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This paper proposes a new electrically controlled magnetic variable-speed gearing (EC-MVSG) machine, which is capable of providing controllable gear ratios for hybrid electric vehicle (HEV) applications. The key design feature involves the adoption of a magnetic gearing structure and acceptance of the memory machine flux-mnemonic concept. Hence, the proposed machine can not only offer a gear-shifting mechanism for torque and speed transmission, but also provide variable gear ratios for torque and speed variation. The electromagnetic design is studied and discussed. The finite-element method is developed with the hysteresis model to verify the validity of the machine design.

Electric machines, which play the essential role of electromechanical energy conversion, are one of the most important components of electric vehicles (EVs) and hybrid EVs (HEVs) [

In the power train of vehicles, mechanical gearing sets have been widely used in modern industrial applications for torque and speed transmission. However, they suffer from the inherent drawbacks of mechanical gears (wear-and tear, annoying noise and need for regular maintenance) and the problems of gearboxes (high transmission losses, bulky size, heavy weight and complicated gear-shifting mechanisms). Recently, magnetic gearing sets (magnetic gears and magnetic gearing machines) have been actively developed. Based on the permanent-magnet (PM) attraction for torque transmission, they naturally display the merits of contactless transmission, silent operation and maintenance free, hence solving the drawbacks of mechanical gears [

Nevertheless, a direct replacement of mechanical gearboxes by magnetic gearing sets with the aim of offering controllable gear ratios is still lacking. Controllable gear ratios are highly desirable for practical applications, such as acting as electric variable transmissions or so-called E-CVTs for HEVs and extended to planetary-geared E-CVTs and dual-machine E-CVTs for HEV or wind power generation [

Recently, a new breed of flux-controllable PM brushless machines, called memory machines, which have the distinct capability to tune the PM magnetization and memorize it, has emerged with considerable attention. In [

The purpose of this paper is to propose a new electrically controlled magnetic variable-speed gearing (EC-MVSG) machine, which can provide controllable gear ratios for HEV applications. Different from the mechanical gearing systems, the proposed machine adopts the magnetic gearing structure and accepts the memory machine flux-mnemonic concept. Hence, the proposed machine can not only offer a gearing mechanism for torque and speed transmission, but also provide variable gear ratios for torque and speed variation. Specifically, the proposed machine will use the topology with two rotors and a stator. Different from the multi-layer airgap structure of existing magnetic gearing machines [

Since the proposed EC-MVSG machine integrates two distinct concepts of magnetic gearing and flux-mnemonics, it has many unique features as follows:

The whole structure is compact and robust, and fully utilizes the machine space for accommodating PMs, windings and MFSs. Both rotors have PMs and magnetizing windings, which means both pole-pairs of rotors can be adjusted. The stator not only comprises MFSs, but also artfully incorporates the MFSs into the air space. In this way, although two concepts are created for the machine design, the flux path is very short from the inner rotor to the outer rotor, and armature windings are bypassed, therefore, it can greatly improve the flux transmission efficiency.

The stator is quite different from those magnetic gearing machines which have separate two parts for the MFSs and the armature windings [

Both rotors accommodate PMs and magnetizing windings, which inherently create the flux-mnemonic feature for PM pole-pairs. Also, it can be found that the rotor space is fully utilized, hence further increasing the material cost-effectiveness. In addition, these 24 pieces of PMs in both rotors can be magnetized or demagnetized to the desired applicable pole-pairs, such as two and four.

The AlNiCo PM is not a rare-earth PM and hence is more abundant and cheap. In addition, it should be noted that two sets of slip rings are needed to access the magnetizing windings of both rotors.

The proposed machine has the capability of gearing effect (with fixed gear ratio) for changing the torque and speed. Namely, if the inner rotor runs at high speed with low-torque output, the outer rotor can run at low speed with high-torque output under a fixed gear ratio.

