# High-Torque Density Design of Small Motors for Automotive Applications with Double Axial-Air-Gap Structures

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## Abstract

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## 1. Introduction

## 2. High Torque Density Design of Axial-Gap Motors

#### 2.1. Prerequisites

#### 2.2. Magnetic Circuit Design of Axial-Gap Motor

_{n}is the number of pole pairs, ϕ is the amount of the total magnetic flux linkage per pole, N is the number of coil turns, and I is an armature current. The magnetic and electrical loading are closely related to ϕ and NI, respectively. Therefore, it is necessary to design the motor structure to maximize the magnetic and electric loading product. The magnetic loading ϕ is roughly determined by the product of the winding factor, the magnetic flux density at the magnet operating point, and the surface area of the magnet facing the teeth. The magnet operating point can be calculated from the permeance of the magnet. The magnet permeance coefficient p

_{u}can be written as:

_{m}is a magnet cross-sectional area, l

_{m}is a magnet thickness, A

_{g}is an air gap surface area, l

_{g}is an air gap length, and K

_{c}is Carter’s coefficient. The higher the permeance of a magnet is, the higher the magnetic flux density of the magnet becomes. Suppose we consider how the magnetic loading ϕ changes when the magnet shape is changed with a constant magnet volume. When the magnet thickness l

_{m}is increased to increase the magnet permeance coefficient, the magnet thickness l

_{m}and the magnet cross-section area A

_{m}contribute to an increase in the magnetic loading ϕ. Still, the air gap surface area A

_{g}and the magnet surface area facing the teeth contribute to the reduction in the magnetic loading ϕ. As described above, each parameter is determined with respect to the change in the magnet shape, and there is a trade-off relationship between each parameter for the magnetic loading ϕ.

#### 2.3. Experimental Results

## 3. High Torque Density of Axial-Gap Motor

#### 3.1. Preconditions and Target

_{dc}is a DC bus resistance, R

_{ac}is a wire harness resistance, η is an inverter efficiency, V

_{dc}is a DC power supply voltage, and I is a line current. The motor diameter is 80 mm, and the motor stack length is 62.5 mm. The benchmark motor has a typical radial-gap configuration: an SPM-type rotor with 8 poles and a 12 slot stator with three-phase concentrated windings. The magnet volume of the benchmark motor is 22,688 mm

^{3}. Under these conditions, we studied increasing the torque density of an axial-gap motor. The study’s goal was to reduce the volume of the motor by half while maintaining the same output as the benchmark motor. Table 3 shows the prerequisites for the designed axial-gap motor.

#### 3.2. Design of Motor Constant for Maximum Output

_{T}is a torque constant, K

_{E}is an induced voltage constant, and ω is an angular velocity of the motor. Because K

_{T}and K

_{E}are equivalent, K

_{E}needed to output target maximum torque T

_{max}is determined from T

_{max}and maximum line current I

_{max}. Therefore, the phase voltage margin V

_{mgn}at I

_{max}is obtained by:

_{mgn}is obtained at the operating point ①, where the influence of E is great among the target speed–torque characteristics, and the effective voltage can be obtained at 68 A

_{rms}or more for I

_{max}.

_{mgn}, the designable armature winding resistance r at I

_{max}is to determine the optimum range of I

_{max}. Winding resistance r is calculated from V

_{mgn}and I considering only the voltage drop of r, and r is also calculated from the calorific value of the driving limit. These equations are shown as follows:

_{mgn}can be ensured with a margin by designing I

_{max}in the range of 80 to 84 A

_{rms}because the impact of voltage drop due to the iron loss, which is not considered in this calculation, is small at the operating point ④, where the rotational speed is low.

_{max}and the maximum current density. Because of the double stator structure, the top and the bottom stator windings must be connected in parallel. Therefore, it is considered that either a 2-parallel or a 4-parallel connection is employed. Using the windings of existing products is necessary to consider the cost. As a result, the winding diameter was determined to be 0.95 mm in a 4-parallel connection or 1.35 mm in a 2-parallel connection.

#### 3.3. Magnetic Circuit Design (Structural Design)

_{n}, ψ

_{a}, and I. ψ

_{a}fluctuates depending on a winding factor, a tooth cross-sectional area, coil turns, and magnetic flux. The parameters to design magnetic circuits affecting these are discussed. However, the parameters to design the magnetic circuit interfere with the parameters which affect the torque because the parameters of the magnetic circuit design and the parameters having an impact on the torque are not independent of each other. Therefore, the changeable parameters must be considered. In this section, the magnetic circuit is designed considering the interference. If an independent parameter is preferentially examined, the optimum value is determined first, and the number of parameters to be determined is reduced. When the parameters interfere with each other, the priority of the design is decided from the torque characteristics with respect to each parameter.

_{n}is the number of slots, and N

_{0}is the number of coil turns per unit slot stack length. Figure 11 shows the normalized number of coil turns with respect to the slot width. This standardization is based on the number of turns in 5.5 mm for a slot width of 10p9s. It is found that the number of coil turns increases in proportion to the slot width in any pole–slot combination. When the slot width increases from 3.7 mm to 3.8 mm, the number of coil turns increases rapidly, this is thought to be due to the space factor. As shown in Figure 12, when the slot width is 3.7 mm, two rows of coils of 1.35 mm for winding diameter are wound, and when the slot width is 3.8 mm, three rows of coils of 0.95 mm for winding diameter are wound. Therefore, it is found that the space factor increases when the number of columns is odd, such as the slot width of 3.8 mm.

