# Axial-Flux PM BLDC Machines with Concentrated Windings: Double-Layer, Single-Layer, and Single-Layer with Unequal Tooth

Min Gu, Zijian Xi

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Min Gu, Zijian Xi. Axial-Flux PM BLDC Machines with Concentrated Windings: Double-Layer, Single-Layer, and Single-Layer with Unequal Tooth. 2017. hal-01498402

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Distributed under a Creative Commons Attribution 4.0 International License
Axial-Flux PM BLDC Machines with Concentrated
Windings: Double-Layer, Single-Layer, and Single-
Layer with Unequal Tooth

Min Gu

Department of Electrical Engineering
Guangdong University of Foreign Studies
Guangzhou, China
min.gu1980@gmail.com

Zijian Xi

Department of Electrical Engineering
Guangdong University of Foreign Studies
Guangzhou, China
z.xi_uni@yahoo.com

***Abstract***—This paper investigates axial-flux permanent-magnet brushless-dc (PM BLDC) machines with concentrated windings and different layer numbers. In order to analyze the influence of layer numbers and unequal tooth on machine performance, three axial-flux PM BLDC machines are considered, and compared with respect to phase back-EMF, winding inductance, cogging torque, and electromagnetic torque. Three-dimensional (3-D) finite-element analysis is used to study the machines precisely.

***Keywords***— axial-flux permanent-magnet, unequal tooth, single-layer, BLDC, 3-D finite-element analysis

I. INTRODUCTION

In term of flux flow, electrical machines can be classified
either as radial-flux machines or axial-flux machines. In radial-
flux machines, the magnetic flux moves along the radius in the
air-gap, while in axial-flux machines the magnetic flux moves
along the axial axis in the air-gap. An axial-flux PM machine
provides higher power density compared with a radial-flux PM
machine, and is a very attractive choice especially when an
electrical machine has to be directly mounted into a mechanical
machine [1-3].

Recently, technology of axial-flux PM machine with concentrated winding is emerging due to their high torque-density, high efficiency, compact construction, high filling factor especially with segmented stators, and good heat removal configuration [1-5]. Also, PM BLDC machines are known for their high efficiency and high torque-density [3,6]. So, axial-flux PM BLDC machines with concentrated windings are excellent choices to be used in applications with restrict space as in direct-driven applications, such as electric vehicles [7-9].

In PM machines with concentrated windings, stator coils
may be wound either on all teeth (double-layer windings) or
only on alternate teeth (single-layer windings). When single-
layer winding is used, number of coils is halved. So the number
of turns per coil must be doubled to have the same number of
total series turns per phase as well as the same winding current
density. In the case of using similar slot number and pole
number, higher winding factor will be achieved which results

in higher torque. Also, similar slot number and pole number
results in low cogging torque. When an axial-flux PMBLDC
motor with high torque density is considered for applications
with limited space, similar slot number and pole number is an
attractive choice. This paper investigates influence of unequal
tooth widths and different layer numbers for axial-flux PM
BLDC machines with similar slot number and pole number.
Hence, the performance of three 3.4 kW 12-slot/10-pole axial-
flux PM BLDC machines with double-layer windings, single-
layer windings, and single-layer windings with unequal tooth
widths are analyzed. In this research cogging torque, back-
EMF, winding inductance, and output torque are obtained for
the three axial-flux PM BLDC machines by 3-D finite element
method.

II. MACHINE DESIGN CONSIDERATION

Axial-flux PM machines have different topologies. A high
efficient axial-flux PM machine with segmented stator
designed for electric vehicles [10-14] is chosen for this study.
This novel axial-flux machine topology has gained attention
and been used in different researches, particularly as in-wheel
electric motors in lightweight urban electric vehicles. The
machine has a single stator that is sandwiched between two
surface-mounted PM rotor discs. The stator segments are
stacked together as an integrated stator by high strength resin
holders. Also parallel slot-opening is employed.

To analyze the influence of layer numbers and tooth widths,
all the considered machines have the same dimensions, and the
same pole and slot combination. In machines with low pole
numbers, such as a 4 pole machine, rotor back-iron length must
be increased to avoid saturation and may exceed the limited
axial length of the motor for different applications with limited
space. In machines with high pole numbers, such as an 18 pole
machine, inter-pole leakage flux increases and will cause the
air-gap flux-density distribution and back-EMF waveform to
be more sinusoidal which is not desired for BLDC operation.
High pole numbers also cause high manufacturing cost. After
careful consideration and analyzing different pole numbers by
3-D finite-element method, 10 pole machines are chosen for
investigation. Number of slots is set to 12 as in machines with
similar slot number and pole number, higher winding factor
<figure><img src="image_2.png" /><figcaption>Figure 1. Winding configurations for 12-slot/10-pole machines (a) double-layer windings (b) single-layer windings (c) single-layer windings with unequal tooth widths</figcaption></figure>

