Design and Optimization of a Novel Wound Field Synchronous Machine for Torque Performance Enhancement

This paper presents the design and optimization of a novel wound field synchronous machine topology, in which permanent magnets (PMs) are introduced into the rotor slot opening with segment configuration for high quality output torque performance. The rotor shape of the proposed PM-assisted wound field synchronous machine with segment configuration is optimized for maximizing the average output torque and decreasing torque ripple under constant PM volume and motor size. The segment configuration can be benefit to improve the reluctance torque. In addition, it is further clarified that the assisted-PM can help to increase the field torque by enlarging the magnetizing synchronous reactance (Xf), as well as increasing airgap flux density. An optimal method combining Kriging method and genetic algorithm is applied for rotor shape optimization of proposed PM-assisted wound field synchronous machine (PMa-WFSM). Then, the 2-D finite-element analysis results, with the aid of JMAG-Designer, are used to confirm the validity. It is determined that the average output torque is improved by 31.66%, and keeps lower torque ripple without decreasing efficiency, increasing PM volume and motor size compared with those of the basic model. Finally, irreversible demagnetization and mises stress analysis verifies the reliability of the novel topology.


Introduction
Recently, development of the industry and the environmental issue are attracting more and more attention [1,2]. Therefore, a series of new techniques about motor system topologies have been developed and applied to obtain high torque density and energy efficiency in most of the industry application and daily life [3,4].
Wound-field synchronous machines (WFSMs) utilize rotor windings to generate flux without the use of magnets. They provide some potential significant benefits and advantages including reducing material cost, higher machine system efficiencies though power factor improvements, loss minimization field control, and improved safety through direct field control during inverter fault conditions [5]. In addition, the effectiveness of WFSMs compared with a Prius Interior Permanent Magnet Motor was analyzed in [6]. It shows WFSMs have two major advantages: one is the controllable field which will make the driver more flexible, and the other one is there are no rare earth magnets. However, the current in the field winding causes significant copper loss, thereby the efficiency is decreased and temperature rise is increased. Additional brushed or brushless methods of transferring power to the rotor field winding are needed which introduces more complexity into the motor's structure.
With the development of permanent magnets (PM) such as Nd-Fe-B, permanent magnet synchronous machines (PMSMs) have been widely used in many industry applications instead of WFSMs because they are very efficient and torque-dense, as well as the size and shape of motor are flexible and varied to meet the corresponding working conditions. However, there are also some problems with PMSMs. The high cost of permanent magnet materials and the limited supply have been signed as its disadvantages [7]. The other problem is that once the magnet is magnetized, it is difficult to achieve flux weakening control [8]. Furthermore, the danger of the irreversible demagnetization should be considered when designing PMSMs.
To overcome these problems, many types of hybrid excited machines have been developed [9], and the PM-assisted wound field synchronous machine (PMa-WFSM) is one of them. In [10], a WFSM was designed for small electric-vehicle traction by inserting the permanent magnets into a predetermined position. Through the comparison of four positions and two kinds of permanent magnet materials, the combination of assisted-PM in slot opening and Nd-Fe-B is the best choice. As mentioned, all the torque ripple values of the PM-assisted models are higher than that of original model. The estimation of assist effects by additional permanent magnets has been done in [11], and these effects vary with load condition. The PM is installed in the pole head to help ensure smooth startup of the machine and improve torque density without any external aid [12]. The paper [13] investigated the mechanism of voltage increased by additional PMs with using a nonlinear magnetic circuit. This expression is useful for the designs of PMa-WFSM. The Rosenbrock's method and time-stepping adaptive FEA are chosen for optimizing the rotor shape of a PMa-WFSM for output maximization [14], while the torque ripple is not considered and the reluctance torque is still negligible.
In reference [15], the single flux barrier is introduced in WFSMs. It is a simple method to improve the motor reluctance torque and widen the operating region. Actually, the single flux barrier can bring about an imbalance of magnetic flux density of the two steel pieces in each pole. Thus, the position of the single flux barrier is considered to be one of the optimal variables [16] to get higher saliency ratio. Nevertheless, the torque ripple is still unsatisfactory because of the asymmetrical single flux barrier.
In this study, PM was introduced into the rotor slot opening of a WFSM with segment configuration for high-quality output torque performance. The rotor shape of proposed PMa-WFSM was optimized for improving the average output torque and keeping lower torque ripple under constant PM volume and motor size. The optimization method mainly comprises Kriging method and a genetic algorithm (GA). Then, JMAG-Designer has been used as the tool of finite-element analysis (FEA) to confirm the validity. Finally, the magnetic saturation under the condition of no-load affected by assisted-PM and its irreversible demagnetization effect and mises stress analysis were analyzed.

