# Optimization of a Permanent Magnet Synchronous Motor for e-Mobility Using Metamodels
## 1 Introduction  
Vehicular pollution has considerably increased in recent years due to urbanization and has become one of the major contributors to environmental pollution. To overcome this problem, electro mobility or e-mobility, which offers an eco-friendly means of transportation, especially in the urban areas, has been gaining considerable traction [1]. The e-mobility industry comprises a wide variety of vehicles, ranging from electric kickboards and Segways, to electric scooters and cars [2]. The key components of any electric vehicle include a motor, battery, and power converter [3]. Among these key components, a traction motor capable of delivering high output at high efficiency was considered in this study. Permanent magnet synchronous motors (PMSMs) have been widely used in a variety of industries (such as appliances, industrial tools, and driving motors for electric vehicles) because of their excellent efficiency, torque density, and low maintenance [4; 5; 6; 7]. PMSMs with rectangular coils in hairpin winding arrangements can reduce the space factor by reducing the unnecessary space in the slots when compared with those with round coils [8]. In addition, since the copper loss is reduced by reducing the end turn of the coils, the efficiency and output density of the motor can be significantly improved [9]. However, torque ripple in PMSM causes vibrations and noise, and there are several studies being conducted to reduce this [10]. There are various methods for reducing the torque ripple as reported in the contemporary literature, such as changing the shape of the stator, rotor, and shoe, and applying a skew and notch. In [11], the torque ripple was minimized by designing a cavity on the rotor. In [12], the shape of the barrier of the rotorwas optimized using a response surface methodology, which is an experimental design method, and a wedge skew was applied to the shoe of the stator to reduce the torque ripple. In another study, the torque ripple was reduced by applying a non-uniform air gap and rotor hole [13]. In [10], the torque ripple was reduced by applying a notch to the rotor. In studies in which the torque ripple was reduced by applying a notch, circular notches were predominantly used [14]. In this study, an elliptical-shaped notch was applied to determine the torque characteristics of a PMSM based on the width and depth of a notch. In addition, the barrier length of the rotor was set as a design variable to improve the performance of the motor. Two methods have been considered as general optimal design methods. In the first method, an approximation function is generated using metamodeling processes based on the design of experiments (DoE) results. Then, the approximated function is combined with an optimal algorithm to determine the optimal values. The second method connects the analysis model and optimal algorithm directly and iteratively analyzes the values until the optimal design values are found. In the former method, the accuracy of the metamodel significantly affects the optimal design results. In most extant studies, the experiments were conducted to approximate the relationship between the input and output variables using only one metamodel technique [15; 16]. However, due to the existence of a variety of metamodeling techniques, it is important to apply the most appropriate one for each design problem. Therefore, in this study, the relationship between the input and output variables is expressed as an approximation function by applying six metamodel techniques for each objective function and constraint. In addition, to compensate for the low accuracy, which is a disadvantage of the optimal design method using metamodels, the best metamodel technique with the lowest error as ascertained by the root mean square error (RMSE) test was applied. The differences between this study and previous studies are as follows.