1. Torque ripple caused by electromagnetic factors
This is the torque pulsation caused by the interaction between stator current and rotor magnetic field, which is directly related to current waveform, induced electromotive force waveform and air gap magnetic flux density distribution. Ideally, the stator current is square wave, the induced electromotive force is trapezoidal wave, the flat top width is 120 electrical angle, and the electromagnetic torque is constant. However, in the actual motor, it is difficult to keep the induced electromotive force as a trapezoidal wave, or the width of the flat top is not 120 electrical angle, or the induced electromotive force and current cannot be kept in strict synchronization due to the insufficient precision of the rotor position detection and control system. Or the current waveform deviates from the square wave and can only change approximately according to the trapezoidal wave. The existence of these factors will lead to electromagnetic torque pulsation. The methods to suppress torque ripple caused by electromagnetic factors include optimization design method, optimal opening angle method, harmonic elimination method, torque feedback method and so on.
(1) Optimization design method. For brushless DC motor, pole shape, pole arc width and pole arc edge shape have great influence on the output electromagnetic torque. When the air gap magnetic flux density is a square wave, that is, the induced electromotive force waveform is an ideal trapezoidal wave, the pole arc width increases, the electromagnetic torque increases and the torque ripple decreases. When the width of polar arc reaches π, the motor power is maximum and the torque ripple is zero. Accordingly, the electromagnetic torque ripple can be effectively eliminated by selecting a reasonable design scheme of motor pole and pole arc without electromagnetic torque ripple, changing the shape of pole or increasing the width of pole arc.
(2) Optimal opening angle method. The electromagnetic torque ripple can be eliminated by the optimal design of the motor, but there are also some shortcomings, such as: due to the limitation of the inductance of the motor winding, even if the motor is powered by a constant current source, the current cannot change suddenly during commutation, and the current waveform flowing into the stator winding cannot be a rectangular wave; In addition, for the actual motor, it is difficult to keep the ideal square wave distribution of air gap magnetic field and the waveform of winding induced electromotive force is not ideal rectangle, so it is impossible to completely eliminate electromagnetic torque ripple from hardware design. Therefore, torque ripple can only be suppressed by control means and strategies. If the optimal opening angle is used to suppress electromagnetic torque ripple, that is, the functional relationship between torque ripple and opening angle is deduced first, and then the optimal opening angle of current is obtained, so that the current waveform and the induced electromotive force waveform can be properly matched, thus achieving the purpose of weakening torque ripple.
(3) Harmonic elimination method. Because the stator current and rotor magnetic field of brushless DC motor are non-sinusoidal, the electromagnetic torque generated by their interaction contains harmonic components, which causes torque pulsation. Electromagnetic torque ripple is formed by the interaction of phase current and induced electromotive force. It can be considered to eliminate the resulting torque ripple by controlling the harmonic component of the current. Because, under ideal conditions, the interaction of flux linkage harmonics and current harmonics (except the third harmonic) of brushless DC motor at the same frequency can produce constant torque, and there is no torque between different harmonics. Of course, in the actual situation, because the inductance of the motor limits the rate of change of current, the current input to the stator winding cannot be a rectangular wave, but often a trapezoidal wave. Moreover, the flat-top width of the flux waveform will be less than the ideal electrical angle 120, so that there is a certain harmonic torque between the flux harmonic and the different current harmonics. Therefore, it is difficult to determine the optimal harmonic current, which also makes harmonics
The application of exclusion method is limited.
(4) Torque feedback method. Harmonic elimination method is an open-loop control method. When the winding impedance is asymmetric and the current measurement error is equal to the disturbance, the control accuracy will be affected. In order to overcome the shortcomings of open-loop control method, people put forward a method to suppress torque ripple from the perspective of feedback, that is, to control the torque as the control object and carry out closed-loop control. The basic principle of the torque feedback method is that the torque feedback signal is obtained by the torque observer according to the position and current signals, and then fed back to the main circuit of the brushless DC motor through the torque controller to realize the real-time control of the torque, thus eliminating the torque ripple. However, the structure of torque feedback method is complex, and it needs to determine the motor parameters in advance. The algorithm is complex and it is difficult to realize.
