A topological-free method for three-axis tool path planning for generalized radiused end milled cutting of a triangular mesh surface

A tool path generation method for a sculptured surface defined by a triangular mesh is presented. Existing tool methods require extensive computer processing power mainly because surface topology for triangular meshes is not provided. The three-axis tool path planning method presented in this paper for generalized radius end mills avoids this problem (and does not need topological information) by offsetting each triangular facet individually. Offsetting a single triangle results in many more triangles, many of which are redundant, increasing the time required for data handling in subsequent steps. To avoid the large number of triangles, the proposed method creates a bounding space to which the offset surface is limited. Applying the boundary space limits the size of the offset surface resulting in a reduction in the number of triangular surfaces generated. The offset surface generation may still result in unwanted intersecting triangles. The tool path planning strategy addresses this issue by applying hidden-surface removal algorithms. Simulation and machining tests are used to validate the tool paths generated using this method.     

Double-spiral tool path in configuration space

Using a spiral tool path is a common strategy in many NC machining applications. It can be used for high-speed machining of pockets or as a space-filling curve for finish applications. When using spirals for finishing application, a double spiral is desired to avoid having a starting or end-point at the center of the workpiece. In this paper, we present an algorithm to create a double spiral from offset curves in a precomputed configuration space (c-space). CAD/CAM systems that operate on NURBS surfaces or on triangular meshes have to deal with the issues of patch-boundary oscillations or long, stretched triangles, respectively. This can be avoided when operating in c-space. The c-space is given in the form of a regular quadrilateral heightfield mesh, which may be adaptively subdivided, where the slope is large. This simple data structure is memory efficient and has proven to be beneficial in CAD/CAM frameworks. Our algorithm creates a double spiral by blending adjacent offset curves. The center of the spiral is filled by a b-spline curve. When given offset curves split into multiple components, the algorithm creates multiple smaller spirals and connects them appropriately. The resulting tool path is one large intersection-free curve with starting and end-point on the boundary of the workpiece.     

任意三角形控制网格的二元四次箱样条曲面算法

二元三方向剖分是方向最少的三角剖分,建立在其上的二元三向箱样条在工程曲面造型等领域有着极为广 泛的应用。规范的二元三向四次箱样条曲面计算仅针对网格中点的价数均为6的情形,从规范的算法出发,提出 了一种任意价数控制点的情形下的曲面计算算法,并对算法进行了较为详细的分析。分析及试验结果表明,按该 算法生成的曲面有较好的整体光顺特性,各面片间是C1连续的,而对某一个三角面片内部则是C2连续的。由于 本算法适用于任意的三角形控制网格,因此在CAD／CAGD等曲面造型中有很高的实用价值。     

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.     

General 3D offsetting of a triangular net using an implicit function and the distance fields

A novel approach which uses the distance fields based on cell subdivision and an implicit surface interpolation based on the radial basis function is proposed in order to get an accurate and error-free offset model of arbitrary shapes composed of a large number of triangle meshes. In the method, the space bounding the original model is divided into smaller cells. For the efficient calculation of distance fields, valid cells which will generate a portion of offset model are selected previously by the proposed detection algorithm. These valid cells are divided again into much smaller voxels which assure required accuracy. At each voxel, the distance fields are created by calculating the minimum distances between the corner points of voxels and the triangle meshes. For the more efficient calculation of distance fields, valid vertices among the triangle meshes which will generate minimum distances with current cell are selected by checking the intersection between current cell and a cone prism generated at each vertex of triangle meshes. In addition, a new approach based on an implicit surface interpolation scheme is proposed to perform two types of offsetting operations including uniform and non-uniform offsetting in the same framework. In the method, a smooth implicit surface is generated from the discrete offset distance values given by the user. After generating the whole distance fields, the offset surface was constructed by using the conventional marching cube algorithm together with mesh smoothing scheme. The effectiveness and validity of this new offset method was demonstrated by performing numerical experiments for the various types of triangle meshes.     

