Hilbert填充曲线用于刀具路径生成的算法及改进研究

对Hibert填充曲线的生成方法进行了研究,建立了平面Hilbert填充曲线与Bezier参数平面之间的映射关系,得到了平面Hilbert填充曲线到空间曲面的映射规则和相应算法。针对该方法用于刀具路径生成时存在转向过于频繁等缺点,为了减小加工过程中对刀具和工件的冲击,提出了用倒角或圆弧进行过渡来代替原来的直角过渡的方法生成加工刀具路径。针对改进后的生成刀具路径的方法编制了仿真程序,对改进前后的刀具路径的长度和生成时间进行对比分析。通过一具体曲面加工路径生成仿真,验证了该方法的有效性。     

基于网格曲面上空间填充曲线刀具路径生成算法研究

在细分网格曲面上,用最短哈密顿回路法通过连接网格节点去寻找最优路径,以形成填充曲线刀具路径。将空间曲面细分成有限四边形网格后,结合无向网上最短哈密顿回路求解算法,通过构建代价树的方法求解最短路径。应用了邻接矩阵的形式描述图形,及基于矩阵法数据存储的度数消减算法判断和处理图形,构建了空间网格曲面上最短哈密顿回路生成算法。通过一个曲面填充实例验证了构建算法的正确性,及用此方法生成曲面加工刀具路径的可行性。     

基于参数线法的填充曲线刀具路径生成方法研究

参数线法刀具路径生成是曲面加工常用的方法,为了缩短走刀路径,将空间填充曲线生成思想融入路径生成过程中,提出基于参数线法的填充曲线刀具路径生成方法.在参数线网格上以最短哈密顿路径算法为指导来生成填充曲线,达到优化参数线刀具路径的目的.通过实例验证了方法的可行性.     

基于Hilbert填充曲线的自由曲面刀具路径规划研究

利用平面Hilbert填充曲线生成方法简单、易于控制填充疏密的优点,将其用于了自由曲面数控加工刀具路径的生成.对平面Hilbert填充曲线的生成原理进行了研究,用矩阵运算的方法生成该曲线.结合自由曲面的形成过程,提出将平面Hilbert曲线通过与曲面参数域相对应的方法映射到曲面上,进而生成加工刀具路径的思想.最后用一个具体应用实例验证了生成平面Hilbert曲线方法的正确性,和用此曲线作为数控加工刀具路径的可行性.通过与经典刀具路径生成方法比较可见该方法具有算法简单,加工余量均匀,加工效率与表面质量高的优点.     

基于MMR的三角网格曲面五轴加工刀轨生成算法

为了提高三角网格曲面五轴加工的加工效率,提出了基于最大材料去除率(maximal materialremoval rate,MMR)的平底刀五轴加工刀轨生成算法。首先计算无曲率干涉且具有最大材料去除率的网格曲面五轴加工的刀具方位角;然后在确定网格曲面可能干涉区域的基础上,提出刀触点处干涉性假设,并以最大材料去除率、刀具无曲率干涉和全局干涉为约束条件,采用二分法确定具有最大材料去除率的无干涉刀具方位角;最后采用截面线法生成三角网格曲面MMR平底刀五轴加工刀轨。通过实验验证了采用文中算法生成的刀轨进行加工能够获得较高的加工效率和表面质量。     

离散曲面慢刀伺服车削刀具路径规划

为解决离散曲面加工的难题,进行了离散曲面慢刀伺服车削刀具路径规划,研究了离散曲面的刀触点生成算法和刀位点生成算法,对比了两种刀位点速度插补算法。提出了基于Zernike多项式局部数据点拟合的刀触点生成方法和Z向刀具形状补偿方法。使用MATLAB软件以环曲面为例进行仿真,验证了该方法的正确性。通过对环曲面和渐进多焦点曲面进行刀具路径规划和加工实验,表明该刀具路径规划方法能够在避免对整个曲面进行拟合的基础上实现离散曲面的高精度加工。     

基于CQEM的海量测量点集刀位轨迹生成算法研究

提出基于约束二次误差度量(CQEM)的海量测量点集刀位轨迹生成算法。算法以大规模测量点集为待加工曲面,依据刀具大小动态生成刀具邻域的插值网格,以平面截交网格交点作为初始刀触点,对其进行CQEM优化并细分该截交网格,在此基础上生成无干涉刀位轨迹。算法不仅利用网格的动态局部构造节约了大量的空间消耗而且通过刀触点集的COEM优化减小了加工曲面逼近测量点所在曲面的误差。     

三角网格曲面加工刀具路径生成等误差步长算法研究

针对三角形网格曲面加工中刀具轨迹的误差均匀性问题,提出了一种等误差步长规划的刀具路径生成算法。该方法将刀具沿网格曲面运动方向的线性误差和转动误差联合作为设计公差,在满足给定精度要求条件下,通过控制设计公差来优化各条刀具轨迹上的刀触点的位置分布,并生成相应的刀位点。在生成完整三角网格曲面刀具路径时充分利用了网格曲面的边界特性,保证了边界一致性。实验表明:该方法生成的刀具路径保持了良好的边界一致性,并显著提高了加工精度和加工质量的均匀性。     

