# Performance Evaluation of Stator/Rotor-PM Flux-Switching Machines and Interior Rotor-PM Machine for Hybrid Electric Vehicles

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Design and Performance of the SPM-FS Machine

#### 2.1. Design Specifications of ISG Application

- PM arrangement

- Stator armature winding

- Rotor

#### 2.2. Design of the SPM-FS Machine

_{pm}and w

_{pm}are variables that describe the size of the PMs in the IPM and SPM-FS machines, where h

_{pm}represents the thickness of the magnetization direction of the PM in both machines, and w

_{pm}represents the width of each pole of the PM in the machine cross-section. g

_{0}represents the single-side length of the air-gap, β

_{st}represents the stator tooth width, and h

_{sy}is the thickness of the stator yoke. In SPM-FS machines, β

_{rt}represents the width of the rotor tooth top, β

_{rty}represents the width of the rotor tooth bottom, and h

_{rt}represents the rotor tooth height. k

_{sio}is the stator split ratio, used to represent the proportion of the stator inner diameter D

_{si}to the stator outer diameter D

_{so}. k

_{sio}= D

_{si}/D

_{s}.

_{so}= 260 mm) and stack length (L

_{a}= 55 mm) of the SPM-FS machine are both larger than that of the IPM machine to satisfy the torque requirement (T

_{N}= 95.5 Nm@150Arms), resulting in a 27.4% larger volume than the IPM-machine due to the significant saturation in stator iron teeth as revealed in [9,12]. As the stator outer diameter is determined, the key stator dimensions in Figure 1c can be obtained initially as followed according to the design procedure [12],

_{slot}= β

_{st}= β

_{pm}= 1/4β

_{sτ}

_{slot}is stator slot width arc, β

_{st}is stator tooth width arc, β

_{pm}is magnet width arc, and β

_{sτ}is the stator pole pitch arc, being equal to D

_{si}/P

_{s}(D

_{si}is the stator inner diameter).

_{ry}= 2β

_{rt}= 2.625β

_{st}

_{rt}is the rotor tooth width arc and β

_{ry}is the rotor yoke width arc as shown in Figure 1c.

#### 2.3. Performance Comparison

#### 2.3.1. Open-Circuit Flux Density Distribution

#### 2.3.2. Open-Circuit Flux-Linkage, Back-EMF and Cogging Torque

_{pm}) of the IPM machine is 0.061 Wb and the total harmonic distortion (THD) is 1.15%, whereas for the SPM-FS machine, they are 0.053 Wb and 0.5%, respectively. Figure 3b shows the phase back-EMF of the two machines at the rated speed of 1000 rpm. It can be clearly seen that the back-EMF of the SPM-FS machine is more sinusoidal with a larger amplitude (E

_{m}= 55.45 V) and a lower THD of 2.34%. However, for the IPM machine E

_{m}= 38.55 V and the corresponding THD value is 7.04%. It can be seen that although the two machines employ concentrated windings, the back-EMF of the SPM-FS machine is significantly more sinusoidal.

#### 2.3.3. Static Rated Torque versus Current Angle

_{d}= 0.578 mH, L

_{q}= 0.448 mH @150Arms), whereas this is negligible for the SPM-FS machines [14] due to the almost equal dq-axes inductances (L

_{d}= 0.467 mH, L

_{q}= 0.431 mH @150Arms). On the other hand, it can be found that at the rated current, the torque of the SPM-FS machine is higher than that of the IPM machine by about 28%. However, it should be noted that the overall volume of the SPM-FS machine is larger than the IPM machine by around 27.4%. For the IPM machine, the effective volume of the machine including the winding end part is 3.3 L, and the volumes of the winding and PM are 0.34 L and 0.1 L, respectively. The volumes of the winding and PM account are 10.43% and 3.03% of the total volume of the machine, respectively. For the SPM-FS machine, the effective volume of the motor including the winding end is 3.98 L, and the volumes of the winding and PM are 0.26 L and 0.29 L, respectively. The volumes of the winding and PM account for 7.96% and 7.37% of the total volume of the machine, respectively. The PM usage of the SPM-FS machine is three times that of the IPM machine.

