数控加工中路径规划与速度插补综述

数控技术在现代制造工业中被广泛使用，相关研究一直为学界和业界共同关注。数控技术的传 统流程主要包含刀具路径规划和进给速度插补。为实现高速高精加工，人们通常将路径规划与速度插补中的若 干问题转换成数理优化模型，针对工程应用问题的复杂性，采用分步迭代优化的思路进行求解，但所得的结果 往往只是局部最优解。其次，路径规划与速度插补都是为了加工一个工件曲面，分两步进行处理虽然简化了计 算，但也导致不能进行整体优化。因此，为了更好地开展路径规划与速度插补一体化设计与全局最优求解的研 究，系统性地了解并学习已有的代表性工作是十分有必要的。所以将逐次介绍数控加工中刀具路径规划与速度 插补的相关方法与技术进展，包括基于端铣的加工路径规划；刀轴方向优化；G 代码加工以及拐角过渡；参数 曲线路径的进给速度规划等国内外相关研究以及最新提出的一些新型加工优化方法。

A survey of path planning and feedrate interpolation in computer numerical control

Numerical control technology is widely employed in the modern manufacturing industry, and related research has been emphasized by academia and industry. The traditional process of numerical control technology is mainly composed of tool path planning and feedrate interpolation. To attain the machining of high speed and precision, several problems in tool path planning and feedrate interpolation are usually transformed into mathematical optimization models. In view of the complexity of engineering application problems, stepwise iterative optimization method is used to address the problems, but the results are usually only locally optimal. Secondly, both tool path planning and feedrate interpolation are designed to process a workpiece surface. Although the calculation is simplified into two steps, the overall optimization cannot be achieved. Therefore, in order to better undertake the research on the integrated design and optimization idea of tool path planning and feedrate interpolation, it is necessary to systematically review and drawn on the existing representative works. We will introduce the relevant methods and technical progress of tool path planning and feedrate interpolation in CNC machining successively, including tool path planning based on end milling, tool orientation optimization, G-code processing and corner transition, feedrate planning of parameter curves, and some new machining optimization methods proposed recently. Among them, the tool path planning methods can be briefly classified into four categories: iso-parametric methods, iso-planar methods, iso-scallop height methods and the newly proposed methods based on vector field. The tool orientation optimization methods can be divided into local optimization methods considering error constraints and global optimization methods based on C-space. And the recent related work of G-code processing and corner transition mainly includes: micro line segments corner transition methods, spline based global fitting methods and finite impulse response-based methods. For parameter curves, the corresponding feedrate planning methods mainly include acceleration/deceleration-based methods, optimization-based approaches and the methods of integrating smoothness and feedrate. After that, we will introduce some emerging methods and techniques like surface segmentation for subtractive/additive manufacturing and the integrated interpolation methods for tool paths.