Comparison and analysis of power and torque performance of PMSM with different rotor structures

In this paper, according to the double reaction principle of permanent magnet synchronous motor (PMSM), the power, torque, and power angle characteristics are derived theoretically. Four motor models of tangential type, radial type, V-type, and U-type PMSM are established by finite element software. The magnetic flux density of the motor is analyzed in detail. At the same time, performance indicators such as efficiency, power factor, and air gap power of permanent magnet synchronous motors were calculated and evaluated, further improving the accuracy and credibility of the research. Based on the comparative study of the analysis results, the advantages and disadvantages of electromagnetic performance corresponding to different rotor structures are obtained, providing the design basis of PMSM.


Introduction
At present, PMSM is one of the latest research focuses on motors.The magnetic field generated by the stator winding interacts with the excitation of a permanent magnet, and converts the energy stored in the electromagnetic field into mechanical energy to provide power for the system.PMSM has the advantages of simple structure, reliable operation performance, and small size, so it is widely used in many fields such as daily life, industrial equipment, and aerospace.However, PMSM still has some problems, such as heat dissipation problems, excessive rotor inertia, high maintenance costs, and so on.Therefore, to further improve the performance and efficiency of PMSM, it is particularly important to improve the rotor structure of the permanent magnet synchronous motor [1][2][3][4] .In Figure 1, PMSM generates losses when operating under load, which mainly include the following aspects: stator copper loss Cu P , stator iron loss Fe P , mechanical loss fw P , and stray loss  P .The composition of input power mainly consists of three parts, namely stator iron loss, stator copper loss, and electromagnetic power.The schematic diagram of input power composition is shown in Figure 1.

Power equation and torque equation of PMSM
The input power equation of PMSM with a solid rotor under asynchronous starting is as follows: The expression of electromagnetic power is where d I and q I are the direct axis component and the quadrature axis component of the current respectively; d X and q X are the direct axis component and the quadrature axis component of reactance, respectively; U is the phase voltage; 0 E is no-load back electromotive force;  is the rotation angle; and m is the phase number.By dividing the mechanical angular velocity at both ends of the above equations, the expression for electromagnetic torque can be obtained: According to the above equation, electromagnetic torque can be divided into two parts: reluctance torque and permanent magnet torque.The reason for the generation of reluctance torque is due to the asymmetry of the magnetic circuit, which occurs when the quadrature axis reluctance and direct axis reluctance are not equal.Permanent magnet torque is generated by the combined action of the armature reaction magnetic field and the magnetic field generated by the permanent magnet [5][6] .
Based on the above theoretical analysis, the electromagnetic performance of different rotor structures will be analyzed and studied in the following content.Four motor models are studied by finite element software, and the eddy current electromagnetic field and output performance of the four motors are compared and analyzed.Four two-dimensional motor models are shown in Figure 2.

Magnetic density distribution of four types of PMSM
Uneven magnetic field distribution can cause vibration and noise during motor operation, while also reducing the efficiency and lifespan of the motor.Through the magnetic density distribution map, it is possible to intuitively understand the uniformity of the internal magnetic field distribution of the motor and determine whether there is an uneven magnetic field.The magnetic density distribution map of four motor models is shown in Figure 3. From Figure 3, it can be seen that the magnetic flux of motor 1 is mainly concentrated at both ends of the rotor axis, which is prone to air gap modulation effect during high-speed operation, resulting in a reduction of the power factor of the motor.The magnetic flux of motor 2 is mainly concentrated in the radial direction of the rotor and distributed in an axisymmetric manner.It is not easy to generate air gap modulation effects during high-speed operation, resulting in high power factor and energy utilization efficiency.The magnetic flux of motor 3 is mainly concentrated at both ends of the rotor, but due to the use of an inclined iron plate design, the magnetic field distribution is more uniform, which reduces the air gap modulation effect and improves the efficiency of the motor.Motor 4 combines the advantages of tangential PMSM and radial PMSM, and has better comprehensive performance.

