# Research on an Axial Magnetic-Field-Modulated Brushless Double Rotor Machine

^{*}

## Abstract

**:**

## 1. Introduction

**Figure 1.**The axial-radial flux compound-structure permanent-magnetic synchronous machine (CS-PMSM) system.

## 2. Theoretical Analysis

#### 2.1. Principle of Operation

_{ph}(z) and λ

_{j}(z). The combination h = 1, k = −1 possesses the comparatively large modulated space harmonic produced by the permanent magnet rotor in the air gap adjacent to the stator. To achieve stable torque transmission in the air gap adjacent to the stator, the pole-pair number of the comparatively large modulated space harmonic produced by the permanent magnet rotor p

_{p}

_{(1, −1)}(h = 1, k = −1) should be equal to that of the stator p

_{s}, which can be expressed by Equation (10):

_{p}

_{(1, −1)}(h = 1, k = −1) should be equal to that of the stator magnetic field ω

_{s}, which can be expressed by Equation (11):

_{sv}(z) and λ

_{j}(z). The combination v = 1, l = −1 possesses the comparatively large modulated space harmonic produced by the stator winding in the air gap adjacent to the permanent magnet rotor. To achieve stable torque transmission in the air gap adjacent to the permanent magnet rotor, the pole-pair number of the comparatively large modulated space harmonic produced by the stator winding p

_{s}

_{(1, −1)}(v = 1, l = −1) should be equal to the pole-pair number of the permanent magnet rotor p

_{p}, which can be expressed by Equation (21):

_{s}

_{(1, −1)}(v = 1, l = −1) should be equal to that of the permanent magnet rotor ω

_{p}, which can be expressed by Equation (22):

_{p}, p

_{s}and p

_{m}can be governed by Equation (23):

_{p}, ω

_{s}and ω

_{m}can be given by Equation (24):

#### 2.2. Torque Transmission

_{p(h, k)}equals p

_{s(v, l)}and ω

_{p(h, k)}equals ω

_{s(v, l)}when the combination of h, k, v and l is determined by Equation (27):

#### 2.3. Torque Ripple

#### 2.3.1. Cogging Torque

_{0p}= 0 and θ

_{0m}= 0, respectively. The flux density due to the permanent magnet rotor in the air gap adjacent to the permanent magnet rotor is regarded as even distribution along z axis. When two rotors rotate at different speeds, the relation between Δθ

_{p}and Δθ

_{m}can be governed by Equations (33) and (34):

_{p}and Δθ

_{m}can be obtained in Equations (35) and (36):

_{m}and 2p

_{p}. It means that when the rotation angles of two rotors differ by 2π, viz. $t=\frac{60}{{\omega}_{\text{m}}-{\omega}_{p}}$, the number of torque ripple on two rotors is LCM (p

_{m}, 2p

_{p}).

_{m}and 2p

_{p}, and the lower the number of poles on the permanent magnet rotor, the smaller the amplitude of the cogging torque will be.

_{p}and Δθ

_{m}can be expressed by Equations (45) and (46):

_{min}and d

_{min}that satisfy the condition of Equation (47) can be achieved. The period of cogging torque waveform t

_{cog}is determined by Equation (48):

_{p}is revolutions per minute, i.e., rpm.

#### 2.3.2. Electromagnetic Torque Ripple

_{p}and p

_{p}

_{(1, 1)}can be expressed by Equations (49) and (50):

_{p}

_{(1, 1)}can be expressed by Equation (51):

_{p}

_{(1, 1)}produced by the permanent magnet rotor is the major harmonic with the rotational speed $\frac{{p}_{p}{\omega}_{p}+{p}_{m}{\omega}_{m}}{{p}_{p}+{p}_{m}}$ while the space harmonic with the number of pole pairs ps(6g+1, 0) produced by the stator winding is the natural space harmonic with the rotational speed $\frac{{\omega}_{s}}{6g+1}$. Since the two space harmonics have the same pole-pair number but different rotational speeds, their interaction will contribute to electromagnetic torque ripple in either air gap under the load operation. As the modulated space harmonic with the pole-pair number p

_{p}

_{(1, 1)}has large amplitude, significant electromagnetic torque ripple arises. It should be notable that the smaller e or g is, the larger amplitude of the natural space harmonic with the number of pole pairs p

_{s}

_{(6g+1, 0)}will be, which results in higher electromagnetic torque ripple.

