*3.1. Flux Distribution*

In this section, the flux paths from the stator to the rotor for points P, R, Q, and S are examined. Only the "M" type is used as illustration since the "N" type will work in the opposite manner. Both motors have the same core material, 50PN440, and the current is adjusted to obtain a similar average torque output. The summary of the point positions is given below.

Figures 7 and 8 show the flux distribution of conventional and proposed motors as the rotor rotates along the circumference passing the stator pole. Each figure from (a) to (d) presents points P, R, Q, S, as described Figure 4, Figure 6, and Table 2. The subsection (e), however, is arbitrarily chosen to observe why the proposed motor has a slightly wider torque positive area, as seen in Figure 6b.



At point P, where the tips of the rotor and stator pole meet, no distinction can be made between the two models other than that the flux is more concentrated at the pole tip for the conventional model. This corresponds to Figures 4b and 6b, in which the value of torque is similar for the four models.

At point R, where the torque convexity corner starts, the stator and rotor overlap in the non-uniform air-gap section. As a result, the flux density of the proposed design is lower, which leads to a lower torque value. In contrast to the conventional type, the sharp increase in torque can be reduced by avoiding high density or saturation in this area, thus obtaining a smoother slope.

**Figure 7.** Flux density of conventional type: (**a**) point P, (**b**) point R, (**c**) point Q, (**d**) point S, (**e**) 87% aligned.

**Figure 8.** Flux density of proposed motor: (**a**) point P, (**b**) point R, (**c**) point Q, (**d**) point S, (**e**) 87% aligned.

After passing point R, the rotation comes to point Q, where the "torque overshoot" curve in the conventional model ends. Relative to point R, the maximum density of the conventional type is reduced here, and so is the torque value. However, this is not the case in the proposed model. The flux density level on the surface of the overlapping section is only higher than that at point R. Therefore, the torque value can be maintained. It can be seen in the figure that this is where the second hole plays an important role in keeping the rotor surface flux density the same; changing the position and/or size will affect the flatness of the torque.

Finally, the end of the convexity is at point S. Here, the average surface flux density in the overlapping section is similar in both models, which explains the torque values in Figure 6b. After point S, the 87% aligned position is chosen arbitrarily. The proposed model still has slightly higher torque compared to the conventional one, resulting in a wider positive area. The reason for this is shown in Figure 8e, where the average surface flux density of the proposed structure is higher because of the positioning of the second hole. In conclusion, the generated torque is closely related to the flux distribution in the overlapping region of the stator and rotor poles. Maintaining a similar flux density level over the excitation period means keeping a constant torque value and thus lowering the torque ripple.

### *3.2. Continuous Torque*

Single-phase excitation alone cannot verify the reduction of the torque ripple. In this section, continuous torque is observed when all phases are excited sequentially. First, the torque ripple equation is given as a percentage of the average torque as follows:

$$T\_{ripple} = \frac{T\_{\text{max}} + T\_{\text{min}}}{T\_{\text{avg}}} \tag{3}$$

Figure 9a shows the continuous torque in the proposed SRM. *T*min occurs at conduction when the exciting phase is turned off and the next phase is turned on. This switching action inevitably creates the inherent high torque ripple in SRM. Reducing *T*max and increasing *T*min for the same *Tavg* is an effective way to reduce the torque ripple. This is the main goal of the proposed structure. However, as shown before, the average torque decreases with each modification. For the torque ripple comparison, the current is adjusted so that the four models have the same average torque of 0.45 Nm. The result is presented in Figure 9b. The corresponding torque ripple is shown in Table 3. The torque ripple is reduced by 7%, and the current of the proposed model is merely 0.5 A higher than the conventional approach. It is shown that the torque of the proposed motor is much flatter at the top, with a wider positive torque area, compared to other models. This confirms that the proposed design can reduce the torque ripple with the same output capability.

**Figure 9.** Continuous torque: (**a**) conventional 12/8 SRM and (**b**) comparison.


**Table 3.** Torque ripple comparison.

### **4. Experimental Results**

After the verification of the reduced torque ripple, the proposed motor was manufactured to evaluate its performance. The prototype of the proposed 12/8 SRM is shown in Figure 10. The punch-holes were distributed into "M" and "N" types, as previously described. The black plate attached on the rotor in Figure 10b contained small magnets. Two Hall-effect sensors were mounted on the back of the motor frame which detected these magnets for rotor position information. Compared to other encoder types, this method results in a much lighter and more compact system.

**Figure 10.** Manufactured motor: (**a**) stator and (**b**) rotor.

The experimental setup is shown in Figure 11a. The motor is mounted on a zig, and its shaft is coupled with a torque sensor, the other end of which is coupled with an electric clutch. By controlling the power of the electric clutch, the load torque could be induced to the motor. A 12 V power supply—corresponding to the battery supply in vehicles—was used for the motor. Figure 11b shows the overall connection diagram involved in the experiment. A microcontroller, TMS320F28335 from Texas Instruments, was used to control the PWM (Pulse Width Modulation) signal to the asymmetric converter and also read the position signal from the Hall sensors. The clutch model was an ZKG-50AN from Mitsubishi. The power to the clutch was controlled manually by adjusting the voltage of a separate DC power supply.

**Figure 11.** Experimental setup: (**a**) test bed and (**b**) connection diagram (eCAP—enhanced capture; MCU—microcontroller unit).

