测点数据生成刀具路径研究

为了提高反求加工的效率，提出由大规模测点数据直接生成粗、精加工刀具路径的算法．粗加工采用层切法分层切削材料，首先构造健壮的数据结构——层切网；然后计算无干涉刀位点，并把整个层切网划分为几个优化的子加工区域；最后应用优化的刀路链接法则得到粗加工刀具路径．精加工由大规模数据点构建三角曲面．为了避免干涉，需计算点、面和边的无干涉刀位点．实验结果表明，粗加工刀具路径算法具有较高的效率，只需要占用较小的内存空间；精加工可以成功地避免干涉并且获得可靠的表面精度．     

Adaptive tool-path generation of rapid prototyping for complex product models

Rapid prototyping (RP) provides an effective method for model verification and product development collaboration. A challenging research issue in RP is how to shorten the build time and improve the surface accuracy especially for complex product models. In this paper, systematic adaptive algorithms and strategies have been developed to address the challenge. A slicing algorithm has been first developed for directly slicing a Computer-Aided Design (CAD) model as a number of RP layers. Closed Non-Uniform Rational B-Spline (NURBS) curves have been introduced to represent the contours of the layers to maintain the surface accuracy of the CAD model. Based on it, a mixed and adaptive tool-path generation algorithm, which is aimed to optimize both the surface quality and fabrication efficiency in RP, has been then developed. The algorithm can generate contour tool-paths for the boundary of each RP sliced layer to reduce the surface errors of the model, and zigzag tool-paths for the internal area of the layer to speed up fabrication. In addition, based on developed build time analysis mathematical models, adaptive strategies have been devised to generate variable speeds for contour tool-paths to address the geometric characteristics in each layer to reduce build time, and to identify the best slope degree of zigzag tool-paths to further minimize the build time. In the end, case studies of complex product models have been used to validate and showcase the performance of the developed algorithms in terms of processing effectiveness and surface accuracy.     

Interference-free tool-path generation in the NC machining of parametric compound surfaces

A method is presented for generating interference-free tool paths from parametric compound surfaces. A parametric compound surface is a surface that consists of parametric surface elements. The method is largely composed of two steps: points are obtained from a compound surface to be converted into a triangular polyhedron; tool paths are then generated from the polyhedron. An efficient algorithm is used in the calculation of cutter-location data, and planar tool paths, which are suitable for metal cutting, are produced. The time taken to obtain all the tool paths from a surface model that consists of a large number of parametric surfaces is short. Some real applications are presented.     

The algorithms for trimmed surfaces construction and tool path generation in reverse engineering

In the duplication of a physical part such as die and mold, aerospace part and so on, most of patches are trimmed surfaces resulting from Boolean manipulations. Direct generation of tool paths from the practical parts is a fundamental problem. This paper presents an efficient method for generating NC tool paths from some trimmed surfaces. Three types of control points are determined to construct an underlying NURBS surfaces. NC tool paths are then generated based on these surfaces. The method can deal efficiently with parts composed of trimmed surfaces. It can be considered as a tool for reverse engineering software integration.     

复杂多曲面高速铣3轴精加工刀轨优化算法

针对高速铣削的特点和现实要求,提出了适合高速铣削面向复杂曲面的3轴精加工可变行距的螺旋线与Zigzag混合刀轨优化算法．该算法生成的刀轨光顺简洁,满足了高速加工的要求．算法中采用的行间NURBS过渡边优化法和跨区域刀轨优化法,具有合理性和实用性．加工结果表明,加工表面无过切．经测试,算法稳定可靠．     

A machining potential field approach to tool path generation for multi-axis sculptured surface machining

This paper presents a machining potential field (MPF) method to generate tool paths for multi-axis sculptured surface machining. A machining potential field is constructed by considering both the part geometry and the cutter geometry to represent the machining-oriented information on the part surface for machining planning. The largest feasible machining strip width and the optimal cutting direction at a surface point can be found on the constructed machining potential field. The tool paths can be generated by following the optimal cutting direction. Compared to the traditional iso-parametric and iso-planar path generation methods, the generated MPF multi-axis tool paths can achieve better surface finish with shorter machining time. Feasible cutter sizes and cutter orientations can also be determined by using the MPF method. The developed techniques can be used to automate the multi-axis tool path generation and to improve the machining efficiency of sculptured surface machining.     

