,23].

Component	Thermal Conductivity [W/(mK)]	Material
Stator/Rotor	48	Silicon steel
Shaft	105	CuBe alloy
Winding	387.6	Copper
Air gap	0.429	Air
Permanent magnet	1	Ferrite
Rotor wedges	0.1	Non-metallic composite

summarizes the thermal conductivity of each component [19,22,23], while

Table 7. Power loss density of the components at maximum power.

Component	Power Loss Density [W/m3]
Stator	1,111,863
Rotor	83,169.6
Winding	1,744,287.42

shows the power loss density of each component. Due to the high resistance of the ferrite PM, the eddy-current loss of the PMs was negligible. Thus, the PM eddy-current loss was not included in the simulation. To cool the motor, the cooling system used in [19] was utilized. The details regarding the cooling system have been described by the authors of [19]. Figure 16 shows the FEA results at the maximum power. As clearly shown, the maximum temperature of the rotor was about 74–76 °C, which is well within the thermal limits of the permanent magnet. In comparison, the maximum temperature of the stator was around 180 °C, which occurred near the copper winding and is within the thermal limits of the class H insulation.

3.5. Demagnetization Analysis

Due to the inherent low coercivity of the ferrite PM and positive temperature coefficient of the intrinsic coercivity, analyzing the irreversible demagnetization rate at the low (−40 °C) and high temperature (80 °C) is essential.

Table 8. Magnetic properties of NMF-12G at −40 and 80 °C.

Magnetic Property	−40 °C	80 °C
Remanent flux density (Br) [T]	0.51	0.38
Coercivity (Hc) [kA/m]	345	299
Intrinsic Coercivity (Hci) [kA/m]	350	414

shows the magnetic properties of NMF-12G at −40 and 80 °C [24]. Further, it should be noted that the PM, whose flux density (B) or magnetic field (H) was below the knee point B value (B_thr) or exceeded knee point H value (H_thr), was irreversibly demagnetized [14]. The B_thr and H_thr were 0.08 T and 330 kA/m at −40, and −0.1 T and 380 kA/m at 80 °C, respectively. Figure 17 and Figure 18 show the B and H distribution of the ferrite PM under 2.6× and 2.8× rated current at −40 °C, and under 2.6× and 3.4× rated current at 80 °C. The simulation results show that the ferrite PM did not experience irreversible demagnetization, i.e., above B_thr and below H_thr, under 2.6× rated current at both temperatures. When the current increased to 2.8× rated current at −40 °C and 3.4× rated current at 80 °C, the corner close to the airgap showed lower B than B_thr and higher H than H_thr. This implies that NMF-12G ferrite PM can safely operate under a 2.8× rated current at −40 °C and 3.4× rated current at 80 °C.

3.6. Fault-Tolerant Capability

One of the advantages of the six-phase winding configuration over the three-phase winding is the fault-tolerant capability [5]. To validate the fault-tolerant capability of the proposed six-phase machine, the motor was simulated when one of the six-phase windings was opened, i.e., I = 0. At the same time, other windings kept the same condition as a healthy case. Figure 19 shows the maximum torque profiles of the proposed machine for healthy and open-phase cases. Compared to the maximum torque for the healthy case, the average maximum torque for the open-phase case was reduced from 2.97 to 2.48 kNm, while the T_rip was increased from 0.9 to 50%. On the other hand, the average maximum torque and T_rip for the one-phase short-circuit case were increased from 2.97 to 3.2 kNm and from 0.9 to 32.5%, respectively. Although the one-phase open-circuit and short-circuit cause significant degradation in the maximum torque and T_rip, it is validated that the proposed motor can still operate even if one of the phases is opened and closed.

4. Electric Truck Simulation Model

The dynamic model of an HDT was built and simulated using MATLAB/Simulink to assess the proposed motor performance under realistic HDT conditions. Figure 20 shows the block diagram for the HDT model, and

Table 9. Specification of the Class-7 Electric Truck Model. Data from [3].

Parameter	Symbol	Value
Vehicle mass [kg]	mveh	15,227
Dynamic wheel radius [m]	Rwheel	0.488
Rolling resistance coefficient	Crr	0.008
Coefficient of aerodynamic drag	Cd	0.6
Vehicle frontal area [m2]	Av	9.0
Initial State-of-Charge [%]	SOCinit	100
Number of battery cell in parallel/series	Nparallel/Nseries	53/225
Final drive gear ratio	GFDR	7.17

summarizes the vehicle specifications used in the simulation. A detailed description of each block in Figure 19 is presented below.

4.1. Driver

The main objective of this block is to convert the reference driving cycle to the required motor traction and braking torque to track the reference driving cycle. The required torque (T_req) was calculated by applying the reference and actual vehicle speed error to a proportional-integral (PI) controller. Then, the output of the PI controller, called the applied pedal position (APP), was converted to the T_req by multiplying the output with the maximum motor torque of 2980 Nm.

