基于随机过程理论短螺旋钻头载荷的数学模型

罗春雷，丁吉，宋长春，范增辉

(中南大学 机电工程学院，湖南 长沙，410083)

摘 要：为了揭示短螺旋钻头载荷随切削厚度和岩石接触强度变化规律，根据岩石的物理力学特性，结合单个镐型截齿切削破岩的工作机理和短螺旋钻头的结构特征，分析短螺旋钻头入岩工况下的受载情况；运用随机过程理论，建立短螺旋钻头随机载荷的数学模型。针对不同的岩石接触强度和钻头切削深度，借助MATLAB仿真求解钻头的扭矩和轴向力，采用数学统计方法对实测结果进行处理分析，并与理论值相比较。研究结果表明：理论求解的钻头扭矩和轴向力的幅值与均值和实际测试值都比较接近，且两者的变化规律一致；在切削厚度一定时，扭矩和轴向力的幅值和均值随着岩石接触强度的增大而迅速增大；在岩石接触强度一定时，扭矩和轴向力的幅值和均值也会随着切削厚度的增大而迅速增大。

关键词：短螺旋钻头；入岩；随机载荷；数学模型

Mathematical model of loads for short helix bit based on random process theory

LUO Chun-lei, DING Ji, SONG Chang-chun, FAN Zeng-hui

(School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China)

Abstract:With regard to the physical and mechanical characteristics of rock, the working principle of single conical bit cutting and the structural characteristics of short helix bit, the load situation of short helix bit in the rock was analyzed to reveal the changing rules of random loads of the short helix bit. Accurate mathematical model of random loading was built according to the random process theory. Based on different contact strengths of rock and cut depths of short helix bit, the MATLAB program was written to get the torque and axial force of short helix bit. The results of the test under the same condition were processed by means of mathematic statistics and were analysized in comparision to those of the theoretical calculation. The results show that the amplitude and average value of torque and axial force from theoretical calculation are quite close to those gotten by practical test，and both the change rules are consistent. When cut depth is kept to some extent, amplitude and average value of torque and axial force increase greatly with the increase of rock contact strength. When contact strength of rock is kept to some extent, amplitude and average value of torque and axial force increase greatly with the increase of the cut depth.

Key words:short helix bit; rock cutting; random loading; mathematical model