# Evaluation of the Acceleration Vibration Signal for Aggregates of the Horizontal Drilling Stand
## 4 Experimental Results and Analysis
### Vibration Signal Processing in the Time Domain  
The basic processing of vibration signals of acceleration in the time domain from the drilling stand aggregates was the display of time waveforms, auto-correlation functions, and the calculation of essential statistical characteristics. In the time domain, the amplitudes \(x(t)\), peak \(x_{p}(t)\), peak to peak \(x_{pp}(t)\), average \(x_{avg}(t)\), and RMS of the vibration signal from individual modes were observed. For idle modes I. to VIII. the stand revolutions were set at 1000 (rpm) or 16.67 (rps) without pressure force, as there was no direct disintegration of the rock, for mode IX, the revolutions were set to 1000 (rpm), and the pressure F = 8000 N.  
The measurement of one experimental mode took \(t\) = 6 s at a sampling frequency of \(f_{s}\) = 18,000 Hz and a sampling period of \(T_{s}\) = 55.5 \(\upmu\)s. All regime measurements were performed by an analogous principle. A segment with the number of samples \(N\) = 2048 was processed from the entire measured signal. Figures 5-7 show the time waveforms and associated auto-correlation functions of the vibration acceleration signals for the set operating modes of the drilling rig. The acceleration signals' time waveforms and auto-correlation functions at the number of samples \(N\) = 2048 are more readable. A more detailed display is chosen for a more straightforward idea of the time waveform of the measured signal. It is possible to deduce the essential statistical characteristics from the time waveforms directly. Figure 5 shows the time waveforms of the separately measured signals of the motor, pump, and hydro-generator units, representing the operating modes I-III. If modes I-III. are compared, then the highest values of significant statistical characteristics are at the vibration signal from the motor, i.e., \(x_{p}(t)\) = 12.753, \(x_{pp}(t)\) = 25.836, and RMS = 3.831 (see Table 1). It is clear that the motor aggregate is the main vibration generator (see Figure 5a). The pump achieves the lowest statistical value. It is clear from the time waveforms that the pump and hydro-generator units have non-harmonic composite periodic signals with a weak stochastic component (see Figure 5c,e). The time waveform of the auto-correlation function also indicates this. In contrast, the waveform of a motor unit is strongly stochastic, but it is assumed to include periodic components even if the random component overlaps a composite signal containing essential diagnostic information. The auto-correlation function of the motor decreases rapidly with increasing \(\tau\), meaning that the signal values have less statistical dependence (see Figure 5b) and assume a broad frequency spectrum. In contrast, the auto-correlation functions of the pump (see Figure 5d) and the hydro-generator (see Figure 5f) have a gradual descent of the samples, representing a greater statistical dependence and a narrow frequency spectrum. Figure 5: Time waveforms of the separately measured signals of the motor, pump, and hydro-generator units (**(a)** the time waveform of the vibration signal of the motor, **(b)** the auto-correlation function of the motor, **(c)** the time waveform of the vibration signal of the pump, **(d)** the auto-correlation function of the pump, **(e)** the time waveform of the vibration signal of the hydro-generator, **(f)** the autocorrelation function of the hydro-generator). Figure 6 shows the time waveforms of the measured signals during the operation of the pair of aggregates in the operating modes IV.-VI. The combinations are motor and pump, motor and hydro-generator, pump and hydro-generator. If the modes IV.-VI. are compared with each other, then the highest values of statistical characteristics are again at the vibration signals where the motor, i.e., motor and pump, motor and hydro-generator, modes IV. enter into the measurement, modes IV. and V. (see Table 1). The position of the motor unit as the primary source of vibration is confirmed.