基于等距法的数控加工刀具轨迹规划
摘要： 本文基于等距思想提出针对不同类型被加工曲面的优化刀具路径规划方法。针对三维自由曲面加工，通过把微分几何中的测地线的短程性与运动平稳性与传统等距偏置法相结合，得到优化的等距偏置法。与传统等距偏置法相比，本文的新方法使得刀具在运动过程中保持比较高的切削速度，大大提高了加工效率和加工质量。对于带岛屿的二维型腔加工，通过引入图形分割理论实现了对被加工型腔的“二分区规划”，避免了等距环间的互交检查，有效地提高了计算效率和加工效率。
首先，论文介绍了曲线等距技术的基本理论。针对平面单一曲线和组合曲线分别给出了计算方法，而空间曲线又分为一般法向等距和测地等距两种，其中一般法向等距是沿曲线法向方向上移动距离为常数的点的轨迹，测地等距是沿正交于曲线且测地线距离常数的点的轨迹。其次，对于自由曲面加工，提出一种基于测地线理论的等距偏置轨迹规划方法。最后，针对二维多岛链型腔内腔加工，给出一种基于图形分割理论的等距偏置轨迹规划方法，通过对岛屿群的合理划分实现了型腔的“二分区规划”等距偏置加工方法。其方法是按照岛屿数量及其分布情况分割成两个待加工曲面，分割后的每一个部分按照传统等距偏置法生成刀具轨迹，最后把两个独立区域的刀具轨迹用直线或圆弧连接起来以得到最后加工所需的刀具轨迹，该方法有效避免了等距环的互交检查。
关键词:轨迹规划 数控加工 等距偏置
Offset Algorithm based tool-path Planning for
NC Machining
Student name:Su Xiao Fan Class:05031307
Supervisor:yu fei
Abstract：Two different kinds of optimal tool path planning methods, which are all based on the conventional offset algorithm, are proposed respectively for freeform surface machining and 2D pocket with island chain in the paper. For freeform surface machining, the formulation of the geodesic, which is corresponding to short path length and high kinematics performance, is introduces to the classical offset method. Comparing with the classical offset method, high federate can be achieved and dynamic of the machine is improved. Comparing with the traditional iso-parametric and iso-planar planning, the distribution of trajectories is even and redundancy is minimized. For 2D pocket with islands machining, the image division technology is used for eliminating the intersection of contours and higher efficiency.
Firstly, the theoretical basis of the offset curve is introduced. The calculation for the single planar curve and combination planar curve is presented. For space curve, there are two different type of offset, separately named general normal offset and geodesic offset. Among of them, the general normal offset means the locus of point at a constant distance measure from orthogonal to curve, while geodesic offset means that the locus of point at a constant distance measured from curve along geodesic drawn orthogonal to the curve. Secondly, for freeform surface machining, the boundary conformed geodesic of the machined surface is firstly calculated, then a set of candidate offset curves are obtained on the general normal offset or the geodesic offset. Finally, for 2D pocket with islands machining, the pocket is firstly divided respect to the island chain basing on the imagine division technology, then the contour offset is formulated for different regions, finally a few of retractions are added for a whole tool path, by which the intersection is eliminated comparing with the traditional contour offset method.
Keyword:trajectory planning；numerical controlled machining;iso-metric offset
Signature of supervisor:
目 录
1 绪论
1.1选题的依据及意义……………………………………………………………( 1 )
1.2数控加工刀具轨迹生成技术…………………………………………………( 2 )
1.3论文的主要研究工作…………………………………………………………( 4 )
2 曲线等距技术
2.1 平面等距线…………………………………………………………………( 5 )
2.1.1 平面等距线的定义………………………………………………………( 5 )
2.1.2 平面等距线的算法………………………………………………………( 6 )
2.2 空间等距线…………………………………………………………………( 7 )
2.2.1 空间一般等距……………………………………………………………( 8 )
2.2.2 测地等距线……………………………………………………………( 10 )
3 自由曲面行切刀轨生成
3.1 概述………………………………………………………………………( 13 )
3.2 与刀具轨迹有关的基本概念……………………………………………( 13 )
3.3 走刀方式的确定…………………………………………………………( 15 )
3.4 路径间距计算公式………………………………………………………( 16 )
3.5 刀具轨迹生成…………………………………………………………( 18 )
3.5.1 刀触点轨迹的具体生成………………………………………………( 18 )
3.5.2 刀位点轨迹生成………………………………………………………( 20 )
4 多岛链型腔环切刀轨生成
4.1 概述………………………………………………………………………( 21 )
4.2 走刀方式的确定…………………………………………………………( 22 )
4.3 区域分割…………………………………………………………………( 24 )
4.4 刀具轨迹的干涉问题……………………………………………………( 26 )
4.5 型腔内腔刀具轨迹生成…………………………………………………( 27 )
4.5.1 轨迹的生成……………………………………………………………( 27 )
4.5.2 刀轨的优越性分析……………………………………………………( 30 )
5 结论………………………………………………………( 32 )
参考文献………………………………………………………………………( 33 )
致谢………………………………………………………………( 35 )
附录……………………………………………………………………………( 36 )
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