The Basic WFSM
To highlight the advantages of the proposed approaches, a WFSM with conventional pole head and segment configuration designated is adopted as the basic model. The stator has six slots with three-phase concentrated coil windings as shown in Figure 1a. The basic rotor of WFSM is shown in Figure 1b. All the specifications of the basic model are listed in Table 1.

The Proposed Model with Assisted-PM
The topology of the proposed model is presented in Figure 2. The PM is assisted in the rotor slot opening and a small protruding piece of steel on the teeth is used for fixing the PM. In this section, NEOMAX-50 (Hitachi, Tokyo, Japan) is selected as the assisted-PM for the hybrid excitation and the PM volume is 4 × 3 mm × 12 mm × 52 mm. It shares the same stator with the basic model. However, the PM needs to be fixed in the opening of the rotor slot, the pole head shape should be changed for adaption. Theoretically, the ratio of pole arc to pole pitch has a range of 0.65 to 0.75 [17]. This will make that the design of field system becomes economical. Therefore, it is necessary to analyze the optimum structure in the following section.

The Proposed Model with Assisted-PM
The topology of the proposed model is presented in Figure 2. The PM is assisted in the rotor slot opening and a small protruding piece of steel on the teeth is used for fixing the PM. In this section, NEOMAX-50 (Hitachi, Tokyo, Japan) is selected as the assisted-PM for the hybrid excitation and the PM volume is 4 × 3 mm × 12 mm × 52 mm. It shares the same stator with the basic model. However, the PM needs to be fixed in the opening of the rotor slot, the pole head shape should be changed for adaption. Theoretically, the ratio of pole arc to pole pitch has a range of 0.65 to 0.75 [17]. This will make that the design of field system becomes economical. Therefore, it is necessary to analyze the optimum structure in the following section.

The Proposed Model with Assisted-PM
The topology of the proposed model is presented in Figure 2. The PM is assisted in the rotor slot opening and a small protruding piece of steel on the teeth is used for fixing the PM. In this section, NEOMAX-50 (Hitachi, Tokyo, Japan) is selected as the assisted-PM for the hybrid excitation and the PM volume is 4 × 3 mm × 12 mm × 52 mm. It shares the same stator with the basic model. However, the PM needs to be fixed in the opening of the rotor slot, the pole head shape should be changed for adaption. Theoretically, the ratio of pole arc to pole pitch has a range of 0.65 to 0.75 [17]. This will make that the design of field system becomes economical. Therefore, it is necessary to analyze the optimum structure in the following section.