复杂参数曲面刀具轨迹铺放算法

结合空间填充曲线法与等残留高度法的优点,提出了一种新的刀具轨迹铺放算法。对u和v方向的等残留高度路径进行叠加求交,用参数变量代替笛卡尔坐标进行自由曲线求交,速度远高于包络面求交法。将每相邻的四个交点作为一个路径回路,通过综合条件判断回路合并方向,使得合并过程满足哈米尔顿回路要求,最终合并得到的哈密尔顿回路即为刀具路径。该方法能够生成近似最短并且连续的刀具轨迹,缩短了自由曲面加工的时间。通过实例验证了该方法的有效性。     

鼓形铣刀侧铣加工叶盘叶片曲面的光顺刀具路径生成方法

鼓形铣刀使用其大弧度切削刃进行切削加工,不仅可以采用大步距加工而仍保持相同表面加工质量,还可以通过改变刀具与工件曲面的切触点在刀具切削刃的位置使刀具和刀柄远离工件,避免碰撞,因此鼓形铣刀特别适合叶盘类零件的叶片曲面加工。现有的光顺刀轴矢量规划方法多使用最短路径算法在机床旋转轴位置的可行空间中求解光顺的刀轴矢量序列。然而,最短路径算法需要把连续问题转化为离散问题求解,在可行空间中的采样间隔越小,所得刀轴矢量序列的质量越高,但计算时间会很长。因此提出了缩短最短路径算法求解光顺刀轴矢量序列的计算时间的方法,并提出了鼓形铣刀侧铣加工叶盘叶片曲面的光顺刀具路径生成方法,该方法同时考虑机床旋转轴和刀具刀尖点运动轨迹的光顺性。试验结果表明,该方法生成的刀具路径能够使机床轴运动平稳。     

基于矩阵运算的Hilbert曲线用于刀具轨迹生成算法研究

基于矩阵运算描述生成平面Hilbert曲线的方法简单,易于编程实现,将其进行了正确的空间矢量化,应用于了曲面加工刀具轨迹的生成.分析了矩阵变化描述曲线的思想,结合曲面加工刀具轨迹的计算过程,提出将平面Hilbert曲线通过与曲面参数域相对应的方法映射到曲面上,进而生成加工刀具路径的思想.建立了二者之间的映射关系,构建了...     

An improved calculation method for cutting contact point and tool orientation analysis according to the CC points

Tool path generation is an important step of five-axis NC milling which plays an important role in parametric surfaces and free-form surfaces manufacturing. Cutter contacting (CC) point calculation is considered as a basic procedure of tool path generation. The step lengths formed by cutter contacting points have an effect on the chord error along feed direction. In traditional calculation method for CC point discretization, the segments connected by adjacent CC points distribute on both sides of the theoretical tool path curve. This situation magnifies the cutting error to some extent and enlarges the expected margin if the surface demands polishing or grinding. Aiming at this issue, this paper proposes an improved constant chord error method for CC point calculation. In the proposed method, the CC points lay on the theoretical tool path curve when the tool path curve is concave and lay on the chord error offset curve when is convex, which ensures the segments connected by the adjacent CC points distribute on one side of design surface, the side of the scallop height between tool paths. Therefore, the actual margin of polishing or grinding can be reduced. The influence of inflection points is also considered in this method to avoid accuracy deterioration caused by the long steps occurring near the inflection points. In part processing, local gouging and global collision must be avoided in tool orientation determination. This paper analyzes tool orientations with no rear gouging and no collision based on the calculated CC points. The novel discretization method for CC points is calculated on a single blade model, and the tool orientations are generated on an open integral impeller. A DMG DMU50 machine tool and a Hexagon three coordinates measuring machine are applied for experiments and measurements. The results show that, the CC point discretization method proposed in this paper offers many advantages over the traditional constant chord error method and commercial software, such as quantity of points, curve fitting, no overcut, and residual margin distributing. At last, blade and tunnel of the open integral impeller with safety tool orientation is machined and verified on the DMG DMU50 machine tool.     

服役破损叶片的曲面重构及刀路生成方法

A model reconstruction and CNC tool path generation of broken blades was proposed for the conditions that damage regions locatesd on the leading/trailing edges and on the tips. Measured data points were sorted, adjusted, and then utilized to construct sectional spline curves. The section curve was smoothed based on the theory of minimized energy, a method of aligning the sectional curves according to the curvatures was proposed. A model reconstruction method based on the lofting strategy was presented for the edge broken blades and the tip broken blades. The damaged regions were extracted, based on which the algorithm for generating zigzag tool path and the spiral tool path was given for CNC machining. Preliminary simulation results reveal that the proposed method guarantees the smoothness of the reconstructed surfaces and the approximation to the blade's real size. The feasibility of the proposed tool path generation method was testifiecl.     