Simulation comparison of efficiency characteristics.
The core material characteristic of PMSM determines its electromagnetic performance, which is also one of the factors affecting its efficiency curve.When the load is small, the magnetic flux density of the core is low, which will cause the electromagnetic performance of the core to decline, thus affecting the efficiency of the motor.When the load is gradually increased, the magnetic flux density of the core is also increased, resulting in an improvement in efficiency.In summary, the efficiency curve of PMSM with torque angle as the independent variable exhibits a single peak characteristic, which is influenced by the characteristics of the motor itself and is also related to factors such as motor load and speed.Efficiency simulation results of four types of motors are as follows: From Figure 4, it can be seen that motor 3 can achieve the highest efficiency of 0.8846 when the torque Angle is 77°.When the torque angle is greater than 100°, the efficiency of the four types of motors decreases rapidly, and the efficiency of motor 1 is the highest.Motor 1 has better performance under heavy-load working conditions.

Simulation comparison of power factor.
When PMSM operates under load, the power factor first decreases, then increases, and then decreases with the variation of the motor torque angle.The fundamental reason is the phase difference change that occurs in the internal magnetic field of the motor as the load changes.Figure 5 shows the simulation results of the power factor for four types of motors.The simulation results show that four different power factor curves can be obtained under the same stator setting conditions.The power factor of motor 3 is maximum at rated torque.Among the four types of motor power factor curves, motor 1 has the smallest slope, while motors 2, 3, and 4 have similar slopes.Therefore, motors 2, 3, and 4 have better response speeds.

Simulation comparison of air gap power.
At low loads, the motor has a higher speed and a smaller air gap between the rotor and stator, resulting in a smaller eddy current power loss in the air gap, so the air gap power curve is lower.As the load increases, the speed of the motor gradually decreases, and the eddy current power loss in the air gap also begins to increase, leading to a gradual increase in the air gap power curve.When the load of the motor reaches a certain degree, due to the saturation effect and thermal effect of the magnetic field, the air gap between the rotor and the stator will change slightly, resulting in the maximum eddy current power loss in the air gap, so that the air gap power curve reaches the peak value.However, when the load continues to increase, the load of the motor will exceed its rated load, producing excessive torque, which will cause the speed of the motor to drop sharply, and the eddy current power loss in the air gap will increase sharply.At the same time, the thermal effect causes the stator coil temperature to rise, the stator resistance to increase, and further increases the eddy current power loss, so that the air gap power curve gradually decreases.The following is the simulation results of air gap power: Figure 6 shows the comparison of air gap power for four motor models at different torque angles.From the comparison of the air gap power curve, it can be seen that the peak value of the curve for motor 1 is the highest, indicating that the motor has the highest output power and efficiency.The slope of the curve mainly reflects the output characteristics of the motor.The curve slope of motor 2 is larger, and the output characteristics of motor 2 are stronger and faster.The curve slope of motor 1 is small, and the output characteristics of the motor are relatively stable.

Conclusion
This paper starts with the theoretical derivation of the torque and power equations and conducts a study on the electromagnetic performance of four different rotor structures of PMSM.It mainly focuses on simulation and comparative analysis of magnetic density distribution, power factor, air gap power, and efficiency.The specific research contents are as follows: 1) Through magnetic flux density simulation analysis, the magnetic flux of tangential PMSM mainly flows in the axial direction, while that of radial PMSM mainly flows in the radial direction.
The magnetic flux of V-type PMSM flows in both radial and tangential directions, and the magnetic flux of U-type PMSM also alternates in the radial and tangential directions.2) Tangential PMSM has higher efficiency and stronger output capacity under high loads.
3) Through simulation analysis of air gap power and power factor, the characteristics of tangential PMSM are relatively smooth, which can be applied to occasions requiring smooth operation.Radial PMSM, V-type PMSM, and U-type PMSM have better response speed, and U-type PMSM has better comprehensive performance.

Figure 2 .
Figure 2. Two-dimensional models of four motors.

Figure 3 .
Figure 3. Magnetic density distribution of four types of motors.

Figure 4 .
Figure 4. Efficiency characteristics of four types of motors.

Figure 5 .
Figure 5. Power factor of four types of motors.

Figure 6 .
Figure 6.Air gap power of four types of motors.