Abstract: The generation mechanism of torque ripple in permanent magnet brushless DC motors is analyzed, and the commutation torque ripple during the sewing machine's stopping process is studied based on the characteristics of the sewing machine controller. A method combining overlapping commutation and stator current fixed-frequency sampling is proposed to suppress torque ripple, and experimental results are given. Keywords: sewing machine; stopping accuracy; brushless DC motor; torque ripple Introduction As a mechatronic device, the power drive system is one of the core technologies of industrial sewing machines. Sewing machine controllers using brushless DC motors have significant performance advantages compared to previous products. This paper analyzes some problems caused by torque ripple in brushless DC motors. Permanent magnet brushless DC motors have many advantages, such as no commutation sparks, reliable operation, convenient maintenance, simple structure, and no excitation loss, and are increasingly widely used in many applications. 1. Torque Characteristics of Brushless DC Motors The equivalent circuit of a brushless DC motor is shown in Figure 1. Torque characteristics are an important indicator of motor performance, among which the most important are average torque and torque smoothness. Brushless DC motors have a higher average torque than conventional motors, but they suffer from torque ripple, a major factor limiting their application. There are three main causes of electromagnetic torque ripple in brushless DC motors: cogging torque ripple, torque ripple caused by non-ideal back electromotive force (EMF), and commutation torque ripple. The first two are related to the motor's manufacturing process or imperfect magnetization of the rotor magnets, and can be suppressed by modifying the motor itself. 2. Theoretical Analysis of Commutation Torque Ripple Assuming a constant motor speed during commutation, an ideal trapezoidal waveform (flat-top width of 120°), and that the amplitude of the back EMF on each phase winding remains constant during commutation, we will analyze the commutation process from phase B to phase C (upper bridge arm commutation), with phase A being a non-commutated winding. Before commutation, S1 and S6 are on, and current flows through the A and B phase windings; after commutation, S1 and S2 are on, S6 is off, and phases A and C are energized. The current in the B phase winding continues upward through the diode. Taking the midpoint of the DC voltage as the reference point, the three-phase voltage balance equation during commutation can be written as: Where: Vsa = (Sa - 1/2)Vdc, Vse = (Sc - 1/2)Vdc, representing the voltages between the A and C phase windings and the reference point N0, respectively; Sa and Sc are switching quantities, for example, Sa = 1 indicates S1 is on and S4 is off; Sa = 0 indicates S1 is off and S3 is on. Vsa = (Sa - 1/2)Vdc is the voltage between the A phase winding and the reference point N0; Vsc = (Sc - 1/2)Vdc is the voltage between the C phase winding and the reference point N0; VNN0 is the voltage between the motor midpoint and the reference point. Considering that in a three-phase Y-connected motor, ia+ib+ic=0, from the voltage balance equation of equation (1), compared with the winding time constant L/R, it can be considered that the PWM period is small enough. Then, ignoring the influence of the resistance of the three-phase winding, we have: where Ka, Kb, and Kc are variables introduced for convenience. Solving this ordinary differential equation, we have: The torque during commutation includes two parts, the first part is the steady-state component, and the second part is the pulsation component caused by commutation. It can be seen that the torque pulsation caused by commutation is related to the parameters of the motor winding, the change law of the three-phase back electromotive force during commutation, the running speed of the motor and the DC voltage, and the modulation method. According to the previous assumption, the waveform of the three-phase back electromotive force is an ideal trapezoidal wave, then we have: Under the ideal back electromotive force waveform condition , the torque pulsation caused by commutation is 3. Suppression of torque pulsation This article is aimed at a brushless DC motor used in a sewing machine controller. Due to the characteristics of the sewing machine, it is required that the motor stop High stopping accuracy is crucial because the accuracy of the stopping position directly affects the overall performance of the sewing machine and the overall evaluation by peers. In the controller design, the motor is already rotating at the predetermined minimum speed before applying braking torque. The load of the motor drive system can be approximated as constant during stopping and is the same each time. In this case, the duration and amplitude of the applied braking torque are assumed to be constant each time stopping, meaning the average power of the applied braking torque is assumed to be constant each time stopping. By adjusting this average braking power, the motor is ensured to stop accurately at the specified position: once the braking power parameter is adjusted, applying the same average braking power during subsequent stops will guarantee a relatively accurate stopping position. However, during actual debugging of the drive system, it was found that if commutation occurs during the application of braking torque, it will affect the stopping accuracy. This is because commutation changes the predetermined average braking torque, thus affecting the stopping accuracy. Therefore, we must suppress torque pulsation in cases of commutation during stopping. First, we introduce a method of delayed commutation (overlapping commutation), in which the off-phase is delayed for a period of time to compensate for the commutation current. To reflect the current of the non-commutated phase (total current) on the DC bus during the delayed off-phase period, a measure is adopted to synchronously modulate the off-phase and non-commutated phases with PWM to keep the on-phase constantly on, as shown in Figure 2. As can be seen from Figure 2, if only the overlapping commutation method is used, the torque ripple suppression effect is not ideal because the overlapping commutation time is difficult to determine and many factors affect torque ripple. To avoid the shortcomings of the conventional overlapping commutation method and obtain better current regulation performance, the literature introduces stator current fixed-frequency sampling current regulation technology, thus forming a current control method combining current fixed-frequency sampling and overlapping commutation technology, as shown in Figure 3. This is the torque ripple suppression method adopted in this paper. In this method, unlike the conventional delayed overlapping commutation method which only extends the conduction of the off-phase by a time interval at the beginning of commutation, the off-phase is modulated at the current sampling point based on the current feedback signal throughout the entire commutation period. As shown in Figure 3, when the current fluctuation of phase A exceeds the set positive threshold, phase C is shut off to reduce the current; when the current fluctuation of phase A is less than the set negative threshold, phase C is turned on to increase the current. Simulation experiments show that, at a current sampling frequency of 200 kHz, compared with conventional overlapping commutation, the torque ripple coefficient is reduced from 43% to 23%. 4. Experimental Results Based on the shutdown conditions of the developed high-speed flat sewing machine brushless motor drive system, a series of experiments were conducted. The experimental results are shown in Figures 4 and 5. The curve at the bottom of both figures is a magnified detail of the upper waveform, representing the DC bus current waveform. Figures 4 and 5 show that during braking, after certain commutation compensation, the instantaneous drop in DC bus current is compensated, and its power is approximately equal to that of the DC bus current without commutation (figure omitted), thus ensuring appropriate reverse torque and keeping the shutdown accuracy within the operating range. It is worth noting that a negative current appears on the DC bus during the commutation of the lower bridge arm. However, no measures were taken to eliminate this negative current during compensation. This is because the reverse torque obtained through the delayed conduction of the off-phase is sufficient to ensure that the stopping accuracy is within the operating range, therefore no further compensation measures were taken. 5. Conclusion This paper takes the brushless DC motor drive system of a high-speed flat sewing machine as an example, mainly discussing the impact of commutation torque pulsation on the stopping accuracy of the motor during braking. Based on actual conditions, a commutation current compensation method combining current fixed-frequency sampling and overlapping commutation technology is proposed to reduce the impact of commutation torque pulsation on stopping accuracy. The designed system and the compensation method adopted have been verified through actual system operation, showing that they can well meet the usage requirements, and the system's technical accuracy requirements are within the specified range.