Optimization of tool positions locally based on the BCELTP for 5-axis machining of free-form surfaces

The Basic Curvature Equations of Locally Tool Positioning (BCELTP) are an accurate description of the relationships between the second order approximations of the cutter surface, the tool envelope surface and the designed surface, which was proposed in our previous paper [Gong Hu, Cao Li-Xin, Liu Jian. Second order approximation of tool envelope surface for 5-axis machining with single point contact. Computer-Aided Design 2008;40:604–15]. Based on them, for a given tool path with single cutter contact point, a new local optimization method of tool positions is presented to maximize the machining strip width by minimizing the relative normal curvature between the tool envelope surface and the designed surface. Since the BCELTP are accurate analytical expressions, the proposed optimization method of tool positions is accurate and effective in computation. Furthermore, another new optimization method of tool positions based on a dual-parameter envelope is subsequently proposed. The most interesting point is that it will result in the same results as the method based on the BCELTP. It also proves the correctness of the method based on the BCELTP from a different angle. Finally, several examples are given to prove its effectiveness and accuracy.