The proposed machine also has the capability of variable gear ratios for torque and speed variation. Namely, the proposed machine has three gear ratios for its outer-rotor speed over its inner-rotor speed, such as 1:1, −2:1 and −1/2.

The AlNiCo PM, created in the 1930s, was widely applied for PM machines due to its high remanence, high thermal stability and high stability [

On the other hand, the AlNiCo PM is suitable for memory machines because of its nonlinear demagnetization characteristics. That is, once the demagnetization current is added for a short time and then removed, the operation point will move along the recoil line and stay at a lower magnetization level. It also means that the magnetization level is memorized. As shown in _{c}, but they have different values of remanence _{rn}.

In detail, the main beelines that represent the magnetizing and demagnetizing processes are marked in _{o}. Subsequently, during the demagnetizing process, the operating point moves leftward along the Line 2, then downward along the Line 3, then rightward along the recoil line until settling at the operating point of _{o} with a lower flux level. The corresponding equations of these beelines can be respectively expressed as [_{0} is the vacuum permeability; μ_{r} is the relative permeability; _{m} is the saturated magnetic field intensity; and _{rn} denotes the remanence of the _{n}

First, during the initial magnetizing state, each AlNiCo PM element is set to have a constant μ_{r} and zero _{r}. Then, if a temporary positive magnetizing current is added, the magnetizing force

Second, during the working state, the magnetizing force _{r} of each element is obtained based on _{rn}. Also, at each time step, the value of _{rn} is modified until it converges using the under-relax iteration method, which is given by:

Since the proposed EC-MVSG machine belongs to the magnetic-gearing machine type, its torque transmission is based on the modulation of the airgap flux density distribution along the radial and circumferential directions, therefore, the airgap flux density space harmonics and the corresponding pole-pair arrangements are governed by [_{ri} is the rotating speed of the machine inner rotor; _{ri} is the pole-pair number of the machine inner rotor; and _{MFS} is the pole-piece number of the MFS. Thus, in order to transmit the torque from the inner rotor to the outer rotor, the outer rotor speed ω_{ro} and the pole-pair number _{ro} of the outer rotor must be equal to ω_{a,}_{b}_{a,}_{b}

Based on the above equation, the so-called magnetic gearing effect will occur, and the gear ratio and speed relationship can be expressed as:

For the proposed machine, the MFS is set to 6. The armature winding is set to three phases with six slots also, which can directly locate in the space between MFSs. The pole-pair numbers of both inner rotor and outer rotor are first set to 12. Then, by magnetizing these PMs to the different directions and amplitudes, the proposed machine will have different pole-pair numbers for both rotors. The first case (_{ri} = 4 and _{r0} = 2. In this case, the outer rotor speed will be twice as the inner rotor speed with contra-rotating direction. The third case (_{ri} = 2 and _{r0} = 4. In this case, the outer rotor speed will be 1/2 as the inner rotor speed with contra-rotating direction. Thus, if the inner rotor speed is set to 500 rpm, the outer rotor speed could be 500 rpm, −1000 rpm or −250 rpm corresponding to the gear ratio of _{r1} = 1, _{r2} = −2 or _{r3} = −1/2.

Electromagnetic field analysis has been widely developed for electric machines. Basically, it can be categorized as analytical field calculation and numerical field calculation. The TS-FEM is the one of the most popular numerical field calculation tools. In this paper, the TS-FEM is incorporated with the above parallelogram hysteresis model and developed for analyzing the proposed EC-MVSG machine.

First, the electromagnetic field equation of the machine is governed by [_{r}_{x}, B_{r}_{y}

Second, the armature circuit equation of the machine at motoring is given by [_{s} is the applied voltage; _{w} is the winding resistance; _{e} is the end winding inductance; _{a} is the axial length; _{e} is the total cross-sectional area of conductors of each phase winding; _{a} is the armature back EMF; _{e} is the coefficient of flux linkage; Φ is the flux linkage; and

Third, the machine motion equation is expressed as [_{m} is the moment of inertia; ω_{m} is the mechanical speed; _{e} is the electromagnetic torque; _{L} is the load torque; and λ is the damping coefficient. After discretizing

By performing the TS-FEM, the machine performance can be calculated and obtained. The corresponding machine data is listed in

First, the basic characteristics of the proposed EC-MVSG machine are calculated and analyzed.

