Multiresolution analysis as an approach for tool path planning in NC machining

Wavelets permit multiresolution analysis of curves and surfaces. A complex curve can be decomposed using wavelet theory into lower resolution curves. The low-resolution (coarse) curves are similar to rough-cuts and high-resolution (fine) curves to finish cuts in NC machining. In this paper, we investigate the applicability of multiresolution analysis using B-spline wavelets to NC machining of contoured 2D objects. High-resolution curves are used close to the object boundary similar to conventional offsetting while lower resolution curves are used farther away from the object boundary. Experimental results indicate that wavelet-based tool path planning improves machining efficiency. Tool path length is reduced, sharp corners are smoothed out thereby reducing uncut areas and larger tools can be selected for rough-cuts.     

Constant scallop-height tool path generation for three-axis sculptured surface machining

This paper presents a new approach for the determination of efficient tool paths in the machining of sculptured surfaces using 3-axis ball-end milling. The objective is to keep the scallop height constant across the machined surface such that redundant tool paths are minimized. Unlike most previous studies on constant scallop-height machining, the present work determines the tool paths without resorting to the approximated 2D representations of the 3D cutting geometry. Two offset surfaces of the design surface, the scallop surface and the tool center surface, are employed to successively establish scallop curves on the scallop surface and cutter location tool paths for the design surface. The effectiveness of the present approach is demonstrated through the machining of a typical sculptured surface. The results indicate that constant scallop-height machining achieves the specified machining accuracy with fewer and shorter tool paths than the existing tool path generation approaches.     

Rough and finish tool-path generation for NC machining of freeform surfaces based on a multiresolution method

Progressive fitting and multiresolution tool path generating techniques are proposed in this paper, by which multi-level (LOD) models fitting for different subsets of sampled points are obtained, and then multiresolution rough-cut and finish-cut tool paths are generated based on the LOD models. The advantages of the proposed method are: (1) the user need not care for data reduction in CAD modeling; (2) final result is obtained by interpolating two lower-level reconstructed surfces, and each lower multiresolution CAD representation can be used to generate rough-cut tool paths; (3) different manufacturing requirements utilize different level models to generate tool paths; (4) selective refinement can be applied by interpolating selceted areas at different levels of details. The key avantage of the prograssive fitting algorithm is that it can use different level surfaces to generate adaptive rough-cut and finishi-cut tool path curves directly. Therefore, based on the proposed techniques, tool path length is reduced. Sharp concers are smothed out and large tools can be selected for rough machining. The efficiency of this algorithm has been demonstrated, and it results in a 20% reduction in machining time.     

Machining feature recognition and tool-path generation for 3-axis CNC milling

This study develops an effective method for identifying machining features. While recognizing features, the workpiece is sliced at some assigned positions. The sectional curves of the workpiece faces and slicing plane constitute the feature profiles. Not only the isolated machining features but also the intersecting machining features can be identified by the information from these intersection profiles. Moreover, the recognized machining features can be employed for scheduling the manufacturing sequence. Different kinds of tool paths can be automatically generated for various machining features to improve the cutting efficiency.     

An optimal approach to multiple tool selection and their numerical control path generation for aggressive rough machining of pockets with free-form boundaries

To machine pockets, especially ones with closed free-form boundary curves, roughing is crucial to part productivity, for this operation alone could take more than 60% of the total machining time. At present, there is a high demand from industry for a new machining technique that can efficiently cut pockets. Aggressive rough machining, in which the largest possible cutters are always employed and are fully immersed in workpieces, can be a solution. Although aggressive roughing is by far the most efficient machining strategy, compared to prior pocketing methods, no computer numerical control (CNC) programming technique has been developed to support it, resulting in few applications in machine shops. To address this urgent industrial need, based on the medial axis transform of a pocket, this work proposes an optimal approach to multiple tool selection and their numerical control (NC) path generation for aggressive roughing of the pocket. First, the NC paths of a specific tool are quickly generated using the pocket’s medial axis transform. Thanks to the unique characteristic of the medial axis transform, the paths can ensure the tool the largest accessible space for pocketing. At the same time, they can guarantee the tool to be free of gouging and interference. Then, an optimization model of selecting multiple cutters and generating their NC paths is built in order to achieve the highest efficiency of the aggressive rough machining. To demonstrate the advantages of this innovative approach, two examples are rendered, and their results are compared to those obtained by the existing methods. This approach can be directly implemented into current CAD/CAM software to promote aggressive rough machining of pockets in industry.     