Adaptive tool-path generation on point-sampled surfaces

In this paper, we present a new approach to generate tool paths for machining point sampled surfaces using a direct projection algorithm, which is based on generating tool paths along planar intersection curves. In our implementation, a guide surface, with simple geometry like planes or cylinder surfaces, is first created according to the bound volume of the point cloud and initial tool paths are planned on it in terms of the motion pattern of the cutters. For each point of the initial tool paths, then, the corresponding cutter contact point (CC) of the point set surface is located by projecting the point onto the point cloud using the direct projection algorithm. In order to obtain adaptive cutter location points (CL), a least squares-based curve fitting method is applied to approximate the CC points using piecewise cubic Bezier, and a numerical method derived to estimate the length of the curve is used to adjust the position of the points along the curve, and make them evenly spaced on the curve with equal arc lengths. In addition, considering that offset curves or surfaces are necessary for locating CL points in many applications, such as machining using ball end milling cutter, torus ended milling cutters, an offset strategy for cubic Bezier curves is also studied. By testing the proposed method on several point clouds, it has been demonstrated to be promising.     

Iso-parametric tool path generation from triangular meshes for free-form surface machining

The polyhedral model is widely used in the manufacturing industry. However, apart from the iso-planar method, the tool path generation methods for polyhedral machining are very limited. In such a case, the given tool paths are no longer boundary-conformed or efficient. This paper presents a new approach to iso-parametric tool path generation for triangular meshes. The strategy proposed herein first parameterizes the triangular faces via a harmonic map. The cutter-contact (CC) points and the path interval are then calculated based on the machining tolerance requirements and the iso-parametric tool paths are finally generated. The method is implemented on a computer and some illustrative examples are provided to show the effectiveness of the developed algorithm. The main advantage of the proposed method is that the tool paths can be generated naturally along the boundary of a polyhedral model, thus eliminating internal tight-radius corners in conventional paths. This leads to substantial reductions of tool wear and machining time. In addition, the proposed method can also be used in other non-iso-parametric tool path planning methods for triangular meshes and compound surfaces machining.     

从测量的散乱数据点云直接生成数控刀具路径的研究

提出了一种直接从测量的散乱数据点云用球头刀对自由曲面进行三轴数控加工时生成刀具路径的方法。不同于现有散乱点云基于逆向工程的刀具路径生成方法,本法考虑并估计了曲面加工误差和粗糙度。将散乱数据点云向XY平面投影,以获得的投影边界为刀具路径的主方向,然后根据曲面所需的加工误差和残留高度要求划分该投影数据点云,得到一系列刀位网格单元。通过最小化每个刀位网格单元的加工误差以确定每个刀位网格的节点位置,加权平均相关联刀位网格节点来对齐相邻刀位网格单元的边缘。为了缩短加工时间,裁去刀位路径上多余的线段,最终生成高效合理的数控加工刀具路径。已用实测的数据点云验证了本法直接生成刀具路径的有效性。     

五轴加工刀具路径生成的有效加工域规划方法

为复杂曲面五轴数控加工的刀具路径优化生成问题提出一种新的有效加工域规划方法。在对工件被加工表面和刀具的几何特征进行分析的基础上,得到在加工件表面上各处的最优可加工域宽度和刀具切削方向。通过采用离散采样和插值计算生成优化的有效加工域集,得到最优化的初始刀具路径;同时建立一种迭代搜索算法,用于解决最优加工域的选择规划问题。采用此算法生成优化的后续刀具路径,使得有效加工域最终完全覆盖整个被加工表面。给出的示例显示相对于传统的五轴加工刀具路径生成算法,有效加工域规划方法可以减少刀具路径的总长度和加工时间,得到更为优化的刀具路径和更好的工件表面质量,因此有效加工域规划方法可以被用于五轴数控加工实践以降低加工成本和提高产品质量。     

Mesh-based tool path generation for constant scallop-height machining

This paper presents a new approach to mesh-based tool path generation for obtaining constant scallop heights. The mesh surface has recently become the focus of considerable interest, because its geometric computation is simpler and more robust than that of the parametric surface. These advantages make it easy to check and remove interference in the process of tool path generation. The previous tool path generation method based on the mesh surface, however, can generate only one topology of iso-planar type where tool paths have evenly spaced tool path intervals. As constant scallop heights cannot be obtained from evenly spaced tool path intervals, unevenly spaced tool paths based on offset meshes are necessary for reducing the machining time and for easy interference removal. This paper proposes and compares four methods to estimate curvatures from the mesh surface; the curvature is essential for calculating unevenly spaced tool path intervals. This paper also proposes an improved drive surface method to propagate CL-paths unevenly and to generate tool paths with various topologies.     

Grind-free tool path generation for five-axis surface machining

This paper discusses automatic tool path generation for five-axis filleted end mill finish-surface machining. A new method of automatic five-axis tool path generation is introduced called Grind-Free (GF) tool path generation. GF surfaces result from tool paths that avoid gouging and have scallops that are within the surface profile or waviness tolerances. New algorithms are presented for determining tool forward step and tool path step-over that produce a GF surface. Gouge-free tool paths can be generated directly from CAD data based solely on local and global machining constraints. The proposed methodology for GF tool path generation has been implemented in the C language using the CODE/Robline system. Surfaces were machined on a Boston Digital 505 five-axis milling machine to confirm this method.