# Locating Sources of Vibration with Harmonics and Pulse Signals in Industrial Machines

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## Abstract

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## 1. Introduction

- operation parameters diagnostics (such as flow rate, energy consumption, efficiency, pressure, etc.) [1];
- overall vibration level control [2];
- spectral diagnostics (analysis of vibration signal) [3];
- infrared thermography [10];
- ultrasound propagation analysis [11];
- acoustic noise signal analysis [12];
- wavelet analysis [13];
- 3D vibration spectra analysis [14];
- location of oscillation defects by remote strain gauge analysis [17];
- and some others.

## 2. Concept of the Method of Locating Defects with Periodical and Non-Periodical Parameters Using Strain Gauge Signal Analysis at Specified Points

- defects with harmonic parameters;
- defects with non-harmonic periodical parameters (pulse periodic signal);
- defects with non-periodical parameters (pulse non-periodical signal).

## 3. Locating Defects with Harmonic Parameters Using Strain Gauge Signal Analysis at Specified Points

_{A}is the oscillation phase of the reaction of the support A; φ

_{B}is the phase of the oscillations of the support reaction B; φ

_{F}—phase of oscillation of the sum of reactions in the supports A and B; R

_{A}—the response amplitude in the support A; R

_{B}—the reaction amplitude in the support B; x and z—horizontal coordinate; y—vertical coordinate.

## 4. Locating Defects with Non-Harmonic Periodical Parameters Using Strain Gauge Signal Analysis at Specified Points

_{2}(t) lags behind the signal from sensor 1 f

_{1}(t) by the value Δt. Given that the amplitude of the signal between them may differ by k times, then using the discrete Fourier transform, the following dependencies can be written for them:

_{i}and β

_{i}are the harmonic phases for the i-th component in the Fourier decomposition; Ai is the harmonic amplitude for the i-th component in the Fourier decomposition; v

_{1}is the pulse frequency; t is the time; n is the number of harmonics in the Fourier decomposition.

_{i}expressed as Δφ

_{i}= β

_{i}− a

_{i}equals to:

_{i}, as a function of the frequency i·v

_{1}, is either a straight line passing through the origin, or a set of straight lines, as shown earlier (Figure 5).

_{i}are the values of the phase difference on the spectra of the two signals (Figure 5) after measurements and transformations.

_{1}frequency, for example, the eccentricity of the rotor, so it is recommended to exclude this frequency from the analysis, so we build a line from a point at the frequency 2·v

_{1}:

## 5. Locating Defects with Non-Periodical Parameters Using Strain Gauge Signal Analysis at Specified Points

_{a}, t

_{b}, t

_{c}, t

_{d}are pulse propagation times to each of the sensors, t

_{0}is pulse movement start time; L

_{x}, L

_{y}and L

_{z}are equipment dimensions; v is speed of wave propagation in material of equipment; x, y, z are the excitation source coordinates that should be obtained.

_{critical}is a critical value of the signal value derivative, R

_{average}is an average value of this variable, σ is its standard deviation. From the theory of probability, it follows that if k = 2, the noise is filtered with 95% probability.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Electric scheme of experimental tools measuring dynamic reaction in supports of equipment.

**Figure 13.**Increase in the signal value derivative for each of four strain gauge sensors (detailed graph).

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**MDPI and ACS Style**

Valeev, A.; Kharrasov, B. Locating Sources of Vibration with Harmonics and Pulse Signals in Industrial Machines. *Acoustics* **2022**, *4*, 574-587.
https://doi.org/10.3390/acoustics4030036

**AMA Style**

Valeev A, Kharrasov B. Locating Sources of Vibration with Harmonics and Pulse Signals in Industrial Machines. *Acoustics*. 2022; 4(3):574-587.
https://doi.org/10.3390/acoustics4030036

**Chicago/Turabian Style**

Valeev, Anvar, and Bulat Kharrasov. 2022. "Locating Sources of Vibration with Harmonics and Pulse Signals in Industrial Machines" *Acoustics* 4, no. 3: 574-587.
https://doi.org/10.3390/acoustics4030036