# Identification of Impact Frequency for Down-the-Hole Drills Using Motor Current Signature Analysis
## 1 Introduction  
Rotary-percussion drilling has been recognized as an efficient drilling method due to its capability to provide a higher rate of penetration (RoP) compared with the conventional rotary drill, especially for high compression strength rock formations composed of dolomite, limestone, sandstone, granite, etc. [1]. Among percussion drilling methods, Down-the-Hole (DTH) drilling is widely used in industrial applications such as mining, blast hole, tunneling, construction, geological exploration, and oil and gas production, among others [2; 3; 4]. Besides high RoP, DTH drilling provides operational and economic advantages, such as low power losses, accurate hole geometry, and reduced drill string stress [5]. One of the most important variables studied in percussion drilling, particularly in DTH drilling, is the impact frequency [6; 7; 8], defined as the number of impacts of the hammer bit over the drilling surface per unit of time. Numerical simulations reported in [9] suggest that a significant increase of RoP can be achieved by increasing the percussive frequency of pneumatic hammers. In [10], authors show simulations to confirm that increasing the impact frequency produces a significant improvement in the RoP but also highlight that high frequencies can also be detrimental to the service life of torsional impact drilling equipment. The impact frequency can also be ranked to establish performance thresholds depending on the characteristics of the equipment and drilling surface. The work in [11] shows that when impact frequency is lower than the threshold frequency, thedetritus removal volume is reduced in the rock breaking process considering polycrystalline diamond drill bits. The adequate operation ranges for the impact frequency vary depending on the mechanic properties of the drilling surface, drilling angle, and hammer type [12; 13; 14; 15]. According to [16], DTH hammers usually operate with impact frequencies ranging from 10 to 28 Hz, generating high-frequency torsional impacts, which produce highly dynamic variations in the magnitude of bit torque. The work in [17] shows that as the hammer vertical deviation angle increases from 0\({}^{\circ}\) (vertical) to 90\({}^{\circ}\) (horizontal), the impact frequency of the pneumatic hammer decreases from 10.8 to 10 Hz, resulting in a reduction of the effective energy per blow of 22.5%. In [18], the authors report that the recommended impact frequency value will depend on different drilling conditions; thus, when considering a back rake angle of 55\({}^{\circ}\), the best penetration performance is achieved for an impact frequency of 30 Hz, while under a crushing efficiency criterion, the recommendation is 50 Hz. Higher impact frequencies can be found in other types of drilling technologies. For instance, in [19], a sonic drill results in an impact frequency of 70 Hz while the hydraulic rock drill dritter analyzed in [20] can reach an impact frequency close to 75 Hz. It is clear that regardless of the type of percussive drilling machine and bit technology, the impact frequency is a crucial variable to be monitored and analyzed for increasing drilling efficiency, stability, and tool life. Typical frequency identification methods rely on complex simulation models or signal analysis using measurements from different sensors (e.g., pressure, sound, strain) installed in specially adapted setups that are difficult to implement in field applications. For instance, the authors in [21] use the acoustic signal recorded by a microphone placed near the impacting system to obtain the experimental data of the impact frequency. In [17], the impact frequency is obtained by the statistical analysis of several waveforms monitored by the data acquisition system, including pressure transducers, photoelectric whirl measuring apparatus, laser rangefinder, and a sensor placed at the end of the rock sample that is capable of monitoring the force acting on the rock during impact.