Abstract: Taking a 10-pole, 30-slot surface-mount permanent magnet synchronous motor as an example, auxiliary slots of different shapes, numbers, and positions are made in the rotor core and the bottom of the permanent magnet below the permanent magnet. The influence of various auxiliary slots on torque ripple and average torque during motor operation under load is analyzed, and the variation law of torque ripple with the size and position of the auxiliary slots is summarized. Finite element analysis shows that making reasonable rotor core auxiliary slots and permanent magnet auxiliary slots can effectively reduce torque ripple.
1 Introduction
Based on the position of the permanent magnets on the rotor, permanent magnet synchronous motors can be divided into three categories: surface type, built-in type, and claw pole type. Surface type rotor magnetic circuit structures are further divided into protruding type and inserted type.
On the other hand, torque ripple can cause motor noise and vibration, affecting the motor's operating performance and even its lifespan. Therefore, reducing torque ripple is one of the main design goals of permanent magnet motors.
Data shows that, based on the expression of cogging torque of surface-protruding permanent magnet synchronous motor derived by the energy method and Fourier decomposition, the influence of some design parameters such as the matching of motor pole number and slot number, permanent magnet pole arc coefficient, and stator slot width on the motor cogging torque was analyzed, and the optimization selection method of these design parameters was derived. Reference [2] established an accurate subdomain analytical model of surface-insertion permanent magnet motor in a two-dimensional polar coordinate system, divided it into three solution regions: stator slot subdomain, air gap subdomain and rotor slot subdomain, solved the vector magnetic potential general solution of each subdomain according to the separation of variables method, and obtained the relevant harmonic coefficients by using the boundary conditions between each subdomain, thus providing conditions for the calculation of cogging torque.
The data proposes to open different types of auxiliary slots such as rectangular slots, triangular slots, and semi-circular slots in the stator crown, and to study the influence of various auxiliary slots on the tooth cogging torque. It was found that the rectangular slot is the most effective in suppressing tooth cogging torque, followed by the semi-circular slot and the triangular slot. The tooth cogging torque decreases with the increase of the auxiliary slot depth and first decreases and then increases with the increase of the slot width.
Many studies have analyzed how auxiliary slots on the stator teeth of surface-mount permanent magnet motors reduce cogging torque, but few have investigated the impact of auxiliary slots on the rotor of such motors on cogging torque. Furthermore, cogging torque is only one source of torque ripple during motor operation under load; simply reducing cogging torque is clearly insufficient. Therefore, this paper focuses on a surface-mount permanent magnet motor with a 10-pole stator and 30 slots, using finite element simulation to study the effects of auxiliary slots on the rotor core below the permanent magnet and the auxiliary slots at the bottom of the permanent magnet on torque ripple during operation under load. By rationally designing the auxiliary slots, torque ripple can be reduced while ensuring a large output torque.
2 Original motor structure
Figure 1 shows a typical structure of a bread-shaped permanent magnet in a surface-insertion rotor structure permanent magnet motor. The outer diameter of the permanent magnet is Rr, and the bottom surface of the permanent magnet is straight rather than curved, which is beneficial for generating a sinusoidal air gap magnetic flux density distribution. The maximum thickness of the permanent magnet is hm, the pole arc width is αm, and parallel magnetization is used. Between adjacent magnetic poles, there are protruding parts in the iron core, which is beneficial for fixing the permanent magnet, so the permanent magnet is a surface-insertion type.
This paper uses the motor shown in Figure 1 as a reference to study the effects of auxiliary slots in the core below the permanent magnet and the bottom of the permanent magnet on the torque ripple during motor operation under load. In the subsequent studies, the finite element method is used to calculate the electromagnetic torque of the motor, and the same three-phase symmetrical sinusoidal rated current is applied to the motor. When the reference motor is subjected to the rated current (51.6 Arms), the average electromagnetic torque is 52.3 Nm, and the torque ripple (defined in this paper as the ratio of peak-to-peak torque to average torque) is 21.4%. It is evident that although a bread-shaped permanent magnet is used, the torque ripple is still significant, necessitating further design optimization to reduce it.
3. Rotor core auxiliary slots below the permanent magnet
Although the motor shown in Figure 1 uses a surface-inserted bread-shaped permanent magnet, the radial excitation magnetomotive force in the motor air gap is still not sinusoidal. Furthermore, the stator slot openings cause uneven distribution of the air gap length in the circumferential direction, thus exacerbating the non-sinusoidal nature of the air gap magnetic flux density. These factors all contribute to the motor's cogging torque and torque ripple during load operation. For surface-inserted permanent magnet motors, creating auxiliary slots on the rotor core below the permanent magnet can alter the equivalent air gap length, thereby changing the air gap magnetic flux density distribution and potentially reducing torque ripple.
3.1 Rectangular auxiliary groove
As shown in Figure 2, two rectangular slots symmetrical about the centerline are made below each magnetic pole of the motor rotor core, with the edges of the slots aligned with the edges of the permanent magnets. Setting the slot width to l1 and the depth to h1, the change in motor torque performance with the size of the rectangular slots is shown in Figure 3. As can be seen from the figure, with an appropriate increase in the depth h1 of the rectangular slots, the motor torque ripple tends to decrease.
Meanwhile, when the slot depth is constant, the magnitude of torque ripple first decreases and then increases with increasing slot width, while the average torque obviously decreases with increasing slot width. As shown in the figure, when l1=7mm and h1=4mm, the torque ripple reaches its optimal value of 6.2%, but the average torque drops to 49.9Nm. Figure 4 shows the no-load air gap radial magnetic flux density waveforms of the reference prototype without auxiliary slots and the motor with the aforementioned optimal auxiliary slots. It is evident that appropriate rectangular auxiliary slots are beneficial for reducing the harmonic components of the air gap magnetic flux density. Of course, opening auxiliary slots will lead to an increase in the equivalent air gap length, which will inevitably cause a decrease in average torque.
