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.     

自由曲面数控加工刀具轨迹生成的约束条件分析

在提出自由曲面数控加工过程和刀具轨迹的规划原则情况下,分析无干涉控制、恒表面速度进给、伺服能力控制和相邻加工曲线影响等轨迹控制的约束条件,实时对轨迹的生成进行系统优化控制。通过系统分析刀具轨迹生成的约束条件,为刀具轨迹优化控制提供决策,对提高自由曲面的切削质量和加工效率具有重要意义。     

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.     

自由曲面五轴变步长数控加工刀轨生成方法

为了在满足逼近误差要求的同时最大程度减少冗余刀轨,对自由曲面提出了一种五轴变步长数控加工刀轨生成方法.首先对刀触点轨迹基于线性误差计算出初始刀触点点集,再以局部干涉调整前倾角的方式计算出无干涉刀位点和刀轴矢量;以最大非线性误差刀位处到刀触点轨迹的最小值作为相邻刀位点之间的逼近误差,并基于数据点自适应离散法计算逼近误差;...     

Tool path generation for machining compound surfaces with extended cut region method

Presented in the paper is a novel tool path generation method for 3-axis NC machining of compound surfaces. Tool path generation procedure consists of two core steps: firstly, the extended cut region (ECR) of every surface is constructed; secondly, CL-curves are computed on every ECR and the final tool paths are achieved by sorting, trimming and connecting the CL-curves. The developed ECR method can solve the gouging problems caused by tangent discontinuity, surface overlap or surface gap among surface elements. The proposed method has been implemented and applied to tool path generation in a general CAM system that has been developed by authors. Our case study has demonstrated the validity of the proposed algorithms.     

组合曲面叶片的螺旋加工刀位轨迹生成

为提高叶片加工质量和改进现有螺旋加工方法,提出了一种新的针对组合曲面造型叶片的四轴螺旋加工方法.该方法在叶片曲面造型过程中,将叶片曲面分割为叶盆、叶背、前缘和后缘四个区域.根据组合曲面叶片造型,提出了组合曲面叶片螺旋加工刀位轨迹生成方法和切触点的计算公式.最后,基于UG软件平台,以二次开发方式编制了相应的数控编程模块.生成了连续光滑的叶片螺旋加工刀位轨迹.试验结果表明,该方法能够实现叶片的四坐标螺旋加工,并可有效提高叶片的加工质量.     

曲面造型及数控加工刀具轨迹生成方法的研究

依据双三次均匀B样条曲面造型理论 ,运用等参数线加工方法 ,给出一种较为简便的曲面造型及数控加工刀具轨迹的生成方法     

空间自由曲面五轴联动数控加工

介绍了五轴数控机床的运动方式,阐述了空间自由曲面五轴联动数控加工中刀具路径规划的基本方法:参数线法、CC路径截面线法、CL路径截面线法、导动面法等。之后对五轴加工中刀具轴向规划进行了论述:垂直于表面方式、平行于表面方式、倾斜于表面方式。最后归纳总结了刀具干涉的检测与处理的方法,并分别说明了其优缺点和适应范围。     

Non-constant parameter NC tool path generation on sculptured surfaces

An algorithm for three-axis NC tool path generation on sculptured surfaces is presented. Non-constant parameter tool contact curves are defined on the part by intersecting parallel planes with the part model surface. Four essential elements of this algorithm are introduced: initial chordal approximation, true machining error calculation, direct gouge elimination, and non-constant parameter tool pass interval adjustment. A software implementation of this algorithm produces graphical output depicting the tool path superimposed over the part surface, and it outputs cutter location (CL) data for further post-processing. Several applications examples are presented to demonstrate the capabilities of the algorithm. The results of this technique are compared to those generated from a commercially available computer-aided manufacturing program, and indicate that equivalent accuracy is obtained with many fewer CL points.Notation C cutting curve - C ¹ cutting curve tangent - CC ₀,CC ₁, ... cutter contact points - d chordal deviation - /_ABC triangle - w incremental step in parameterw - ABC angle - a small quantity - l chord length - n _s ,n _p , ... normal vectors - P, P _r ,P _c ,P ₁ ,P ₂ , ... space point - Q parametric equation of a surface - R radius of a ball-end milling tool - TC ₀,TC ₁, ... tool center points - u, v, u _s ,u _c ,w, t parameters - angle - curvature - h cusp height - T machining tolerance     

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.     

Incomplete two-manifold mesh-based tool path generation

This paper presents a new paradigm for three-axis tool path generation based on an incomplete two-manifold mesh model; namely, an inexact polyhedron. When geometric data is transferred from one system to another system and tessellated for tool path generation, the model does not have any topological data between meshes and facets. In contrast to the existing polyhedral machining approach, the proposed method generates tool paths from an incomplete two-manifold mesh model. In order to generate gouge-free tool paths, cutter-location meshes (CL-meshes) are generated by offsetting boundary edges, boundary vertices, and facets. The CL-meshes are sliced by machining planes and the calculated intersections are sorted, trimmed, and linked. The grid method is used to reduce the computing time when range searching problems arise. The method is fully implemented and verified by machining an incomplete two-manifold mesh model.     