4.2. Battery Pack

The main goal of the battery pack block is to calculate (1) the current state-of-charge (SOC_current), and (2) V_bat from the motor current (I_mot) and calculated SOC_current. First, SOC_current is calculated by Equation (9).

$$SO{C}_{current}=SO{C}_{init}-100·{{\displaystyle \int }}^{ }\frac{I_{mot}}{3600·N_{parallel}}dt,$$

(9)

where SOC_init is the initial SOC of the battery pack, and N_{cell_parallel} is the number of battery cells in parallel. These values are listed in Table 9. Based on SOC_current, V_bat is computed by Equation (10).

$$V_{bat}=N_{series}\left(V_{oc}\left(SO{C}_{current}\right)-\frac{R\left(SO{C}_{current}\right)·I_{mot}}{N_{parallel}}\right)$$

(10)

where V_oc and R are the open-circuit cell voltage and resistance as a function of SOC_current, respectively, and N_series is the number of battery cells in series. Figure 21 shows V_oc and R as a function of SOC_current. Since both V_oc and R change significantly at 10% of SOC_current, the simulation stops when SOC_current reaches 15%.

4.3. Motor Drive

The motor drive block was used to calculate (1) T_m from T_req from the driver block, and (2) I_mot to produce T_m. A lookup table determined T_m with the maximum allowable torque at a given speed (T_thr), indicated by the solid black line shown in the motor efficiency map in Figure 14. If T_req is below T_thr, then T_m equals T_req. On the other hand, if T_req is higher than T_thr, then T_m equals T_thr.

I_mot is calculated by Equation (11).

$$I_m=\frac{T_m{\omega }_m}{\left(V_{dc}/\sqrt{3}\right)·{\eta }_m}$$

(11)

where η_m is each motor efficiency, as shown in Figure 14.

4.4. 3-Speed Gearbox and Final Gear

This block converted the T_m and wheel speed (ω_wheel) from the wheel block to the gear torque (T_gear) and ω_m, respectively. T_gear and ω_m were determined by Equations (12) and (13), respectively.

$$T_{gear}=T_m·G_{1,2,3}·G_{FDR},$$

(12)

$${\omega }_m={\omega }_{wheel}·G_{1,2,3}·G_{FDR},$$

(13)

where G_1,2,3 are the optimal three-speed gear ratios obtained in [3] under four drive cycles, and G_FDR is the final drive ratio of 7.66. These gear ratios of the three-speed gearbox are listed in

Table 10. The 3-speed optimal gear ratio under the drive cycle.

Drive Cycle	1st	2nd	3rd
CILCC	1.01	0.539	0.241
OCC	1.16	0.584	0.302
UDDSHDV	1.09	0.489	0.302
HWFET	1.01	0.416	0.259

. Figure 22 describes the flowchart for the three-speed gear shifting strategy. The details of the drive cycles are presented in the following section.

4.5. Wheel

The wheel block was used to convert (1) the T_gear from the three-speed gearbox and final gear block to the traction force (F_trac), and (2) the vehicle speed (V_veh) from the vehicle dynamic block to the ω_wheel. F_trac and ω_wheel were calculated by Equations (14) and (15).

$$F_{trac}=T_{wheel}/R_{wheel},$$

(14)

$${\omega }_{wheel}=V_{veh}/R_{wheel},$$

(15)

where R_wheel is the wheel radius, listed in Table 9.

4.6. Vehicle Dynamics

Lastly, this subsystem converted F_trac from the wheel block to the V_veh. The V_veh was calculated using the following equations.

$$V_{veh}=\frac{1}{M_i}{\displaystyle \int }\left(F_{trac}-F_{loss}\right)dt,$$

(16)

$$F_{loss}=\frac{1}{2}\rho A_v{C}_d{\left(V_{veh}\right)}^2+m_{veh}g{C}_{rr},$$

(17)

where g is the gravity (9.8 m/s²), and ρ is the air density (1.204 kg/m³). Additional parameters are listed in Table 9.

5. Performance Evaluation of Proposed Motor in Electric Truck Simulation

5.1. Traction Performance

Generally, the class-7 HDTs are driven in two modes: city and inter-city. The city mode is driven like a utility service truck, requiring frequent start-stop operations, while the inter-city mode requires high-speed driving and few start-stop operations [3]. For the city mode, the Advanced Heavy Hybrid Propulsion Systems (AHHPS) program uses the combined international local and commuter cycle (CILCC) to evaluate HDTs [25]. The AHHPS is sponsored by the U.S. Department of Energy. To further evaluate in the city mode, the Urban Dynamometer Driving Schedule for Heavy Duty Vehicle (UDDSHDV) and Orange County Bus Cycle (OCC) were used. For the inner-city transportation, the Highway Fuel Economy Test (HWFET) was utilized. Figure 23 shows the driving cycles with the tracking performances of the reported and proposed PMSM. Both the reported and proposed PMSMs closely followed the reference driving cycles.

5.2. Energy Consumption

Table 11. Energy consumption of the reported and proposed motor with a 3-speed gearbox under 4 drive cycles.