_{p}

_{(1, 1)}can be expressed by Equation (52):

_{p}(1, 1) produced by the permanent magnet rotor is the major harmonic with the rotational speed $\frac{{p}_{p}{\omega}_{p}+{p}_{m}{\omega}_{m}}{{p}_{p}+{p}_{m}}$ while the space harmonic with the number of pole pairs p

_{s}(6g−1, 0) produced by the stator winding is the natural space harmonic with the rotational speed $-\frac{{\omega}_{s}}{6g-1}$. Their interaction will contribute to electromagnetic torque ripple in either air gap under the load operation. As the modulated space harmonic with the pole-pair number p

_{p}

_{(1, 1)}has large amplitude, significant electromagnetic torque ripple arises. It should be notable that the smaller e or g is, the larger amplitude of the natural space harmonic with the number of pole pairs p

_{s}

_{(6g−1, 0)}will be, which results in higher electromagnetic torque ripple.

_{p}and p

_{p}

_{(1, 1)}can be expressed by Equations (53) and (54):

_{p}

_{(1, 1)}produced by the permanent magnet rotor is the major harmonic with the rotational speed $\frac{{p}_{p}{\omega}_{p}+{p}_{m}{\omega}_{m}}{{p}_{p}+{p}_{m}}$ while the space harmonic with the number of pole pairs p

_{s}(6g−1, 0) produced by the stator winding is the natural space harmonic with the rotational speed $-\frac{{\omega}_{s}}{6g-1}$. Moreover, the natural space harmonic with the number of pole pairs p

_{p}produced by the permanent magnet rotor is the fundamental harmonic with the rotational speed ω

_{p}while the space harmonic with the number of pole pairs p

_{p}(3g−1, 0) produced by the stator winding is the natural space harmonic with the rotational speed $-\frac{{\omega}_{s}}{3g-1}$. Therefore, two kinds of non-ignorable harmonic interactions will contribute to electromagnetic torque ripple. As the modulated space harmonic with the pole-pair number p

_{p}

_{(1, 1)}and the fundamental harmonic with the pole-pair number p

_{p}both have large amplitudes, significant electromagnetic torque ripple arises. It should be notable that the smaller e or g is, the larger amplitudes of the natural space harmonics with the number of pole pairs p

_{s}

_{(6g−1, 0)}and p

_{s}

_{(3g−1, 0)}will be, which results in higher electromagnetic torque ripple.

_{p}

_{(1, 1)}can be expressed by Equation (55):

_{p}produced by the permanent magnet rotor is the fundamental harmonic with the rotational speed ω

_{p}while the space harmonic with the number of pole pairs p

_{s}

_{(3g+1, 0)}produced by the stator winding is the natural space harmonic with the rotational speed $\frac{{\omega}_{s}}{3g+1}$. Their interaction will contribute to electromagnetic torque ripple in either air gap under the load operation. As the natural space harmonic with the pole-pair number p

_{p}

_{(1, 1)}has large amplitude, significant electromagnetic torque ripple arises. It should be notable that the smaller e or g is, the larger amplitude of the natural space harmonic with the number of pole pairs p

_{s}

_{(3g+1, 0)}will be, which results in higher electromagnetic torque ripple.

## 3. FEM Simulation

**Figure 2.**Three-dimensional (3D) simulation model of the axial magnetic-field-modulated brushless double rotor machine (MFM-BDRM): (

**a**) overall view; and (

**b**) exploded view.

#### 3.1. Flux Density Waveform and Harmonics Analysis

**Figure 3.**Axial flux density waveforms due to the permanent magnet rotor, in the air gap adjacent to the stator and corresponding space harmonic spectra: (

**a**) axial flux density waveform without the modulating ring rotor; (

**b**) the space harmonic spectrum without the modulating ring rotor; (

**c**) axial flux density waveform with the modulating ring rotor; and (

**d**) the space harmonic spectrum with the modulating ring rotor.

**Figure 4.**Axial flux density waveforms due to the stator winding, in the air gap adjacent to the stator and corresponding space harmonic spectra: (

**a**) axial flux density waveform without the modulating ring rotor; (

**b**) the space harmonic spectrum without the modulating ring rotor; (

**c**) axial flux density waveform with the modulating ring rotor; and (

**d**) the space harmonic spectrum with the modulating ring rotor.

**Figure 5.**Axial flux density waveforms due to the permanent magnet rotor, in the air gap adjacent to the permanent magnet rotor and corresponding space harmonic spectra: (