When using four rectangular auxiliary slots symmetrical about the centerline as shown in Figure 5, the five parameters l1, h1, x1, l2, and h2 are optimized. Figure 6 shows that when the slot size remains constant, the torque ripple of the motor increases with the increase of the distance x1 between two rectangular auxiliary slots. Furthermore, it can be seen that the motor performance is significantly affected by the auxiliary slots closer to the magnetic pole edge. The optimal simulation result is when l1=7mm, h1=4mm, x1=0.5mm, l2=1mm, and h2=2mm, with an average motor torque of 49.6 Nm and a torque ripple of 5.5%. Compared to adding only a symmetrical single rectangular auxiliary slot, adding an inner auxiliary slot can further reduce torque ripple, but the average torque will also decrease. A simple optimization method is to optimize the inner slot only after the outer slot has reached its optimal value.
Based on the symmetrical four-slot design, a pair of auxiliary slots are added to the inner side, forming a symmetrical six-rectangular auxiliary slot structure. The slot positions x2 and sizes l3 and h3 are optimized. For simplicity, l1=7mm, h1=4mm, x1=0.5mm, l2=1mm, and h2=2mm are pre-fixed. Finite element analysis results show that adding the inner slots does not reduce torque pulsation; on the contrary, as the distance between the inner slots increases, the motor performance decreases. Therefore, adding a third pair of rectangular auxiliary slots is not very meaningful.
3.2 Semi-circular auxiliary groove
To investigate the effect of semi-circular auxiliary slots on the torque of a surface-mount permanent magnet motor, two semi-circular auxiliary slots symmetrical about the centerline were created on the rotor core below the magnets, as shown in Figure 7. Their position and size could be constrained and optimized using l1 and r1, and the results are shown in Figure 8. The minimum torque ripple was 4.9%, but the average torque decreased to 49.3 Nm. It can be seen that the torque ripple first decreases and then increases as the slot radius increases.
When the outer semi-circular auxiliary groove reaches its optimal state, another pair of semi-circular auxiliary grooves are then created on the inner side. The inner auxiliary grooves are then constrained and optimized using parameters x1 and r2. However, finite element analysis shows that creating the inner auxiliary grooves does not reduce torque pulsation, therefore they are not illustrated.
4 Permanent Magnet Bottom Auxiliary Groove
Besides creating auxiliary slots in the rotor core, auxiliary slots can also be created at the bottom of the permanent magnet. We first studied two symmetrical semi-circular slots, as shown in Figure 9. By constraining the position and size of the auxiliary slots with parameters x1 and r1, optimization analysis yielded the results shown in Figure 10. It can be seen that adding appropriate auxiliary slots to the permanent magnet can effectively reduce torque ripple; however, improper placement of the auxiliary slots can significantly worsen the motor's torque ripple. When x1 = 3mm and r1 = 1.5mm, the optimal torque ripple reaches 8.2%, with an average torque of 50.4 Nm.
With the outer slot optimized, a pair of inner slots are added (see Figure 11). The inner slots are then optimized using parameters x2 and r2, yielding the results shown in Figure 12. It can be seen that appropriately placed inner auxiliary slots are beneficial for further reducing motor torque ripple. When the radius r2 of the inner auxiliary slot remains constant, the torque ripple first decreases and then increases with the increase of the inner auxiliary slot position x2. When x2 = 2.5 mm and r2 = 1.5 mm, the torque ripple can be reduced to 4.8%, while the average torque is 48.0 Nm.
If a third pair of slots is added to the bottom of the permanent magnet, finite element calculations show that the torque pulsation not only does not weaken but worsens. Detailed calculation results are not given here.
5. Conclusion
This paper investigates the influence of rotor auxiliary slots on torque ripple during operation of a surface-mount permanent magnet motor (SPM) under load. First, rectangular and semi-circular auxiliary slots are created on the rotor core beneath the permanent magnet. The effects of the size, position, and number of these slots on the motor's torque ripple are studied. When the rotor core's auxiliary slots are symmetrical double rectangular slots, the motor's torque ripple decreases with increasing slot depth, and initially decreases then increases with increasing slot width. Adding a pair of inner rectangular slots, with appropriate slot size, can further reduce the motor's torque ripple; when the inner slot size is fixed, the torque ripple increases with increasing distance from the inner to the outer slot. Adding more rectangular slots no longer reduces torque ripple. When the rotor core's auxiliary slots are semi-circular slots with fixed positions, the torque ripple initially decreases then increases with increasing slot radius. Adding another pair of inner slots reveals that the torque ripple increases with increasing inner slot distance. Finally, the effect of adding auxiliary slots at the bottom of the bread-shaped permanent magnet on motor performance was investigated. When a pair of semi-circular slots were added, if the slot size was fixed, the torque ripple initially decreased and then increased as the distance between the slot edge and the permanent magnet edge increased. When another pair of inner slots were added, it was found that the torque ripple initially decreased and then increased as the distance between the two slots increased. Overall, the inner slots helped reduce torque ripple. However, when a third pair of semi-circular auxiliary slots were added to the permanent magnet, the torque ripple actually worsened.
Based on the above analysis, it can be seen that the auxiliary slots on the rotor core or permanent magnet can be reasonably designed to effectively reduce torque pulsation, and of course, the average torque will also decrease.
