# Identification of Impact Frequency for Down-the-Hole Drills Using Motor Current Signature Analysis
## 3 Results
### Side bands Approach  
Figures 7 and 8 show the time and frequency domain representation of the motor current signals during the NP and SP stages, respectively. Figure 7a shows the expected sinusoidal signal with a nearly fixed amplitude of 3 A. The plotted motor current corresponds to the sum of the magnetizing current and mechanical friction associated with the rotating components of the drill rig, including gearbox and bottomhole assembly. The spectrum in Figure 7b shows that the motor current signal has a fundamental component around 47.9 Hz with an amplitude of 2.96 A. The fundamental frequency corresponds to the stator voltage frequency that feeds the induction motor from the VFD. Since the VFD implements its own control law, the voltage frequency reaching the motor differs slightly from the 50 Hz of the grid, considering the speed reference and the instantaneous motor  
Figure 5: Hammer pressure signal analysis during SP-stage: (**a**) P\({}_{h}\) signal; (**b**) zoom of P\({}_{h}\) signal; (**c**) frequency spectrum of P\({}_{h}\).  
Figure 6: Frequency spectrum of the sound signal during SP-stage.  
load. Figure 7c shows a zoomed-in view of the spectrum around the fundamental frequency, showing that during the NP-stage, there are no additional frequency components other than the fundamental associated with the power supply.  
The current signal in the temporal domain plotted in Figure 8a, shows that, once the drilling starts, the current presents a variable amplitude with peaks reaching around 4 A. The frequency spectrum in Figure 8b shows a fundamental component at 48.2 Hz, slightly higher than the frequency obtained previously during the NP-stage due to the increment of the load torque in the SP-stage that reduces the motor speed. As a result, the VFD control law increases the feed frequency to keep motion at the constant reference speed. The amplitude of the fundamental component is only 2.51 A, which suggests that amplitudes higher than 2.51 A observed in the temporal domain are associated with additional frequency components present during the stable percussion drilling operation. Effectively, the zoomed-in view in Figure 8c shows the presence of two groups of side bands around the fundamental frequency originating from different operational dynamics. According to the analysis to detect defects in the cage of induction motors presented in [37], the pair of side bands close to the fundamental frequency represents the \"_twice slip frequency side bands_\" whose values and related current amplitudes are defined by the drive train inertia and torque and speed oscillations. The same work states that the farther group of side bands can be associated with oscillations of mechanical loads, which, for our case study, are produced by the percussive action of the hammer. This group of symmetrically spaced side bands is located at 34.07 Hz and 62.27 Hz and is related to the cyclic variation around the mean average speed caused by the hammer operation. The average distance of these bands to the fundamental frequency is 14.10 Hz, corresponding to the impact frequency.  
Figure 7: Motor current signal analysis during stage-a: (**a**) zoom of I\({}_{m}\) signal; (**b**) frequency spectrum of I\({}_{m}\); (**c**) zoom of frequency spectrum of I\({}_{m}\).  
From a practical perspective, this method requires the user to know the rated range of variations of the impact frequency, which can usually be found in the technical specifications provided by the hammer's manufacturer. If the range of rated frequency is unknown, it may be difficult to discriminate the side bands related to the impact frequency from the other side bands expected to appear in the current frequency spectrum.