and hence higher output torque is achieved. Also, similar slot number and pole number results in low cogging torque due to high LCM (least common multiple) of pole number and slot number. Therefore the research is carried out for a 12-slot/10-pole axial-flux PM motor with double-layer windings (motor A), a 12-slot/10-pole axial-flux PM motor with single-layer windings (motor B), and a 12-slot/10-pole axial-flux PM motor with single-layer windings with unequal tooth widths (motor C). Figure 1 (a)-(c) shows motor A, motor B, and motor C; respectively. It is seen in Figure 1 (c) that the coils are wound on alternate teeth which are wider than unwound teeth. The widths of the wound teeth are set equal to the pole pitch so that pitch factor of 1 would be achieved.

<table><caption>TABLE I. MOTOR PARAMETERS</caption><thead><tr><th>Motor type</th><th>A</th><th>B</th><th>C</th></tr></thead><tbody><tr><td>No-load Voltage, V</td><td>50</td><td>50</td><td>50</td></tr><tr><td>Rated phase current, A</td><td>34</td><td>34</td><td>34</td></tr><tr><td>Rated rotational speed, rpm</td><td>1200</td><td>1200</td><td>1200</td></tr><tr><td>Stator outer radius, mm</td><td>95</td><td>95</td><td>95</td></tr><tr><td>Stator inner radius, mm</td><td>55</td><td>55</td><td>55</td></tr><tr><td>Slot-opening, mm</td><td>4</td><td>4</td><td>4</td></tr><tr><td>Tooth width at average radius, mm</td><td>35.27</td><td>35.27</td><td>43.12<br>27.41</td></tr><tr><td>pole-arc to pole-pitch ratio</td><td>0.7</td><td>0.7</td><td>0.7</td></tr><tr><td>Air gap, mm</td><td>1.5</td><td>1.5</td><td>1.5</td></tr><tr><td>Magnet axial length, mm</td><td>5</td><td>5</td><td>5</td></tr><tr><td>Magnet remanence, T</td><td>1.22</td><td>1.22</td><td>1.22</td></tr><tr><td>Number of turns per coil</td><td>25</td><td>50</td><td>50</td></tr></tbody></table>

The derivation of the sizing equation follows a similar form to the sizing equation as in [15-18]:

$$P = \frac{\pi^2 npl_m (R_o^2 - R_i^2) R_i}{60(l_m + g')} l_{bar} JK_f \alpha_s B_r \left(1 - \frac{\alpha_s l_m B_r}{(l_m + g') B_s}\right) (1)$$

where P is the output power, n is machine speed, $R_o$, $R_i$ are stator outer and inner radius respectively, $l_{bar}$ is winding axial length, J is winding current density, $K_f$ is winding fill factor, $l_m$ is magnet thickness and g' is effective air gap length, $B_r$ and $B_s$ are magnet residual flux density and maximum no load stator core flux density. The stator, magnet outer to inner diameter ratio is chosen as 0.58 for maximum specific torque, in equation (1). The main design parameters are summarized in Table I.

Cogging torque is one of the main contributors to the torque ripple in PM motors, which is caused by the interactions between PMs and stator teeth. Beside pole and slot combination, pole arc has significant effect on cogging torque. In this research cogging torque of three machines are set at their minimum for different configuration. The optimum ratios of pole arc to pole pitch for minimizing cogging torque for a given slot and pole number is [18-21]:

$$\alpha_p = \frac{N - k_1}{N} + k_2, \quad k_1 = 1, 2, \dots, N - 1 \quad (2)$$

where $N=N_c/2p$, $N_c$ is the least common multiple between pole number and slot number, and $k_2$ is a constant that ranges from 0.01 to 0.03 depending on air-gap length [22-26]. Equation (2) is for a regular machine with equal tooth widths. Optimum pole arc to pole pitch ratios of a 12-slot/10-pole machine with unequal tooth widths is equal to the optimum pole arc to pole pitch ratios of a 6-slot/10-pole machine with equal tooth widths. Hence, the optimum ratios of pole arc to pole pitch for minimizing cogging torque is shown in Table II. The common pole arc to pole pitch ratio of 0.7 was chosen for this study.
<table><caption>TABLE II. OPTIMUM POLE ARC TO POLE PITCH RATIOS</caption><tr><td>12-slot/10-pole</td><td>0.19, 0.36, 0.53, 0.7, 0.86</td></tr><tr><td>12-slot/10-pole with unequal tooth widths</td><td>0.36, 0.7</td></tr></table>