Adaptive iso-planar tool path generation for machining of free-form surfaces

The iso-planar (Cartesian) tool path generation method has been used for several decades. However, it suffers an inherent drawback: in the region where the direction of the surface normal is close to that of the parallel intersecting planes, the intersecting plane intervals have to be reduced because of the influence of surface slopes. This causes redundant tool paths in the associated flatter regions and results in lower machining efficiency. This paper presents an algorithm that overcomes the disadvantage of the iso-planar method while keeping its advantages of robustness and simplicity. In this algorithm, the concept of isophote is applied to partition the surface into different regions. In each region the tool path side steps are adaptive to the surface features. Therefore redundant tool paths are avoided. By applying the region-by-region or global-local machining strategy, the machining efficiency is increased.     

Adaptive restoration of complex geometry parts through reverse engineering application

After a certain number of hours of running, no two mechanical components are completely the same due to normal wear or foreign object damage. A nominal CAD model from a component designer is different from its corresponding worn one and therefore cannot be directly used for tool path generation for build up and machining repair processes. This is the main reason that most repair process used for complex geometry parts, such as gas turbine blades, is currently carried out manually and is called the “Black Art”.This paper proposes a defects-free model-based repair strategy to generate correct tool paths for build up process and machining process adaptive to each worn component through the reverse engineering application. Based on 3D scanning data, a polygonal modelling approach is introduced in this paper to rapidly restore worn parts for direct use of welding, machining and inspection processes. With this nominal model, this paper presents the procedure to accurately define and extract repair error, repair volume and repair patch geometry for the tool path generation, which is adaptive to each individual part. The tool paths are transferred to a CNC machine for the repairing trials. Further research work is performed on repair geometry extraction algorithm and repair module development within the reverse engineering environment.     

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 smooth spiral tool path for high speed machining of 2D pockets

We introduce a new algorithm for generating a spiral tool path for high-speed machining of pockets without islands. The pocket may be an arbitrary simply-connected 2D shape bounded by straight-line segments and circular arcs. The tool path is generated by interpolating growing disks placed on the medial axis of the pocket. It starts inside the pocket and spirals out to the pocket boundary. The tool path is guaranteed to be free of self-intersections and allows machining of the pocket without tool retractions. The start point of the spiral may be chosen freely by the user anywhere within the pocket. Most importantly, the spiral tool path complies with a user-specified maximum cutting width. The output of our algorithm is a G¹-continuous spiral path. However, in a post-processing step, a properly adapted variant of the recent “PowerApx” package [Heimlich M, Held M. Biarc approximation, simplification and smoothing of polygonal curves by means of Voronoi-based tolerance bands. International Journal of Computational Geometry & Applications 2008;18(3):221-50] can be used to boost the tool path to C²-continuity. Our new algorithm was implemented and tested successfully on real-world data. We conclude our paper by an analysis of sample tool paths produced by our implementation.     

Linear and angular feedrate interpolation for planar implicit curves

In multi-axis CNC machining, a cutting tool combines translation and rotational movements with respect to a workpiece. This entails CNC interpolation to take angular feedrates defining the speed of the rotational movement into account, while current interpolations are overwhelmingly based on linear feedrates defining the speed of the translation movement. This paper considers linear and angular feedrate interpolations of 2D tool paths for multi-axis machining. A 2D tool path is identified by a position curve assumed to be a 2D implicit curve and a tool orientation curve based on the implicit curve. The paper will relate the angular feedrate to the linear feedrate along the tool paths. The result is then used to develop the angular feedrate interpolation from the linear feedrate interpolation. Detailed interpolation schemes for such hybrid feedrates as a constant linear feedrate with constrained angular feedrate (CLCA) and a constant angular feedrate with constrained linear feedrate (CACL) have further been constructed. A corrected interpolation scheme is further present to augment the initial interpolation. Example interpolations including a quadric curve, the nodal cubic and a quartic curve are carried out to illustrate the feasibility and effectiveness of the proposed approach.     

