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

Abstract

This paper describes the results of studies on higher torque density of automotive auxiliary motors based on electromagnetic field analysis. Dual stator axial-gap PM motors achieve higher torque density than radial-gap motors in a flat motor shape. Therefore, an axial-gap motor was designed based on a design policy different from that in the past to reduce its volume by half of the radial-gap motors for automotive applications and was experimentally evaluated using a prototype motor. In order to improve the torque density, a double axial-gap motor structure was adopted to achieve wide torque generation areas and was optimally designed, reducing the volume by 44% compared with the existing model. It was experimentally evaluated using a prototype motor.

1. Introduction

Recently, the number of small in-vehicle motors has been increasing yearly due to the electrification of various vehicle functions and the spread of hybrid electric vehicles (HEV). In addition, the development of battery electric vehicles (BEV) and plug-in hybrid electric vehicles (PHEV) is also being actively carried out. Currently, the number of auxiliary motors installed in automobiles is approximately 50 per car in the mass-market class and 130 per car in the luxury class. The worldwide production of small automotive motors is estimated to be three billion units in recent years and is expected to exceed four billion units by 2025 [1,2]. The number of small in-vehicle motors is expected to increase further. However, the increase in the small motors causes deterioration of fuel efficiency (mileage) and electricity consumption because the lightweight and compact design of the vehicles is hampered. Therefore, the small in-vehicle motors are required to be smaller and lighter. Small motors for automotive applications are used in various car areas, such as the steering wheel area, air conditioning, engine and brake systems, and doors and seats. The output of these motors ranges from a few W to several kW, depending on the application. For example, among motors for electric water pumps, the motor output is less than 20 W for air conditioning and heating applications that ensure heating function when the engine of idling-stop vehicles is stopped, 20 W~100 W for motor generator and inverter cooling applications, and the motor output for engine cooling applications is 100 W or more. The output of electric cooling fan motors for radiators is 200 W or more, and the output of electric brake motors and electric power steering motors varies from several hundred W to several kW, depending on the vehicle’s specifications [2,3]. In-vehicle small motors are often not required to be as high efficiency as traction motors (output: 50 kW–80 kW, efficiency: 95–97%) [2] since the small motors are used less frequently than the traction motors and have a smaller absolute value of the loss. Rather, there is a need for smaller motor designs due to higher torque—for example, reported cases include blower motors with efficiencies of 70–75% [4], electric oil pump motors with efficiencies of 75–80% [5], and electric power steering motors with efficiencies of 83% [6]. From the standpoint of miniaturization, electric water pump motors are required to be smaller because the space in the engine compartment is shrinking due to the expansion of the vehicle cabin and the increase in the amount of auxiliary equipment installed. In electric power steering motors, which are located in the column, rack, and pinion sections of the steering shaft, there is a demand for downsizing motors because of the layout restrictions around the steering. In addition, as motor characteristics, electric power steering motors require high torque for turning the steering wheel when the car is stopped and high rotation to cope with the reaction force of the steering wheel when avoiding an emergency or climbing up a step; that is, a wide driving range from high to low load is required. Furthermore, low-vibration motor characteristics are needed to avoid discomfort when operating the steering wheel. In addition, with the recent electrification of automobiles and future automatic driving in mind, the introduction of various by-wire systems that transmit steering operation by electric signals is desired. Redundancy, such as multiple drive systems, is also required to ensure the reliability and safety of auxiliary motors for automotive applications [7,8].

In recent years, axial-gap type PM motors have been actively studied in motor hardware research and development. For its use, there are traction motors such as BEV and HEV [9,10,11,12,13,14,15], in-wheel motors [16,17,18,19], and motors for collaborative robots [20]. Axial-gap motors, especially pancake-type motors, have a larger torque generation surface area than radial-gap motors, so higher torque density can be expected in some applications such as in-vehicle auxiliary machines [21,22]. The authors have studied double-stator axial-gap type PM motors [23,24,25]. The stator and rotor configurations of axial-gap motors include single-rotor and single-stator types [26], two-rotor and single-stator types [16,27,28], and even multi-layered stator–rotor structures [29]. The authors have studied two-stator and single-rotor structures that allow the stator to be easily fixed and ensure the windings’ redundancy and high heat dissipation. The axial-gap motor has a 3D magnetic circuit, and soft magnetic composite (SMC) is often employed as a stator core material [13,27,30] against the background of material performance improvement [31,32]. The stator almost always has an open-slot tooth structure from the viewpoint of the manufacturing process. Axial-gap motors have more structural parameters which affect each other in designing magnetic loading (rotor) and electric loading (stator) compared with radial-gap motors with pole horns in the stator. Therefore, it is tough to design the stator and the rotor separately in axial-gap motors. It is necessary to design the entire magnetic circuit of the motor in consideration of electrical and magnetic loading simultaneously.