交叠网格的检测与合并

提出了一种新的多片网格重叠区域的检测方法。首先对欲合并的网格采用基于栅格六面体和k-d树搜索的方法进行交叠区域的检测;然后删除交叠区域冗余的三角面片,在删除后的网格缝隙处建立连接桥三角面片;最后提取出建立连接桥后的孔洞并进行补洞处理,从而达到缝合网格的目的。由于拼接后的网格在缝合处会存在“台阶”等不光顺情况,因此通过光顺算法实现缝合处的光滑过渡。实例表明该网格拼合算法在处理速度和网格质量上都有很好的表现。     

Contour-parallel offset machining for trimmed surfaces based on conformal mapping with free boundary

The parametric surfaces of some manufactured parts are often subjected to the Boolean operation of other objects; generating suitable NC tool paths from such trimmed surface remains a challenge. This paper presents a new planar development-based method to generate contour-parallel offset paths of trimmed surfaces. To avoid direct frequent identifications and removals of interferences of offset curves on 3D-trimmed surface possibly with multiple holes or restricted regions, the original surface is flattened in the plane domain using a two-stage approach which consists of conformal mapping with free boundary and further nonlinear accuracy improvement. Then, sequent offsets of the boundary curves of the planar region are generated, and the global interferences are detected and removed using an efficient and robust divide-and-conquer strategy. Based on a tree data structure, a tool-path linking algorithm is also given with less or no tool retractions, and subsequently, the resulting planar paths are inversely mapped to the physical space. Illustrated examples have been conducted to testify the affectivity and the applicability of the proposed contour-parallel offset machining method.     

Computer-aided design of experiments: an enabler of agile manufacturing

The generation of feature curves or curve network from the digitized points of an object is very important for successful surface reconstruction. Owing to the shape complexity of industrial parts and the random nature of scanned points, the feature curves detected are generally not smooth or accurate enough for the subsequent use. The purpose of this study was to present an algorithm for extracting geodesic or feature lines on triangular meshes provided that the initial and final points of the path are given. The proposed algorithm is essentially developed from a heuristic search algorithm where a cost function composed of distance and curvature information is employed to guide the search of the optimized path. When the distances between the points dominate the cost function, it will result in a geodesic path between the initial and final points. On the contrary, when the curvature cost dominates, the optimized path will track the feature edges or rounded edges appropriately. Successful examples are presented to illustrate the feasibility of the proposed algorithm.     

Development of automatic surface reconstruction technique in reverse engineering

The computer-aided design model reconstruction process is generally very complex, as it requires substantial efforts in planning and editing data points, curves, and surfaces. A novel method is developed in this study for automatic surface reconstruction from a huge number of triangular meshes. The proposed method is mainly composed of the following five steps: mesh simplification, quadrilateral mesh generation, curve net construction, connectivity data preparation, and multiple surfaces fitting with G¹ continuity across the boundaries. The first three steps build the boundary curves of the surfaces. The fourth step prepares the data needed for surface fitting, which includes segmented points, continuity conditions on the boundaries, and topological relationship of the data. In the final step, all regions of points are fitted into appropriate surfaces, with the accuracy and smoothness of the surfaces controlled and G¹ continuity between the surfaces. A detailed discussion for each of the above algorithms is provided. Successful examples are also presented to demonstrate the feasibility of the proposed method.     

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.     

一种基于子域分解的表面混合网格生成方法

提出了一种新的基于子域分解的混合网格生成方法。该方法首先用映射法生成结构化背景网格,并确定实体表面上包含的小孔、键槽等小特征在背景网格中的位置,然后删除这些小特征覆盖的背景网格,并在这些区域内生成三角形网格,最后将剩余的背景网格和生成的三角形网格合并,得到整个目标域的网格。该算法综合了映射法效率高、网格质量好、四边形网格计算精度高,以及三角形网格几何适应能力强的优势。数值实验表明,针对复杂的实体表面,新方法能够全自动地生成质量较好的混合网格,生成的网格质量及算法效率均优于传统的推进波前法和铺砖法。     

全冠义齿网格过渡算法研究与应用

针对全冠义齿数字化设计时外冠和内冠过渡融合的问题,提出了一种新的网格过渡算法。首先提取外冠和内冠网格边界进行桥接形成封闭孔洞;然后根据定义的三角片插入规则插入新的三角片填充孔洞,构造初始过渡网格;最后投影到由边界顶点插值得到的隐式曲面上,投影点构成新的过渡网格,将其与外冠和内冠拓扑合并形成完整的全冠义齿修复体。用过渡算法得到的网格面片分布均匀,三角片质量较好,而且过渡边界光顺自然,具有较好的连续性。     

