The Micro-Vibration Equation of Rock and Its Analysis Basing on the Principle of Least Action

In order to study the effect of impact frequency of percussion drilling tools,natural frequency of rock and other factors on rock breaking effect in percussion drilling,the research on vibration mechanism of rock under harmonic excitation was carried out.In this paper,the micro-vibration equation of rock under the impact of indenter is established based on the principle of least action.Then the effect of mass and natural frequency of rock,impact force,impact time and impact frequency of indenter on vibration displacement were analyzed.The vibration displacement of rock fluctuates up and down at the equilibrium position.When the impact force of indenter is 30 kN or the density of rock is 2.39 g/cm3,the vibration displacement of rock will be the largest,1.3 mm and 2.8 mm respectively.Rocks with natural frequency of 1 000 Hz,1 500 Hz and 2 000 Hz generate maximum vibration displacement of 16 mm,13 mm and 6 mm at impact frequency of 1 000 Hz,1 500 Hz and 2 000 Hz respectively.The results show that the curve of vibration displacement of rock is a kind of cosine curve.The vibration displacement of rock is proportional to the impact force of indenter and is inversely proportional to the density(quality)of rock.When the impact frequency of indenter is equal to the natural frequency of rock,the maximum vibration displacement would be reached.