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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.