Causes of cogging torque & how to reduce cogging torque?（2）

2. Rotor Pole Arc Coefficient

The pole arc coefficient (α) refers to the ratio of the magnetic pole arc width to the pole pitch. For integral-slot motors, when using surface-mounted permanent magnets, it is generally considered beneficial to reduce cogging torque when the magnetic pole arc width closely approximates an integer multiple of the slot pitch. For fractional-slot motors, finite element simulation analysis shows that cogging torque is minimized when the pole arc coefficient is 0.89/0.78/0.67 for a 9-slot 8-pole motor, and 0.67 for a 4-pole 6-slot motor.

3. Non-Uniform Air Gap

Motor designs typically feature a uniform air gap between the stator and rotor. In such cases, the magnetic flux density under the magnets often resembles a trapezoidal waveform with significant harmonic components. By introducing a non-uniform air gap, where the air gap is smaller at the center of the magnet and larger at the edges, the magnetic flux density can approach a sinusoidal waveform, which helps reduce cogging torque.

For internal rotor surface-mounted motors, when the inner and outer diameters of the arc-shaped magnets are concentric, the magnets have uniform thickness, resulting in a uniform air gap. If the inner and outer diameters are non-concentric, the magnet thickness varies, creating a non-uniform air gap and reducing cogging torque.

4. Skewed Rotor Poles and Stator Slots

The fundamental period of cogging torque is determined by the least common multiple (N) of the stator slot number (Z) and the rotor pole number (2p). This corresponds to a mechanical angle of 360°/N. Skewing the stator core slots or rotor pole angles by 360°/N can effectively eliminate the fundamental component of cogging torque.

However, using skewed poles or slots can reduce back electromotive force (EMF) and electromagnetic torque. Skewed stator slots also increase winding complexity and may generate axial forces in the motor. A common manufacturing alternative is to achieve skewed poles by offsetting rotor sections. Parametric analysis indicates that dividing the rotor into five sections eliminates cogging torque entirely.

5. Magnetic Pole Shifting

Magnetic pole shifting is similar to segmented rotor pole offsets. For 2p magnetic poles, instead of uniformly distributing the poles, they are circumferentially shifted. This effectively creates segmented poles within one cogging torque fundamental period, suppressing cogging torque components except for the 2p-th harmonic and its multiples. However, magnetic pole shifting can introduce rotor unbalanced magnetic pull issues. For instance, in a 4-pole 24-slot motor, magnetic pole shifting reduced cogging torque from 0.2 Nm to 0.02 Nm.

6. Auxiliary Slots on Stator Teeth

Adding auxiliary slots on stator teeth reduces cogging torque by increasing the fundamental period of cogging torque. The cogging torque introduced by auxiliary slots compensates for the original cogging torque, reducing its overall amplitude. Auxiliary slots also increase the effective air gap, further lowering cogging torque. For example, in an 18-slot 12-pole motor, adding two auxiliary slots increased the cogging torque period by three times and reduced its amplitude by threefold. In a 4-pole 6-slot motor, adding two auxiliary slots reduced cogging torque from 1.04 Nm to 0.2 Nm.

7. Optimization of Slot Opening Width

The presence of slot openings is the primary cause of cogging torque. Generally, smaller slot openings are preferred for integral-slot motors. Finite element simulation analysis shows that cogging torque increases monotonically with slot opening width. For fractional-slot motors, such as a 12-slot 14-pole motor, when the slot opening width is optimized at 3.45 mm, cogging torque is only 6% of that with a slot opening width of 2 mm and 10% of that with a slot opening width of 4 mm. This indicates that there exists an optimal slot opening width for fractional-slot motors.

8. Slotless Winding

The most straightforward and effective method to eliminate cogging torque is to adopt slotless winding structures. Armature windings may be bonded to a smooth rotor surface, designed as moving coils, or configured as printed circuit windings in disc motors. Regardless of the form, the thickness of the armature winding becomes part of the effective air gap. Consequently, slotless motors have a significantly larger equivalent air gap than slotted motors, requiring much higher excitation magnetomotive force. This limited the capacity and development of slotless motors in the early stages.

If you are interested in learning more about techniques for eliminating cogging torque, feel free to reach out to Santroll's technical team. Contact us!