## 1 Introduction  
**Interior permanent magnet (IPM) synchronous motors are widely used in various industrial applications such as automotive applications, pumps, compressors, centrifuges and many other fields** **[**1; 2; 3; 4**]****. The most important advantages of IPM over their counterparts are high power density, high efficiency, wide range and adjustable speed operation, high power factor, and low weight** **[**2**]****. **  
**The interior permanent magnet (IPM) synchronous motor rotors are more mechanically robust as opposed to the surface mounted permanent magnet synchronous motors; however, the permanent magnet-based machines might be in general less mechanically robust compared to induction machines due to the fact that they contain relatively fragile mechanical components, such as permanent magnets and their protecting metal sleeves and aluminum alloy shields for eddy current reduction [2]. These components reduce the rotor stiffness, which may lead to undesirable resonance critical speeds close to the operation range, which need to be precisely calculated and foreseen during the process of the development and design of the electrical machine [2]. The optimal mechanical design of a low vibration, low noise and stable rotational movement interior permanent magnet (IPM) synchronous motor intended for a wide range of operating speeds is a challenging task. This is particularly important for automotive applications as well as in similar industrial sectors in which a wide speed range is needed. For such applications the optimum mechanical vibration response of all motor components has to be carefully foreseen in the design stage. The mechanical structure of both stator and rotor assembly and their components needs to be analyzed in detail in addition to other important physical phenomena such as magnetic and thermal properties. Such complete mechanical analysis should include both static modal analysis for vibration analysis of geometrical and material properties of the machine components and the rotor dynamics in order to investigate the vibration of the rotating parts. The modal analysis of the machines' stator has already been extensively reported for different types of electrical machines [5; 6; 7; 8; 9; 10; 11; 12; 13; 14], while the rotor dynamic has mostly studied for the mechanical design of high speed machines constructed for special applications [1; 2; 4; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. To the best of the authors' knowledge, the complete mechanical analysis of the stator and rotor components of the same machine by the modal and rotor dynamic analysis has not been reported. In the present study, a complete mechanical analysis of an interior permanent magnet (IPM) synchronous motor designed for a wide range of operating speeds was performed by numerically, analytically and experimentally investigating mechanical vibrations of all stator and rotor components of the electrical motor. One of the major objectives was to derive and comprehensively summarize the key parameters related to mechanical vibrations response phenomena, which is important when designing rotating electrical machines. Specifically, the present study was focused on the static modal and the rotor-dynamic analysis of the IPM components and its assembly. First, a finite element-based model for modal analysis of the IPM stator stack was built and compared with the analytical and experimental results. Second, the numerical modal analysis was performed for the stator with the slot windings and the end-windings and compared to the experimental measurement data. The influence of the presence of the motor housing on the natural frequencies of the stator was analyzed by numerical modal analysis. The numerical and experimental modal analyses were further carried out on the machine rotor assembly in order to investigate the influence of magnets on its mechanical vibration behavior.