中文摘要：

研究五轴联动数控机床侧铣加工中铣刀的形状确定和运动路径的规划问题.利用旋转曲面铣刀和设计曲面呈相切关系的事实,将一个铣刀的刚体运动描述为一个带约束的优化问题并给出求解方法.该方法以用户交互给出的一个线段作为铣刀轴的初始位置,通过计算铣刀的最优刚体运动生成一个轴线段的运动序列,并再通过对旋转曲面的经线做最小二乘拟合得到一个旋转曲面铣刀.实验结果表明,文中方法得到的刀具的运动生成的加工曲面与设计曲面具有较小的逼近误差,从而提供了一种铣刀运动路径优化算法的初始化方法,对提高已有路径优化算法的效率和结果的质量有重要作用.

英文摘要：

We study cutter shape determination and tool path generation in 5-axis CNC flank milling. According to the fact that the cutting tool with a revolution surface is tangent to the target surface, we formulate the rigid motion of a cutter as a constrained optimization problem. We analyze this problem in details and give an algorithm to determine moving direction of cutting tool. The movement of the cutter gives a sequence of tool axes which forms a ruled surface. The least squares fitting to meridian curves of all revolution surfaces leads to a revolution surface which determines the shape of the cutting tool. By experiments, we show that the machined surface by the proposed method has small approximation error to the target surface.