**a**) axial flux density waveform without the modulating ring rotor; (

**b**) the space harmonic spectrum without the modulating ring rotor; (

**c**) axial flux density waveform with the modulating ring rotor; and (

**d**) the space harmonic spectrum with the modulating ring rotor.

**Figure 6.**Axial flux density waveforms due to the stator winding, in the air gap adjacent to the permanent magnet rotor and corresponding space harmonic spectra: (

**a**) axial flux density waveform without the modulating ring rotor; (

**b**) the space harmonic spectrum without the modulating ring rotor; (

**c**) axial flux density waveform with the modulating ring rotor; and (

**d**) the space harmonic spectrum with the modulating ring rotor.

#### 3.2. Operating Principle

_{d}= 0 control strategy is suitable for the axial MFM-BDRM to get the maximum torque transmission capability.

_{s}= 10,250 rpm, to meet the operation demand. It can be found that stable torque transmission can be achieved. The electromagnetic torque on the modulating ring rotor, on the permanent magnet rotor and on the stator is 62.71 Nm, −50.44 Nm and −12.27 Nm, respectively. The torque ratio of the modulating ring rotor with respect to the permanent rotor is −1.24, approximately equal to −21/17. As will be evident from Figure 9, the axial MFM-BDRM can realize speed decoupling between the permanent magnet rotor and the modulating ring rotor by adjusting the frequency of the stator winding. Moreover, the machine can transfer torque by a torque ratio.

**Figure 9.**No-load back electromotive force (EMF) waveforms and torque transfer waveforms: (

**a**) no-load back EMF waveforms; and (

**b**) torque transfer waveforms.

#### 3.3. Torque Transmission

**Figure 10.**Torque transmission characteristics: (

**a**) variation of torque with the number of pole pairs of the permanent magnet (PM) rotor; and (

**b**) Variation of torque ratio with the number of pole pairs of the PM rotor.

#### 3.4. Torque Ripple Characteristics

_{m}and 2p

_{p}is also 48, the fundamental order of the cogging torque is equal to the least common multiple between p

_{m}and 2p

_{p}. Therefore, Equation (44) is verified through 3D FEM.

**Figure 11.**Cogging torque waveforms: (

**a**) cogging toque waveform of the permanent magnet rotor; and (

**b**) cogging torque waveform of the modulating ring rotor.

- when ω
_{p}= 1000 rpm, ω_{m}= 2000 rpm: $\frac{c}{d}=\frac{2\times 12\times 1000}{16\times 2000}=\frac{3}{4}\text{\hspace{0.17em}\hspace{0.17em}}\Rightarrow \text{\hspace{0.17em}}{c}_{\mathrm{min}}=3\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\Rightarrow {t}_{cog}=3\frac{30}{12\times 1000}\text{s}=7.5\text{ms}$; - when ω
_{p}= 2000 rpm, ω_{m}= 3000 rpm: $\frac{c}{d}=\frac{2\times 12\times 2000}{16\times 3000}=\frac{1}{1}\text{\hspace{0.17em}\hspace{0.17em}}\Rightarrow \text{\hspace{0.17em}}{c}_{\mathrm{min}}=1\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\Rightarrow {t}_{cog}=\frac{30}{12\times 2000}\text{s}=1.25\text{ms}$; - when ω
_{p}= 5000 rpm, ω_{m}= 6000 rpm: $\frac{c}{d}=\frac{2\times 12\times 5000}{16\times 6000}=\frac{5}{4}\text{\hspace{0.17em}\hspace{0.17em}}\Rightarrow \text{\hspace{0.17em}}{c}_{\mathrm{min}}=5\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\Rightarrow {t}_{cog}=5\frac{30}{12\times 5000}\text{s}=2.5\text{ms}$.

**Figure 12.**Cogging torque waveforms: (

**a**) cogging toque waveform of the permanent magnet rotor; and (

**b**) cogging torque waveform of the modulating ring rotor.

_{p}and ΔT

_{m}. Models with the greatest common divisor between the pole-pair number on the permanent magnet rotor and the pole-pair number on the stator 1 exhibit low ΔT

_{p}and ΔT

_{m}.

**Figure 13.**Variation of cogging torque and $\frac{LCM({p}_{m},2{p}_{p})}{2{p}_{p}}$ with the number of pole pairs of the PM rotor.

