**5. Vibration simulation using finite element method (FEM)**

As already indicated in the previous sections of the chapter, the vibration of electric machines is a phenomenon that interferes with several physical areas (mechanics, electromagnetism, etc.) [8–10]. Therefore, the entire calculation process needs to be divided into several parts:


**Figure 2.** The Ansys workbench modules.

The frequency spectrum of these vibrations has discrete character. Vibrations caused by the electrical causes occur mainly in the radial direction. Vibrations are occurred in the case of more varied air gap size in the axial direction, for example, due to non-symmetrical rotor

Mechanical vibrations are mainly caused by bearings, rotor balancing, machining of rotating parts and rotor mounting. Mechanical vibrations produced into electrical machines are also caused by connected devices. These external vibration sources include clutch misalignment

The basic aerodynamic source of vibration is the fan in electric machine. Any obstruction that is exposed to air flow can generate vibration. The main cause of fan noise is the formation of

As already indicated in the previous sections of the chapter, the vibration of electric machines is a phenomenon that interferes with several physical areas (mechanics, electromagnetism, etc.) [8–10]. Therefore, the entire calculation process needs to be divided into several parts:

**a.** Determining Vibration Sources: at first, it is necessary to decide which resources to count. In the case of this chapter, the calculation is simplified only for the occurrence of vibrations by the effect of a time-dependent electromagnetic field. For this reason, it is possible to use Maxwell 2D or Maxwell 3D. This module allows to calculate the time-varying effect of the force in the magnetic circuit depending on the change of the electric current. The use of this program also allows to connect to a simulator of electrical circuits (program Simplorer). After connecting the supply current to the Maxwell model on the simpler electric circuit, it is possible to calculate the changes in the magnetic circuit caused by the control

**b.** Model creation: creating a model of an electric machine is one of the most important parts of the calculation itself. The user must choose between 2D and 3D model. The 2D model is much simpler, and therefore, the calculation itself takes a very short time. On the other hand, this is a great simplification of the calculation. The 3D model will allow for a more accurate calculation and consideration of the more influences affecting the calculation. However, the calculation of 3D models is considerably more demanding for computa-

**c.** Calculation of forces caused by selected sources: the next step is to determine the forces that act on the electrical machine. In this chapter, this is defined as a force of electromagnetic

tional power, and therefore, the calculation time is considerably longer.

or gearing, wedge gears or vibrations caused by connected loads [1].

198 Finite Element Method - Simulation, Numerical Analysis and Solution Techniques

**5. Vibration simulation using finite element method (FEM)**

mounting [1].

**4.2. Mechanical sources**

**4.3. Aerodynamic sources**

logic, that is, speed control.

turbulent airflow around the fan blades [1, 2, 4].

origin. The Maxwell program is used to determine them. These calculations can be supplemented by the calculation of the actual frequencies of the electric machine and also by external influences (such as asymmetry, etc.). An important factor is determining the right time step.

**d.** Determining vibration on the model: determination of vibration on a particular model is the result of a mechanical analysis [8–10] (**Figure 2**).