#### 2.3.4. Torque-Current Capacity

_{e}− J

_{sa}) curves are compared in Figure 5, where the maximum torque per ampere (MTPA) control is used based on the optimal current angle. It can be seen that the T

_{e}− J

_{sa}curve of the IPM machine is always linear, even when the current is beyond the rated value of 150 Arms (corresponding to J

_{sa}= 20 A/mm

^{2}) and the torque is 109.5 Nm. However, for the SPM-FS machine, the torque values are always higher than that of the IPM machine [15,16]. However, as the current increases beyond 105 A (J

_{sa}= 14 A/mm

^{2}), the slope of torque significantly decreases due to the stronger stator iron saturation, as revealed in Ref. [17]. Another fact that should be emphasized is that the magnets consumed for the SPM-FS machine is almost three times that of the IPM machine as listed in Table 1, which indicates the SPM-FS machine is not a competitive candidate from the viewpoint of cost. Hence, in the next section a novel RPM-FS machine is introduced to address the above issues.

## 3. Optimization Design of the RPM-FS Machine

_{pm}and w

_{pm}are variables that describe the size of permanent magnets in RPM-FS machines, where h

_{pm}represents the thickness of the magnetization direction of the permanent magnet in both machines, and w

_{pm}represents the width of each pole of the permanent magnet in the machine cross-section. β

_{st}represents the stator tooth width, and h

_{sy}is the thickness of the stator yoke. g

_{0}represents the length of the air-gap. β

_{rtt}represents the width of the rotor tooth top, and β

_{rtb}represents the width of the rotor tooth bottom. Due to the moving of PMs from stator to rotor, a significantly improved torque capability and overload capacity has been witnessed in the applications in a Toyota Prius [11]. However, for ISG applications where a low DC voltage (U

_{dc}= 144 V) and a large current (I

_{rms}= 150 A) are required, the feasibility of RPM-FS machines should be evaluated further.

_{1}, x

_{2}, x

_{3}…, x

_{n}, each performance index is a function of f(x) = (x

_{1}, x

_{2}, x

_{3},…, x

_{n})

^{T},

_{st}× π/P

_{s}, where k

_{st}is the stator tooth width coefficient, the initial value is 1 and P

_{s}is the number of stator slots. The same thickness of the stator yoke is k

_{sy}× πD

_{si}/(4 × P

_{s}), where k

_{sy}is the thickness coefficient of the stator yoke, with an initial value of 2, and D

_{si}is the inner diameter of the stator. The width of the top of the rotor teeth is k

_{rtt}× π/P

_{r}, where k

_{rtt}is the coefficient of the top width of the rotor teeth and P

_{r}is the number of rotor teeth. In the optimization design, the parameter variation ranges are listed in Table 4.

_{Cu}, M

_{PM}, M

_{S}and M

_{R}are mass of copper, PMs, stator and rotor silicon steel sheet, respectively. The coefficients 7.25, 29 and 1.45 in Equation (4) represent the prices of copper, permanent magnet and stator/rotor core during optimization (in $), respectively.

## 4. Performance Comparison of the Three Machines

#### 4.1. PM Flux Field Distribution and Air-Gap Flux Density

_{PM}, n = 1 and 3), whereas the other harmonics with 4, 8, 16 and 28 pole-pairs (|nP

_{PM}± kP

_{r}|, (n = 1, k = 1, and n = 3, k = 1) are generated since the PM-MMF is modulated by the salient rotor teeth in the air-gap field. Similarly, for the RPM-FS machine, the dominant harmonics produced by the PM-MMF are only the 10th component (nP

_{PM}, n = 1 and 5); meanwhile, if the modulation of salient stator teeth to rotor PM-MMF is taken into consideration, the harmonics of the 14th and 34th components (|nP

_{PM}± kP

_{s}|, n = 1, k = 1) are generated. However, for the IPM machine, the dominant harmonics produced by the PM-MMF are only the 6th component (nP

_{PM}, n = 1) and multiples of the sixth component.

#### 4.2. Cogging Torque

_{s}and rotor pole number of P

_{r}, the period of cogging torque T

_{cog}yields [20],

_{s}, P

_{r}) is lowest common multiple of P

_{s}and P

_{r}.

_{r}, P

_{s}), the peak–peak value of the IPM, SPM-FS and RPM-FS machines is, respectively 9.28 Nm, 5.91 Nm and 2.65 Nm, indicating that the two flux-switching machines exhibit lower cogging torque.

