The back-EMF waveform of a brushless DC motor is one of the key factors affecting its torque ripple characteristics. Its waveform characteristics directly determine the smoothness and efficiency of the motor's operation. Back-EMF is generated by the rotating rotor permanent magnets cutting the stator windings, following Faraday's law of electromagnetic induction. Its waveform shape, flat-top width, and harmonic content significantly influence torque ripple.
Ideally, the back-EMF waveform of a brushless DC motor should be a trapezoidal wave with a flat-top width of 120° electrical degrees. When this waveform is matched with a rectangular current, constant torque output can be achieved during the non-commutation period. However, in actual motors, the back-EMF waveform often exhibits distortion due to design or manufacturing errors, such as a flat-top width less than 120° or inconsistent rising/falling edge slopes. When the flat-top width is less than 120°, even with an ideal rectangular current drive, electromagnetic torque ripples due to the phase mismatch between the back-EMF and the current. In this case, the torque ripple coefficient increases significantly as the flat-top width decreases, leading to unstable motor operation.
The harmonic content of the back-EMF waveform is another key factor in torque ripple. Trapezoidal back-EMF waveforms contain numerous odd-order harmonics, particularly the 3rd, 5th, and 7th harmonics. These harmonics interact with the current waveform to generate additional harmonic torque components. For example, the 6th harmonic torque is one of the primary sources of ripple in brushless DC motors, and its amplitude is directly related to the back-EMF harmonic content. When the back-EMF waveform is severely distorted, the harmonic torque component increases significantly, exacerbating torque ripple and impacting the motor's low-speed performance and positioning accuracy.
The impact of the commutation process on torque ripple is closely related to the back-EMF waveform. During commutation, current switches from one phase to another. If the back-EMF waveform were an ideal trapezoidal waveform, commutation-induced torque ripple could be suppressed. However, actual back-EMF waveforms often exhibit non-ideal characteristics, such as plateau fluctuations or offset zero crossings. This leads to a mismatch between the rate of change of current and the back-EMF during commutation, thus causing torque ripple. Furthermore, the accuracy of the back EMF zero-crossing point is crucial for sensorless control. Large errors in zero-crossing detection can further exacerbate commutation torque ripple.
To minimize the impact of the back EMF waveform on torque ripple, various control strategies can be employed. For example, when the back EMF plateau width is small, using sinusoidal current drive can effectively reduce torque ripple. This is because the interaction between the sinusoidal current and the distorted trapezoidal back EMF reduces harmonic torque components. Furthermore, overlapping commutation control smoothes current transitions during commutation by extending the time that both phases are simultaneously on, thereby suppressing commutation torque ripple. Current hysteresis control and PWM chopping algorithms reduce the impact of current fluctuations on torque by adjusting the current amplitude in real time.
Optimization during the motor design phase is also an important means of reducing torque ripple. Adjusting the stator winding layout and rotor magnetic circuit structure can improve the plateau width and symmetry of the back EMF waveform. For example, using concentrated windings or skewed pole designs can reduce back EMF distortion caused by cogging, thereby reducing cogging torque ripple. Furthermore, selecting permanent magnet materials with high magnetic properties can improve the stability of the back EMF waveform and reduce torque ripple caused by inconsistent magnetic properties.
The back EMF waveform of a brushless DC motor directly influences torque ripple characteristics through its shape, flattop width, and harmonic content. While an ideal trapezoidal back EMF waveform can achieve low torque ripple operation, the actual waveform often exhibits distortion due to design or manufacturing errors, leading to increased harmonic torque and commutation torque ripple. By optimizing control strategies and motor design, the impact of the back EMF waveform on torque ripple can be effectively suppressed, improving motor operation smoothness and efficiency.