Principle
In fact, because of the adaptive pole head shape due to the assisted-PM, the length of q-axis flux path in the steel core will be increased. This will make the saliency reduced. It is not good for the high torque density. Therefore, the segment configuration and pole head should be paid more attention.
The Figure 3a shows the phasor diagram of proposed model derived from d-q rotor frame equivalent circuit using the Park transformation, where winding resistances and space harmonics are neglected. The terminal voltage in the circuit can be expressed as follows: where, U d and U q are the d-axis and the q-axis terminal voltages, I d and I q are the d-axis and the q-axis magnetizing currents, X d and X q are the d-axis and the q-axis synchronous reactance, X f is the magnetizing synchronous reactance, I f is the DC field current, ψ PM is the maximum flux linkages by the PM, w 0 is the electrical frequency. The electromagnetic torque can be calculated from the circuit as expressed in Equation (2).
where, I s is the peak value of the phase current, γ is the angle of the stator current vector measured with respect to the q-axis designated as the current phase angle. The first term is the field torque, the second is the PM torque, and the last is the reluctance torque. Theoretically, the three torques are both benefit for the total torque of the motor. The high X f , ψ PM and X d − X q will increase the total torque. In fact, because of the adaptive pole head shape due to the assisted-PM, the length of q-axis flux path in the steel core will be increased. This will make the saliency reduced. It is not good for the high torque density. Therefore, the segment configuration and pole head should be paid more attention.
The Figure 3a shows the phasor diagram of proposed model derived from d-q rotor frame equivalent circuit using the Park transformation, where winding resistances and space harmonics are neglected. The terminal voltage in the circuit can be expressed as follows: where, Ud and Uq are the d-axis and the q-axis terminal voltages, Id and Iq are the d-axis and the q-axis magnetizing currents, Xd and Xq are the d-axis and the q-axis synchronous reactance, Xf is the magnetizing synchronous reactance, If is the DC field current, ψPM is the maximum flux linkages by the PM, w0 is the electrical frequency. The electromagnetic torque can be calculated from the circuit as expressed in Equation (2).
where, Is is the peak value of the phase current, γ is the angle of the stator current vector measured with respect to the q-axis designated as the current phase angle. The first term is the field torque, the second is the PM torque, and the last is the reluctance torque. Theoretically, the three torques are both benefit for the total torque of the motor. The high Xf, ψPM and Xd − Xq will increase the total torque.
(a) (b)  Figure 3b shows the magnetic flux path on the rotor of proposed PMa-WFSM. The PM flux is separated by part 1 and part 2 in the assisted position. The PM flux part 1 not only increases the air gap flux density directly, but also can decrease the q-axis flux path in the pole head that can reduce the inductance of q-axis, which has the same function of the segment configuration. The PM flux part 2 in Figure 3b can be seen that it can mitigate the flux in the iron core and the Xf will be increased because of low magnetic saturation.
The segment rotor pole can decrease the Xq which can be benefit for the saliency. The d-axis and q-axis flux distribution are shown in Figure 4. Assume that the position where the rotor pole is opposed to the stator teeth is the d-axis. In addition, turning counterclockwise 90-degree electrical angle along the d-axis is the q-axis. The q-axis flux line closed to the segmental edges form a zigzag  Figure 3b shows the magnetic flux path on the rotor of proposed PMa-WFSM. The PM flux is separated by part 1 and part 2 in the assisted position. The PM flux part 1 not only increases the air gap flux density directly, but also can decrease the q-axis flux path in the pole head that can reduce the inductance of q-axis, which has the same function of the segment configuration. The PM flux part 2 in Figure 3b can be seen that it can mitigate the flux in the iron core and the X f will be increased because of low magnetic saturation.
The segment rotor pole can decrease the X q which can be benefit for the saliency. The d-axis and q-axis flux distribution are shown in Figure 4. Assume that the position where the rotor pole is opposed to the stator teeth is the d-axis. In addition, turning counterclockwise 90-degree electrical angle along the d-axis is the q-axis. The q-axis flux line closed to the segmental edges form a zigzag leakage path, which shows the flux lines find a low reluctance path to be a circle. In addition, from the view of the rotor pole head, the q-axis flux line is also limited by the PM flux. leakage path, which shows the flux lines find a low reluctance path to be a circle. In addition, from the view of the rotor pole head, the q-axis flux line is also limited by the PM flux.
(a) (b) To verify the above analysis, the 2-D FEA (JMAG-Designer) is used. Figure 5a shows the total magnetic flux distributions of proposed model under no-load condition. In addition, the frozen permeability method (FPM) [18] is used to obtain the separated magnetic flux produced by the rotor field windings (FWs) or produced by the assisted-PM, as indicated in Figure 5b,c. It is observed that the magnetic flux direction of the PM in the rotor core is opposite to that produced by the FWs. It can reduce the magnetic saturation of the pole core, which further influence Xf. It is benefit for the enhancement of the field torque. Some of magnetic flux produced by the assisted-PMs flow through the air gap into the stator core. Its direction is the same as that of the flux flows produced by the FWs. The magnetic flux of this part will increase the airgap flux density. It is benefit for improving electromagnetic torque.  Figure 6 shows the torque characteristics of basic model and proposed model, respectively. At the current phase angle of −25°, the output torque can reach their maximum values. Compared with the basic model, additional magnet torque is added and contributes 9.9% of the total torque, meanwhile the average output torque is increased by 17.55%. Meanwhile, the reluctance torque is increased by only 6.9%. It is enough to verify that the assisted-PM flux can effectively decrease the Xq reduction, which is caused by the change of the pole head shape for installing PM. However, as To verify the above analysis, the 2-D FEA (JMAG-Designer) is used. Figure 5a shows the total magnetic flux distributions of proposed model under no-load condition. In addition, the frozen permeability method (FPM) [18] is used to obtain the separated magnetic flux produced by the rotor field windings (FWs) or produced by the assisted-PM, as indicated in Figure 5b,c. It is observed that the magnetic flux direction of the PM in the rotor core is opposite to that produced by the FWs. It can reduce the magnetic saturation of the pole core, which further influence X f . It is benefit for the enhancement of the field torque. Some of magnetic flux produced by the assisted-PMs flow through the air gap into the stator core. Its direction is the same as that of the flux flows produced by the FWs. The magnetic flux of this part will increase the airgap flux density. It is benefit for improving electromagnetic torque. leakage path, which shows the flux lines find a low reluctance path to be a circle. In addition, from the view of the rotor pole head, the q-axis flux line is also limited by the PM flux.

