基于最小作用量原理的岩石微振动方程及分析

摘要

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 .T hen the effect of mass and natu-ral 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 frequen-cy of 1 000 Hz ,1 500 Hz and 2 000 Hz respectively .T he results show that the curve of vibration displace-ment 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 in-denter is equal to the natural frequency of rock ,the maximum vibration displacement would be reached .%为了研究冲击钻井中钻具冲击频率、岩石固有频率等对破岩效率的影响，基于最小作用量原理，建立了岩石在压头冲击作用下的微振动方程，并以此为基础，分析了岩石的质量和固有频率、压头的冲击力和冲击频率以及时间等因素与岩石振动位移的关系。分析研究发现，岩石振动位移在平衡位置处上下变化，当压头冲击力为30 kN、岩石密度为2.39 g／cm3时，岩石的振动位移最大，分别为1.3和8 mm ；固有频率为1000，1500和2000 Hz的岩石，分别在1000，1500和2000 Hz左右冲击频率下产生16，13和6 mm的最大振动位移。研究结果表明：岩石的振动位移曲线类似余弦曲线，振动位移与压头的冲击力成正比，与岩石的密度（质量）成反比；当压头的冲击频率与岩石的固有频率共振时，振动位移最大。