_{p}and ΔT

_{m}vary with the number of pole pairs of the permanent magnet rotor when the number of stator pole pairs remains to be 4. Each model is simulated under the condition that the permanent magnet rotor operates at the rotational speed of 5000 rpm and the modulating ring rotor operates at the rotational speed of 6000 rpm. The same stator structure, the same number of winding turns per phase and the same overall dimension are presumed. ΔT

_{p}under no-load condition is almost the same with ΔT

_{p}under load condition, except for models with the number of pole pairs of the permanent magnet rotor being 4, 8, 12 and 20. Moreover, there is non-ignorable difference between ΔT

_{m}under no-load condition and ΔT

_{m}under load condition for models with the number of pole pairs of the permanent magnet rotor being 4, 8, 12 and 20. It can be seen clearly that models with the number of pole pairs of the permanent magnet rotor being 4, 8, 12 and 20 have significant electromagnetic torque ripple.

**Figure 14.**Variation of ΔT

_{p}and ΔT

_{m}with the number of pole pairs of the PM rotor: (

**a**) ΔT

_{p}and (

**b**) ΔT

_{m}.

Circumstance | Constraint | Model with p_{p} in study | |
---|---|---|---|

p_{p} = 3g·p_{s}, g = 1, 2, 3… | p_{p}_{(1, 1)} = p_{s}_{(6g+1, 0)} $\frac{{p}_{p}{\omega}_{p}+{p}_{m}{\omega}_{m}}{{p}_{p}+{p}_{m}}\ne \frac{{\omega}_{s}}{6g+1}$ | 12 | |

p_{p} = (3g − 1)p_{s}, g = 1, 3, 5… | p_{p}_{(1, 1)} = p_{s}_{(6g−1, 0)} $\frac{{p}_{p}{\omega}_{p}+{p}_{m}{\omega}_{m}}{{p}_{p}+{p}_{m}}\ne -\frac{{\omega}_{s}}{6g-1}$ | 8 | |

p_{p} = (3g − 1)p_{s}, g = 2, 4, 6… | p_{p} = p_{s}_{(3g-1, 0)} ${\omega}_{p}\ne -\frac{{\omega}_{s}}{3g-1}$p _{p}_{(1, 1)} = p_{s}_{(6g−1, 0)} $\frac{{p}_{p}{\omega}_{p}+{p}_{m}{\omega}_{m}}{{p}_{p}+{p}_{m}}\ne -\frac{{\omega}_{s}}{6g-1}$ | 20 | |

p_{p} = (3g + 1)p_{s}, g = 0, 2, 4… | p_{p} = p_{s}_{(3g+1)} ${\omega}_{p}\ne \frac{{\omega}_{s}}{3g+1}$ | 4 |

#### 3.5. Operation Performance

_{p}= 20.

**Figure 15.**No-load back EMF waveforms: (

**a**) one-phase no-load back EMF waveforms for four schemes; and (

**b**) three-phase no-load back EMF waveforms for the scheme with p

_{p}= 20.

_{p}= 20 is much larger than the other three schemes.

**Figure 16.**Cogging torque waveforms: (

**a**) cogging torque on the modulating ring rotor; and (

**b**) cogging torque on the permanent magnet rotor.

_{p}= 20 is very significant.

**Figure 17.**Electromagnetic torque waveforms: (

**a**) electromagnetic torque on the modulating ring rotor; and (

**b**) electromagnetic torque on the permanent magnet rotor.

_{p}= 17 and p

_{p}= 19 are pretty good, while the scheme with p

_{p}= 20 is worst. In consideration of ΔT

_{p}and ΔT

_{m}under no-load condition, the best scheme is that with p

_{p}= 19, and then p

_{p}= 17, and then p

_{p}= 18, and the scheme with p

_{p}= 20 is the worst. $\frac{LCM({p}_{m},2{p}_{p})}{2{p}_{p}}$ from large to small in order is the scheme with p

_{p}= 19, the scheme with p

_{p}= 17, the scheme with p

_{p}= 18 and the scheme with p

_{p}= 20. When $\frac{LCM({p}_{m},2{p}_{p})}{2{p}_{p}}$ is smaller, the cogging torque is larger. Cogging torque for the scheme with p

_{p}= 20 is 7 times as large as the scheme with p

_{p}= 19. Under load condition, the torque ripple on the modulating ring for the scheme with p

_{p}= 20 is approximately seven times as high as the other schemes, which is in accordance with electromagnetic torque ripple analysis.

