Arithmetic solution for the axial vibration of drill string coupling with a down-the-hole hammer in rock drilling

Down-the-hole hammer (DTH) drilling is an air hammer drilling technique designed for drilling through bedrock and features a typical drill string length of 200 m or shorter due to its technical specifications. During DTH drilling of granitelike hard rocks, the impacts of the piston-bit-rock system cause the drill string to generate severe vibration and noise pollution. In addition, the rapid wear of the button bit and drill string significantly decreases the drilling efficiency. Based on a distributed parameter drill string model of a DTH, this paper studies the phenomenon of the drill string's axial forced vibration with a periodic impacting force under DTH drilling in an innovative manner. With the focus of study on the DTH button bit, the transient impact force on the button bit during the drilling of the piston-bit-rock system is determined, and the impact force is converted to a periodic excitation force function using polynomial fitting. Then, the periodic impulse is transformed into a harmonic series using Fourier transforms, and finally, the drill string vibration response under the harmonic excitation force series is determined. The results reveal that a periodic impulse can mainly be determined by the nature of the DTH drill string and rock and the impact frequency during drilling. Further evidence demonstrates that at least one frequency component of the impulse harmonic series will be equal to the modal frequencies of the drill string insofar as the condition 2nf(0)l = i root E/rho is met; the coupling of the short drill string with the DTH may cause resonance at a specific hole depth, whose resonance regions are adjacent to but not continuous with the extension of the drill string. This work should serve as an important theoretical guide for designers in the dynamic design, modification, and use of a DTH drilling system.