The Performance Comparison between the Basic and Proposed Models
(a) (b) To verify the above analysis, the 2-D FEA (JMAG-Designer) is used. Figure 5a shows the total magnetic flux distributions of proposed model under no-load condition. In addition, the frozen permeability method (FPM) [18] is used to obtain the separated magnetic flux produced by the rotor field windings (FWs) or produced by the assisted-PM, as indicated in Figure 5b,c. It is observed that the magnetic flux direction of the PM in the rotor core is opposite to that produced by the FWs. It can reduce the magnetic saturation of the pole core, which further influence Xf. It is benefit for the enhancement of the field torque. Some of magnetic flux produced by the assisted-PMs flow through the air gap into the stator core. Its direction is the same as that of the flux flows produced by the FWs. The magnetic flux of this part will increase the airgap flux density. It is benefit for improving electromagnetic torque.  Figure 6 shows the torque characteristics of basic model and proposed model, respectively. At the current phase angle of −25°, the output torque can reach their maximum values. Compared with the basic model, additional magnet torque is added and contributes 9.9% of the total torque, meanwhile the average output torque is increased by 17.55%. Meanwhile, the reluctance torque is increased by only 6.9%. It is enough to verify that the assisted-PM flux can effectively decrease the Xq reduction, which is caused by the change of the pole head shape for installing PM. However, as  Figure 6 shows the torque characteristics of basic model and proposed model, respectively. At the current phase angle of −25 • , the output torque can reach their maximum values. Compared with the basic model, additional magnet torque is added and contributes 9.9% of the total torque, meanwhile the average output torque is increased by 17.55%. Meanwhile, the reluctance torque is increased by only 6.9%. It is enough to verify that the assisted-PM flux can effectively decrease the X q reduction, which is caused by the change of the pole head shape for installing PM. However, as is known in the published papers [10][11][12][13][14][15][16], the torque ripple has the challenge of deterioration. As far as this motor is concerned, the torque ripple is increased by 44.5%, it can be shown in Figure 7 and Table 2. Figure 8 shows the calculated no-load saturation curves of the basic model and proposed model. It is revealed that the saturation field current of the basic and proposed model is changed from 1.7 A to 2.6 A. It is observed that it benefits from reduction in the magnetic saturation of the core by assisted-PM. In the following section, the segment distance and segment displacement, the shape of magnet and pole head will be optimized to realize higher average torque and lower torque ripple. is known in the published papers [10][11][12][13][14][15][16], the torque ripple has the challenge of deterioration. As far as this motor is concerned, the torque ripple is increased by 44.5%, it can be shown in Figure 7 and Table 2. Figure 8 shows the calculated no-load saturation curves of the basic model and proposed model. It is revealed that the saturation field current of the basic and proposed model is changed from 1.7 A to 2.6 A. It is observed that it benefits from reduction in the magnetic saturation of the core by assisted-PM. In the following section, the segment distance and segment displacement, the shape of magnet and pole head will be optimized to realize higher average torque and lower torque ripple.

