中文摘要：

三维曲面加工制造是通过刀具刃口的运动扫掠面逼近设计曲面来实现的。针对单行侧铣加工,定义用于评价设计曲面与加工曲面之间偏差的点—刀具包络面有向距离函数。基于刀具包络面的双参数球族包络表示,提出无须构造包络面而直接计算该有向距离的方法,并推导出其关于刀轴轨迹面形状控制参数的一阶梯度表达式,以定量刻画刀具路径的改变对加工曲面法向误差的影响。在此基础上构造基于导数信息的刀具包络面向设计曲面的离散点云的最佳一致逼近算法,并应用序列线性规划算法来求解该约束优化问题,实现圆锥刀五轴侧铣加工刀具路径的整体优化,应用于叶轮叶片加工的实例表明该方法能够显著提高加工精度。有关理论和方法同样也适用于一般回转刀具的侧铣加工规划。

英文摘要：

Optimum positioning of the conical tool for five-axis flank milling of non-developable ruled surface is modeled as approximation of the tool envelope surface to the data points on the design surface following the minimum zone criterion recommended by ANSI and ISO standards for tolerance evaluation.Based on the observation that conical surface can be treated as a canal surface,i.e.the envelope surface of a one-parameter family of spheres,the swept envelope of a conical tool is represented as a sphere-swept surface.Then,an approach is presented to efficiently compute the signed distance between the swept surface and a point in space without constructing the swept surface itself,and the first order differential increment of the signed point-to-surface distance with respect to the differential deformation of the tool axis trajectory surface is also derived.By using the distance function,tool path optimizations for semi-finish and finish millings are formulated as two constrained optimization problems in a unified framework,and a sequential approximation algorithm along with a hierarchical algorithmic structure is developed to solve them.Numerical example is given to confirm the validity of the proposed approach.