# Research on Influence of Switching Angle on the Vibration of Switched Reluctance Motor
## 2 Principle of Switching Angle control Method  
A typical structure of stator and rotor for a 12-8 SRM is shown in Figure 1a. As can be seen from the figure, both the stator and the rotor of the SRM are doubly salient structures. If a specific phase of the motor (e.g., phase 1) is excited, the magnetic field force is generated due to the distortion of the electromagnetic field, which makes the rotor rotate to the position where the pole axis of the rotor and the pole axis of the stator coincide. When the phases 2, 3, 1 and 2 in Figure 1a are sequentially energized, the rotor will continuously rotate in a counterclockwise direction, and, vice versa, in a clockwise direction. Due to the double salient pole structure and unique switching mode of the switched reluctance motor, the flux linkage of the switched reluctance motor has strong nonlinearity, which makes the mathematical model of the switched reluctance motor very complex. In order to facilitate the analysis, on the basis of ignoring the flux saturation effect and reluctance edge effect, this section linearizes and simplifies the flux linkage characteristics of switched reluctance motor. In the linearized model, the inductance is related to the rotor position and independent of the current. For a phase of the switched reluctance motor, during the rotation, the relative positions of salient poles of stator and rotor change periodically, and the inductance also changes periodically between the maximum value \(L_{\text{max}}\) and the minimum value \(L_{\text{min}}\). The change curve of inductance relative to rotor position is shown in Figure 1b, where \(\beta_{r}\) is the length of stator pole arc, \(\beta_{  
B coincide, \(\theta_{4}\) is the position where side a of stator and side a of rotor coincide, \(\theta_{5}\) is the position where stator side B and rotor side a coincide and \(\theta_{6}\) is the coincidence position of stator side a and rotor side B. Figure 1b also shows the variation curve of the inductance with respect to the rotor angle position \(\theta\) under the linear model, where \(\theta_{1}\) to \(\theta_{5}\) is an electrical cycle. When \(\theta_{1}\leq\theta<\theta_{2}\), the stator salient pole and rotor groove overlap, and the air gap between stator and rotor is the largest, so the magnetic resistance is the largest and the inductance is the smallest. When \(\theta_{2}\leq\theta<\theta_{3}\), the rotor salient pole begins to overlap with the stator salient pole, the air gap between the stator and rotor decreases, and the inductance increases linearly. When the stator salient pole coincides with the rotor salient pole, the inductance reaches the maximum. When \(\theta_{3}\leq\theta<\theta_{4}\), the rotor salient pole and stator salient pole remain coincident, the air gap is the smallest, and the inductance is always the maximum. When \(\theta_{4}\leq\theta<\theta_{5}\), the rotor salient pole gradually separates from the stator salient pole, and the inductance value linearly decreases to the minimum value. The inductance expression is [24]:  
\[L(\theta)=\left\{ \begin{array}{ll}L_{\min},&\theta_{1}\leq\theta<\theta_{2} \\ L_{\min}+\frac{L_{\max}-L_{\min}}{\beta_{r}}(\theta-\theta_{2}),&\theta_{2} \leq\theta<\theta_{3}\\ L_{\max},&\theta_{3}\leq\theta<\theta_{4}\\ L_{\max}-\frac{L_{\max}-L_{\min}}{\beta_{r}}(\theta-\theta_{4}),&\theta_{4} \leq\theta<\theta_{5}\\ \end{array} \right.