The Performance Comparison between the Basic and Proposed Models
(a) (b)    is known in the published papers [10][11][12][13][14][15][16], the torque ripple has the challenge of deterioration. As far as this motor is concerned, the torque ripple is increased by 44.5%, it can be shown in Figure 7 and Table 2. Figure 8 shows the calculated no-load saturation curves of the basic model and proposed model. It is revealed that the saturation field current of the basic and proposed model is changed from 1.7 A to 2.6 A. It is observed that it benefits from reduction in the magnetic saturation of the core by assisted-PM. In the following section, the segment distance and segment displacement, the shape of magnet and pole head will be optimized to realize higher average torque and lower torque ripple.

The Process of Rotor Shape Optimization
The abovementioned proposed PMa-WFSM was designed only by adding PMs in the slot opening of the WFSM segmented rotor. It not only brings the increase of the average output torque but also causes the deterioration of the torque ripple. This characteristic is more obvious in the segment configuration. It is expected that the average output torque and torque ripple can be improved by optimizing the shape of the proposed rotor. Therefore, an effective optimization approach combining Kriging method [19] and genetic algorithm (GA) [20] is applied for rotor shape optimization in order to improve torque characteristic and decrease torque ripple under constant PM volume and motor size without the deterioration of efficiency. Figure 9 shows the five design variables assigned to the rotor. The width h of the assisted-PM is selected as one of the design variables, whereas the length w of the assisted-PM is automatically changed in order to maintain the volume of assisted-PM as a constant. m and l are the main parameters that define the rotor slot area and the magnetic flux path of the assisted-PM. d is the segment distance that can determine the ability of hindering the q-axis flux. x is the segment displacement between the rotor pole center and segment distance center which can adjust the magnetic imbalance of the two pieces in each rotor pole. Because the assisted-PM changes the across-sectional area of the FWs, in order to maintain the slot filling ratio, the number of turns is proportionately changed. The stator is fixed during the entire optimization process of the motor.
Firstly, according to the requirements of the motor, the objective functions, constraints, and design variables are obtained. The main optimal design process can be classified as roughly two steps as shown in Figure 10.
(1) The Latin Hypercube Sampling (LHS) [21] step of process 1 in Figure 10 is the first step of searching the optimized design variables in the design range of design variables h, m, l, d, and x. By using the LHS within the design range corresponding to the determined design variables, the sampling values are randomly and evenly distributed in all areas. The model approximated by the 2D FEA analysis results is composed by using the Krigging method in the PIAnO software (v.3.6, PIDOTEC Inc, Seoul, South Korea) by PIDOTEC Inc. [22].
(2) For this paper, the Generic Algorithm step of process 2 in Figure 10 evaluates the fitness from the modeling function developed by the Kriging model; thus, the optimal results were determined by the population. The fitness modeling function F(i) used in GA is expressed as [23] where f (i) is the multi-objective function, P(i) is the penalty function, ε is the penalty coefficient, and i is vector of the design variables.
Finally, the optimal design results were verified by FEA. If the FEA results were not satisfied with the target requirements, the range of design variables should be adjusted and do the above steps again, until it is satisfied.  The objective functions for maximizing the total torque and minimizing the torque ripple are shown in Equation (4), which are implemented with the same weight value to each objective function. Compared with proposed model, the constraints are set to limit the total torque to a higher value, and the torque ripple should be lower, as shown in Equation (5). It is simple and easy implementation to be conducted through the commercial optimization tool-PIAnO. The ranges for the design variables are shown in Equation (6) • Design variables:  The objective functions for maximizing the total torque and minimizing the torque ripple are shown in Equation (4), which are implemented with the same weight value to each objective function. Compared with proposed model, the constraints are set to limit the total torque to a higher value, and the torque ripple should be lower, as shown in Equation (5). It is simple and easy implementation to be conducted through the commercial optimization tool-PIAnO. The ranges for the design variables are shown in Equation (6).
Maximize the total torque.
Minimize the torque ripple (4) • Constraints: . . % Torque 0 37 Nm Torque ripple 44 7 • Design variables: The objective functions for maximizing the total torque and minimizing the torque ripple are shown in Equation (4), which are implemented with the same weight value to each objective function. Compared with proposed model, the constraints are set to limit the total torque to a higher value, and the torque ripple should be lower, as shown in Equation (5). It is simple and easy implementation to be conducted through the commercial optimization tool-PIAnO. The ranges for the design variables are shown in Equation (6)

Convergence Results of Variables
In the optimization process, the optimal values of the variables for the objective functions can be obtained. The convergence results of the design variables are shown in Figure 11a. The five design variables (h, l, m, d, x) are 5.612 mm, 3.662 mm, 2.289 mm, 1.075 mm, 0.003 mm, respectively. When the average torque and torque ripple are kept the same weight value, the segment displacement x is closed to 0, which indicates that the segment displacement x is the contradictory between the average torque and torque ripple. Figure 11b shows the convergence procedure and results of the optimized design of torque and torque ripple of the objective function. The determined average output torque and torque ripple after the iteration are 0.425 Nm and 27.72%, respectively.

