# A Multi-Physics Modeling-Based Vibration Prediction Method for Switched Reluctance Motors
## 2 Vibration of the Switched Reluctance Motor  
SRM mainly consists of a stator unit, a rotor unit and corresponding structural components, as shown in Figure 1a. The stator unit includes iron core, winding, slot wedge, insulating material and motor lead, while the rotor unit contains rotor shaft and rotor core. Both the stator and the rotor use a salient pole structure that was formed by laminating silicon steel sheets. In addition, the windings are installed only at the stator pole. Furthermore, the structural components are mainly composed of housing, end cover, bearing cover, bearing, junction box, and junction column. Figure 1b illustrates the stator and rotor structure for a 12-8 SRM. Four radial relative windings at the stator pole form a phase. If current is applied to a specific phase of the motor (e.g., phase A), 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. At this time, the magnetic resistance is at a minimum. When the phases B, C, A and B in Figure 1b are sequentially energized, the rotor will continuously rotate in a counterclockwise direction, and, vice versa, in a clockwise direction.  
Currently, the vibration problem is one of the research hotspots of the SRM. It is mainly caused by the change of the electromagnetic force between air gap magnetic fields of the stator and rotor. When the stator winding of SRM is energized, an induced magnetic field is formed at the stator pole, which further magnetizes the rotor. At this time, electromagnetic forces are generated between the stator and rotor, as shown in Figure 2. The electromagnetic forces acting on the stator and rotor, namely \(F_{s}\) and \(F_{r}\), are a pair of forces and reaction forces. The electromagnetic force \(F_{s}\) can be decomposed into tangential magnetic force \(F_{st}\) and radial magnetic force \(F_{sr}\). When the stator winding is excited, the radial magnetic force \(F_{sr}\) increases, stretching the stator along the radial direction. However, if the current is cut, the radial magnetic force \(F_{sr}\) is reduced to zero, and the stator rebounds in the radial direction. With the continuous commutation of the excitation winding for the SRM, the radial magnetic force \(F_{sr}\) of the different phases repeatedly attracts and releases the stator, causing structural deformation of the motor stator. If the frequency of \(F_{sr}\) is close to the natural frequency of the motor, it will excite the resonance of the motor body and cause strong radial vibration. Similarly, the electromagnetic force \(F_{r}\) can be also decomposed into tangential magnetic force \(F_{rt}\) and radial magnetic force \(F_{rr}\). Due to the doubly salient construction and fundamental excitation principles, the majority of the flux in SRM is in the radial direction. Although the torque ripple caused by fluctuations of \(F_{rt}\) during motor excitation and demagnetization may also induce tangential vibration, it can be neglected compared with radial vibration, which has been also verified by the works of several researchers [18; 1; 26]. For instance, [PERSON] et al. [18] designed a series of experiments to investigate the vibration in SRM, and the experimental results showed that radial vibration of the stator frame caused by radial electromagnetic forces is the dominant source of vibration in SRM. The authors in [1; 26] also proved that the acceleration response of SRM mainly resulted from the sudden change of radial electromagnetic forces. Consequently, this paper focuses on the establishment of a radial vibration prediction model.  
Figure 1: Structure and working principle of switched reluctance motor (SRM): (**a**) structure of SRM; (**b**) working principle of a 12-8 SRM.