#### 4.3. End-Effect

_{a}/D

_{so}) of the three machines are all around 1/5, and hence the 3D end-effect cannot be neglected.

_{2D}and S

_{3D}represent the area of the envelope of the air-gap flux density along the axial direction of the machine based on 2D FEM and 3D FEM, respectively. The ratio of the area contained in the calculation of 2D and 3D flux densities is defined as the end effect. It can be seen that the amplitude of the air-gap flux density (B

_{gap}) is almost unchanged along the axis in the iron region (half of stack length), while it tends to decrease around the end-part region of the iron. As shown in Figure 11, by comparing the surrounded areas composed of 3D- and 2D-FEM flux density waveforms, namely S

_{2D}and (S

_{2D}+ S

_{3D}), respectively, the end-part factor can be calculated as 0.88, 0.89 and 0.87 for the IPM, SPM-FS and RPM-FS machines, respectively, which means during the initially design stage the influence of end-effect on performance should be considered to be approximately 10% quantitatively.

#### 4.4. Torque Characteristic

_{ave}) is 109.5 Nm, 136 Nm, 106.7 Nm and 129 Nm, respectively. Obviously, due to the 27.4% larger volume, the torque of the SPM-FS machine is maximum. For the RPM-FS machine, the torque is larger than the IPM machine by 17.8% with the same volume, which means the torque density is strongest. Moreover, the rated torque ripple of the IPM machine is largest, which is a drawback of the IPM machine.

#### 4.5. Flux-Weakening Ability

_{fw}[22].

_{dc}= 158 V and I

_{ph}= 150 Arms, the torque-speed (T

_{e}− n) and power-speed (P − n) characteristics of the three machines are simulated via MTPA control in constant torque region and flux weakening control in constant power region [23], and the results are shown in Figure 14. It can be found that the rated speed of 1000 rpm can be achieved by all three machines. The average torque of the RPM-FS machine is larger than that of the IPM machine within the full speed range (0, 6000 rpm). Correspondingly, the output power of the RPM-FS machines is slightly and remarkably larger than that of the SPM-FS and IPM machines, respectively. Considering the same volume of the RPM-FS and IPM machines, the torque density and power density of the RPM-FS machines are both best and offer promising potential for ISG applications.

#### 4.6. Thermal Analysis

#### 4.7. Stress Deformation Analysis

#### 4.8. Comprehensive Efficiency

^{2}, the rolling resistance coefficient is 0.0054, the wheel radius is 0.2 m, the transmission efficiency is 90% and the gear ratio is 4.1. The selected cycle condition is China Automotive Test Cycle (CLTC), as shown in Figure 17a, under which the comprehensive efficiency of the three motors is 90.1%, 88.7% and 91.6%, respectively.

#### 4.9. Cost Analysis

## 5. Experimental Verification

## 6. Conclusions

- Both the stator- and rotor-PM flux-switching machines exhibit comparable torque capability with that of the IPM machine. However, the SPM-FS machine suffers from limited overload ability due to stator tooth saturation and unfavorable consumption of magnets when the PMs are located in the stator.
- The RPM-FS machine exhibits a larger torque and overload capability without the space competition pressure from armature windings and PMs. Meanwhile, the amount of PMs has also been greatly reduced, which is favorable for cost. Hence, the RPM-FS machine is a promising candidate for ISG applications.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Topologies of the IPM machine and the SPM-FS machine with different PM locations. (

