**4. Noise measurement**

For measurement noise of induction machines can be used several techniques. The basic method for the measurement noise is the sound meter. It is a device which measures sound pressure.

## **4.1. Measurement process**

Measurement of noise can be divided into three main parts. The first part is data capture. For this purpose, the most commonly used microphones, or specialized equipment to measure noise (sound level meter). Their output is usually an analog signal, which must be further processed. When choosing of microphone is needed careful heed on certain parameters that can affect measurement accuracy. One of the most important parameter is the sensitivity of frequency. Worse microphones not recorded of the entire spectrum of the measured noise. Thanks to this complicates achieve it of accurate analysis results. Other parameters include the microphone sensitivity, which indicates the size of the output voltage (mV / Pa), depending on the pressure acting on the membrane. In addition, the structural dimensions of the measurement microphone and also the type of sound field that which is measured. Computers are most frequently use for Signal processing. For this reason it is necessary to convert from analog signal to digital form.

Large numbers of types A/D converters is on the market. Some are stand-alone converters; others are integrated to the specialized measurement cards. In both cases, the measurement depends on the three main parameters. The first is the measuring range of the converter. It gives the minimum, respectively maximum, measurable value. Because the signal is weak from a microphone, there should be used an amplifier for its amplification. Another parameter of the A/D converter is the bit depth conversion. This parameter defines the limitations of this device.

**Figure 3.** Block diagram of measurement process


$$\mathbf{I} = \int\_{\mathbf{f}\_1}^{\mathbf{f}\_2} \mathbf{I}(\mathbf{f}) \mathbf{d}\mathbf{f} \tag{32}$$

$$L\_{IS} = 10 \log \left[ \frac{l(f)}{l\_{ref}} \right] \tag{33}$$

$$L\_I = L\_{Is} + 10\log(\Delta f) \tag{34}$$

$$L\_p = L\_{ps} + 10\log(\Delta f) \tag{35}$$

$$
\Delta f = f\_u - f\_l \tag{36}
$$

$$\mathfrak{x}\_{\mathfrak{c}}(f) = \int\_{-\infty}^{\infty} \mathfrak{x}(t) . e^{-j2\,\pi f \,t} dt \tag{37}$$

$$\mathbf{x}(t) = \int\_{-\infty}^{\infty} \mathbf{x}\_c(f) . e^{j2\,\pi.f.t} dt \tag{38}$$

$$\mathbf{x}(f) = 2 \int\_{-\infty}^{\infty} \mathbf{x}(t) . \cos \{2. \pi.f.t + \Theta(f)\} dt \tag{39}$$
 
$$\text{Where: } \Theta(f) = \begin{cases} 0, & f \ge 0 \\ \frac{\pi}{2}, & f < 0 \end{cases}$$

$$\mathbf{x}(t) = \int\_{-\infty}^{\infty} \mathbf{x}(f) . \cos \{2. \pi.f. \mathbf{t} + \Theta(t)\} df \tag{40}$$

$$\mathbf{x}\_1(f) = 2 \int\_{-\infty}^{\infty} \mathbf{x}(t) . \cos(2.\pi.f.t)dt \tag{41}$$

$$\mathbf{x}\_0(f) = 2 \int\_{-\infty}^{\infty} \mathbf{x}(t) . \sin(2.\pi.f.t)dt \tag{42}$$

$$\mathbf{x}(t) = \int\_{-\infty}^{\infty} [\mathbf{x}\_1(t). \cos(2.\pi.f.t) + \mathbf{x}\_0(t). \sin(2.\pi.f.t)] df \tag{43}$$

$$
\begin{bmatrix}
\chi\_c(f) \\
\chi\_c(-f)
\end{bmatrix} = \frac{1}{2} \cdot \begin{bmatrix}
1 & -j \\
1 & j
\end{bmatrix} \cdot \begin{bmatrix}
\chi\_1(f) \\
\chi\_{10}(f)
\end{bmatrix}, f \neq 0 \tag{44}
$$

$$
\begin{bmatrix}
\boldsymbol{\chi}\_1(f) \\
\boldsymbol{\chi}\_0(-f)
\end{bmatrix} = \begin{bmatrix}
1 & 1 \\
1 & -j
\end{bmatrix} \cdot \begin{bmatrix}
\boldsymbol{\chi}\_c(f) \\
\boldsymbol{\chi}\_c(-f)
\end{bmatrix} \tag{45}
$$