Convergence Results of Variables
In the optimization process, the optimal values of the variables for the objective functions can be obtained. The convergence results of the design variables are shown in Figure 11a. The five design variables (h, l, m, d, x) are 5.612 mm, 3.662 mm, 2.289 mm, 1.075 mm, 0.003 mm, respectively. When the average torque and torque ripple are kept the same weight value, the segment displacement x is closed to 0, which indicates that the segment displacement x is the contradictory between the average torque and torque ripple. Figure 11b shows the convergence procedure and results of the optimized design of torque and torque ripple of the objective function. The determined average output torque and torque ripple after the iteration are 0.425 Nm and 27.72%, respectively.

Characteristics Analysis Results by 2-D FEA
The design variables obtained by iteration have been used to verify in JMAG-2D designer as the optimal model. Figure 12 shows the torque characteristics of the optimal model, and the detail analysis results from simulation is revealed in Table 3. At the current phase angle of −25° that is the same with basic model and proposed model, the output torque can reach its maximum value. The assisted-PM in the optimal model is better utilized than that in proposed model. Compared with the proposed model results, the total torque is increased by 12%, apparently. The sum of the reluctance torque and the magnet torque increases from 23.4% of the total torque to 38.3%.
The electromagnetic torques of proposed model and optimal model at the maximum torque condition are compared in Figure 13. The torque ripple of the optimal model, defined as the peak to peak torque value versus the average torque value is reduced by 35.1% compared to that of the proposed model.
The electromotive force is produced by the field current and the assisted-PM. Figure 14 shows the calculated no-load saturation curves of the proposed model and optimal model. It is revealed that the phase voltage of proposed model and optimal model has an increase of around 1.8 V. This is mainly caused by the direct flux linkage of the armature winding from the assisted-PM.

Characteristics Analysis Results by 2-D FEA
The design variables obtained by iteration have been used to verify in JMAG-2D designer as the optimal model. Figure 12 shows the torque characteristics of the optimal model, and the detail analysis results from simulation is revealed in Table 3. At the current phase angle of −25 • that is the same with basic model and proposed model, the output torque can reach its maximum value. The assisted-PM in the optimal model is better utilized than that in proposed model. Compared with the proposed model results, the total torque is increased by 12%, apparently. The sum of the reluctance torque and the magnet torque increases from 23.4% of the total torque to 38.3%.
The electromagnetic torques of proposed model and optimal model at the maximum torque condition are compared in Figure 13. The torque ripple of the optimal model, defined as the peak to peak torque value versus the average torque value is reduced by 35.1% compared to that of the proposed model.
The electromotive force is produced by the field current and the assisted-PM. Figure 14 shows the calculated no-load saturation curves of the proposed model and optimal model. It is revealed that the phase voltage of proposed model and optimal model has an increase of around 1.8 V. This is mainly caused by the direct flux linkage of the armature winding from the assisted-PM.                 Figure 15 shows the comparison of Back-EMFs for each phase. Due to the optimization of the pole head, the Back-EMF of the optimal model exhibit considerable distortion but contain highly enhanced fundamental value. Figure 16 shows the corresponding Fast Fourier Transform (FFT) analysis, while the Total Harmonics Distortion (THD) for the three models are 6.5%, 3.13% and 1.51%, respectively.  Figure 15 shows the comparison of Back-EMFs for each phase. Due to the optimization of the pole head, the Back-EMF of the optimal model exhibit considerable distortion but contain highly enhanced fundamental value. Figure 16 shows the corresponding Fast Fourier Transform (FFT) analysis, while the Total Harmonics Distortion (THD) for the three models are 6.5%, 3.13% and 1.51%, respectively.