Additionally, there is no textbook approach to the design of magnetic circuits in PMSM. However, in many cases, some mechanical load device is assumed and designed to meet the specifications required by that load. Specifically, rotation speed and torque at the motor’s operating point are given first. At the same time, the outer diameter of the motor due to mounting constraints and the power supply (voltage, current) become design specifications. Then, using the torque equation, the permanent magnet armature flux linkage ${\psi }_a$ is calculated from the torque and current specifications. The maximum speed and fundamental frequency determine the number of poles. Next, using the voltage equation, the upper limit of inductance is obtained from the rotational speed and voltage specifications. The approximate dimensions of the motor are tentatively determined using an empirically obtained ratio, and the permeance of the main magnetic circuit is estimated by the permeance method. Then, the winding resistance can be calculated from the current density, stator shape, and winding factor. Finally, the magnet specifications (the type of PM, thickness) are determined from the required armature flux linkage and inductance. A motor model is created with these selected motor parameters, and motor characteristics are calculated by electromagnetic field analysis. In many cases, motors are designed in this way. If the calculated voltage exceeds the limit, review the magnet specifications and the number of coil turns and recalculate the motor characteristics. Furthermore, if the desired characteristics are not met, the motor dimensions, and even the number of poles, will be changed retroactively. Additionally, the motor characteristics need to be recalculated [33].

In this paper, a motor was designed based on a design policy different from the past to achieve high torque density for miniaturization. Precisely, the required torque constant is calculated from the target operating point, and the minimum required current value is calculated from the relationship of voltage to current using a voltage equation. The drivable winding resistance value is calculated within that current range, and the winding specification is determined within a certain voltage margin. Considering the electrical specifications first and designing the motor, there is no need for a review calculation due to the voltage exceeding the limit, which was the case in the past. The magnetic circuit is designed based on the assumption of such electrical specifications. Still, the dimensional parameters of the motors interfere with each other, and the optimum value cannot be determined by the individual parameters only. Therefore, we separate the motor parameters into independent combinations that do not interfere with each other. Among these parameters, the characteristics of several patterns of parameter combinations are calculated and compared by electromagnetic field analysis using FEM, and the optimal parameter values are determined in the order. Suppose a motor is designed using the above calculation method. In that case, it is necessary to calculate several models to determine each parameter. Still, the parameters close to the optimum value can be specified in the order of consideration. The final motor structure can be determined without recalculation as in the conventional method, thus reducing the number of trials.

In Section 2 of this paper, the axial-gap motor was designed to achieve high torque while considering the axial-gap structure’s unique structure compared with a radial-gap motor in a flat shape. In Section 3, considering a motor structure design specialized for the axial-gap motors, a prototype motor was developed to achieve higher torque density than radial-gap motors, which have conventionally been designed for automotive auxiliary machines.

2. High Torque Density Design of Axial-Gap Motors

2.1. Prerequisites

Considering the possibility of increasing the torque of an axial-gap motor compared to a general radial-gap motor.

Table 1. Preconditions.

Items	Value
Motor outer diameter	84 mm
Stack length	25 mm
Maximum current density	30 Arms/mm2
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

shows the preconditions of a radial-gap motor and axial-gap motor. The motor outer diameter D is 84 mm, and the motor stack length L is 25 mm. Thus, the flatness ratio of motors is 0.3. The flatness ratio is defined by:

$$\mathrm{flatness} \mathrm{ratio}=\frac{\mathrm{stack} \mathrm{length} L}{\mathrm{motor} \mathrm{diameter} D},$$

(1)

The kind of magnet is ferrite magnets. The volume of magnets and the current density should also be constant. The winding method is concentrated winding, the driving system is a three-phase sinusoidal AC drive, and the magnet arrangement is SPM-type.

