Optimization of the cutter size and tool orientation for reaching the critical state with multi-constraints in deep and narrow channel parts machining

Abstract

Increasing the cutter size to enhance its stiffness is of great significance for improving the machining efficiency and precision of deep and narrow channel parts. In this paper, the concept of cutter size critical sphere (CSCS) is presented, which is a specified sphere and tangent to several geometric constraints of tool accessible regions. With this concept, the complex multi-constraints of the workpiece can be transformed into several simple but precise geometric conditions to optimize the size and tool orientation of a conical cutter. The conical cutter generated by CSCS can reach a critical state with multi-constraints simultaneously. Firstly, the mathematical principle of the conical cutter generated by a cylindrical cutter is deduced based on the motion envelope theory. Secondly, the concept of CSCS is proposed based on the deduced mathematical principle and the calculation method of the CSCS with the general situation is provided. Thirdly, the CSCS with special situations is discussed and the calculation method is proposed. Fourthly, the mathematical model and solving algorithm for the max-size CSCS is given. The solving algorithm is designed based on the 3D Medial Axis Transformation (3D MAT) theory. Finally, the proposed method is verified by three simulation experiments and a comparison experiment. The results show that the proposed method can efficiently and accurately calculate the max size and tool orientation of the conical cutter simultaneously. The optimized conical cutter can be tangent to the multi-constraints of the workpiece but do no interfer with them.