# A Multi-Physics Modeling-Based Vibration Prediction Method for Switched Reluctance Motors
## 1 Introduction  
Due to its simple structure, low cost and high reliability, a switched reluctance motor (SRM) has been highlighted for many industrial applications [1; 2]. For instance, SRM is considered as a promising candidate for the distributed-driven electric vehicle [3; 4]. Based on the analytical Fourier fitting method, [PERSON] et al. [5] presented a convenience method for modeling an in-wheel switched reluctance motor. To alleviate the harmful effects of vibration induced by the unbalanced electromagnetic force, [PERSON] and co-workers [6] developed a vibration mitigation method based on a dynamic vibration absorbing structure. Despite its many advantages, SRM suffers from inherent vibration and acoustic noise, which limits its application in the industrial potential market. Therefore, researchers have investigated the vibration and acoustic noise problem for SRM from various aspects: stator and rotor pole shaping [7], motor topology optimization [8; 9], switching angle adjustment [10], insert of zero voltage loop during switching [11], and current waveform profiling [12]. In order to predict the vibration of SRM, accurate modal analysis and radial force calculation are of vital significance. The natural frequencies and vibration modes of SRM can be calculated by modal analysis, which are used to analyze the vibration characteristics. [PERSON] et al. [13] showed that the vibration is largest when the harmonic frequency of electromagnetic force coincides with the modal frequency. [PERSON] et al. [14] recommended a phase radial force shaping method based on harmonic content analysis, which was experimentally validated with experiments at different speed and load conditions. [PERSON] and co-workers [15] analyzed the mechanical coupling path of stator and rotor and itsinfluence on vibration modes. Taking into account the electromagnetic characteristics, mechanical vibration, and acoustic noise, [PERSON] et al. [16] proposed a numerical modeling method for classical SRM and mutually coupled SRM. In [17], FEA methods were used to determine the modal shapes and natural frequencies for SRM, and the influence of end-bell and self-weight were also considered. However, the above methods only analyzed the modal of the motor stator, and did not consider the influence of windings, end cover, bearings, and other components on the system modal. Radial electromagnetic force is the main excitation source for the vibration and noise of SRM [18]. Calculation of electromagnetic force can be categorized into analytical methods and finite element analysis (FEA) methods. [PERSON] et al. [19] and [PERSON] et al. [20] derived the electromagnetic field distribution of SRM by dimension parameters and calculated the radial force according to the virtual displacement principle. However, the analytical methods require precise system parameters, and the corresponding derivation process of the radial force is quite complicated. In [21, 22], the finite element-based multi-physics analysis method was adopted to calculate the electromagnetic force, and the electromagnetic force was used as the excitation of the vibration model. [PERSON] et al. [23] and [PERSON] et al. [24] proposed a multi-physical field numerical simulation method, in which only the vibration characteristics of the stator were considered. With the obtained electromagnetic force and modal information, the vibration of the motor can be determined quantitatively. By utilizing the modal information and electromagnetic force, [PERSON] et al. [23] calculated the stator vibration response by a modal superposition method. [PERSON] and co-workers [25] established the transfer function model of vibration based on impulse excitation experiment and employed the transfer function model to calculate and analyze the vibration. [PERSON] et al. [19] and [PERSON] et al. [26] computed the SRM vibration by convolution method. When the number of switching actions in a cycle is relatively large, the computational time will also increase.