2.2. Magnetic Circuit Design of Axial-Gap Motor

Figure 1 shows a typical radial-gap type benchmark motor and an illustration of an axial-gap motor. The radial-gap motor’s number of poles and slots is 8 poles and 12 slots (8p12s). The axial-gap motor structure was designed using electromagnetic field analysis simulation based on the finite element method (FEM). The axial-gap motor’s number of poles and slots was 16p12s because the winding factor is the same as the radial-gap motor, and the torque can be increased by increasing the number of poles. The axial-gap motor has dual open-slot stators with concentrated windings.

The torque of the motor can generally be expressed by:

$$T\propto P_n{\psi }_{a}I=P_n\varphi NI,$$

(2)

where P_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:

$$p_u={\mu }_0\frac{A_g{l}_m}{K_c{l}_g{A}_m},$$

(3)

where A_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.

On the other hand, if we consider maximizing the electrical loading NI, the stator shape must be determined to maximize the number of coil turns N, since the current I is constant. The number of coil turns N is determined by the slot volume. Dimensional parameters determining the slot volume are a slot width and a back yoke thickness. If the stator’s slot width is increased to increase the number of coil turns, the amount of armature flux linkage is increased; hence, it is necessary to increase the back yoke thickness. In addition, since the stator of the axial-gap motor has an open-slot tooth structure, if the slot width is increased, the tooth surface area becomes small, resulting in a smaller magnet surface area facing the tooth. As a result, the magnetic loading ϕ becomes small. Thus, there is a trade-off relationship between each dimensional parameter of the stator for the number of coil turns (electric loading). Furthermore, there is a trade-off relationship between electrical and magnetic loading.

In the examination of this section, in order not to complicate factors of torque fluctuation, the effect of each dimensional parameter represented by the electric and magnetic loading on the torque was verified by the FEM under the condition that some dimensional parameters interfered with by the electric and magnetic loading are fixed. Figure 2 shows the torque with respect to the magnet thickness, where the slot width is fixed at 9.8 mm. It is found that the maximum torque is obtained at around 2.5 mm, which is a manufacturing limit. It is considered that this is due to the fact that the thinner the magnet is, the larger the slot volume is because the motor size is kept constant.

Figure 3 shows an average torque and a torque ripple with respect to the slot width. The magnet thickness is fixed at 2.5 mm. It can be seen that the torque is the highest when the slot width is 9.2 mm, and the torque ripple is the lowest. From Figure 3, it can be seen that the slot width in which the product of the electric loading and the magnetic loading becomes the largest is 9.2 mm. Furthermore, the torque ripple tends to have a low value because of a structure peculiar to the axial-gap motor in which the end surfaces extend in the radial direction of the magnet, and the stator teeth are relatively skewed. In particular, the slot width of 9.2 mm is considered to be caused by the fact that the instantaneous torque generated by each tooth has a countervailing relation.

Based on the above results, the mechanical dimensions of the motor were determined to be 2.5 mm for the magnet thickness and 9.2 mm for the slot width.

2.3. Experimental Results

The axial-gap motor was designed in the preceding paragraph, the radial-gap benchmark motor was manufactured, and the torque characteristics of prototype motors were measured.

Table 2. Specifications of radial-gap motor and axial-gap motor.

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

shows the specifications of a radial-gap motor and an axial-gap motor. The air gap length of the radial-gap motor is 1.0 mm. On the other hand, the air gap length of the axial-gap motor is 0.5 mm on each side. Because the axial-gap motor has a two-stator and single-rotor structure, there is an air gap of 0.5 mm above and below the rotor. Considering the two air gaps of the axial-gap motor and one air gap of the radial-gap motor, the axial-gap motor’s air gap length is equivalent to the radial-gap motor. The rotor structure of the axial-gap motor consists of magnets pasted on the upper and lower surfaces relative to the core. The magnet is fixed in such a way that the magnetic flux direction penetrates the rotor’s top and bottom.

Figure 4 shows the average torque with respect to the current density obtained in the analysis and the measurement. The analysis value is the electromagnetic field analysis simulation result based on the FEM. It shows that the torque density of the axial-gap motor is twice that of the radial-gap motor. It can also be seen that the analytical value and the measured value are almost the same. As described above, it has been found that the axial-gap motor can have a higher torque density than the radial-gap motor at a flatness ratio of 0.3.

3. High Torque Density of Axial-Gap Motor

3.1. Preconditions and Target

Figure 5 shows a benchmark motor and its motor drive circuit for small in-vehicle motor applications [25], and Figure 6 shows the operating characteristics of the benchmark model. In Figure 5b, R_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 mm³. 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. Preconditions.