**a**) IPM machine, (

**b**) SPM-FS machine, (

**c**) modular stator elements of the IPM machine and the SPM-FS machine.

**Figure 3.**PM flux-linkage, back-EMF @1000 rpm and cogging torque waveforms of the two machines. (

**a**) PM flux-linkage, (

**b**) back-EMF. (

**c**) cogging torque.

**Figure 7.**Optimization results of RPM-FS machine. (

**a**) Considering torque, torque ripple, and efficiency, (

**b**) considering torque, efficiency and material cost.

**Figure 9.**Open-circuit performance of the three machines. (

**a**) PM field distribution, (

**b**) radial air-gap PM flux density, (

**c**) radial air-gap PM flux density harmonic distributions, (

**d**) tangential air-gap PM flux density, (

**e**) tangential air-gap PM flux density harmonic distributions.

**Figure 11.**Amplitude variations of air-gap PM flux density in axial direction. (

**a**) IPM machine, (

**b**) SPM-FS machine, (

**c**) RPM-FS machine.

**Figure 14.**Electromagnetic torque and power vs. speed of the three machines @ Udc = 158 V and Iph = 150 Arms.

**Figure 15.**Temperature distribution of the three machines. (

**a**) IPM machine, (

**b**) SPM-FS machine, (

**c**) RPM-FS machine.

**Figure 16.**Stress and deformation of the three machines. (

**a**) IPM machine rotor, (

**b**) SPM-FS machine rotor, (

**c**) RPM-FS machine rotor, (

**d**) IPM machine rotor, (

**e**) SPM-FS machine rotor, (

**f**) RPM-FS machine rotor.

**Figure 17.**Comprehensive efficiency based on cycle conditions. (

**a**) CLTC drive cycle, (

**b**) SPM-FS machine, (

**c**) RPM-FS machine, (

**d**) IPM machine.

Parameters | IPM | SPM-FS |
---|---|---|

DC-link voltage, U_{dc} (V) | 144 | 144 |

Base speed, n_{N} (rpm) | 1000 | 1000 |

Rated torque, T_{N} (Nm) | 95.5 | 95.5 |

Max speed, n_{max} (rpm) | 6000 | 6000 |

PM remanence at 25 °C, B_{r} (T) | 1.2 | 1.2 |

PM coercive force at 25 °C, H_{c} (A/m) | −868,292 | −868,292 |

Stator/Rotor Iron material | 35WW300 | 35WW300 |

Stator outer diameter, D_{so} (mm) | 253 | 260 |

Stack length, L_{a} (mm) | 45.6 | 55 |

Stator slot number, P_{s} | 18 | 12 |

Rotor pole number, P_{r} | 12 | 10 |

PM pole-pair number, P_{PM} | 6 | 6 |

Electromagnetic pole-pair number, P_{fe} | 6 | 10 |

Air-gap length, g_{0} (mm) | 0.9 | 0.9 |

Stator split ratio (D_{si}/D_{so}), k_{sio} | 0.672 | 0.6 |

Stator slot width, β_{slot} (deg.) | 6.7 | 8 |

Stator tooth width, β_{st} (deg.) | 13.3 | 8 |

Rotor tooth width, β_{rt} (deg.) | / | 10.5 |

Rotor yoke width, β_{rty} (deg.) | / | 21 |

Width of the magnet, w_{pm} (mm) | 34.77 | 39 |

Thickness of the magnet, h_{pm} (mm) | 5.35 | 11.65 |

Number of winding layers | 2 | 2 |

Number of turns in series per phase | 60 | 48 |

Number of strands | 20 | 17 |

Number of parallel branches | 1 | 1 |

Wire diameter, (mm) | 0.78 | 0.87 |

Winding connection type | Y | Y |

Magnet volume, V_{pm} (mm^{3}) | 101,790 | 299,871 |

Stator tooth width, W_{st} (mm) | 20.3 | 12.4 |

Stator yoke thickness, T_{sy} (mm) | 12.4 | 9.5 |

Turns number per coil, N_{c} | 10 | 12 |

Performance Index | RPM-FS |
---|---|

Peak cogging torque, T_{cog} (Nm) | f(cog) |

Rated torque, T_{N} (Nm) | f(torque) |

Rated torque ripple, T_{rip} (%) | f(rip) |

Material cost, ($) | f(cost) |

Material mass, Q (kg) | f(mass) |