The Magnetic Flux Density Distribution
The magnetic flux density distribution of basic model, proposed model and optimal model at the maximum torque condition are shown in Figure 17a-c, respectively. It is shown that the magnet flux density of the rotor core has been reducing effectively and the magnetic flux density of the stator core has been increased, under on-load condition. To investigate the reality clearly, there are four working points chosen for comparison as the following results.  Figure 15 shows the comparison of Back-EMFs for each phase. Due to the optimization of the pole head, the Back-EMF of the optimal model exhibit considerable distortion but contain highly enhanced fundamental value. Figure 16 shows the corresponding Fast Fourier Transform (FFT) analysis, while the Total Harmonics Distortion (THD) for the three models are 6.5%, 3.13% and 1.51%, respectively.

The Magnetic Flux Density Distribution
The magnetic flux density distribution of basic model, proposed model and optimal model at the maximum torque condition are shown in Figure 17a-c, respectively. It is shown that the magnet flux density of the rotor core has been reducing effectively and the magnetic flux density of the stator core has been increased, under on-load condition. To investigate the reality clearly, there are four working points chosen for comparison as the following results.

The Magnetic Flux Density Distribution
The magnetic flux density distribution of basic model, proposed model and optimal model at the maximum torque condition are shown in Figure 17a-c, respectively. It is shown that the magnet flux density of the rotor core has been reducing effectively and the magnetic flux density of the stator core has been increased, under on-load condition. To investigate the reality clearly, there are four working points chosen for comparison as the following results.

Demagnetization Analysis
When the motor suffers the sudden three phase short circuit condition, the field and armature current would be very large to keep the flux linkage as a constant. Therefore, it is necessary to analyze the irreversible demagnetization of the PM to ensure the reliability of the novel topology.
To assure the reliability of the PM utilization, the analysis of the magnet irreversible demagnetization for the optimal model is performed within seven times of the rated input current. To investigate the effect of magnet irreversible demagnetization for PM torque and field torque, the EMF demagnetization ratio is defined as where E1 is the Root-Mean-Square (RMS) value of the terminal voltage in phase before inputting the phase current, and E2 is the RMS value of the terminal voltage in phase after inputting the phase current.
The analysis results of the EMF demagnetization ratios are depicted in Figure 18. It indicates that the EMF demagnetization ratio is 0.73% with seven times of the input current indicating that only a slight demagnetization occurs to the peak of the magnet.

Demagnetization Analysis
When the motor suffers the sudden three phase short circuit condition, the field and armature current would be very large to keep the flux linkage as a constant. Therefore, it is necessary to analyze the irreversible demagnetization of the PM to ensure the reliability of the novel topology.
To assure the reliability of the PM utilization, the analysis of the magnet irreversible demagnetization for the optimal model is performed within seven times of the rated input current. To investigate the effect of magnet irreversible demagnetization for PM torque and field torque, the EMF demagnetization ratio is defined as where E 1 is the Root-Mean-Square (RMS) value of the terminal voltage in phase before inputting the phase current, and E 2 is the RMS value of the terminal voltage in phase after inputting the phase current. The analysis results of the EMF demagnetization ratios are depicted in Figure 18. It indicates that the EMF demagnetization ratio is 0.73% with seven times of the input current indicating that only a slight demagnetization occurs to the peak of the magnet.