A mapping-based approach to eliminating self-intersection of offset paths on mesh surfaces for CNC machining

Geometrically, a tool path can be generated by successively offsetting its adjacent path on the surface with a given path interval, which preferably starts from one of the surface boundaries or a primary curve. The key issues involved in offset path planning are the generation of raw offset paths and the elimination of the self-intersection of raw offset paths. Most researches available in this area are focused on how to generate the raw offset paths, however, the latter, especially how to eliminate the self-intersection of the offset paths on mesh surfaces, has not been sufficiently addressed. In this paper, a mapping-based approach to eliminating the self-intersection of offset paths is proposed for the CNC machining of mesh surfaces. The method first flattens the mesh surface onto a predefined plane by using a mesh mapping technique, and then taking the mapping as a guide, the offset paths are also naturally mapped onto the plane, from which those invalid self-intersection loops can be effectively identified and eliminated. To handle the issue of self-intersection for all types of offset path, a notion of local loop is introduced to detect and eliminate the invalid self-intersection loops. After that the planar paths are inversely mapped into the physical space and the final tool paths used for the machining of mesh surface are obtained. Meanwhile, in order to improve the kinematic and dynamic performance of the machine tool when machining along the generated offset paths, a method for rounding the sharp corners of tool paths, which result from the process of eliminating the self-intersection of raw offset paths, is also preliminarily investigated. Finally, the proposed method is validated by the results of simulations and machining experiments.     

Tool-path generation of planar NURBS curves

It has been widely used in CAD field for many years and gradually applied in CAM area with the prevalence of NURBS interpolator equipped in CNC controllers. But few of them provide the tool radius compensation function. In order to achieve the goal of generating tool-path, an algorithm was presented to offset NURBS curves by an optimum process for CAD/CAM systems in this paper. NURBS format is ideal for HSM applications, but not all NURBS outputs are equal and standard. Basically, there are two different ways to generate NURBS tool-paths; one is to fit a NURBS curve to the conventional tool-path output, the other one is to generate a NURBS tool-path from the start. The main targets for the tool-path of this paper are: (1) To keep a constant distance d between progenitor curve C(t) and offset curve C_d(t) on the normal direction of C(t); (2) to alternate the order k of the basis function in offset curve C_d(t); (3) to oscillate the number of control points of offset curve C_d(t) and compare it with progenitor curve C(t). In order to meet the tolerance requirements as specified by the design, this study offsets the NURBS curves by a pre-described distance d. The principle procedure consists of the following steps: (1) construct an evaluating bound error function; (2) sample offset point-sequenced curves based on first derivatives; (3) give the order of NURBS curve and number of control points to compute all initial conditions and (4) optimize the control points by a path searching algorithm.     

Tool path planning for compound surfaces in spray forming processes

Spray forming is an emerging manufacturing process. The automated tool planning for this process is a nontrivial problem, especially for geometry-complicated parts consisting of multiple freeform surfaces. Existing tool planning approaches are not able to deal with this kind of compound surface. This paper proposes a tool-path planning approach which optimizes the tool motion performance and the thickness uniformity. There are two steps in this approach. The first step partitions the part surface into flat patches based on the topology and normal directions. The second step determines the tool movement patterns and the sweeping directions for each flat patch. Based on the above two steps, optimal tool paths can be calculated. Experimental tests are carried out on automotive body parts and the results validate the proposed approach. Note to Practitioners-This paper was motivated by the problem of automatically planning tool paths for spray forming using Programmable Powdered Preforming Process (P4) technology. However, the proposed approach can be applied to other surface manufacturing applications such as spray painting, spray cleaning, rapid tooling, etc. Existing tool planning approaches are not able to handle complicated, multi-patch surfaces. This paper proposes a methodology to partition complicated surfaces into easy-to-handle patches and generate tool paths with optimized thickness uniformity and tool motion performance. We tested the approach using simulation on sample automotive body parts and proved its feasibility. However, this approach requires that the parts to be sprayed belong to the sheet-metal type so that the part geometry can be analyzed on a plane. In our future research, we will run physical tests on actual parts and investigate the deposition effects on the thickness uniformity.     