Efficiency, η (%) | f(eff) |

Loss, (W) | f(loss) |

Optimal Variables | RPM-FS |
---|---|

Stator split ratio, (D_{si}/D_{so}) | k_{sio} |

Rotor split ratio, (R_{ri}/R_{ro}) | k_{rio} |

Stator tooth width factor | k_{st} |

Stator yoke width factor | k_{sy} |

Rotor tooth top width factor | k_{rtt} |

Rotor tooth bottom width factor | k_{rtb} |

Magnet width factor | k_{pmw} |

Magnet length factor | k_{pmh} |

Stator tooth width arc, (k_{st} × π/P_{s}) | β_{st} (deg.) |

Stator yoke thickness, (k_{sy} × πD_{si}/(4 × P_{s})) | h_{sy} (mm) |

Magnet width, (k_{pmw} × (R_{ro} − R_{ri})) | w_{pm} (deg.) |

Magnet length, (D_{ri} × sin(k_{pmh} × π/4 × P_{r})) | h_{pm} (mm) |

Rotor tooth top width arc, (k_{rtt} × π/P_{r}) | β_{rtt} (deg.) |

Parameters | Initial Value | Variation Range |
---|---|---|

k_{sio} | 0.64 | 0.55~0.8 |

k_{st} | 0.96 | 0.8~1.2 |

k_{sy} | 1.9 | 1.8~2.4 |

k_{rio} | 0.68 | 0.6~0.7 |

k_{rrb} | 0.69 | 0.7~0.85 |

k_{rrt} | 0.7 | 0.7~0.85 |

k_{pmw} | 0.95 | 0.8~0.98 |

k_{pmh} | 0.855 | 0.7~1.2 |

Indexes | Objective | Boundaries |
---|---|---|

Efficiency (%) | 0.64 | 0.55~0.8 |

Torque (Nm) | 0.96 | 0.8~1.2 |

Cogging torque (Nm) | 1.9 | 1.8~2.4 |

Torque ripple (Nm) | 0.68 | 0.6~0.7 |

Material cost ($) | 0.69 | 0.7~0.85 |

Phase current (A) | 0.7 | 0.7~0.85 |

Current density (A/mm2) | 0.95 | 0.8~0.98 |

Mass PM (kg) | 0.855 | 0.7~1.2 |

Design Parameter | Initial Design | Optimal Design |
---|---|---|

k_{sio} | 0.64 | 0.7464 |

k_{st} | 0.96 | 1.1813 |

k_{sy} | 1.9 | 2.3143 |

k_{rio} | 0.68 | 0.6133 |

k_{rrb} | 0.69 | 0.7045 |

k_{rrt} | 0.7 | 0.7206 |

k_{pmw} | 0.95 | 0.8897 |

k_{pmh} | 0.855 | 0.7223 |

Performance Index | Initial Design | Optimal Design |
---|---|---|

Cogging torque, T_{cog} (Nm) | 5.38 | 2.65 |

Rated efficiency, η (%) | 90.5 | 92.1 |

Rated torque, T_{N} (Nm) | 93.4 | 129.1 |

Rated torque ripple, T_{rip} (%) | 8.9 | 6.8 |

Cost, ($) | 48.44 | 41.42 |

Parameters | IPM | SPM-FS | RPM-FS |
---|---|---|---|

Stator lamination mass (kg) | 7.19 | 6.23 | 5.9 |

Rotor lamination mass (kg) | 2.06 | 4.98 | 2.06 |

Copper mass (kg) | 2.56 | 2.36 | 1.45 |

PM mass (kg) | 0.75 | 2.2 | 0.668 |

Cost of silicon steel sheet (USD) | 13.4 | 16.3 | 11.5 |

Cost of permanent magnets (USD) | 18.6 | 17.1 | 10.5 |

Cost of copper (USD) | 21.75 | 63.8 | 19.4 |

Total effective mass (kg) | 12.6 | 15.77 | 10.07 |

Maximum power (kW) | 14.1 | 15.8 | 16.7 |

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## Share and Cite

**MDPI and ACS Style**

Yu, W.; Wu, Z.; Hua, W.
Performance Evaluation of Stator/Rotor-PM Flux-Switching Machines and Interior Rotor-PM Machine for Hybrid Electric Vehicles. *World Electr. Veh. J.* **2023**, *14*, 139.
https://doi.org/10.3390/wevj14060139

**AMA Style**

Yu W, Wu Z, Hua W.
Performance Evaluation of Stator/Rotor-PM Flux-Switching Machines and Interior Rotor-PM Machine for Hybrid Electric Vehicles. *World Electric Vehicle Journal*. 2023; 14(6):139.
https://doi.org/10.3390/wevj14060139

**Chicago/Turabian Style**

Yu, Wenfei, Zhongze Wu, and Wei Hua.
2023. "Performance Evaluation of Stator/Rotor-PM Flux-Switching Machines and Interior Rotor-PM Machine for Hybrid Electric Vehicles" *World Electric Vehicle Journal* 14, no. 6: 139.
https://doi.org/10.3390/wevj14060139