Scheme | p_{p} = 17 | p_{p} = 18 | p_{p} = 19 | p_{p} = 20 |
---|---|---|---|---|

RMS value of A-phase no-load back EMF (V) | 122.8 | 127.1 | 123.1 | 126.2 |

THD of no-load back EMF (%) | 7.14 | 12.05 | 8.1 | 46.27 |

ΔT_{p} under no-load condition (Nm) | 3.13 | 5.1 | 2.19 | 14.85 |

ΔT_{m} under no-load condition (Nm) | 3.0 | 4.97 | 2.27 | 15.45 |

LCM(p_{m}, 2p_{p})/2p_{p} | 21 | 11 | 23 | 3 |

Average torque on the modulating ring rotor (Nm) | 62.71 | 62.94 | 61.71 | 68.33 |

Torque ripple on the modulating ring rotor (%) | 4.68 | 6.54 | 3.90 | 33.62 |

Average torque on the permanent magnet rotor (Nm) | −50.44 | −50.76 | −50.51 | −54.91 |

Torque ripple on the permanent magnet rotor (%) | 3.35 | 4.75 | 4.01 | 25.35 |

_{p}. The space harmonic with the pole-pair number 44 (h = 1, k = 1) is the dominant harmonic in either air gap with the rotational speed $\frac{{p}_{p}{\omega}_{p}+{p}_{m}{\omega}_{m}}{{p}_{p}+{p}_{m}}$.

**Figure 18.**Axial flux density waveforms due to the permanent magnet rotor, in two air gaps and corresponding space harmonic spectra: (

**a**) axial flux density waveform in the air gap adjacent to the permanent magnet rotor; (

**b**) the space harmonic spectrum in the air gap adjacent to the permanent magnet rotor; (

**c**) axial flux density waveform in the air gap adjacent to the stator; and (

**d**) the space harmonic spectrum in the air gap adjacent to the stator.

**Figure 19.**Axial flux density waveforms due to the stator winding, in two air gaps and corresponding space harmonic spectra: (

**a**) axial flux density waveform in the air gap adjacent to the permanent magnet rotor; (

**b**) the space harmonic spectrum in the air gap adjacent to the permanent magnet rotor; (

**c**) axial flux density waveform in the air gap adjacent to the stator; and (

**d**) the space harmonic spectrum in the air gap adjacent to the stator.

## 4. Conclusions

- (1)
- The matching relation of p
_{s}, p_{p}and p_{m}, and the relation of ω_{s}, ω_{p}and ω_{m}have been deduced. It is found that the axial MFM-BDRM provides speed difference between the shaft of the modulating ring rotor and that of the permanent magnet rotor by adjusting the frequency of stator winding current. - (2)
- The torque transmission relation has been deduced. The result shows that the axial MFM-BDRM transfers torque by a certain torque ratio.
- (3)
- The cogging torque characteristics have been mathematically formulated. The result demonstrates that the order of the cogging torque is LCM (p
_{m}, 2p_{p}) and there is good correlation between the amplitude of cogging torque and $\frac{LCM({p}_{m},2{p}_{p})}{2{p}_{p}}$. The smaller $\frac{LCM({p}_{m},2{p}_{p})}{2{p}_{p}}$ is, the larger the cogging toque will be. - (4)
- The performance analysis verifies that the adoption of the scheme that the greatest common divisor between the pole-pair number of the permanent magnet rotor and that of the stator is 1 can prominently reduce torque ripple and make the no-load back EMF more sinusoid, resulting in good performance of the machine.

## Nomenclature:

p_{p} | number of pole pairs of the permanent magnet rotor |

p_{s} | number of pole pairs of the stator |

p_{m} | number of ferromagnetic pole pieces |

ω_{p} | rotational speed of the permanent magnet rotor |

ω_{s} | rotational speed of the stator magnetic field |

ω_{m} | rotational speed of the modulating ring rotor |

θ_{op} | initial phase angle of the permanent magnet rotor |

θ_{om} | initial phase angle of the modulating ring rotor |

θ_{os} | initial phase angle of the stator magnetic field |

p_{p}_{(h, k)}, ω_{p}_{(h, k)} | number of pole pairs in the space harmonic magnetic field distribution produced by the permanent magnet rotor and its rotational speed |

p_{s}_{(v, l)}, ω_{s}_{(v, l)} | number of pole pairs in the space harmonic magnetic field distribution produced by the stator winding and its rotational speed |

