## 2 Structure of Flared-Shaped IPM and Proposed Flared-Type CP IPM Motor
### Proposed Flared-Type CP IPM Motor  
Figure 2 shows the basic model of the proposed FCPM in this study, in which the magnets that constitute the S pole are removed from the typical flared IPM motor, as shown in Figure 1. An electric steel plate is placed at the position of the removed S pole. As shown in Figure 2, magnet usage can be reduced by half compared to the typical flared-shaped IPM motor.  
In a flared IPM motor with conventional flared-shaped PM rotor structure (Figure 1), the magnetizing directions of the magnets are alternately arranged such that the N and S poles are alternately present. However, the consequent-pole-type rotor structure removes the permanent magnets constituting the S pole and makes the N and S poles alternately formed in the rotor by using the magnetic flux lines of the permanent magnets forming the N pole. Therefore, there is an advantage of reducing the usage of permanent magnets by half. However, the CP-type rotor structure has the disadvantage of increasing the torque ripple because of the asymmetry of the back-EMF.  
Figure 3 shows the two-dimensional (2D) finite element method (FEM) analysis results of the basic proposed FCPM model under the no-load condition, and Table 2 shows the comparison results of the no-load analysis of the standard flared-type IPM model with that of the basic FCPM model. (In Table 2, \(\blacktriangle\) indicates an increase in value, and \(\blacktriangledown\) indicates a decrease in value.)  
Figure 3: Analysis results of no-load conditions (7500 [rpm]): (**a**) back-EMF, (**b**) cogging torque.  
Figure 2: Proposed flared-type CP IPM motor (1/4 model).  
The basic FCPM model has the advantage of halving the number of magnets used, compared with the standard flared-shaped IPM model. However, as shown in Figure 3, the back-EMF waveform is asymmetrical, and this significantly increases the total harmonic distortion (THD) of the back-EMF to 29.5%. THD represents the ratio of total harmonic components to the fundamental component. If the THD is large, it affects the back-EMF and torque waveform, causing the distortion of the waveform. This causes the motor performance to deteriorate [23].  
In addition, a 37.7% reduction can be observed in the back-EMF. Therefore, owing to a decrease in the back-EMF, an increase in the current and a decrease in the efficiency at the rated load are expected. However, due to the decrease in the amount of PMs, the cogging torque ripple decreases by 36.2% and the torque ripple is also expected to decrease at the rated load.  
The flared-structured rotor comprises one polarity with four magnets, so it conveniently enables control over the polar angle that conveys a single polarity. Therefore, by optimizing the polar angle to form one polarity and the angle of individual PMs, the waveform of the back-EMF can be made symmetrical. Accordingly, it is possible to minimize the THD and performance reduction. Therefore, in this study, we propose the shape of the basic FCPM model and optimize it. The purpose of this study is to improve the performance while taking advantage of the CP model, thereby reducing the use of PMs. As design variables, the polar angle formed by the PM and the angles of the individual PMs were set as variables to proceed with the design optimization. Through this, an optimal model with a high torque performance and low torque ripple was designed to reduce the use of PMs.