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基于极限分析上限定理的凿型截齿水平切割力预测方法研究

Research on prediction method of horizontal cutting force of chisel pick based on upper bound theorem of limit analysis

  • 摘要: 轮斗挖掘机是露天煤矿连续开采工艺系统的关键装备,截齿设计及切割力预测是轮斗挖掘机研制关键技术难题。为了指导轮斗挖掘机的机械设计,优化铲斗截齿设计,更准确的预测开采过程中截齿所受切割阻力,基于极限分析理论提出了预测凿型截齿水平切割力的上限法。基于库伦屈服准则相关联流动法则,建立以对数螺旋线为破坏面的旋转运动机构;通过输入荷载功率与破坏区的能量耗散率相等,推导凿型截齿的水平切割力表达式;通过数值求导获得水平切割力系数图,显示了切割前角和岩石内摩擦角对凿型截齿的水平切割力的影响,简化了凿型截齿水平切割力预测计算。不同于以切屑-截齿作用力学分析为基础的凿型截齿拉伸或剪切破坏模型,上限法优势是无需假设破坏面上应力分布。采用7组实验数据对上限法和其他传统方法预测结果进行对比验证,14个统计指标结果表明:上限法在预测精准度方面同半经验法和Evans法相近,优于Nishimatsu法,验证了上限法对凿型截齿切割岩石水平切割力的有效性和适用性。上限法预测效果可通过考虑三维破坏运动机构和采用拉伸截断的流动法则进行改进。

     

    Abstract: The wheel bucket excavator is the key mining equipment in the continuous process system of open-pit coal mines, pick design and cutting force prediction are key technical problems in the development of wheel bucket excavators. In order to guide the mechanical design of wheel excavators, optimize the design of bucket picks, and more accurately predict the cutting resistance of wheel excavators during mining, an upper limit method for the horizontal cutting force of chisel picks is proposed based on the limit analysis theory. The upper limit method is based on the flow law associated with the Coulomb yield criterion and establishes a rotary motion mechanism with a logarithmic spiral as the failure surface; by equating the input load power with the energy dissipation rate of the failure zone, the horizontal cutting force expression of the chisel pick is derived; The horizontal cutting force coefficient diagram is obtained through numerical derivation, which shows the influence of the cutting rake angle and the internal friction angle of the rock on the horizontal cutting force of the chisel pick, and simplifies the prediction calculation of the horizontal cutting force of the chisel pick. Different from the chisel pick tensile or shear failure model based on the mechanical analysis of chip-pick interaction, the advantage of the upper limit method is that there is no need to assume the stress distribution on the failure surface. Seven sets of experimental data are used to compare and verify the prediction results of the upper limit method and other traditional methods. The results of 14 statistical indicators show that the upper limit method is similar to the semi-empirical method and Evans method in terms of prediction accuracy, and is better than the Nishimatsu method. The effectiveness and applicability of the upper limit method to the horizontal cutting force of rock cutting with chisel picks is verified. The prediction performance of the upper limit method can be improved by considering the three-dimensional failure motion mechanism and using the flow law of stretch truncation.

     

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