Machining, Measurement, and Control Laboratory

Algorithm to Optimize Cutting Path for Minimizing Workpiece Displacement at Cutting Point
Yusuke Koike, Atsushi Matsubara, Shinji Nishiwaki, Kazuhiro Izui, Iwao Yamaji

Vibrations of a tool or a workpiece in cutting cause a relative displacement between the tool and the workpiece, which leads to a variation of a cutting force. The vibration deteriorates a surface roughness and shortens tool life. In this research, we propose a method to reduce vibrations of the workpiece at a cutting point. An algorithm that generates a cutting path to minimize workpiece displacements without reducing material removal rate is developed. The cutting path is generated by considering workpiece stiffness matrices, cutting force vectors and feed directions. In this algorithm, an anisotropy analysis of workpiece stiffness matrices is mainly conducted and the direction that maximizes the stiffness is calculated at every cutting point. A material is attached in a stepwise manner from the final shape to the initial shape. Therefore, the calculating process (material attaching process) is reverse to the cutting process (material removal process). Appropriate cutting conditions to cut the rigid workpiece and the cutting force vector are to be prepared before calculations. Suppose that an initial workpiece shape and a final workpiece shape are given, the stepwise flow to generate an optimized cutting path is as follows. First, candidate points to attach a next material are calculated from a current workpiece shape, and workpiece stiffness matrices at these points are calculated by using FEM (Finite Element Method). Second, the direction which has the highest stiffness in a workpiece at each cutting point is calculated by using SVD (Singular Value Decomposition). Third, feed directions are changed to align a cutting force vector to the highest stiffness direction while taking some restrictions into account. Restrictions are defined from a mechanical structure and an interference between a tool and a workpiece. Finally, workpiece displacements at candidate points to which a next material is attached are calculated from cutting force vectors and workpiece stiffness matrices, and the optimal point is selected from candidate points, which has the smallest workpiece displacement. Such calculating processes are repeated until a workpiece shape comes to the initial shape. As a result, the cutting path is generated as the reverse of a material attaching process, which minimizes a workpiece displacement at each cutting point. The algorithm is applied to the design of end milling and the designed process is compared with a cutting process with a conventional cutting path.
Keywords: Cutting Path, Workpiece Displacement, Compliance, FEM, SVD.