Moreover,

Second, the generating performances of the machine are discussed.

Third, the torque performances of the machine are evaluated and discussed.

In addition, the corresponding cogging torques are not small due to the flux interaction of both rotors, but the cogging torques can be offset to a certain extent. In

Moreover,

Finally,

In addition, the machine's loss and efficiency are calculated and discussed. The copper loss of the machine at rated conditions is 14.4 W. In

In this paper, a new type of EC-MVSG machine is presented, which possesses electrically controllable gear ratios for automobile driving. First, the machine structure, design principle, and operation principle are discussed and analyzed in detail. The idea is to change the magnetization of the AlNiCo PM to achieve different rotor pole-pair numbers of the machine. Meanwhile, the machine design adopts the magnetic gearing effect. Thus, the proposed machine not only offers a gearing mechanism for torque and speed transmission, but also provides variable gear ratios for torque and speed variations. Namely, the ratio of the outer-rotor speed to the inner-rotor speed has three values: _{r1} = 1, _{r2} = −2 and _{r3} = −1/2, which means that the machine has three operation cases. In this way, the machine is highly promising for automotive applications. The results demonstrate the effectiveness of the proposed machine design.

This work was supported by a research grant (Project No. HKU710612E) from the Research Grants Council in Hong Kong Special Administrative Region, China.

The authors declare no conflict of interest.

Proposed electrically controlled magnetic variable-speed gearing (EC-MVSG) machine: (

Operating principle of different PMs: (

Flux distribution under inner rotor of 500 rpm: (

Airgap flux density under different pole-pair numbers: (

Flux linkage waveforms under inner-rotor speed of 500 rpm: (

No-load EMF waveforms under inner-rotor speed of 500 rpm: (

Basic torque performances with

Basic torque performances with

Basic torque performances with

Rated torque waveforms under inner-rotor speed of 500 rpm: (

Machine key data. MFSs: modulated ferromagnetic segments.

Outer rotor outside diameter | 280.0 mm | Number of MFSs | 6 |

Outer rotor inside diameter | 221.2 mm | 4 | |

Inner rotor outside diameter | 190.0 mm | 4 | |

Inner rotor inside diameter | 80.0 mm | 4 | |

Stator outside diameter | 220.0 mm | 2 | |

Stator inside diameter | 191.2 mm | 2 | |

Outside airgap length | 0.6 mm | 4 | |

Inside airgap length | 0.6 mm | Number of phases | 3 |

Shaft length | 80.0 mm | Number of stator slots | 6 |

Volume | 4,926,017 mm^{3} |
- | - |

Torque performances.

Maximum value of torque-angle capability in |
30.2 Nm | 30.0 Nm |

Maximum value of torque-angle capability in |
30.0 Nm | 19.2 Nm |

Maximum value of torque-angle capability in |
20.2 Nm | 30.2 Nm |

Cogging torque in |
0.9 Nm | 1.3 Nm |

Cogging torque in |
6.9 Nm | 5.9 Nm |

Cogging torque in |
6.1 Nm | 8.8 Nm |

Rated torque in |
32.2 Nm | 31.8 Nm |

Rated torque in |
28.2 Nm | −9.2 Nm |

Rated torque in |
12.5 Nm | −26.5 Nm |

Torque ripple in |
20.4% | 30.6% |

Torque ripple in |
56.2% | 208.2% |

Torque ripple in |
179.8% | 79.8% |

Torque density in |
6.54 kNm/m^{3} |
6.46 kNm/m^{3} |

Torque density in |
5.73 kNm/m^{3} |
1.87 kNm/m^{3} |

Torque density in |
2.54 kNm/m^{3} |
5.38 kNm/m^{3} |