2. Torque ripple caused by current commutation
When the brushless DC motor works, the stator windings are commutated in a certain order. Due to the inductance in each phase winding, the instantaneous change of current is hindered. Every time it passes through a magnetic state, the current in the armature winding will cause the pulsation of electromagnetic torque when switching from one phase to another. The methods of restraining torque ripple caused by current commutation include current feedback method, hysteresis current method, overlapping commutation method and pulse width modulation (PwM) chopping method.
(1) current feedback method. This method is to keep the non-commutated phase current constant and make the commutation torque ripple zero, because the existence of non-commutated phase current will lead to certain torque ripple. Generally speaking, current feedback control can be divided into two forms, namely DC side current feedback control and AC side current feedback control. The current feedback signal of DC side current feedback control is taken from DC side and mainly controls the current amplitude. Because the DC side current feedback control is based on the current signal flowing through the DC power supply, only one current sensor is needed to obtain the current feedback signal. The current feedback signal controlled by current feedback on the AC side is taken out by the AC side. At this time, the phase current to be controlled is determined according to the position of the rotor to make it follow the given value. In the commutation process, when the non-commutation phase current does not reach the given value, PwM control does not work; When the non-commutation current exceeds the set value, PwM control begins to work. Turn off all switching devices to reduce the current value until it is lower than the set value, then turn off the turned-off switching devices to increase their values, and so on, to realize the adjustment of non-commutated phase current until commutation is completed.
(2) Hysteresis current method. Among the commonly used current control methods, besides the above methods, there are hysteresis current control methods. Its basic principle is. Hysresis current regulator (HcR) is used in the current loop. By comparing the reference current with the actual current, an appropriate trigger signal can be given during commutation. The amplitude of actual current and the width of hysteresis loop determine the output of HcR control signal. When the actual current is less than the lower limit of the hysteresis width, the switching device is turned on; When the current rises and reaches the upper limit of hysteresis width, the switching device is turned off, which makes the current drop. The actual current can be the phase current or the input current of the inverter. Hysteresis current method has the characteristics of simple application, good rapidity and strong current limiting ability. Hysteresis current control methods can be divided into three situations: HcR controlled by rising phase current, HcR controlled by non-commutating phase current and HCR controlled by three-phase phase current independently. Comparing the effects of these three methods to suppress commutation torque ripple, it is proved that the latter two cases have the same commutation torque characteristics, have good suppression effect on commutation torque ripple, and are suitable for low speed.
(3) Overlapping commutation method. Although the current feedback method and hysteresis current method solve the torque ripple problem of commutation at low speed, they are usually not ideal at high speed. At present, overlapping commutation method is a mature method to suppress commutation torque ripple in high-speed section. Its basic principle is. The power switching devices that should be turned off immediately during commutation are not turned off immediately, but the time interval is extended, and the switching devices that should not be turned on are turned on in advance. In the traditional overlapping commutation method, it is necessary to determine the overlapping time in advance, but it is difficult to choose the appropriate overlapping time and to minimize the torque ripple.
(4)PwM chopping method. The PwM chopping method is similar to the AC side current feedback control method, that is, the switching devices chop at a certain frequency before turning off and after turning on, so as to control the terminal voltage of the winding in the commutation process, make the rising and falling rates of each commutation current equal, compensate the change of the total current amplitude, and suppress the commutation torque ripple. Compared with the overlapping commutation method, this method has smaller torque ripple and is suitable for occasions with high accuracy requirements.
