# Evaluation of the Acceleration Vibration Signal for Aggregates of the Horizontal Drilling Stand
## 4 Experimental Results and Analysis
### Vibration Signal Processing in the Frequency Domain  
The processing of vibration acceleration signals from individual aggregates in the frequency domain requires the construction of amplitude and power spectra. It is possible to differentiate dominant frequencies, frequency clusters, and frequency bands from the spectra. An algorithm of FFT constructed the resulting operating mode frequency spectra. The algorithm of FFT was used for a vibration signal with a sampling frequency of \(f_{s}=18\) kHz, a sampling period of \(T_{s}=55.5\) us, and a segment length of \(N=2048\) samples. Frequency spacing must be considered when analyzing and constructing signal spectra. The frequency spacing between the spectral lines indicates the density of the spectral lines. Denser spectral lines increase the frequency resolution of the constructed spectra. The frequency spacing in the spectra was determined by the following equation:  
\[\Delta f=\frac{f_{s}}{N}=\frac{18000\;\mathrm{Hz}}{2048}=8.7\;\mathrm{Hz}. \tag{8}\]  
Significant dominant frequencies and frequency bands are recognizable from the amplitude spectra of individual operating modes. Dominant frequencies have a significant amplitude. The following figures (see Figures 9 and 10) present the resulting amplitude spectra for the operating modes I.-IX. when the individual units are running idle and with a load. A more detailed display of the constructed spectra (i.e., zoom factor) is chosen for easier and clearer identification and differentiation of dominant frequencies and frequency bands. From the amplitude-frequency spectrum for mode I. if only the motor unit were in operation, it is clear that the dominant frequency components are in the frequency band 0-4000 Hz. Several clusters have significant frequency components in this frequency band (see Figure 9a). Table 2 lists the significant frequency components. In the frequency spectrum of the motor, it was possible to determine approximately ten dominant frequencies that are characteristic of this aggregate. The spectrum can be said to be broad-spectrum because it contains the basic low frequencies \(f_{1}=52.7\) Hz, \(f_{2}=149\) Hz, \(f_{3}=386\) Hz, and \(f_{4}=483\) Hz. In the mid-frequency band from 1 kHz, there are several significant frequencies \(f_{6}=1274\) Hz and \(f_{7}=1336\) Hz with high amplitude. The spectrum also contains a high frequency \(f_{10}=4000\) Hz. From amplitude-frequency spectra for operating mode II., i.e., only the pump is running, and mode III. when in operation is the hydro-generator unit, it is clear that significant frequency components are located in the low-frequency band 0-1000 Hz with one frequency above 1 kHz at the hydro-generator \(f_{8}=1318\) Hz. Operating mode spectrum II. has five dominant frequencies that are characteristic of the aggregate. The fundamental frequencies are \(f_{1}=52.7\) Hz, \(f_{2}=149\) Hz, and \(f_{3}=246.1\) Hz, the other frequencies are non-integer multiples of the fundamental revolutions frequencies (see Figure 9b). Operating mode spectrum III. has 5 to 7 dominant frequencies in detailed view. It contains the fundamental frequencies and the essential frequencies \(f_{7}=878.9\) Hz and \(f_{8}=1318\) Hz. They represent the significant frequencies that differentiate the pump spectrum from the hydro-generator spectrum. These frequencies are only characteristic of the hydro-generator unit (see Figure 9c). In operational modes IV. and V., the spectra of 8 to 13 dominant frequencies in a detailed view (see Figure 10d,e) can be observed. Motor vibrations strongly influence the spectra. The frequency band is in the range of 0-4000 Hz. The basic common frequencies are the low frequencies \(f_{1}=52.7\) Hz, \(f_{2}=149\) Hz, \(f_{3}=439\) Hz, and higher 1723 and 4000 Hz. The middle frequency band of both modes is in the range of 1000-3000 Hz. Also in this band are frequencies with high amplitudes of 1230, 1248, 1362, 1485, and 1529 Hz.