Items	Value
Motor outer diameter	80 mm
Supply voltage Vdc	11 V
Maximum current density	30 Arms/mm2
Volume of magnet	less than benchmark

shows the prerequisites for the designed axial-gap motor.

3.2. Design of Motor Constant for Maximum Output

As a design policy, motor constants that satisfy the preconditions are designed roughly, and then a drive voltage and winding specifications with sufficient electrical margin are determined. Finally, a magnetic circuit is designed under these conditions. Thus, the number of trials and errors in the magnetic circuit design, which occupies a large part of the motor design process, can be reduced.

First, the driving conditions under which the voltage drop of the driving circuit and the back e.m.f. can be allowed are examined. When the armature current is I, the motor input voltage V (phase) can be calculated by the following equation:

$$V=\frac{\left(V_{dc}-\sqrt{2}{R}_{dc}I\right)\eta }{\sqrt{6}}-R_{ac}I.$$

(4)

Figure 7 shows the result calculated from the above equation. The voltage calculated by subtracting the back e.m.f. from the motor input voltage is a voltage margin. However, iron loss and reactive power are ignored because these are complicated. The torque T and the line-to-line electromotive force E are expressed by:

$$T=3K_{T}I,\mathrm{and}$$

(5)

$$\frac{E}{\sqrt{3}}=K_E\omega ,$$

(6)

where K_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:

$$V_{mgn}=V-\frac{E}{\sqrt{3}}=V-K_E\omega =V-\frac{T_{max}}{3I_{max}}.$$

(7)

Figure 8 shows the result calculated from the above equation. The minimum V_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.

Next, the armature winding is examined. Using the obtained V_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:

$$r=\frac{V_{mgn}}{I}, \mathrm{and}$$

(8)

$$r=\frac{Calorific Power}{3I^2}.$$

(9)

Figure 9 shows the designable r with respect to the maximum line current. Numbers indicate the operating points used in the calculation in Equation (8) in Figure 9. It is considered that V_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.

In addition, the coil diameter is determined, which can be designed from the preconditions, i.e., the range of I_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)

The magnetic circuit is examined based on the winding diameter determined in the previous section. In general, the torque can be expressed by Equation (2). From Equation (2), torque is proportional to P_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.

First, the pole–slot combination is examined. The number of poles and the winding factor are determined only by the pole–slot combination. However, the outer diameter of the motor is limited in this study. If the number of slots is changed under the condition where the ampere turn is constant, the tooth cross-sectional area changes, and parameters other than the winding factor may affect the torque; thus, the pole–slot combination cannot be an independent parameter. Therefore, to make them independent parameters, the number of coil turns, the inner and outer diameters of the magnets, the quantity of the magnets, the cross-sectional area of the teeth, and the inner and the outer diameters of the teeth were kept constant for each number of slots to be designed so as not to be affected by any parameters other than the number of poles and the winding factor.

Figure 10 shows the torque with respect to the pole–slot combination. Since it is not possible to compare models with different numbers of slots, an appropriate number of poles in each number of slots is chosen.

Table 4. Winding factor for each number of poles and slots in concentrated winding.

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

shows the winding factor for each number of poles and slots in a concentrated winding and the basic order of torque ripple at each number of poles. The smaller the number of slots is, the less difficult it is to make the stator, and the smaller the insulator volume of the entire stator. Therefore, a smaller number of slots increases the ratio of windings to slot area, leading to an increase in the number of coil turns. The larger the number of poles is, the higher the torque is, but at the same time, the amount of flux leakage between the poles increases, which also results in lower torque. In addition, the larger the number of poles is, the larger the order of torque ripple is, the smaller the torque ripple rate is, and the lower the motor’s vibration. Slot specifications of 6 slot or less are unbalanced considering the motor outer diameter dimensions, and 18 slot or more are out of consideration due to high manufacturing difficulty. The number of poles is chosen in the range of 8 pole to 16 pole with the same idea. For each number of slots, the number of poles with a large winding factor was selected to be compared for torque characteristics. The 9 slot structure was analyzed for 8 pole and 10 pole; the 12 slot structure for 10 pole, 14 pole, and 16 pole; and the 15 slot structure for 14 pole and 16 pole. Since the stator teeth shape is an open slot shape in the axial-gap motors, it is considered that the winding factor is slightly different from the general winding factor shown in Table 4, and this effect is believed to be reflected as torque. As a result, 10p9s (10 poles, 9 slots), 14p12s, and 16p15s, were selected for the pole–slot combination.

