矩阵算子法构建切削滑移线场的分析

Analysis of Cutting Slip-line Field Constructed by Using Matrix-operator Method

刀具与切屑接触的摩擦因数呈不均匀分布增加了正交切削分析的难度,缺少一个完善的解析模型。针对于此,本文采用矩阵算子法构建了一种考虑在刀-屑接触面上变摩擦因数的滑移线场。通过Oxley的剪切切削理论找出工件表面材料塑性剪切变形的位置,为滑移线场的添加几何约束条件,从而求解滑移线参数。根据滑移线场,导出刀-屑接触长度,推算出切削力的解析式。模型计算结果与GH4169切削有限元仿真结果对比发现:刀-屑接触长度误差在9.8%内,两者的切削力在变化趋势上一致且数值上相近,验证了滑移线场的准确性。上述研究成果为变摩擦因数的正交切削分析刀-屑接触长度和切削力提供了理论方法。

The friction coefficient between the tool and the chip is unevenly distributed which increases the difficulty of orthogonal cutting analysis and lacks an analytical model.A slip-line field with variable friction coefficient on the tool-chip contact surface is constructed with matrix operator method.Geometric constraints,which obtain from the position of plastic shear deformation of workpiece surface found in terms of the Oxley's shear cutting theory,are added to the slip-line field to determine the parameters in the slip-line field.According to the above model,the tool-chip contact length is derived and the analytical formula of the cutting force is deduced.By comparing with the model and the finite element results in the cutting of GH4169,it is found that the error of tool-chip contact length is within 9.8%,the change in cutting force is slight,which verifies the accuracy of the model via slip line field method.The above results provide a theoretical method for orthogonal cutting with variable friction coefficient analysis of tool chip contact length and cutting force.