**2. Vibration fundamentals**

Vibrations are a mechanical phenomenon. It can be said that this is the movement of a flexible body or environment whose individual body vibrates around the equilibrium position.

The forces acting on the vibrating body define the motion equation:

$$m.\frac{d^2\mathbf{x}}{dt^2} = (F(t) - k.\mathbf{x} - b.\frac{d\mathbf{x}}{dt})\tag{1}$$

This relationship applies to very simple oscillations. There are a number of sources and influences in electric machines that affect the vibration generation. The actual course of vibration displacement is, therefore, the sum of forces that change over time with different frequencies. The vibration displacement of the electric machine is shown in **Figure 1**. Fast Fourier Transformation is used to convert the signal into the frequency area and the result of this transformation is shown in **Figure 1**. **Figure 1** also shows the proportion of individual har-

Vibration Simulation of Electric Machines http://dx.doi.org/10.5772/intechopen.72266 195

**Figure 1.** Induction motor vibration - a) Displacement of electric machine. b) FFT of vibration signal

For the calculation of vibrations in electrical machines, it is necessary to get basic information about their basic construction. The electric machine consists of a magnetic circuit. The magnetic circuit focuses most of the magnetic field into a defined area. The magnetic circuit itself is made of steel plates connected to the stator, respectively into the rotor. There are grooves cut on the internal circumference of the stator, into which the winding is inserted. The winding itself is one of the most important parts of electric machines. Copper with good electric conductivity and with 99% purity is used as a material of winding. In some applications, aluminum alloy of similar purity is used as a material. All electric motors have many other mechanical parts. These include a shaft on which the rotor plates are mounted. Although the shaft is, in most cases, a simple component that is made of a machined steel rod, it can have a great effect on the vibration of the machine. The main parameter that can affect the vibration is the quality of the processing and the quality of the whole rotor balancing. Due to the possible inhomogeneity of the material, the so-called mass unbalance can occur, causing the unwanted vibrations generated by the machine. The vibration level and frequency depend on the rotation speed of the rotor itself. Rotors are balancing in production to reduce this phenomenon. Another important part of electrical machines is bearings. Many types of bearings are used in electrical machines. Ball bearing or roller bearings are commonly used. Nowadays, electromagnetic bearings are also used in special applications. From the vibration point of view, two separate phenomena occur in the bearings. The first is generating vibrations. This is in

monics on the vibration signal [2–4].

**3. Electric machine construction**

where *m* is body mass, *x* is deviation from the steady state of the body, *F*(*t*) is force dependent on time, *k* is stiffness of the spring, and *b* is coefficient of damping.

The forces acting on any system create the oscillation itself. In a simple case, the oscillation has a harmonic character. This occurs when system is exposed to a single source with a constant exciting force. For the description of harmonic oscillation, the relationship is used:

$$\mathbf{x}(t) = \mathbf{x}\_{\text{max}}.\sin(2\pi f\_{\text{f}}t) \tag{2}$$

where *x*(*t*) is displacement value, *x*max is maximum displacement value and *f* is vibration frequency.

**Figure 1.** Induction motor vibration - a) Displacement of electric machine. b) FFT of vibration signal

This relationship applies to very simple oscillations. There are a number of sources and influences in electric machines that affect the vibration generation. The actual course of vibration displacement is, therefore, the sum of forces that change over time with different frequencies. The vibration displacement of the electric machine is shown in **Figure 1**. Fast Fourier Transformation is used to convert the signal into the frequency area and the result of this transformation is shown in **Figure 1**. **Figure 1** also shows the proportion of individual harmonics on the vibration signal [2–4].