Next, the slot width is examined. Since the tooth cross-section area and the number of coil turns vary if the slot width is changed, the examination is carried out in the number of coil turns and tooth cross-section areas, respectively. First, regarding the examination of the number of coil turns, the number of coil turns is proportional to the torque, and this can be understood from Equation (2). Since the number of coil turns varies with the slot width and stack length, it cannot be determined only by the slot width. Therefore, the characteristics of the number of coil turns with respect to the slot width are examined so that it can be referred to in the final stage of determining the motor parameter. The stator shape is not decided only by these data. Since the winding diameter was determined in Section 2, the slot width, which can be manufactured with 0.95 mm or 1.35 mm for the winding diameter, is examined. The ratio of the number of coil turns in each slot width is determined by:

$$N=\frac{S_n{N}_0}{P_n},$$

(10)

where S_n is the number of slots, and N₀ 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.

Next, the tooth cross-section is examined. As mentioned in Section 2, the magnetic loading also changes with the change of the tooth cross-section area, so the tooth cross-section is not an independent parameter. Therefore, the relationship between the tooth cross-sectional area and the shape of the magnet is freely determined in each model. However, the overhang of the magnet shall be 0 mm. Additionally, to be independent of the number of coil turns, the ampere turn is constant, and the torque characteristics with respect to tooth cross-sectional area are calculated. Figure 13 shows the change in torque due to the effect of the tooth cross-sectional area, with the horizontal axis being the slot width. It is normalized based on the torque when the slot width is 2.0 mm in 10p9s, which has the largest tooth cross-section. The torque increases as the slot width are narrower because the magnet shape is changed by the stator shape, which increases the amount of magnet used. Thus far, the number of coil turns and the tooth cross-section, which varies with the slot width, have been examined. Finally, torque with respect to slot width is shown in Figure 14. It is calculated by the product of the number of coil turns and torque with respect to the tooth cross-sectional area. It is considered that the number of coil turns (N) affects the torque in the first study in Figure 11. In the next study of the tooth cross-sectional area, the magnet flux $\varphi$ due to the change in magnet shape accompanying the change in stator shape affects the torque, and the difference in the number of pole pairs (P_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.

Since the magnet overhang has been kept constant in the previous study, there is a margin in the magnet quantity. Therefore, the characteristics of torque with respect to magnet overhang are examined. Considering that the position of the tooth outer diameter and the slot cross-sectional area may have an effect, the slot width was set to 3 points of 6 mm, 7.5 mm, and 9 mm. Figure 15 shows the result of examining the torque with respect to magnet overhang. The torque for the overhang quantity is expected to increase about 1.2 times on the outside and about 1.1 times on the inside. It is also found that the relationship between the overhang amount and the torque tends to be the same for all the slot widths. In the final stage of determining the motor parameter, it is designed to allocate the usable magnet quantity to the inner and outer diameters’ overhang to maximize the torque. Increasing torque is greater in the overhang on the outer diameter side than on the inner diameter side because more magnet volume is used when magnets are placed on the outer diameter side. In addition, in the case of an axial-gap motor, the distance between the point at which the force and the point on the axis of rotation are longer in the outer diameter section than in the inner diameter section, so that overhang on the outer diameter side results in greater rotational force. Therefore, if there is a limit to the volume of magnets, it is considered that increasing the overhang amount on the outer diameter side is more effective in increasing torque.

Based on the result examined, several magnetic circuits are selected (pole–slot combination, winding diameter, number of rows), and various parameters which can expect the highest torque for each magnetic circuit are decided. The number of rows is a parameter roughly determined by the winding resistance value with respect to the slot width. The magnet shape is obtained by examining the magnet overhang quantity, the magnet thickness, and the usable magnet quantity. Still, since the effect of the magnet thickness on the torque is small, the torque is mainly obtained by the magnet overhang. The analysis results are shown in Figure 16. This model is determined as a magnetic circuit structure. As a result, it was found that the maximum torque was obtained when the winding diameter was 0.95 mm at 14p12s and the number of rows was three. The final motor product thickness was 34.8 mm and could be reduced by 44% compared to the radial-type benchmark motor.