T_{p} | electromagnetic torque on the permanent magnet rotor |

T_{s} | electromagnetic torque on the stator |

T_{m} | electromagnetic torque on the modulating ring rotor |

T_{cog} | cogging torque of interaction between the permanent magnet rotor and ferromagnetic pole pieces of the modulating ring rotor |

W | total magnetic energy |

B | magnetic flux density in the air gap adjacent to the permanent magnet rotor |

V | volume of the air gap adjacent to the permanent magnet rotor |

Α | relative position angle between the permanent magnet rotor and modulating ring rotor |

R_{i} | inner radius of the axial MFM-BDRM |

R_{o} | outer radius of the axial MFM-BDRM |

δ | length of the air gap adjacent to the permanent magnet rotor |

Δθ_{p} | rotation angle of the permanent magnet rotor |

Δθ_{m} | rotation angle of the modulating ring rotor |

t_{cog} | period of the cogging torque waveform |

LCM(p_{m}, 2p_{p}) | the least common multiple between p _{m} and 2p_{p} |

f_{ph}(z) | Fourier coefficient for the magnetomotive force produced by the permanent magnet rotor |

F_{A}(z, θ, t) | magnetomotive force produced by A-phase winding |

F_{B}(z, θ, t) | magnetomotive force produced by B-phase winding |

F_{C}(z, θ, t) | magnetomotive force produced by C-phase winding |

f_{sv}(z) | Fourier coefficient for the magnetomotive force produced by one-phase winding |

b_{ph}(z) | Fourier coefficient for the axial component of the flux density distribution produced by the permanent magnet rotor without the modulating ring rotor |

b_{sv}(z) | Fourier coefficient for the axial component of the flux density distribution produced by the stator winding without the modulating ring rotor |

λ_{0}(z), λ_{j}(z) | Fourier coefficient for the modulating function |

B_{0}, B_{h} | Fourier coefficient for the square of flux density produced by the permanent magnet rotor along z axis without the modulating ring rotor |