Tool-path generation from measured data

Presented in the paper is a procedure through which 3-axis NC tool-paths (for roughing and finishing) can be directly generated from measured data (a set of point sequence curves). The rough machining is performed by machining volumes of material in a slice-by-slice manner. To generate the roughing tool-path, it is essential to extract the machining regions (contour curves and their inclusion relationships) from each slice. For the machining region extraction, we employ the boundary extraction algorithm suggested by Park and Choi (Comput.-Aided Des. 33 (2001) 571). By making use of the boundary extraction algorithm, it is possible to extract the machining regions with O(n) time complexity, where n is the number of runs. The finishing tool-path can be obtained by defining a series of curves on the CL (cutter location) surface. However, calculating the CL-surface of the measured data involves time-consuming computations, such as swept volume modeling of an inverse tool and Boolean operations between polygonal volumes. To avoid these computational difficulties, we develop an algorithm to calculate the finishing tool-path based on well-known 2D geometric algorithms, such as 2D curve offsetting and polygonal chain intersection algorithms.     

Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution

We introduce a new method that approximates free-form surfaces by envelopes of one-parameter motions of surfaces of revolution. In the context of 5-axis computer numerically controlled (CNC) machining, we propose a flank machining methodology which is a preferable scallop-free scenario when the milling tool and the machined free-form surface meet tangentially along a smooth curve. We seek both an optimal shape of the milling tool as well as its optimal path in 3D space and propose an optimization based framework where these entities are the unknowns. We propose two initialization strategies where the first one requires a user’s intervention only by setting the initial position of the milling tool while the second one enables to prescribe a preferable tool-path. We present several examples showing that the proposed method recovers exact envelopes, including semi-envelopes and incomplete data, and for general free-form objects it detects envelope sub-patches.     

One-sided offset approximation of freeform curves for interference-free NURBS machining

Generating valid tool path curves in NURBS form is important in realizing an efficient NURBS machining. In this paper, a method for computing one-sided offset approximations of freeform curves with NURBS format as tool paths is presented. The approach first uses line segments to approximate the progenitor curve with one-sided deviations. Based on the obtained line approximating curve and its offsets, a unilateral tolerance zone (UTZ) is constructed subsequently. Finally, a C¹-continuous and completely interference-free NURBS offset curve is generated within the UTZ to satisfy the required tolerance globally. Since all of the geometric computations involved are linear, the proposed method is efficient and robust. Interference-free tool path generation thus can be achieved in NURBS based NC machining.     

Iso-planar interpolation for the machining of implicit surfaces

The paper presents an approach for on-line path generation and interpolation for the machining of implicit surfaces. For a given implicit surface, once the cutting plane direction and cut-in points have been selected, iso-planar tool paths and interpolated points can be calculated on-line according to the feedrate and scallop height requirements. The approach enables the tool position and orientation to be correctly calculated at each interpolated point. Validation examples are provided for the interpolation of cyclide surfaces with planar and curved boundaries.     

Automated surface subdivision and tool path generation for -axis CNC machining of sculptured parts

As an innovative and cost-effective method for carrying out multiple-axis CNC machining, -axis CNC machining technique adds an automatic indexing/rotary table with two additional discrete rotations to a regular 3-axis CNC machine, to improve its ability and efficiency for machining complex sculptured parts. In this work, a new tool path generation method to automatically subdivide a complex sculptured surface into a number of easy-to-machine surface patches; identify the favorable machining set-up/orientation for each patch; and generate effective 3-axis CNC tool paths for each patch is introduced. The method and its advantages are illustrated using an example of sculptured surface machining. The work contributes to automated multiple-axis CNC tool path generation for sculptured part machining and forms a foundation for further research.     

An adaptive process planning approach of rapid prototyping and manufacturing

This paper presents an adaptive approach to improve the process planning of Rapid Prototyping/Manufacturing (RP/M) for complex product models such as biomedical models. Non-Uniform Rational B-Spline (NURBS)-based curves were introduced to represent the boundary contours of the sliced layers in RP/M to maintain the geometrical accuracy of the original models. A mixed tool-path generation algorithm was then developed to generate contour tool-paths along the boundary and offset curves of each sliced layer to preserve geometrical accuracy, and zigzag tool-paths for the internal area of the layer to simplify computing processes and speed up fabrication. In addition, based on the developed build time and geometrical accuracy analysis models, adaptive algorithms were designed to generate an adaptive speed of the RP/M nozzle/print head for the contour tool-paths to address the geometrical characteristics of each layer, and to identify the best slope degree of the zigzag tool-paths towards achieving the minimum build time. Five case studies of complex biomedical models were used to verify and demonstrate the improved performance of the approach in terms of processing effectiveness and geometrical accuracy.     