3. Torque ripple caused by cogging effect
The stator core of brushless DC motor must have teeth and implants in order to place the stator winding. Due to the existence of stator tooth slot, the air gap is uneven, and the magnetic flux within a tooth pitch is relatively concentrated in the teeth, which makes the air gap permeability not constant. When the rotor rotates. The air gap magnetic field will change, resulting in cogging torque. Cogging torque is related to rotor position, which causes torque pulsation. Cogging torque is an inherent characteristic of permanent magnet motor. When the motor is running at low speed and light load, cogging torque will cause obvious speed fluctuation, which will lead to vibration and noise. Therefore, how to weaken the cogging torque is one of the more important goals in the design of permanent magnet motor.
The reason of cogging torque is different from the above two reasons of torque pulsation. The above two causes of torque ripple are the interaction between stator current and rotor magnetic field, while cogging torque is produced by the interaction between stator core and rotor magnetic field. The most common method to reduce cogging torque ripple is stator chute or rotor inclined pole. In addition, increasing the air gap and using fractional and magnetic slot wedge are also helpful to reduce the fluctuation of cogging torque. Of course, the best way to eliminate the cogging effect is to adopt the slotless motor structure.
No matter what form the armature winding of slotless motor takes, its thickness is always a part of the actual air gap, so the actual equivalent air gap of slotless motor is much larger than that of slotted motor, and the required excitation magnetomotive force is also much larger. This limited the ability and development of slotless motor in the early stage. In recent years, with the rapid development of magnetic materials, especially the application of rare earth permanent magnet materials with high magnetic energy products such as NdFeB, it has created conditions for the practical use of slotless motors. The slotless structure is adopted because it has a super air gap at the same time, which can not only completely eliminate the torque ripple caused by cogging effect, but also greatly weaken the torque ripple caused by armature reaction and mechanical eccentricity.
4. Torque ripple caused by armature reaction
The influence of armature magnetomotive force on the main magnetic field of air gap is called armature reaction. The armature reaction of brushless DC motor is complex. According to the nature of armature reaction, the magnetomotive force of armature reaction can be decomposed into quadrature axis component and direct axis component.
The response of the quadrature-axis armature to the magnetomotive force will distort the waveform of the main magnetic field in the air gap, so that the magnetic induction intensity of the main magnetic field in the air gap is no longer the square cross when it is empty, and the induced electromotive force will also be distorted. This leads to the mismatch between induced electromotive force and armature current, which in turn causes torque ripple. At present, brushless DC motors are all made of high-performance rare earth permanent magnet materials. If the tile surface-mounted type is adopted, the influence of the cross-axis armature reaction on the main magnetic field of the air gap will be very weak. This is because the reaction magnetic circuit of the quadrature-axis armature passes through the air gap and the permanent magnet [see Figure 6 8(a)], and the permeability of the permanent magnet material is very close to that of air, which makes the magnetic resistance of the reaction magnetic circuit of the quadrature-axis armature very large, and the magnetic flux of the reaction of the quadrature-axis armature is very small, so the influence on the main magnetic field of the air gap can be ignored.
In the process of rotor rotation, the direct axis armature reacts with the magnetomotive force to demagnetize the main magnetic field and then increase the magnetic field, so that the total magnetic flux of each pole of the load changes near the total magnetic flux of each pole under no load. In this way, the induced electromotive force and electromagnetic torque will also change, but the influence is not great.
5. Torque fluctuation caused by machining
The inconsistency between machining and material is also one of the important reasons for torque ripple of brushless DC motor. For example, the size and shape deviation of the motor during machining and assembly, the uneven distribution of slots on the stator punching sheet, the unilateral magnetic pull caused by the eccentricity of the inner and outer circles of the stator, the misalignment of the stator and the rotor, the uneven friction torque of the bearing system, the torque pulsation caused by the inaccurate positioning of the rotor position sensor, the torque pulsation caused by the asymmetry of winding parameters in each phase and the difference of performance parameters of electronic components, and the torque pulsation caused by the inconsistency of parts materials in the magnetic circuit, especially the performance of permanent magnets. Therefore. Improving machining level is also an important measure to reduce torque ripple.