G_{0}, G_{j} | Fourier coefficient for the square of the modulating function |

ΔT | torque difference between the maximum and minimum value |

ΔT_{p} | ΔT of the permanent magnet rotor |

ΔT_{m} | ΔT of the modulating ring rotor |

## Acknowledgments

## Conflicts of Interest

## References

- Ehsani, M.; Gao, Y.; Miller, J.M. Hybrid electric vehicles: Architecture and motor drives. IEEE Proc.
**2007**, 95, 719–720. [Google Scholar] [CrossRef] - Chau, K.T.; Chan, C.C. Emerging energy-efficient technologies for hybrid electric vehicles. IEEE Proc.
**2007**, 95, 821–835. [Google Scholar] [CrossRef] - Magnussen, F.; Sadarangani, C. Electromagnetic Transducer for Hybrid Electric Vehicles. In Proceedings of the Nordic Workshop on Power and Industrial Electronics, Stockholm, Sweden, 12–14 August 2002; pp. 5–6.
- Magnussen, F.; Thelin, P.; Sadarangani, C. Design of Compact Permanent Magnet Machines for a Novel HEV Propulsion System. In Proceedings of the 20th International Electric Vehicle Symposium and Exposition (EVS), Long Beach, CA, USA, 15–19 November 2003; pp. 1–12.
- Nordlund, E.; Eriksson, S. Test and Verification of a Four-Quadrant Transducer for HEV Applications. In Proceedings of the IEEE Vehicle Power and Propulsion Conference, Chicago, IL, USA, 2–5 September 2005; pp. 37–41.
- Zheng, P.; Liu, R.R.; Thelin, P.; Nordlund, E.; Sadarangani, C. Research on the parameters and performances of a 4QT prototype machine used for HEV. IEEE Trans. Magn.
**2007**, 43, 443–446. [Google Scholar] [CrossRef] - Sun, X.K.; Cheng, M. Thermal analysis and cooling system design of dual mechanical port machine for wind power application. IEEE Trans. Magn.
**2013**, 60, 1724–1733. [Google Scholar] - Frank, N.W.; Toliyat, H.A. Gearing Ratios of a Magnetic Gear for Wind Turbines. In Proceedings of the Electric Machines and Drives Conference (IEMDC ’09), Miami, FL, USA, 3–6 May 2009; pp. 1224–1230.
- Frank, N.W.; Toliyat, H.A. Gearing Ratios of a Magnetic Gear for Marine Applications. In Proceedings of the Electric Ship Technologies Symposium (ESTS 2009), Baltimore, MD, USA, 20–22 April 2009; pp. 477–481.
- Zheng, P.; Liu, R.R.; Wu, Q.; Tong, C.D.; Tang, Z.J. Compound-Structure Permanent-Magnet Synchronous Machine Used for HEVs. In Proceedings of the International Conference on Electric Machines and Systems (ICEMS 2008), Wuhan, China, 17–20 October 2008; pp. 2916–2920.
- Eriksson, S.; Sadarangani, C. A Four-Quadrant HEV Drive System. In Proceedings of the IEEE 56th Vehicular Technology Conference (VTC 2002), Vancouver, BC, Canada, 24–28 September 2002; Volume 3, pp. 1510–1514.
- Hoeijmakers, M.J.; Ferreira, J.A. The electric variable transmission. IEEE Trans. Ind. Appl.
**2006**, 42, 1092–1010. [Google Scholar] [CrossRef] - Cui, S.M.; Huang, W.X.; Cheng, Y.; Ning, K.W.; Chan, C.C. Design and Experimental Research on Induction Machine Based Electrical Variable Transmission. In Proceedings of the IEEE Vehicle Power and Propulsion Conference (VPPC 2007), Arlington, TX, USA, 9–12 September 2007; pp. 231–235.
- Cui, S.M.; Yuan, Y.J.; Wu, Q.; Wang, T.C. Research on Switched Reluctance Double-Rotor Motor Used for Hybrid Electric Vehicle. In Proceedings of the International Conference on Electric Machines and Systems (ICEMS 2008), Wuhan, China, 17–20 October 2008; pp. 3393–3396.
- Xu, L.Y.; Zhang, Y. Design and Evaluation of a Dual Mechanical Port Machine and System. In Proceedings of the CES/IEEE 5th International on Power Electronics and Motion Control Conference (IPEMC 2006), Shanghai, China, 14–16 August 2006; Volume3, pp. 1–5.
- Liu, R.R.; Zhao, H.; Tong, C.D.; Chen, G.; Zheng, P.; Gu, G. Experimental evaluation of a radial-radial-flux compound-structure permanent-magnet synchronous machine used for HEVs. IEEE Trans. Magn.
**2009**, 45, 645–649. [Google Scholar] [CrossRef] - Zheng, P.; Zhao, J.; Liu, R.R.; Tong, C.D.; Wu, Q.; Shi, W. Comparison and Evaluation of Different Compound-Structure Permanent-Magnet Synchronous Machine Used for HEVs. In Proceedings of the 2010 IEEE Energy Conversion Congress and Exposition (ECCE), Atlanta, GA, USA, 12–16 September 2010; pp. 1707–1714.
- Zheng, P.; Bai, J.G.; Tong, C.D.; Lin, J.; Wang, H.P. Research on Electromagnetic Performance of a Novel Radial Magnetic-Field-Modulated Brushless Double Rotor Machine. In Proceedings of the 2011 International Conference on Electrical Machines and Systems (ICEMS), Beijing, China, 20–23 August 2011; pp. 1–6.
