Geometry of chip formation in circular end milling
Geometry of chip formation in circular end milling
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DOI：
10.1007/s00170-011-3478-0
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发表时间：
2012-03
期刊：
影响因子：
--
通讯作者：
A. Banerjee;Hsi-Yung Feng;E. Bordatchev
中科院分区：
文献类型：
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作者：
A. Banerjee;Hsi-Yung Feng;E. Bordatchev
沿着连续的圆形刀具轨迹加工，避免了刀具停刀和进给量的变化。这有助于减少机床机械结构和切削过程动力学的影响，特别是在高速铣削。随着这种加工概念的日益普及，对圆立铣削中有效切屑形成的详细研究对于切削过程的精确运动学和动力学建模是必要的。本文研究了圆端铣削过程中切屑的形成，重点研究了每齿进给量和未变形切屑厚度，并给出了它们的解析推导和数值解。首先，介绍了沿直线和圆刀路轨迹的端铣每齿进给量配方的差异。在此基础上，推导了考虑宽刀路半径范围内的齿形轨迹的圆端铣刀屑未变形厚度的有效公式。在推导过程中遇到的复杂超越方程，通过基于实例的方法得到封闭形式的解析解。通过对圆端铣刀齿轨迹的数值模拟，并与直线端铣刀齿轨迹进行比较，验证了未变形切屑厚度解析解的正确性。圆立铣削未变形切屑厚度的解析计算与数值计算非常相似，表明了所提解析公式的有效性。作为一个实例，基于推导的切屑厚度公式和现有的机械模型，计算了圆立铣削的切削力。计算结果重申，需要考虑调整的每齿进给量和有效的切屑厚度公式在圆立铣削，特别是对于小的刀具轨迹半径，更现实的过程建模。
Machining along continuous circular tool-path trajectories avoids tool stoppage and even feed rate variation. This helps particularly in high-speed milling by reducing the effect of the machine tool mechanical structure and cutting process dynamics. With the increase in popularity of this machining concept, the need for detailed study of a valid chip formation in circular end milling is becoming necessary for accurate kinematic and dynamic modeling of the cutting process. In this paper, chip formation during circular end milling is studied with a major focus on feed per tooth and undeformed chip thickness along with their analytical derivations and numerical solutions. At first, the difference in the feed per tooth formulation for end milling along linear and circular tool-path trajectories is presented. In the next step, valid formulation of the undeformed chip thickness in circular end milling is derived by considering an epitrochoidal tooth trajectory with a wide range of the tool-path radius. The complex transcendental equations encountered in the derivation are dealt with, by a case-based approach to obtain closed-form analytical solutions. The analytical solutions of undeformed chip thickness are validated with results of numerical simulations of tool and tooth trajectories for circular end milling and also compared to the linear end milling. The close resemblance between analytical and numerical calculations of the undeformed chip thickness in circular end milling suggests validity of the proposed analytical formulations. As a case study, the cutting forces in circular end milling are calculated based on the derived chip thickness formulations and an existing mechanistic model. The calculation results reiterate the need of taking into account adjusted feed per tooth and valid chip thickness formulations in circular end milling, especially for small tool-path radii, for more realistic process modeling.