# Multi-Step Design Optimization for the Improvement of an Outer-Rotor Brushless Direct Current Motor
## 1 Introduction  
BLDC motors are becoming popular for electrical applications and industrial processes and are replacing traditional induction motors. According to the International Energy Agency (IEA) analysis report, the global electricity consumption in motors accounts for more than 46% of the total electricity [1, 2]. The significance of traditional motors in industrial production is that they account for the most significant power consumption. This power consumption is one of the facts of global warming and climate change. The Paris Agreement, with Intended Nationally Determined Contributions (INDCs), is aimed at contributing to carbon dioxide reduction [3], and we also supported the industrial process to replace the BLDC motor instead of using a traditional motor. The BLDC motors can be used in many electrical applications, such as electric fans, water pumping, rolling machines in various industries, and electric vehicles [4]. The performance of BLDC motors is better than that of other motors, and their electricity consumption is lower. BLDC motors can also help save energy, slow global warming, and be eco-friendly [5]. In the worldwide market of electric fans, the BLDC motor demand is increasing yearly. In 2023, a report predicted that the US dollar would go from USD 9.6 billion to USD 15.2 billion by 2025. Increasing the demand for BLDC motors is a big jump [6]. Moreover, the BLDC motor can achieve higher efficiency and lower operation noise than other motors [3].  
There are several studies on optimizing the design of the BLDC motors using either Taguchi or RSM methods. In [7, 8, 9, 10], the BLDC motor design was optimized by using the Taguchi method, whereas the studies presented in [11, 12] used the RSM approach to achieve the optimal design of a motor. Most of the studies used either the Taguchi method or RSM alone. However, in [13], the author combined these two approaches to achieve amulti-step optimization of an Interior Permanent Magnet Synchronous Motor. However, this approach has yet to be applied to optimize BLDC motors.  
A novel two-step optimization algorithm for a BLDC motor design was developed to fill the research gap. The first step uses the Taguchi method to optimize seven parameters of the motor and then passes it on to the FEM analysis to obtain the preliminary optimal settings. The second step applies the RSM to refine the design, focusing on the top three critical variables that significantly impact the performance. This multi-step approach leverages the strengths of both methods: the Taguchi method, which can be used for a wide range of variables, and RSM for a small number of variables. The effectiveness of this hybrid strategy is validated by comparing the proposed model's motor design's performance using the FEM with previous results. This method efficiently combines the benefits of each optimization technique to improve motor performance. This proposed optimization approach is used to develop the optimized motor design by following the framework shown in Figure 1.  
As a preliminary study, we conducted a market survey on electric fans to select our reference motor systematically. According to the market survey, 54.7% of the participants had agreed to use the energy-saving BLDC motor electric fan, as shown in Figure 2. Based on the survey result, the BLDC motor was selected as a reference design, and the measured parameter of the reference motor was used to optimize the design using the multi-step optimization approach.  
Figure 1: Flow diagram of proposed motor design.