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Cogging torque of permanent magnet synchronous motor

source：未知 time：2024-09-30 10:08nbsp; click：

Cogging torque is the torque generated by the interaction between the permanent magnet and the stator core when the permanent magnet motor winding is not energized. It is caused by the pulsation of the tangential component of the interaction force between the permanent magnet and the stator teeth. When the motor rotor rotates, the magnetic permeance in a small range of the stator slots on both sides of the permanent magnet changes significantly, causing the magnetic field energy storage to change, thereby generating cogging torque.

Cogging torque can cause torque pulsation in the permanent magnet motor, which in turn causes speed fluctuations. Torque pulsation can also cause vibration and noise in the motor. When the frequency of the pulsating torque is consistent with the resonant frequency of the armature current, resonance will occur, which will inevitably amplify the vibration and noise of the cogging torque. It seriously affects the positioning accuracy and servo performance of the motor, especially at low speeds.

Cogging torque reduction method Scholars have conducted a lot of research on reducing cogging torque. The methods are summarized into three categories:

Overall consideration of the motor: using fractional slot winding; considerations on the stator side: stator skew slots, stator tooth auxiliary slots, slot width optimization; considerations on the rotor side: rotor magnetic pole arc coefficient, uneven air gap, rotor skew pole, magnetic pole offset.

Using fractional slot winding

Considering the relationship between the combination of slot number Z and pole number 2p and cogging torque, it is generally believed that the larger the number of fundamental wave cogging torque cycles, the smaller its amplitude, so the combination of stator slot number Z and rotor pole number 2p with a larger least common multiple should be selected.

The principle that the use of fractional slot winding motors is beneficial to reducing cogging torque is that the magnetic field positions of each slot of its stator are different, so the cogging torque phases generated by each are different. The superposition result not only increases the number of fundamental wave cogging torque cycles, but also may produce mutual compensation. The number and position of tooth slots under each magnetic pole of the integer slot winding motor are the same, and the cogging torque generated under all poles has the same phase. The cogging torque of 2p poles is superimposed to greatly increase the total cogging torque.

The author has simulated the same 9-slot stator punching, and the rotor is 6-pole and 8-pole. Both schemes are fractional slot motors, but the cogging torque is also very different because their least common multiples of Z and 2p are 18 and 72 respectively. The peak cogging torque of the 9-slot 6-pole motor is 30mNm, while the cogging torque of the 9-slot 8-pole motor is 2mNm.

Rotor pole arc coefficient

The pole arc coefficient α refers to the ratio of the pole arc width to the pole pitch. In the case of integer slot motors, for surface mounted permanent magnet poles, it is generally believed that it is beneficial to reduce the cogging torque when the pole arc width is close to an integer multiple of the slot pitch. In the case of fractional slot motors, such as 9-slot 8-pole motors, through finite element simulation analysis, when the pole arc coefficient is selected as 0.89/0.78/0.67, the cogging torque is small; for 4-pole 6-slot motors, when the pole arc coefficient is 0.67, the cogging torque is small.

Uneven air gap

The air gap between the stator and rotor of the motor is usually designed to be uniform, and the air gap flux density distribution under the magnet will be closer to a trapezoidal wave with more harmonics. If it is changed to an unequal air gap, that is, the air gap is small at the center of the magnet and there is a larger air gap at the pole tip, the air gap flux density distribution under the magnet will be close to a sine wave, which is beneficial to reduce the cogging torque.

In the inner rotor surface mounted motor, if the inner and outer diameters of the arc-shaped permanent magnet are concentric circles, the thickness of the permanent magnet is equal and the air gap is uniform. If the inner and outer diameters are not concentric, the magnet thickness is unequal, which can make the motor air gap uneven, thereby reducing the cogging torque.

Rotor skewed poles, stator skewed slots

The fundamental period of the cogging torque is equal to the least common multiple N of the number of stator slots Z and the number of rotor poles 2p, that is, the fundamental period of the cogging torque corresponds to a mechanical angle of 360/N. Therefore, if the stator core skew angle or the rotor magnetic pole skew angle is 360/N, the fundamental wave of the cogging torque can be eliminated.

The use of skewed poles and skewed slots will lead to a decrease in the motor's back electromotive force and electromagnetic torque. The stator skewed slots will increase the difficulty of winding embedding, and the motor will generate axial force. The rotor segment staggered method is usually used to approximate the skewed pole. For example, if the number of rotor segments is parametrically analyzed, when the number of rotor segments reaches 5, the cogging torque can be completely ignored.

Pole offset

Pole offset is similar to the segmented misalignment of the rotor poles. Only when there are 2p poles can the original evenly distributed position be changed to a circumferential offset. This is equivalent to having 2p segments of segmented poles in a fundamental wave tooth slot cycle. Except for the 2p harmonics and its multiples, other tooth slot torques are weakened. However, pole offset will introduce the problem of unbalanced magnetic pull of the rotor. For example, for a 4-pole 24-slot motor, the tooth slot torque is reduced from 0.2Nm to 0.02Nm after using the pole offset method. The author has disassembled Reno's servo motor, which uses pole offset to reduce the tooth slot torque.

Auxiliary slots in stator teeth

The principle of reducing cogging torque by opening auxiliary slots in stator teeth is to increase the number of fundamental wave cycles of cogging torque. The cogging torque caused by the auxiliary slots compensates for the original slot cogging torque, thereby reducing the amplitude of the total cogging torque. Opening auxiliary slots also increases the equivalent air gap, which is also beneficial to reducing the cogging torque. The literature mentions that for 18-slot 12-pole motors, when two slots are opened in the stator, the number of cogging torque cycles increases three times, and the cogging torque decreases by about 3 times. For 4-pole 6-slot motors, when two auxiliary slots are opened in the stator, the cogging torque decreases from 1.04Nm to 0.2Nm.

Slot width optimization

The existence of stator slots is the main reason for the generation of cogging torque. It is generally believed that the smaller the slot width, the better. For integer slot motors, through finite element simulation analysis, the cogging torque increases monotonically with the slot width. For fractional slot motors such as 12-slot 14-pole motors, finite element simulation analysis is performed. When the slot width is 3.45mm, the cogging torque is about 6% of the slot width of 2mm and about 10% of the slot width of 4mm. For fractional slot motors, the smaller the slot width, the better. There are optimizable slot width options.

Slotless winding

The most thorough and simple method is to use a slotless winding structure. The armature winding is either pasted on the smooth rotor surface, or made into a moving coil, or a printed circuit winding of a disc motor. Regardless of the form used, the thickness of the armature winding is always a component of the actual air gap. Therefore, the actual equivalent air gap of the slotless motor is much larger than that of the slotted motor, and the required excitation magnetic potential is also much larger, which limited the capacity and development of the slotless motor in the early days. This has indeed been studied and trial-produced in China for a long time, but I have not heard of any company that has mass-produced products. There is a company in the UK that specializes in this type of motor, which is widely used in some aviation fields.

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