**1. Introduction**

Automotive x-by-wire systems have undergone a significant technological development over the last few decades. The "x" refers to the function segment of a car, such as parking, shifting, and braking, and varies widely. In shift-by-wire (SBW), the traditional mechanical connection between the gearshift activator (e.g., shift lever) and transmission is replaced with electric components. There are four common shifting modes—parking (P), reverse (R), neutral (N), and driving (D)—which the driver can switch to easily. When a command is given, it activates the electronic control that rotates the actuator to change the gear. SBW systems are easier to assemble and require less space, so there will is more room for interior design. Moreover, it adds convenience and comfort in driving [1]. According to [2], the three most important aspects in designing and manufacturing vehicle transmissions are their long service life, low repair cost, and low production costs, each of which score 9.00, 4.89, and 4.59 out of 10 points, respectively. In other words, the robustness of the system is the most essential factor.

Switched reluctance motors (SRMs) satisfy the three top requirements. The structure is simple and resilient. The core is doubly-salient with no permanent magnets, and the windings are only wound on the stator in a concentrated way. Moreover, the end-coil length is short, and so the motor is relatively small and compact overall. In terms of its structure, SRM is highly robust. SRM has been reported to be used by Toyota and Lexus as the motor is reliable and highly responsive [3,4].

SRMs are singly-excited and inherently generate a high torque ripple compared to AC machines running on sinusoidal voltage. Figure 1 shows a general 6/4 SRM drive system with an asymmetric half bridge converter and ideal torque generation. As the name suggests, SRM generates only reluctance torque and it pulsates according to the rotor position due to the switching operation and structure. In other words, the torque generation is based on the tendency of the rotor to be aligned with the excited stator pole pair [5]. Therefore, the reduction of torque ripple is a major topic in SRM research. The methods vary from design to control and simple to complicated approaches. From the design perspective, it is common to change the stator and/or rotor pole shape to form either a non-uniform air-gap or wide arc [6–8]. A unique semi-elliptical core is proposed in [9], in which both sides of each rotor pole are somewhat rounded instead of being straight lines. Rounded rotor pole tips are also presented as a design to reduce torque ripple in [10]. The inclusion of holes on the pole are also viable, as shown in [11–15], but this is usually done to reduce the noise and vibration. Various hole shapes have been studied; the effect of the height, width, and location of rectangular holes can be seen in [12]. Circular holes are preferred in [13], which prevent local saturation in the corners of square-shaped holes. Small diamond-shaped holes are placed strategically in the stator yoke in [14] to enhance the oscillation damping, leading to lower vibration. Triangular shapes are presented in [15] based on the flux path to reduce the stress during excitation. In addition, multi-objective shape optimization using intelligent algorithms (e.g., genetic algorithm, particle swarm, etc.) is usually implemented in the geometry optimization process [16–18]. With this method, various losses and thermal factors can be considered in combination to generate the optimum model. The inherent torque ripple of SRM is due to the nonlinear coupling between the phase current, rotor position, and overlapping angle as well as the complete machine geometry determined in the initial design process [17,19]. Therefore, to effectively reduce the torque ripple, it is best to undertake both design alterations and a control strategy. However, this study solely focuses on the design.

**Figure 1.** (**a**) General 12/8 switched reluctance motor (SRM) with parallel winding connection and (**b**) constant current excitation.

In this paper, a rotor pole design combining a non-uniform air-gap and circular holes near the tip is proposed to reduce torque ripple. The SBW system actuator is equipped with a cycloidal speed reducer to increase the output torque up to hundreds of Nm. Depending on the gear ratio, many rotations of the motor can only translate to one tooth being moved at the transmission gear. Smooth rotation is necessary to ensure accurate movement and increase the reliability of the SBW. The selection of a non-uniform angle and hole position is described. The finite element method (FEM) is used to analyze the electromagnetic characteristics of the design. The proposed SRM was manufactured and experiments were performed to verify the performance of the motor. Two simple Hall-effect sensors mounted on the back of the motor frame are used as rotation angle sensors to ensure a compact design. The simulation and experiment results show a reduction in torque ripple while maintaining the average torque output.

A similar structure, with holes drilled on the corners of stator and rotor poles, is proposed in [20]. The stator poles have a small shoe-like design, and a conventional uniform air-gap was implemented. The authors also suggested a tapered pole and skewed rotors. However, the rotor positioning method is not clearly described, and the design optimization approach is complicated. A non-uniform air-gap

is also used in [21], which also targets the SBW application, but the design is complex. The rotor pole surface is castle-shaped using a plurality of concavities and convexities. A complicated structure is more prone to possible manufacturing errors. The proposed design simply adopts an arched non-uniform air-gap and two holes in the non-uniform air gap section. A hole placement method to modify the torque profile is also presented. Since SRM has no permanent magnet, its torque magnitude depends largely on the length of the air-gap. A non-uniform air-gap results in a larger gap length, and the holes are positioned so that saturation level at the surface can be maintained while still reducing the peak torque, leading to a lower torque ripple. Compared to previous literature, the proposed design is simple and straightforward and can serve as a guideline for modifying the torque profile by design.