Parallel stator slot-openings are used so that high filling factor can be achieved. When parallel slot-openings are employed, the ratio of the slot-opening width to the slot-pitch is a function of radius. In the case of machines A and B, the tooth widths at every radius (r) can be obtained as:

$$w = r \left( \frac{2\pi}{N_s} - 2\sin^{-1}\left(\frac{ds}{2r}\right) \right) \quad (3)$$

while in the case of machines with unequal tooth widths as machine C, the tooth widths at every radius (r) can be obtained as:

$$w_c = r \left( \frac{\pi}{p} - 2 \sin^{-1} \left( \frac{ds}{2r} \right) \right) \quad (4)$$

$$w_n = r \left( \frac{4\pi}{N_s} - \frac{\pi}{p} - 2 \sin^{-1} \left( \frac{ds}{2r} \right) \right) \quad (5)$$

where $w_c$ is the width of teeth that carries a coil, $w_n$ is the width of teeth that does not carry a coil, $P$ is the number of pole pairs, $N_s$ is the number of slot, and $ds$ is the parallel slot-opening.

There are different ways to realize a motor with concentrated windings. It is assumed that the design is performed for three-phase motors with balanced windings which have two coils sides in each slot. The angles of the $k$th coil for the double-layer concentrated windings are defined as:

$$\begin{gathered} \theta_c(k) = (k-1) \frac{P}{N_s} 180^\circ E \quad (6) \\ \text{for } k=1, 2, \dots, N_s \end{gathered}$$

while for the single-layer winding as:

$$\begin{gathered} \theta_c(k) = (k-1) \frac{P}{N_s} 360^\circ E \quad (7) \\ \text{for } k=1, 2, \dots, \frac{N_s}{2} \end{gathered}$$

with respect to (6) and (7), in a double-layer 12-slot/10-pole machine the 3-phase winding arrangement is AA'C'CBB'A'ACC'B'B; and for a single-layer 12-slot/10-pole machine, either for equal or unequal tooth widths, it is AC'BA'CB'.

The winding factors $K_{wn}$ can be achieved as:

<table><caption>TABLE III. WINDING FACTOR</caption><thead><tr><th rowspan="2">Motor Type</th><th colspan="4">Harmonic order</th></tr><tr><th>n = 1</th><th>n = 3</th><th>n = 5</th><th>n = 7</th></tr></thead><tbody><tr><td>Motor A</td><td>0.933</td><td>0.5</td><td>0.067</td><td>0.067</td></tr><tr><td>Motor B</td><td>0.966</td><td>-0.707</td><td>0.259</td><td>0.259</td></tr><tr><td>Motor C</td><td>1</td><td>1</td><td>1</td><td>1</td></tr></tbody></table>

$$k_{wn} = \frac{1}{N_{cph}} \sum_{k=1}^{N_{cph}} e^{-jn\theta_c(k)} \quad (8)$$

where $N_{cph}$ represents number of coils per phase.

### III. SIMULATION RESULTS

The finite-element method allows a precise analysis of magnetic devices taking into account geometric details and magnetic nonlinearity. As axial-flux PM machines are inherently 3-D machines, 3-D finite-element model was developed to simulate the performance of the machines. Phase back-EMF, winding inductance, cogging torque, and output torque are obtained for three machines with precise 3-D finite-element simulation.

Table III shows the winding factors for the fundamental and harmonics of the motors. It can be seen that motor C, having single-layer windings with unequal tooth widths has highest fundamental winding factor. This could result in higher flux linkage and consequently higher torque compared to other two motors.

Torque quality of AFPM machines, which is directly related to the torque ripple components, is of high importance. Torque ripple, which is the torque pulsation caused by the periodic components in the instantaneous torque of the machine, could result in vibration, noise, and even failure. The torque ripple of PM BLDC machine constitutes two different components, back-EMF related torque ripple, and cogging torque which is unaffected by the load. The contribution of these components in torque ripple is investigated in following.

#### A. Phase back-EMF and Line back-EMF

Phase back-EMF is computed by the no-load change rate of flux linkage through the corresponding coils. Phase-back-EMF and line back-EMF waveforms of the three motors are obtained by using 3-D finite-element model and are shown in Figures 2 and 3; respectively. It is seen that machines with single layer windings has more trapezoidal phase back-EMF waveforms. Also unequal tooth widths will increase the flat top area and hence machine C has the most trapezoidal phase back-EMF waveform. As in brushless-dc operation, only two phases conduct at each time, line back-EMF waveform will define the average electromagnetic torque and also back-EMF related torque ripple. It is seen that motors B and C have a high line back-EMF value, while motor A with double-layer windings has the lowest value. Also it is seen from Figure 3 that machine B has the least flat top area. So machine B with single layer winding and equal tooth widths will have higher back-EMF related torque ripple.
<figure><img src="image_3.png" /><figcaption>Figure 2. Phase back-EMF waveforms by 3-D finite-element</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 3. Line EMF waveforms by 3-D finite-element</figcaption></figure>

## B. Winding Inductances and Cogging Torque

Table IV shows self and mutual inductances of the three machines obtained by 3-D finite-element model. It is seen that machines B and C have higher self-inductance which can limit short circuit current better than machine A. Also machines B and C have lower mutual-inductance which will isolate phases from each other more effectively compared to motor A. So motors B and C which have single layer windings provide higher fault tolerance capability.