曲面数控加工中面向NURBS刀具路径生成的刀位点分段算法

曲面数控加工中,NURBS刀具路径生成技术需要在大量有序刀位点中提取适合于NURBS刀具路径表示的刀位点段,刀位点的分段质量是决定NURBS刀具路径生成的前提.通过分析NURBS刀具路径的特点,对由刀位点表示的刀具路径之间的连接方式和边界点进行分类,提出通过层次聚类法将刀具路径进行分段的算法.在此基础上,通过判断连接点的类型来提取合适的刀位点段以进行NURBS刀具路径的生成.实例结果表明,该算法分段可靠、快捷,对不同曲线曲面轮廓刀具轨迹点进行分段的适应性强,分段结果可以满足NURBS刀具路径的生成.     

Quart-parametric interpolations for intersecting paths

The intersecting path is an important tool path generation method. This paper proposes an approach for the quart-parametric interpolation of intersecting paths. The objective of our approach is that the intersecting paths for surface machining can be directly interpolated within the computer numerical control (CNC) system. This enables the CNC interpolator to process the intersecting paths without geometric approximation as in existing approaches and take into consideration any specific feedrate profiles and further machining dynamical issues along the path.The interpolation of the intersection of two general parametric surfaces is transferred into interpolation of its projection curves and the time trajectories of four parameters along the intersecting curves are obtained. Our strategy is to carry out the quart-parametric interpolation based on the projection interpolation. The feedrate control method is developed, and then the interpolation algorithms for two projection curves are proposed. An error reduction scheme is presented to alleviate point deviation from the drive parametric surface. Simulations of quart-parametric interpolation have been carried out to verify the effectiveness of the proposed algorithm.     

Tool path generation for clean-up machining by a curve-based approach

This paper presents a new efficient and robust tool-path generation method that employs a curve-based approach for clean-up machining. The clean-up machining discussed in this paper is pencil-cut and fillet-cut for a polyhedral model of the STL form with a ball-end mill. The pencil-cut and fillet-cut paths are obtained from the curve-based scanning tool paths on the xz, yz, and xy planes. The scanning tool path has exact sharp-concave points and bi-contact vectors, both of which are very useful to detect ‘pencil-points’, to trace the pencil-cut path, and to generate the fillet-cut path. In the paper, some illustrative examples are provided, and the characteristics of the proposed method are discussed.     

An artificial immune system approach to CNC tool path generation

Reduced machining time and increased accuracy for a sculptured surface are both very important when producing complicated parts, so, the step-size and tool-path interval are essential components in high-speed and high-resolution machining. If they are too small, the machining time will increase, whereas if they are too large, rough surfaces will result. In particular, the machining time, which is a key factor in high-speed machining, is affected by the tool-path interval more than the step size. The present paper introduces a ‘system software’ developed to reduce machining time and increased accuracy for a sculptured surface with Non-Uniform Rational B-Spline (NURBS) patches. The system is mainly based on a new and a powerful artificial intelligence (AI) tool, called artificial immune systems (AIS). It is implemented using C programming language on a PC. It can be used as stand alone system or as the integrated module of a CNC machine tool. With the use of AIS, the impact and power of AI techniques have been reflected on the performance of the tool path optimization system. The methodology of the developed tool path optimization system is illustrated with practical examples in this paper.     

Coverage based tool-path planning for automated polishing using contact mechanics theory

Presented in this paper is a tool-path planning method for automated polishing. This work is an integral part of research program on automated polishing/deburring being carried out at Ryerson University. Whereas tool-path planning for machining is treated as a geometry problem, it is shown here that tool-path planning for polishing should be treated as a contact mechanics problem because of contact action between the polishing tool and the part. To develop this method, contact mechanics is applied for contact area modeling and analysis. Once the contact area is determined for multiple points along the given polishing path, a Contact Area Map (CAM) is established and used to show the coverage area during polishing. This map is then used to plan polishing paths that ensures a complete coverage for polishing. Simulation has been conducted to show the effectiveness of this new tool-path method.