Purpose There are still a number of challenges to be addressed for the harmonic vibro-impacting drilling technology to become the norm in the industry. The change mechanism of energy response of rock under harmonic vibro-impacting is one of the problems that needs to be solved, which is also an indispensable part of the rock-breaking mechanism of the technology. Thus, this study focuses on the modelling of energy response of rock under harmonic vibro-impacting. Methods Modelling of energy response of rock with and without damping under harmonic vibro-impacting is undertaken and the corresponding equations of energy dissipation are presented in this study. Subsequently, the results of numerical calculation are given and the effects of natural frequency of rock, impacting frequency, impacting force and other parameters of energy response of rock are analyzed. Finally, a practical case is given to demonstrate the rock-breaking effect under harmonic vibro-impacting drilling.
ResultsThe results show that energy response of rock with damping decays regularly over time in the harmonic form under harmonic vibro-impacting. Also, it increases with the increase of natural frequency and mass of rock, impacting frequency and force, and is not affected by the stiffness of the rock. In addition, the penetration rate in practice has been greatly improved under harmonic vibro-impacting. Conclusions Based on the analysis undertaken, the variation mechanism of energy response of rock under harmonic vibroimpacting was found and the rock-breaking effect of the technology was verified. The study on the modelling of energy response of rock under harmonic vibro-impacting can provide a theoretical basis for applying harmonic vibro-impacting drilling technology.
List of SymbolsL Lagrange function q Generalized coordinates, ṁ q Generalized velocity (m/s) p Generalized momentum (kg m/s) t Time (s) H Hamiltonian function Ideal natural frequency of rock (rad/s) 1 Actual natural frequency of rock (rad/s) i Impacting frequency (rad/s) T Kinetic energy (J) U 1 Potential energy (J) U 2 External potential energy (J) x Vibration displacement of rock (m) x Vibration velocity of rock (m/s) x Vibration acceleration of rock (m/s 2 ) k Stiffness of rock (N/m) m Mass of rock (kg) c Damping coefficient of rock (N s/m) f Amplitude of impacting force (N) F Impacting force (N)Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.