Noise of Induction Machines 221

determine the proportion of individual harmonics. These harmonic then they can be the

The next part of the measurement was performed on the induction motor which worked without a load. The electric motor was loosely placed on a foam board. This board was for suppression the transmission of vibrations from the surroundings. External vibrations are

Measurement noise of electric machine, that is run, is shown in Fig. 5. As seen from the

<sup>0</sup> <sup>1000</sup> <sup>2000</sup> <sup>3000</sup> <sup>4000</sup> <sup>5000</sup> <sup>6000</sup> <sup>7000</sup> <sup>8000</sup> <sup>9000</sup> <sup>10000</sup> -0.4

Samples

On Fig. 7 is an analysis of the measured noise using MATLAB. Specifically, was carried Fast Fourier Transform (FFT). Dominant frequency is 600 Hz. This frequency is multiple of power supply frequency. It is a frequency of radial forces. In measurement signal can be

6. . *<sup>v</sup>*

*f k f* (48)

involved many harmonics frequencies of radial forces. Than we can write equation

"subtracted" from the noise levels of electrical machines.

measured values, that the noise level is constantly fluctuating.


not desirable for accurate measurements.

**Figure 5.** Noise of induction machines - no load

**Figure 6.** Noise of induction machine – 1 rotation

*f* … Frequency of radial force [Hz] - *f* … Power supply frequency [Hz] - *k* … Number (k=1, 2, 3, …..)

For ݂ ൌ ͷͲݖܪ are frequencies of radial forces݂௩ ൌ ͵ͲͲǡ ͲͲǡ ͻͲͲǡ ǥ ݖܪ.

**6.2. Noise of induction machine** 

Where


Equations (44) and (45) are very useful to convert from one representation to the other. When �(�)is real, ��(�) and ��(�)are also real. Then, (44) shows that ��(�) and ��(��) are complex conjugates of each other. Equations (44) and (45) are also valid in the case of the discrete time Fourier transformation. In addition, they are valid for Fourier series and the discrete Fourier transforms with the replacement of fby the frequency index n. The RFT relations given by (43) can be proven by using (44), and writing (38) as

$$\mathbf{x}(t) = \int\_{0}^{\infty} \frac{1}{2} \left[ \mathbf{x}\_{1}(f) - j\mathbf{x}\_{0}(f) \right]. \, e^{j\,2\pi f \cdot t} df + \int\_{0}^{-\infty} \frac{1}{2} \left[ \mathbf{x}\_{1}(-f) - j\mathbf{x}\_{0}(-f) \right]. \, e^{j\,2\pi f \cdot t} df \tag{46}$$

Then

$$\mathbf{x}(t) = \int\_{0}^{w} [\mathbf{x}\_{1}(f), \cos(2.\pi.f.t) + \mathbf{x}\_{0}(f), \sin(2.\pi.f.t)] df \tag{47}$$

### **6. Measurement noise of induction machines**

### **6.1. Disturbed surroundings**

Surrounding noise sources have an impact on the measurement of electrical machinery. It is not always possible to perform measurements in specialized laboratories, which are perfectly sound-insulated. To laboratory measurement can penetrate the noise from nearby sources (see Fig. 4), which is inaudible to the human ear. The interference from other sources can be created undesirable frequencies in the frequency band.

**Figure 4.** Noise measurement in the laboratory when the machine is switched off

Interference of other sources in the neighborhood of workplace cannot be directly prevented, but you can minimize their impact on analysis of the measured signal. Before the measurements it must be made measurement ambient noise before the main measurements. It is necessary to determine whether the background noise is random, or it is periodically repeated. In the case of random noise is preferable to wait to other time of measurement or it must count with errors in the measurement. In the event that can be measurement of noise repeated. Can be recorded the extent of spectral interference with which will be calculate when evaluating the measured results. From Spectral analyses of interference is possible to determine the proportion of individual harmonics. These harmonic then they can be the "subtracted" from the noise levels of electrical machines.

The next part of the measurement was performed on the induction motor which worked without a load. The electric motor was loosely placed on a foam board. This board was for suppression the transmission of vibrations from the surroundings. External vibrations are not desirable for accurate measurements.

Measurement noise of electric machine, that is run, is shown in Fig. 5. As seen from the measured values, that the noise level is constantly fluctuating.

**Figure 5.** Noise of induction machines - no load

**Figure 6.** Noise of induction machine – 1 rotation