The number of cogging torque periods per rotor revolution is equal to the LCM (least common multiple) of poles number and slots number. Higher cogging torque frequency leads to lower magnitude. It is clear that machines A and B have the same cogging torque as winding layer numbers do not influence cogging torque. Also the cogging torque waveform of the 12-slot/10-pole machine C with unequal tooth widths is similar to that of a 6-slot/10-pole machine with equal tooth widths. It should be mentioned that for computing cogging torque waveforms having extremely low amplitude, mesh density in the finite element analysis has to be significantly high. Cogging torque waveforms of the three axial-flux PM machines are obtained using 3-D finite-element analysis as shown in Fig. 4. In machines A and B, the number of cogging

<table><caption>TABLE IV. SELF AND MUTUAL INDUCTANCES</caption><thead><tr><td>Motor Type</td><td>Self-inductance (mH)</td><td>Mutual inductance (mH)</td></tr></thead><tbody><tr><td>Motor A</td><td>1.21</td><td>0.106</td></tr><tr><td>Motor B</td><td>1.95</td><td>-0.026</td></tr><tr><td>Motor C</td><td>2.15</td><td>-0.037</td></tr></tbody></table>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>Figure 4. Cogging torque waveforms for (a) motors A and B, (b) motor C</figcaption></figure>

torque periods per revolution is 60, while it is 30 for machine C. As can be seen in Figure 4, higher cogging torque frequency results in lower level of the cogging torque. The peak to peak cogging torque of all three motors is extremely low, about 0.2 Nm for machines A and B with equal tooth widths, and about 0.4 Nm for machine C with unequal tooth widths.

## C. Output Torque

The instantaneous electromagnetic torque of the machine can be calculated from:

$$T = \frac{1}{w_r} (e_a i_a + e_b i_b + e_c i_c) \quad (8)$$
<figure><img src="image_7.png" /><figcaption>Figure 5. 3-D finite-element output torque waveforms</figcaption></figure>

<table><caption>TABLE V. MOTOR PERFORMANCES</caption><thead><tr><th>Type</th><th><i>T</i><sub>max</sub> (Nm)</th><th><i>T</i><sub>min</sub> (Nm)</th><th><i>T</i><sub>ave</sub> (Nm)</th><th><i>T</i><sub>ripple</sub> (%)</th></tr></thead><tbody><tr><td>Motor A</td><td>24.05</td><td>20.8</td><td>22.60</td><td>14.37</td></tr><tr><td>Motor B</td><td>25.51</td><td>19.73</td><td>22.84</td><td>25.31</td></tr><tr><td>Motor C</td><td>26.27</td><td>21.49</td><td>24.56</td><td>19.46</td></tr></tbody></table>

where $e_a$, $e_b$, $e_c$, $i_a$, $i_b$, and $i_c$ are back-EMFs and currents in phases A, B, and C, respectively. Also $w_r$ is the rotor speed (rad/s). Torque waveform has dominant information about motor performance including torque average and torque ripple, and the motor choice for different applications can be based on it. All of the three machines considered in this research are supplied with 120° rectangular phase current waveforms (brushless-dc operation) with 34-A amplitude. The torque was obtained by using 3-D finite-element analysis as shown in Figure 5. Maximum torque, minimum torque, average torque and torque ripple of the motors are given in Table V. It is seen that motor C with single layer windings and unequal tooth widths has highest torque value with medium torque ripple which makes it appropriate for applications requiring high torque-density. Also, motor A with double layer windings has the least torque ripple which makes it a good candidate for applications where low noise and vibration is important. Motor B with single layer windings and equal tooth widths has the highest torque ripple.

## IV. CONCLUSION

Analysis and comparison of axial-flux PM BLDC machines by 3-D finite-element analysis was presented in this paper. The comparison is done for three 10-pole machines with the same dimensions, magnetic and electric loading. It is shown that although all three axial-flux PM machines have good fault tolerance capability, but axial-flux PM machines with single layer windings can better fulfill fault tolerance capability. Also all machines, having similar slot number and pole number and chosen pole arc to pole pitch ratio, produced low cogging torque. Axial-flux PM machines with single layer windings and unequal tooth widths have the highest torque average, while axial-flux PM machines with double-layer windings had the lowest torque ripples.

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