The Micro Vibration Equation of Rock and Its Analysis in Flat Indenter Basing on the Principle of Least Action

Advances in Petroleum Exploration and Development Pub Date : 2018-09-26 DOI:10.3968/10681

Guodong Ji, Haige Wang, L. Liu, Siqi Li, L. Sun, Zihe Chen

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Abstract

Impact frequency of drill tools, vibration displacement of rock and other factors play a key role on the impact efficiency of vibration and rock breaking effect in the percussion drilling. In this paper, the micro vibration equation of rock in the impact of indenter was established based on the principle of least action. Then the relationship among vibration displacement of rock and quality and natural frequency of rock, impact force and impact frequency of indenter and time were analyzed. The results show that the curve of vibration displacement is kind of shape of cosine function, its size fluctuates up and down in the equilibrium position with the changes in various factors; The greater the impact of flat indenter is, The smaller the quality of rock is, the greater the vibration displacement of rock is; The closer the impact frequency of indenter and natural frequency of rock are, the greater the vibration amplitude of rock is, and it is significantly higher than the situation which the difference of impact frequency of indenter and natural frequency of rock is large.

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基于最小作用原理的扁压头岩石微振动方程及其分析

在冲击钻井中，钻具的冲击频率、岩石的振动位移等因素对振动的冲击效率和破岩效果起关键作用。基于最小作用量原理，建立了岩石在压头冲击下的微振动方程。分析了岩石振动位移与岩石质量、岩石固有频率、压头冲击力和冲击频率与时间的关系。结果表明:振动位移曲线呈余弦函数形状，其大小随各因素的变化在平衡位置上下波动;扁压头的冲击越大，岩石的质量越小，岩石的振动位移越大;压头冲击频率与岩石固有频率越接近，岩石振动幅值越大，明显高于压头冲击频率与岩石固有频率差异较大的情况。

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Advances in Petroleum Exploration and Development

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