Axis path planning of five-axis surface machining by optimizing differential vector of the axis movement considering tool posture limits

Two rotating axes of the five-axis machine tools complicate the kinematics, which increases the difficulty of trajectory planning of five-axis CNC machining. In the process of machining a free-form surface with a ball-end cutter, the tool is required to follow the tool tip path of the surface and the restriction of tool orientation is only constrained within a certain range. This paper proposes a planning algorithm based on differential vector optimization for generating a smooth trajectory of each axis for five-axis machining. Firstly, the kinematic model of the five-axis CNC machine tool and the Jacobian matrix are built. Secondly, the optimization objectives combined with the smoothness optimization requirements and the limits of the tool axis vector are established. Then, the trajectory of the moving axis is generated by integrating the optimized differential vector. At last, a waveform surface machining process is simulated in the VERICUT software with the trajectory generated by the proposed optimization method. To prove the feasibility and superiority of the method, the real part machining experiment is conducted in an A-C type five-axis CNC machine. The experiments verify the smoothness and optimal of the proposed path planning method.