3.4. Results of Verification of Equipment

Figure 17 shows the structure of a prototype axial-gap motor, and Figure 18 shows a prototype axial-gap motor.

Table 5. Specifications of prototype axial-gap motor.

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 mm3
drive system		Three-phase sinusoidal voltage

shows the specifications of the axial-gap motor. The motor diameter is 80 mm, stack length is 34.8 mm, and the prototype motor has an SPM type rotor with 14 poles, and a 12 slot stator with a three-phase concentrated winding. Since the magnetic circuit in the stator core is three-dimensional, Soft Magnetic Composite (SMC) is used for the stator core, and an insulator for insulation is used. The B–H characteristics of SMC are shown in Figure 19. It can be seen that the maximum saturation magnetic flux density of the SMC used in the axial-gap motor is about 1.8 T, while the maximum saturation magnetic flux density of the magnetic steel sheet used as the stator core in the radial-gap motor is about 2.0 T. The magnet material is SmFeN magnet, and the magnets are adhered to and held to a rotor core having a circular lattice shape. The windings are connected in two parallel and four lines with a star configuration. A resolver is used to sense the rotor position.

After the unmagnetized magnet of the prototype axial-gap motor was bonded to the rotor core, the magnet was magnetized by the magnetizing system. Figure 20 shows the rotor’s surface magnetic flux density waveform on the up and downside when the measured radial center radius r is 27 mm. It can be seen that there is little variation in each pole and the ups and downsides. Figure 21 shows the back e.m.f. waveform at a rotating speed of 1000 r/min. Total harmonic distribution (THD) of the back e.m.f. was calculated by:

$$THD=\frac{\sqrt{V_2{}^2+V_3{}^2+V_4{}^2\cdots +V_n{}^2}}{V_1},$$

(11)

where V_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.

Figure 22 shows the instantaneous torque waveform at 78 Arms around the maximum torque. The torque ripple calculated by dividing the difference between the maximum and minimum values of the torque by the average torque was 1.57%. As described in Section 2, this is due to the structure in which the stator teeth of the axial-gap motor and the magnet are relatively skewed. It can be seen that a low torque ripple can be realized even in an actual machine of the axial-gap motor by magnetizing the magnet with high accuracy.

Figure 23 shows the target operation characteristics and the speed–torque characteristics of the simulation value and the experiment value of the axial-gap motor and the radial benchmark motor. Figure 24 shows the measurement system configuration. The prototype of the axial-gap motor was found to have the same maximum torque as the benchmark motor. The torque per magnet volume improved by 47%. It is confirmed that the axial-gap motor has a motor structure that can effectively use magnets than the benchmark motor. Figure 22 shows that the characteristics of the designed axial-gap motor exceed the target. Additionally, it can be seen that the analytical values and the experimental value are almost the same.

Figure 25 shows the measured efficiency with respect to torque for the benchmark motor and axial-gap motor at maximum power control and a breakdown of losses at 0.9 Nm near maximum efficiency. However, iron loss is defined as all remaining losses after subtracting the output calculated from the torque and rotation, copper loss, and mechanical loss from the input power of the motor. The maximum efficiency of both motors is found to be about 85% at around 1 Nm. In recent years, SMC material development has progressed. Although the maximum magnetic flux density of SMC is inferior to that of electrical steel, the iron loss characteristics of SMC are almost the same characteristics as those of electrical steel (depending on frequency). It indicates no significant difference in parts due to iron loss. Since the winding resistance of both motors in this study is almost the same, the inductance is not significantly different due to the SPM type; it can be seen that the loss characteristics of the axial-gap motor are similar to those of the benchmark motor. However, there are slight differences due to the ratio of electrical and magnetic loading, heat dissipation, and core material.

4. Conclusions

In this paper, the potential of the axial-gap motor to increase the torque density in the flat motor shape was discussed, and it was shown that the axial-gap motor’s torque becomes two times that of the radial-gap motor at the flatness ratio of 0.3. In addition, to reduce the motor volume by half by increasing the torque density, a flat-type double stator axial-gap PM motor was applied to the small automotive auxiliary motor, and miniaturization was studied.

As a result, the optimized motor satisfied the specifications with a small size, i.e., 80 mm motor outer diameter and 34.8 mm motor stack length. The double stator type axial-gap motor with a higher torque density achieved excellent performance equivalent to the benchmark model while the volume was reduced by 44%.