- Zheng, P.; Bai, J.G.; Tong, C.D.; Sui, Y.; Song, Z.Y.; Zhao, Q.B. Investigation of a novel radial magnetic-field-modulated brushless double rotor machine used for HEVs. IEEE Trans. Magn.
**2013**, 49, 1231–1341. [Google Scholar] [CrossRef] - Mezani, S.; Atallah, K.; Howe, D. A high-performance axial-field magnetic gear. J. Appl. Phys.
**2006**, 99, 08R303:1–08R303:3. [Google Scholar] [CrossRef] - Niguchi, N.; Hirata, K.; Zaini, A.; Nagai, S. Proposal of an Axial-Type Magnetic-Geared Motor. In Proceedings of the 2012 International Conference on Electrical Machines (ICEM), Marseille, France, 2–5 September 2012; pp. 738–743.
- Atallah, K.; Howe, D. A novel high-performance magnetic gear. IEEE Trans. Magn.
**2001**, 37, 2844–2846. [Google Scholar] [CrossRef] - Jian, L.N.; Chau, K.T.; Gong, Y.; Jiang, J.Z.; Yu, C.; Li, W.L. Comparison of coaxial magnetic gears with different topologies. IEEE Trans. Magn.
**2009**, 45, 4526–4529. [Google Scholar] [CrossRef] [Green Version] - Rasmussen, P.O.; Andersen, T.O.; Jørgensen, F.; Nielson, O. Development of a high-performance magnetic gear. IEEE Trans. Ind. Appl.
**2005**, 41, 764–770. [Google Scholar] [CrossRef] - Atallah, K.; Calverley, S.D.; Howe, D. Design, analysis and realization of a high performance magnetic gear. IEE Proc. Electr. Power Appl.
**2004**, 151, 135–143. [Google Scholar] [CrossRef] - Atallah, K.; Rens, J.; Mezani, S.; Howe, D. A novel “Pseudo” direct-drive brushless permanent magnet machine. IEEE Trans. Magn.
**2008**, 44, 4349–4352. [Google Scholar] [CrossRef] - Wang, L.L.; Shen, J.X.; Luk, P.C.K.; Fei, W.Z.; Wang, C.F.; Hao, H. Development of a magnetic-geared permanent magnet brushless motor. IEEE Trans. Magn.
**2009**, 45, 4578–4581. [Google Scholar] [CrossRef] [Green Version] - Ho, S.L.; Niu, S.X.; Fu, W.N. Transient analysis of a magnetic gear integrated brushless permanent magnet machine using circuit-field-motion coupled time-stepping finite element method. IEEE Trans. Magn.
**2010**, 46, 2074–2077. [Google Scholar] [CrossRef] - Lubin, T.; Mezani, S.; Rezzoug, A. Analytical computation of the magnetic field distribution in a magnetic gear. IEEE Trans. Magn.
**2010**, 46, 2611–2621. [Google Scholar] [CrossRef] - Zhu, Z.Q.; Howe, D. Analytical prediction of the cogging torque in radial-field permanent magnet brushless motors. IEEE Trans. Magn.
**1992**, 28, 1371–1374. [Google Scholar] [CrossRef] - Niguchi, N.; Hirata, K. Cogging torque analysis of magnetic gear. IEEE Trans. Ind. Electron.
**2012**, 59, 2189–2197. [Google Scholar] [CrossRef] - Niguchi, N.; Hirata, K. Torque Ripple Analysis of a Magnetic-Geared Motor. In Proceedings of the 2012 International Conference on Electrical Machines (ICEM), Marseille, France, 2–5 September 2012; pp. 789–794.
- Jian, L.N.; Chau, K.T. A coaxial magnetic gear with halbach permanent-magnet arrays. IEEE Trans. Energy Convers.
**2010**, 25, 319–328. [Google Scholar] [CrossRef] [Green Version] - Li, Y.; Xing, J.W.; Lu, Y.P.; Yin, Z.J. Torque analysis of a novel non-contact permanent variable transmission. IEEE Trans. Magn.
**2011**, 47, 4465–4468. [Google Scholar] [CrossRef] - Niguchi, N.; Hirata, K. Torque-speed characteristics analysis of a magnetic-geared motor using finite element method coupled with vector control. IEEE Trans. Magn.
**2013**, 49, 2401–2404. [Google Scholar] [CrossRef] - Van Wyk, J.D.; Skudelny, H.-Ch.; Müller-Hellmann, A. Power electronics control of the electromechanical energy conversion process and some application. IEE Proc. B Electr. Power Appl.
**2008**, 133, 369–399. [Google Scholar] [CrossRef] - Liu, C.; Chau, K.T. Electromagnetic design and analysis of double-rotor flux-modulated permanent-magnet machines. Prog. Electromagn. Res.
**2012**, 131, 81–97. [Google Scholar] [CrossRef]

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## Share and Cite

**MDPI and ACS Style**

Zheng, P.; Song, Z.; Bai, J.; Tong, C.; Yu, B.
Research on an Axial Magnetic-Field-Modulated Brushless Double Rotor Machine. *Energies* **2013**, *6*, 4799-4829.
https://doi.org/10.3390/en6094799

**AMA Style**

Zheng P, Song Z, Bai J, Tong C, Yu B.
Research on an Axial Magnetic-Field-Modulated Brushless Double Rotor Machine. *Energies*. 2013; 6(9):4799-4829.
https://doi.org/10.3390/en6094799

**Chicago/Turabian Style**

Zheng, Ping, Zhiyi Song, Jingang Bai, Chengde Tong, and Bin Yu.
2013. "Research on an Axial Magnetic-Field-Modulated Brushless Double Rotor Machine" *Energies* 6, no. 9: 4799-4829.
https://doi.org/10.3390/en6094799