The experiment was performed by implementing a 100% duty cycle of PWM, also known as single-pulse control, as shown in Figure 12. The phase currents are also presented in the figure. The rated value of the proposed motor, which was 0.245 Nm at 1800 RPM, was achieved, as can be seen in Figure 12a. A much higher torque could be obtained at the lower speed level of 600 RPM, at which the motor was able to generate 0.70 Nm of output torque. Nevertheless, the maximum current was under 30 A in any condition. Finally, the speed vs. torque and efficiency curves are shown in Figure 13. The efficiencies at 1800 and 600 RPM were 70.7 and 32.5%, respectively. However, efficiency was not a necessary requirement, since the motor only rotates for a short amount of time with each shift gear command from the driver. The phase RMS (Root-Mean Square) current required to produce the torque is given in Figure 13b. All values were under 15 A and thus met the design target. Therefore, it could be confirmed that the proposed motor satisfies all the requirements presented in Table 1.

**Figure 12.** Experimental result: (**a**) 1800 RPM–0.245 Nm and (**b**) 600 RPM–0.70 Nm.

**Figure 13.** Performance curves: (**a**) speed vs. torque, efficiency and (**b**) speed vs. torque, phase current RMS.

The calculation of the torque ripple is difficult to perform in real-time during an experiment. Therefore, FEM can be used to estimate the actual torque. A dynamic simulation using the SRM circuit configuration shown in Figure 1a could be set according to the experimental setup. The same control properties (initial position, excitation angle, etc.) were applied in the simulation to obtain a similar phase current to that of the experiment. Thus, the torque output of the experiment could be predicted. The result is shown in Figure 14. The experimental and simulation phase currents are shown in the top and middle plots, respectively. The resulting torque from the middle plot is shown at the bottom. The torque ripple was calculated to be 26.65%.

**Figure 14.** Comparison of phase currents and estimated torque.

### **5. Discussions**

The effectiveness of the proposed design combining a non-uniform air-gap and hole placement and its performance have been confirmed through FEM simulations and experiment. However, an optimization algorithm was not performed, and it is possible that a more optimal model could be designed. The closer the hole is to the surface, the greater the impact on the torque. If the hole is too close, however, then the structure is at risk of breaking during operation. An additional mechanical structural analysis could therefore also be useful. It is also feasible to only use one hole or more than two holes to modify the torque waveform as required. The same principle should be applied, maintaining the flux density on the surface. Another factor to be considered is that it is important to discuss how accurate the motor prototype will be with the corresponding manufacturer; in this case, this relates to the possible size of the hole and air-gap. Nevertheless, the viability of the proposed SRM as an SBW actuator is shown in this study.

SRM has a large number of advantages because of its simple structure, but the implementation of the motor in practical everyday use is still low compared to other machines. In [3,4], the authors presented a 12/8 SRM for an actual SBW application; however, the improvement of the drawbacks of SRM such as torque ripple were not clearly discussed and/or shown. Other than the design method and analysis, it is hoped that this study can guide researchers and industries to utilize and improve SRMs to make it competitive in the market.

Furthermore, various control methods can be applied to increase the performance. As can be seen in the experimental results, the phase currents have a "tail" at the end before decreasing to zero. This is due to the slightly long excitation time allowing more current to flow so that the desired torque can be reached. Even a simple turn-on and turn-off angle control method can be implemented to further reduce the torque ripple; however, this is beyond the scope of this paper.

### **6. Conclusions**

In this paper, a rotor design to reduce torque ripple while maintaining the average torque value and bi-directional rotation is proposed. SRM is a low-cost, robust motor but suffers from relatively high torque ripple, which can hinder its performance. Low torque ripple and smooth operation are necessary for shift-by-wire applications for safety and accuracy in moving the shifting gear.

A non-uniform air-gap is utilized to reduce the "torque overshoot" which occurs in the conventional structure. This is then combined with the positioning of two holes, meaning that the average flux density at the overlapping region of the stator and rotor poles can be kept close to constant during the period of excitation. The rotor pole tip is cut in a mirrored way to maintain a symmetrical property for bi-directional rotation. FEM is used to check the characteristics of the motor, and it is shown that the torque ripple can be reduced by 7% for the same output power by modifying the design alone.

A prototype motor of the proposed design was manufactured to verify its performance. It was shown that the motor satisfied the requirement of 0.245 Nm of torque at 1800 RPM. Moreover, the maximum current was kept below 30 A. The estimated torque ripple by matching the simulation to the experimental result was shown to be low, at 26.65%. The efficiency at rated conditions was 70.7%, but this was not a requirement due to the designated application, which demands the motor only to be run for a short amount of time and not to be in continuous operation. Both simulations and experiments showed the viability of the proposed 12/8 SRM as an actuator for a shift-by-wire system.

SRM has no brushes and commutators, and so there is little—or no—problem with maintenance compared to DC and universal motors. However, compared to permanent magnet motors, the power density and efficiency are generally relatively low. SRM makes up for this with its low manufacturing cost and high robustness (due to its simple structure). When efficiency is not the main issue and a long lifespan and high robustness are prioritized, an SRM with a low torque ripple design is a good actuator candidate that can meet the output requirements, as presented in this paper.

**Author Contributions:** Conceptualization, X.S.N.; Data curation, G.F.L.; Formal analysis, G.F.L.; Investigation, G.F.L.; Methodology, X.S.N.; Supervision, J.-W.A.; Validation, J.-W.A.; Writing—original draft, G.F.L.; Writing—review & editing, G.F.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by "Human Resources Program in Energy Technology" of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), and was granted financial resources from the Ministry of Trade, Industry & Energy, Republic of Korea. (No. 20184010201700), and Kyungsung University Research Grants in 2020.

**Conflicts of Interest:** The authors declare no conflict of interest.
