# Research on Influence of Switching Angle on the Vibration of Switched Reluctance Motor
## 3 Influence of Switching Angle on Vibration
### Influence of Switching Angle on Current  
Switching angle control strategy achieves the purpose of controlling the operation of the motor by adjusting the turn-on and turn-off angles of each phase of the motor. As can be seen from the previous section, the inductance of the motor is at a minimum value before \(\theta_{2}\) (the rotor angle at which the stator salient poles of the motor and the rotor groove begin to disengage), and the current increases linearly between the turn-on angles \(\theta_{on}\) and \(\theta_{2}\). Therefore, by changing the turn-on angle \(\theta_{on}\), the amplitude of the phase current in the inductance rising region is different, and the generated torque is also different. When the turn-off angle \(\theta_{off}\) of the motor is fixed, different turn-on angles will cause the current to have different waveforms, as shown in Figure 4.  
When the turn-on angle \(\theta_{on}<\theta_{2}-L/[(L_{\max}-L_{\min})/\beta_{r}]\) and \(di/d\theta<0\), the current drops in the inductance rising region, as shown by curve a in Figure 4. This is because when  
Figure 4: Current curves with constant turn-off angles and different turn-on angles. the turn-on angle is too small, the current rises too fast, and when the motor turns to \(\theta 2\), the current amplitude is too large, making the torque too large. At this time, the amplitude of the back EMF is greater than the bus voltage, and so the current decreases. When the turn-on angle \(\theta_{on}=\theta_{2}-L/[(L_{\max}-L_{\min})/\beta_{r}]\) and \(di/d\theta=0\), the current amplitude remains unchanged, as shown by curve b in Figure 4. Since the back EMF is equal to the bus voltage, the current does not change. When the turn-on angle \(\theta_{on}>\theta_{2}-L/[(L_{\max}-L_{\min})/\beta_{r}]\) and \(di/d\theta>0\), the phase current amplitude continues to increase when the motor turns to \(\theta_{2}\), as shown by the curve c in the Figure 4. Due to the delay in the turn-on of the phase winding, the phase current is too small, and the rotating electromotive force is smaller than the bus voltage. The curve of the current harmonic components with the turn-on angle can be obtained by performing a Fourier transform on the current waveform. Figure 5 shows the current harmonic variation when the turn-off angle is fixed at \(120^{\circ}\) and the turn-on angle varies from \(15^{\circ}\) to \(45^{\circ}\). Figure 5: Influence of turn-on angle to current harmonic magnitude (**a**) DC (**b**) 3 rd order (**c**) 9 th order (**d**) 18 th order (**e**) 36 th order (**f**) 48 th order. As can be seen from Figure 5, with the increase of harmonic order, the harmonic amplitude shows a decreasing trend. The DC component of the current waveform decreases with the increase of the turn-on angle, and other harmonic components first decrease and then increase with the change of the turn-on angle. There is a minimum value at a specific angle, such as the current harmonic amplitude, which has a minimum value at 30 centigrade as shown in Figure 5.  
Similarly, if the turn-on angle of the motor is fixed, the change of turn-off angle will also cause the change of current waveform, as shown in Figure 6. It can be seen from the figure that the turn-off angle determines the position where the current is reduced to zero. In Formula (9), let \(i(\theta)=0\), and get the zero point of the current \(\theta_{0}=2\theta_{off}-\theta_{on}\). When \(\theta_{0}<\theta_{3}\), i.e., \(\theta_{off}<(\theta_{3}+\theta_{on})/2\), the current has decreased to zero before the inductance increases to the maximum, as shown in curve C in Figure 6. When \(\theta_{0}>\theta_{3}\), i.e., \(\theta_{off}>(\theta_{3}+\theta_{on})/2\), the current decreases to zero in the maximum inductance area, as shown in curve B in Figure 6. When the turn-off angle continues to increase, the current is still not zero in the inductance drop area, as shown in curve A in Figure 4.0 It can be known from the electromagnetic torque characteristics that braking torque will be generated at this time.