_{n}) at each number of slots affects the torque. Thus, it can be seen from the torque equation in Equation (2) that each study can make an independent study. In the study of the number of coil turns in Figure 11, the number of coil turns increases (torque increases) in proportion to the slot width. In contrast, in the study of the tooth cross-sectional area in Figure 13, the torque decreases with the slot width. This trade-off relationship results in a change in torque characteristics that peaks for a change in the slot width in each model, as shown in Figure 14. Therefore, the slot width where the torque peaks are considered the maximum torque in each model. As a result, it was found that the slot width of 3.8 mm with 14p12s was the largest torque.

#### 3.4. Results of Verification of Equipment

_{n}is each order component of back e.m.f. From this equation, the calculated THD was 0.0067. From there, it can be seen that the back e.m.f. waveform has mostly the primary component and has a sinusoidal waveform with few harmonic components.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 25.**Efficiency with respect to torque of benchmark motor and axial-gap motor: (

**a**) efficiency with respect to torque; (

**b**) loss analysis at 0.9 Nm.

Items | Value |
---|---|

Motor outer diameter | 84 mm |

Stack length | 25 mm |

Maximum current density | 30 Arms/mm^{2} |

Volume of PM | constant |

Kind of PM | Ferrite magnet |

Magnet arrangement | SPM |

Winding method | Concentrated windings |

Winding connection method | Star configuration |

Motor driving system | Three-phase sinusoidal AC drive |

Items | Radial-Gap Motor | Axial-Gap Motor | |
---|---|---|---|

number of poles and slots | 8 poles, 12 slots | 16 poles, 12 slots | |

Motor outer diameter | 84 mm | ||

stack length | 25 mm | ||

Air gap length | 1.0 mm | 0.5 mm (one side) | |

stator | stator outer diameter | 84 mm | 84 mm |

stator inner diameter | 45.4 mm | 44.2 mm | |

width of tooth/width of slots | 7.2 mm/− | −/8.3 mm | |

width of backyoke | 5 mm | 2 mm | |

rotor | rotor outer diameter | 43.4 mm | 82 mm |

thickness of PM | 9.4 mm | 2.5 mm | |

outer diameter of PM | 43.4 mm | 80 mm | |

inner diameter of PM | 24.6 mm | 32 mm |

Items | Value |
---|---|

Motor outer diameter | 80 mm |

Supply voltage V_{dc} | 11 V |

Maximum current density | 30 Arms/mm^{2} |

Volume of magnet | less than benchmark |

Slot | 6 | 9 | 12 | 15 | 18 | Torque Ripple |
---|---|---|---|---|---|---|

Pole | ||||||

4 | 0.866 | 0.617 | 0.433 | 0.389 | 0.328 | 12 |

6 | 0.866 | 0.38 | 0.433 | 18 | ||

8 | 0.866 | 0.946 | 0.866 | 0.711 | 0.616 | 24 |

10 | 0.5 | 0.946 | 0.933 | 0.866 | 0.735 | 30 |

12 | 0.866 | 0.91 | 0.866 | 36 | ||

14 | 0.5 | 0.617 | 0.933 | 0.952 | 0.902 | 42 |

16 | 0.866 | 0.328 | 0.866 | 0.952 | 0.946 | 48 |

18 | 0.91 | 54 | ||||

20 | 0.866 | 0.328 | 0.433 | 0.866 | 0.946 | 60 |

22 | 0.5 | 0.902 | 0.711 | 0.617 | 0.902 | 66 |

Items | Value | |
---|---|---|

Number of Poles and Slots | 14poles, 12slots | |

motor diameter | 80 mm | |

axial length | 34.8 mm | |

stator | winding method | Concentrated windings |

winding connection method | Star connection 2 series, 4 parallel | |

wire diameter | 0.95 mm | |

stator core material | Soft Magnetic Composite (SMC) | |

rotor | slot width | 3.8 mm |

rotor frame material | SUS303 | |

material of magnets | SmFeN | |

magnet arrangement | SPM type | |

thickness of magnets | 5.7 mm | |

volume of magnets | 15,349 mm^{3} | |

drive system | Three-phase sinusoidal voltage |

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**MDPI and ACS Style**

Hattori, A.; Noguchi, T.; Kamiyama, H.
High-Torque Density Design of Small Motors for Automotive Applications with Double Axial-Air-Gap Structures. *Energies* **2022**, *15*, 7341.
https://doi.org/10.3390/en15197341

**AMA Style**

Hattori A, Noguchi T, Kamiyama H.
High-Torque Density Design of Small Motors for Automotive Applications with Double Axial-Air-Gap Structures. *Energies*. 2022; 15(19):7341.
https://doi.org/10.3390/en15197341

**Chicago/Turabian Style**

Hattori, Akihisa, Toshihiko Noguchi, and Hiromu Kamiyama.
2022. "High-Torque Density Design of Small Motors for Automotive Applications with Double Axial-Air-Gap Structures" *Energies* 15, no. 19: 7341.
https://doi.org/10.3390/en15197341