Demagnetization Analysis
When the motor suffers the sudden three phase short circuit condition, the field and armature current would be very large to keep the flux linkage as a constant. Therefore, it is necessary to analyze the irreversible demagnetization of the PM to ensure the reliability of the novel topology.
To assure the reliability of the PM utilization, the analysis of the magnet irreversible demagnetization for the optimal model is performed within seven times of the rated input current. To investigate the effect of magnet irreversible demagnetization for PM torque and field torque, the EMF demagnetization ratio is defined as where E1 is the Root-Mean-Square (RMS) value of the terminal voltage in phase before inputting the phase current, and E2 is the RMS value of the terminal voltage in phase after inputting the phase current.
The analysis results of the EMF demagnetization ratios are depicted in Figure 18. It indicates that the EMF demagnetization ratio is 0.73% with seven times of the input current indicating that only a slight demagnetization occurs to the peak of the magnet.  Because the reluctance torque is affected by the assisted-PM in the optimal model, the EMF demagnetization ratio cannot describe the influence. To investigate the effect of magnet irreversible demagnetization for total torque, the torque demagnetization ratio is defined as where T 1 is the average value of the output torque before inputting the phase current, and T 2 is the average value of the output torque after inputting the phase current. The analysis results of the torque demagnetization ratios are depicted in Figure 19. It indicates that the torque demagnetization ratio is under 0.01% with seven times of the input current. In another word, when the motor suffers the sudden three phase short circuit condition, the demagnetization caused by the large instantaneous current will not affect the output torque of the optimal model. From the above analysis, the demagnetization that occurs on the peak of the magnet with seven times of the input current has a negligible impact on the output performance of the optimal model. It has superior endurance against the magnet irreversible demagnetization, which especially benefits of the reluctance torque resisting the effect of demagnetization. Because the reluctance torque is affected by the assisted-PM in the optimal model, the EMF demagnetization ratio cannot describe the influence. To investigate the effect of magnet irreversible demagnetization for total torque, the torque demagnetization ratio is defined as where T1 is the average value of the output torque before inputting the phase current, and T2 is the average value of the output torque after inputting the phase current. The analysis results of the torque demagnetization ratios are depicted in Figure 19. It indicates that the torque demagnetization ratio is under 0.01% with seven times of the input current. In another word, when the motor suffers the sudden three phase short circuit condition, the demagnetization caused by the large instantaneous current will not affect the output torque of the optimal model. From the above analysis, the demagnetization that occurs on the peak of the magnet with seven times of the input current has a negligible impact on the output performance of the optimal model. It has superior endurance against the magnet irreversible demagnetization, which especially benefits of the reluctance torque resisting the effect of demagnetization.

Mises Stress Analysis
Due to the combined rotor structure, the mechanical stress of the machine at the rated speed-1500 r/min has to be investigated. The material properties of the rotor core are listed in Table 4. The structural strength of the optimal model is evaluated by using FEA simulations. The maximum allowable fatigue stress (Yield strength) of the used rotor material is 304 MPa. In addition, the mises stress analysis is shown in Figure 20. It can be seen that the highest stress is about 0.5 MPa, which is so far below the maximum allowable fatigue stress of the used rotor material.

Mises Stress Analysis
Due to the combined rotor structure, the mechanical stress of the machine at the rated speed-1500 r/min has to be investigated. The material properties of the rotor core are listed in Table 4. The structural strength of the optimal model is evaluated by using FEA simulations. The maximum allowable fatigue stress (Yield strength) of the used rotor material is 304 MPa. In addition, the mises stress analysis is shown in Figure 20. It can be seen that the highest stress is about 0.5 MPa, which is so far below the maximum allowable fatigue stress of the used rotor material.

Conclusions
This paper proposes a novel rotor structure named proposed PMa-WFSM and then optimizes the rotor shape to improve average output torque and decrease torque ripple under a constant PM volume and motor size. It is revealed that the inflection point of iron magnetic saturation has been effectively widened, and the torque performance has been a nice enhancement. The segment distance and segment displacement, the shape of magnet and pole head should be designed and optimized for a better combination to realize the targets.
The results obtained by FEA show that the optimized model has greatly increased the total average torque by 31.66%. It is also clarified that the optimum structure can significantly reduce the torque ripple that caused by the assisted-PM. All the operations are without a decrease in efficiency or an increase on PM volume and motor size. Finally, irreversible demagnetization and mises stress analysis verified the reliability of the novel topology.

Conclusions
This paper proposes a novel rotor structure named proposed PMa-WFSM and then optimizes the rotor shape to improve average output torque and decrease torque ripple under a constant PM volume and motor size. It is revealed that the inflection point of iron magnetic saturation has been effectively widened, and the torque performance has been a nice enhancement. The segment distance and segment displacement, the shape of magnet and pole head should be designed and optimized for a better combination to realize the targets.
The results obtained by FEA show that the optimized model has greatly increased the total average torque by 31.66%. It is also clarified that the optimum structure can significantly reduce the torque ripple that caused by the assisted-PM. All the operations are without a decrease in efficiency or an increase on PM volume and motor size. Finally, irreversible demagnetization and mises stress analysis verified the reliability of the novel topology.