Drive Cycle	Energy Consumption in Wh		Energy Consumption in Wh/km		Consumption Savings [%]
	Reported 6Φ-FSCW-Nd-FIPMSM	Proposed 6Φ-SS-FSCW-Fer-SIPMSM	Reported 6Φ-FSCW-Nd-FIPMSM	Proposed 6Φ-SS-FSCW-Fer-SIPMSM
CILCC	8485.7	8430.7	441.1	438.3	0.64
OCC	4719.6	4692.0	452.1	449.4	0.60
UDDSHDV	5658.0	5583.6	451.6	445.6	1.33
HWFET	452.0	446.5	452.0	446.5	1.22

shows the energy consumption in Watt-hour (Wh) and Wh per km for the reported and proposed motor with the three-speed gearboxes. The proposed motor can save the energy by 55, 74, 28, and 90 Wh and 2.9, 5.9, 2.6, and 5.5 Wh per km in the CILCC, UDDSHDV, OCC, and HWFET driving cycle, respectively, compared to the reported motor. This implies that the proposed motor can save 1.8, 4.3, 1.9, and 3.7 kWh of energy when a 300 kWh battery is used. According to Bloomberg New Energy Finance, the average price of the battery per kWh in 2020 was USD 137 per kWh [26]. Based on this price and the calculated energy savings, the proposed motor can save USD 243.7, 589.3, 262.9, and 504 in the CILCC, UDDSHDV, OCC, and HWFET driving cycles, respectively.

5.3. Cost

A significant advantage of the ferrite motor over the RE-PM motor is the cost. Thereby, the costs of the reported RE-PM and proposed ferrite motor were compared to show the effectiveness of the proposed motor quantitatively. The motor cost was calculated by Equation (18):

$$\mathrm{Machine} \mathrm{Cos}\mathrm{t}=\left(A_{mag}{\rho }_{mag}{C}_{mag}+A_{ro}{\rho }_{M19}{C}_{M19}+A_{st}{\rho }_{M19}{C}_{M19}+A_{nm}{\rho }_{nm}{C}_{nm}\right)L+M_{cu}{C}_{cu},$$

(18)

where A denotes the area for each material, ρ is the density, and C is the material cost per kg. The subscripts correspond to mag = magnet (NdFeB for the reported motor and NMF-12G for the proposed motor), M19 = M19–29G (non-oriented Si-steel), Cu = copper, nm = nonmagnetic wedge for the proposed motor only, L = the stack length of the motor, and M = the mass of the material. The cost and density of each material are listed in

Table 12. Material cost and density.

Material	Cost ($/kg)	Density (g/cm3)
NdFeB	100	7.5
Ferrite	7	5
Copper	7.03	8.96
CuBe alloy	165	1
M19–29G	1.0	7.85

[13,14]. The costs of the shaft, lamination between stacked cores, and housing with liquid cooling are excluded. Based on the prices listed in Table 12, the volume, weight, and cost of the reported and proposed motor are calculated and summarized in

Table 13. Volume, weight, and cost of the reported and proposed motor.

Part	Reported			Proposed			Cost Savings [%]
	Volume [cm3]	Weight [kg]	Cost [$]	Volume [cm3]	Weight [kg]	Cost [$]
Stator	31,105	244.1	244	31,261	245.4	245	0
Rotor	19,819	155.6	156	14,234	111.8	112	28
Magnet	3570	26.8	2677	5467	27.4	191	92.9
Coil	15,066	135	949	15,066	135	949	0
Wedges	0	0	0	100.5	0.15	16.6	−16,600
Total		561	4026		519	1514	62.4

. These results show that the proposed motor can be fabricated not only 42 kg lighter but also with a USD 2512 lower cost than the reported motor. This cost reduction is mainly attributed to the significantly lower price of the ferrite PM than the RE-PM.

6. Conclusions

This paper proposed a 6-phase (dual 3-phase) 24-slot/10-pole stator-shifted fractional-slot concentrated winding spoke-type ferrite permanent magnet motor for class-7 electric truck application. By adopting a stator-shifting concept and an 11 mm diameter circular notch embedded in the rotor, the proposed motor generated a maximum torque of 2980 Nm and a torque ripple of 0.9%. This low torque ripple is attributed to the significantly reduced MMF harmonic order of the 7th, 17th, 19th, and 29th, resulting in 86% torque ripple reduction with 28% torque improvement. The simulated results of the stator-shifted motor were in good agreement with the measured results of the stator-shifted prototype. The irreversible demagnetization and mechanical analysis showed that the proposed motor could operate up to the operating current of 3.8× of the rated current under extreme temperature and at its maximum speed of 3750 rpm without any issue. An electric truck model was constructed and simulated using MATLAB/Simulink to evaluate the proposed motor performance. The simulation results showed that compared to the reported NdFeB-based motor, the proposed ferrite motor could save not only the battery capacity of 2.6–5.9 Wh/km, which is equivalent to USD 244–589 when a 300 kWh battery is used, but also the motor cost of USD 2512 while showing similar motor performance.

7. Patents

The U.S. provisional patent entitled “Ferrite Spoke-type Permanent Magnet Synchronous Motor for Electric Truck” is under review by the U.S. patent office.