Updating 3D triangular mesh models based on locally added point clouds

In a manufacturing area, design changes for an original surface model are frequently required: for example, when the physical parts are modified or when the parts are partially manufactured from analogous shapes. In this case, an efficient surface updating method by locally adding scan data for the modified area is highly desirable. For this purpose, this paper presents a new procedure to update an initial model that is composed of combinatorial triangular facets based on a set of locally added point data. Nowadays, many people are using surface models that are represented by triangular facets in reverse engineering, since it is fast and easy to create the triangular meshes directly from large amounts of point data. The initial surface model is first created from the initial point set by tight cocone, which is a water-tight surface reconstructor; and then the point cloud data for the updates is locally added onto the initial model maintaining the same coordinate system. In order to update the initial model, the special region on the initial surface that needs to be updated is recognized through the detection of the overlapping area between the initial model and the boundary of the newly added point cloud. After that, the initial surface model is eventually updated to the final output by replacing the recognized region with the newly added point cloud. The proposed method has been implemented and tested with several examples. This algorithm will be practically useful to modify the surface model with physical part changes and free-form surface design.     

基于“薄膜变形”的牙齿曲面重建算法研究与实现

牙齿曲面重建是口腔修复CAD/CAM系统的核心内容之一。本文提出了一种基于"薄膜变形包围"牙齿曲面重建算法,首先对简化后的牙齿三角网格模型进行Loop细分以提高模型的变形逼近的能力;然后对细分后的网格施加"吸引力"使细分网格逼近原始密集的网格模型;接着施加"松弛力"消除网格变形后的褶皱;最后通过不断的异步迭代循环调整网格顶点的位置,直到满足预设的误差精度后停止。通过对两类典型牙齿模型的网格重建的算例,验证了本文算法的可行性。     

基于Pro／E提高三角曲面品质的解决方案

介绍了一种三角曲面的构建方法,首先以三条边和其中一条边对应的预角创建三角曲面;接着在顶角收敛处创建投影曲线,并用投影曲线将收敛的部分曲面裁剪掉;然后以四条边界曲线创建曲面,并使曲面和原曲面相切;最后合并两曲面。通过曲面偏距网格分析可知,曲面的U、V方向网格线不再相交于一点,表明曲面品质在收敛角处得到改善。     

Surface offsetting using distance volumes

Proposed in this paper is a new approach for offset surface construction using three- dimensional (3D) distance volumes. After converting an original compound surface into a triangular mesh, the approach creates a distance volume of the triangular mesh. With this distance volume and a given offset value, it extracts the offset points in each slice to create a sequence of two dimensional (2D) cross-sections. The approach then performs offset surface construction using the serial cross-sections. For more accurate and efficient computation of the distance volume, the concept of space division is combined with the concept one of distance propagation to the whole space of interest. The resulting offset surface is a G¹ composite surface consisting of three kinds of surfaces: skinned, capped, andor branched surfaces. The proposed approach provides offset surfaces that are accurate and free of degeneracy. Some experimental results demonstrate its usefulness and quality.     

薄板冲压成形中基于数控轨迹点的全自动四边形网格生成

基于模具型腔表面的数控轨迹点,提出了一种适用于薄板冲压成 形计算机仿真的全自动四边形网格生成方法。该方法首先利用最大弦长偏差法删除冗余轨迹 点,接着根据相邻特征曲线插值法来重新分布轨迹点,最后生成四边形网格。算法简单、稳 定,能处理任意无孔洞冲压模具型腔表面的数控加工轨迹点的自动四边形网格生成问题。     

基于复合三角Bezier曲面/平面交线的裁剪

提出一种复合三角Ｂｅｚｉｅｒ曲面与平面的求交算法,这种算法能处理多条交线、交线环的情况,在自由曲面数控加工编程中具有广泛的应力场合,对提高汽车等领域的曲面ＮＣ加工精度具有重要的工程价值。将交点作为型值点插入相应的三角网格,通过三角网 重新划分和分离,实现复合曲面的裁剪。试用显示,这种裁剪方法在工程上是行之有效的。