一种用于多面体加工的圆弧刀轨生成算法

为提高多面体模型的加工效率,提出了一种用于多面体加工的圆弧刀轨生成算法。采用截平面和多面体模型的等距模型求交来计算初始直线刀轨;由等距模型的顶点曲率估算刀位点处沿刀轨方向和刀轨间隔方向的曲率半径,并根据残留高度确定刀轨行距。提出了基于刀位点曲率半径调节的圆弧拟合算法,算法引入拟合约束条件和曲率半径调节系数;在拟合精度范围内,迭代确定曲率半径调节系数,从而确定拟合圆弧。实验结果表明文中方法生成的刀轨保持G1连续且包含的圆弧段数量较少,有利于提高加工效率。     

Tool path generation for machining free-form pockets using Voronoi diagrams

Voronoi diagrams for closed shapes have many practical applications, ranging from numerical control machining to mesh generation. Curve offsetting based on Voronoi diagrams avoids the topological problems encountered in the traditional offsetting algorithms. In this paper, we propose a procedure using Voronoi diagram-based tool-path generation for machining pockets with free-form boundaries. A pocket can be bounded by 2D free-form curve elements that are differentiable twice. The procedure consists of three steps:

Tool path generation for pattern sculpting on free-form surfaces

Sculpting pattern onto free-form surfaces is a potential method for many applications such as jewelry, glass blowmolding, injection molding, even automatically spray painting on the surfaces, etc. In this paper, a method of tool path generation for pattern sculpting on free-form surfaces is developed. First, 2D pattern is converted into discrete data points for tool path generation from digital image using image processing technique. To map the discrete pattern onto the part surface, mesh mapping is introduced, which is used for flattening the part surfaces onto a plane. On this plane, the discrete pattern is scaled, rotated, and translated to a desirable location. Then using the mapping of the part surface to the plane as a guide, the pattern to be sculpted is inversely mapped back onto the part surface. On this basis, according to the selected cutter and the depth of cut, the tool path is generated. Since the method does not rely on processing on the surface parametric domain, it is not limited to single surface patch, and is also equally applicable to multiple trimmed surfaces and mesh surfaces, etc. During calculation of the projected pattern, the proposed method does not involve any iterative numerical procedures, thus it is also robust and efficient. Finally, the method is implemented and tested on several typical examples to verify its validity.     

自由曲面数控加工动态仿真研究

在VC++6.0平台上采用OpenGL技术开发一种自由曲面数控加工过程仿真系统。该系统可根据自由曲面的不同造型,规划出适当的刀位轨迹,生成G代码;实现交互控制,完成设计曲面的成型加工,并动态显示加工路径。     

离散点云等残留高度数控加工刀轨生成方法

为了最大化刀轨行间距,从而减少刀轨总长度,针对离散点云提出了一种等残留高度刀轨生成方法。提出以点云局部轮廓点集直接生成残留高度点的迭代计算方法,再根据残留高度点和点云局部点集迭代计算出下一行等残留高度刀位点,从而获得等残留高度刀轨。算法无需点云等距或曲面重构,为了提高算法效率,提出了算法所需数据初值的优化计算方法。最后对典型的点云模型生成刀轨,与等行距刀轨相比,提出的算法生成的等残留高度刀轨总长度大幅减少,验证了算法的可行性和有效性。     

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.     

A CL surface deformation approach for constant scallop height tool path generation from triangular mesh

In this paper, we present a cutter location (CL) surface deformation approach for constant scallop height tool path generation from triangular mesh. The triangular mesh model of the stereo lithography (STL) format is offset to the CL surface and then deformed in accordance with the deformation vectors, which are computed by the slope and the curvature of the CL surface. In addition, the tool path, which is computed by slicing the deformed CL surface, is inversely deformed by those same deformation vectors to a tool path with a constant scallop height. The proposed method is implemented, and a tool path is generated and tested by simulation and by numerical control (NC) machining. The scallop height was found to be constant over the entire machined surface, demonstrating much better quality than that of mesh slicing, under the same constraints for machining time.     

A novel iso-scallop tool-path generation for efficient five-axis machining of free-form surfaces

Weld cladding is a process of depositing a thick layer of a corrosion resistance material over carbon steel plate to improve the corrosion resistance properties. The main problem faced in stainless steel cladding is the selection of process parameters for achieving the required clad bead geometry and its shape relationships. This paper highlights an experimental study carried out to develop mathematical models to predict clad bead geometry and its shape relationships of austenitic stainless steel claddings deposited by gas metal arc welding process. The experiments were conducted based on four-factor, five-level central composite rotatable design with full replication technique. The mathematical models were developed using multiple regression method. The developed models have been checked for their adequacy and significance. The direct and interaction effects of process parameters on clad bead geometry and its shape relationships are presented in graphical form.     

自由曲面加工中NURBS曲线的插补实现

针对复杂型面零件的高精度曲面加工,传统上应用直线、圆弧和螺旋线等插补。由于曲面轮廓离散成大量微段直线或圆弧来加工,这不仅使编程复杂、代码量膨胀,而且不可避免地带来逼近误差,影响零件的加工精度、表面粗糙度和生产效率。提出一种NURBS曲线的实时插补算法,它基于NURBS曲线的参数表示法来求出优化的曲线参数,实现了NURBS曲线高速、高精度加工的插补控制。试验的结果表明,这种插补方法是有效的。