**9. Mechanical simulation**

The mechanical analysis itself in the Ansys program serves to determine the deformations based on the forces applied to the model. The main variable, which in this case describes the vibration, is the displacement of the individual components of the model. It also serves to determine a deformation and displacement of the body at each point in the mesh when finite element method is used. The calculation is based on the following equation:

$$\{M\}.\\\langle\mu\rangle + \{C\}.\\\langle\upsilon\rangle + \{K\}.\\\langle\mathbf{x}(t)\rangle = \{F(t)\}\tag{15}$$

machines but also with program Maxwell's control and adjustment. The actual modeling of the machine itself is also quite demanding. Whether the user uses a classical CAD system or RMxprt, it needs a lot of information that can have a detrimental effect on the calculation. One of the most important information is the dimensions of the electric machine. This information can be obtained from the technical documentation. Another factor that can influence the calculation is the knowledge of the materials used and especially their properties. Much information about these materials can be found on the Internet. In many cases, the values of material properties are measured in specific conditions (e.g., at temperature 22°C) and then these values do not have to match the calculation conditions. The ideal source of information on material

Vibration Simulation of Electric Machines http://dx.doi.org/10.5772/intechopen.72266 205

Once a model has been created, it is necessary to set-up individual analyses. It should be noted that, for example, electromagnetic analysis has different mesh quality requirements than mechanical analysis. There are automatic features for mesh creation in Ansys Workbench and Maxwell environment. For vibration calculations, it is necessary to edit the quality mesh on certain parts of the model manually in many cases. However, this requires knowledge not only of the procedures for both types of calculations but also of some experience with different types of analyses. Another non-negligible part of the calculation is the time step selection for transient analysis. If the time step is too long, there is a loss of data that could be critical to the calculation. Conversely, when setting a small time step, an unreasonable load on the computing hardware will occur and an increase in the computational time will be necessary. Given the number of calculations that need to be made to achieve the relevant results, a minor

It can be said that modern programs using finite element methods allow the calculation of a wide range of physical problems. As far as the calculations of vibrations of electric machines are concerned, it is a very complex issue, which affects many areas (electricity, magnetism, mechanics, thermal). The calculation of the complete vibrational spectrum of the electric machine with all vibration sources is possible, but it is very time consuming. Therefore, it is always necessary to focus on solving a certain part of this issue. Based on the analysis of the results, requirements and the analysis of the input parameters, it is possible to simplify the solution considerably, which allows to achieve reasonable results in a sufficiently short time. An ideal solution to the vibration problem of electric tools using finite element method is to build a team of workers with knowledge and experience from different industries who will

This research work has been carried out in the Centre for Research and Utilization of Renewable Energy (CVVOZE). Authors gratefully acknowledge the financial support from the Ministry of Education, Youth and Sports of the Czech Republic under NPU I program

properties is the supplier of construction materials.

change may mean an extension of day calculations.

cooperate.

**Acknowledgements**

(project No. LO1210).

**Figure 7.** Vibration results from FEM.

where *F*(*t*) is load vector, *M* is mass, *C* is damping, *K* is stiffness, *x* is displacement vector, *a* is acceleration vector (*a* = *x*¨(*t*)), and v is velocity vector (*v* = *x*̇ (*t*)).

On the basis of this equation, the individual displacements of the bodies are then determined. Several other parameters have to be taken into account to set the calculation correctly. One of the things that need to be set is the material properties of the individual parts of the simulated machine. The material properties are the material density, the Poisson's ratio and the Young's modulus for mechanical analysis. These material properties can be found on the Internet or requested from the material supplier.

Another parameter that affects the quality of the result is the final set-up of the mesh. There is a need to focus on to focus on where forces work or where there is a small cross-section on model. At these points of the model, it is necessary to manually adjust the strength of the mesh to avoid any unwanted effect on the result.

Another parameter is to determine the properties of the contact surfaces. Particularly, for more complex models, results are poor where there is a poor contact surface setting. The Ansys mechanical analysis module uses five types of contact surfaces such as bounded, without separation, without friction, friction and pulping. Their choice depends on the knowledge of the construction of the electrical machine and on the way of the mechanical connection of its individual parts [4, 8] (**Figure 7**).
