基于Z-MAP方法的球头铣刀铣削力的建模

瞬时刚性切削力的建模是铣削加工物理仿真的基础，然而，球头铣刀的刀齿形状复杂，加工过程中姿态多变，瞬时刚性铣削力的建模难度较大。在考虑刀具姿态调整的情况下，通过齐次坐标变换建立了刀齿的运动轨迹，提出了一种识别刀具和工件瞬时接触区的改进Z-MAP算法，通过计算当前刀齿的参考线与工件的边界面或刀齿扫掠面的交点求出瞬时未变形切屑厚度，并采用非线性回归的方法辨识了切削力系数，在此基础上使用微元积分法建立了瞬时切削力的计算模型。为了验证仿真模型的可靠性，分别进行了垂直加工和倾斜加工试验，试验和仿真结果具有较高的一致性，表明该建模仿真方法是有效的，可以为实际加工中参数的选择和优化提供理论依据。

Modeling on the Milling Force of Ball-end Milling Cutter Based on Z-MAP Method

The modeling of instantaneous rigid cutting force is the basis of physical simulation of milling. However, it is difficult to model due to the complex shape of the cutter teeth of ball-end milling cutter and the changeable posture during machining. Under the condition of considering the cutter posture adjustment, trajectory of cutter teeth is established based on the homogeneous coordinate transformation, an improved Z-MAP algorithm of recognition of instantaneous cutter and workpiece engagement area is proposed. By calculating the intersection point between the reference line of the cutter tooth and the boundary of the workpiece surface, or the one between the reference line and cutter teeth's sweeping surface, the instantaneous undeformed chip thickness is derived. And the cutting force coefficients are identified by non-linear regression method. On these bases, the calculation of the instantaneous cutting force model is established by using the infinitesimal integral method. In order to validate the reliability of the simulation model, vertical machining and inclined machining tests are carried out respectively. The results of experimental and simulated results are highly consistent, it is therefore indicated that the modeling simulation method is effective and could provide theoretical basis for the selection and optimization of parameters in actual machining.