基于Evans截割模型的镐型截齿峰值截割力的计算

为了能对镐型截齿在平面截割截槽对称条件下的峰值截割力进行较为准确的预测,基于Evans的截割模型,通过分析截割时齿头的锥形表面因岩石的夹制效应而接触应力分布有所不同,理论推导出了一个新的峰值截割力计算公式以及公式应满足的截割边界条件。相比现有其他截割力计算公式,除了考虑截齿半锥角θ、煤岩抗拉强度σt及齿岩之间摩擦因数f等参数的影响,且将煤岩的脆性指数m引入其中,计算结果与试验值更为接近。公式所应满足的截割边界条件,可用截深h和加载位置与相邻自由边界垂直距离s比值的最低限值smin/h表示,且值大小受截齿半锥角θ影响较小,而主要与煤岩脆性指数m有关,当m介于5~15时,smin/h介于2~3,符合既有试验所得结果。所得公式和结论可为进一步分析和推导镐型截齿在实际采掘条件下包含更多参数的峰值截割力提供理论基础和指导。

Calculation of peak cutting force of conical picks based on Evans’cutting model

In order to forecast peak cutting force of conical picks more accurately under conditions of plane cutting and symmetrical slotting，a new formula for calculating the peak cutting force and the formula which should satisfy the cutting boundary conditions are deduced theoretically.The derivation of the formulas were based on Evans’ cutting model and assumed the stress distribution of conical surface of pick tip are different due to the clip effects of rocks when cutter cutting.Compared to other existing theoretical formulas，the calculation results are closer with the experimental value.In addition to considering the influence of some factors on the cutting force，such as half-cone angle θ of picks，tensile strength σt of rocks and friction coefficient f between picks and rocks，the brittleness index m of coal and rock is introduced.The formula should satisfy the cutting boundary condition which is represented by minimum limit of the ratio between cutting depth h and the vertical distance s from the loading position to the adjacent free border.That is smin/h，which mainly related to brittleness index m and almost unaffected by half-cone angle θ of picks.When m is 5 to 15，smin/h is between 2 and 3 and consistent with the existing experiments results.The derived formulas and conclusions can provide theoretical basis and guidance for the further analyzing and deducing of real peak cutting force containing more parameters of conical picks under actual mining condition.