复杂曲面笔式加工的直接插补算法

复杂曲面笔式加工时的工具轨迹是位于曲面上的自由曲线轨迹．针对此类形式的轨迹，给出一种复杂曲面笔式加工时的自由曲线型刀轨的直接插补算法，即对位于曲面上以投影方式形成的任意自由曲线形式的刀轨进行插补计算，生成控制机床运动的指令．该方法的实现扩充了CNC系统的轨迹控制功能，提高了复杂曲面的加工效率．仿真和试切的结果证明算法可行而且有效．该算法也可以应用到整体曲面加工中．     

Fast Constrained Surface Extraction by Minimal Paths

In this paper we consider a new approach for single object segmentation in 3D images. Our method improves the classical geodesic active surface model. It greatly simplifies the model initialization and naturally avoids local minima by incorporating user extra information into the segmentation process. The initialization procedure is reduced to introducing 3D curves into the image. These curves are supposed to belong to the surface to extract and thus, also constitute user given information. Hence, our model finds a surface that has these curves as boundary conditions and that minimizes the integral of a potential function that corresponds to the image features. Our goal is achieved by using globally minimal paths. We approximate the surface to extract by a discrete network of paths. Furthermore, an interpolation method is used to build a mesh or an implicit representation based on the information retrieved from the network of paths. Our paper describes a fast construction obtained by exploiting the Fast Marching algorithm and a fast analytical interpolation method. Moreover, a Level set method can be used to refine the segmentation when higher accuracy is required. The algorithm has been successfully applied to 3D medical images and synthetic images.     

Iso-planar piecewise linear NC tool path generation from discrete measured data points

This article presents a method of generating iso-planar piecewise linear NC tool paths for three-axis surface machining using ball-end milling directly from discrete measured data points. Unlike the existing tool path generation methods for discrete points, both the machining error and the machined surface finish are explicitly considered and evaluated in the present work. The primary direction of the generated iso-planar tool paths is derived from the projected boundary of the discrete points. A projected cutter location net (CL-net) is then created, which groups the data points according to the intended machining error and surface finish requirements. The machining error of an individual data point is evaluated within its bounding CL-net cell from the adjacent tool swept surfaces of the ball-end mill. The positions of the CL-net nodes can thus be optimized and established sequentially by minimizing the machining error of each CL-net cell. Since the linear edges of adjacent CL-net cells are in general not perfectly aligned, weighted averages of the associated CL-net nodes are employed as the CL points for machining. As a final step, the redundant segments on the CL paths are trimmed to reduce machining time. The validity of the tool path generation method has been examined by using both simulated and experimentally measured data points.     

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.     

An algorithm for the interpolation of hybrid curves

Real time tool path generation consists of off-line design and real time interpolation of tool paths. An hybrid curve is the intersection of a parametric surface and an implicit surface. Previous work in tool path interpolation focused mainly in the interpolation of parametric curves. Tool paths designed by drive surface methods are hybrid curves which, in general, cannot be represented as parametric curves. An algorithm for the interpolation of hybrid curves is proposed in this paper. The algorithm is based on interpolation of the projection of the hybrid curve into the parametric domain. Each increment involves a second-order interpolation step augmented by iterative error reduction.Simulations of hybrid curve interpolation have been carried out. They are based on practical surfaces represented as NURB surfaces and implicit surfaces including a plane, a cylinder and a high order algebraic surface. They demonstrate that under typical machining conditions, interpolation error is well within the accuracy requirements of typical machining and that the use of one iteration error reduction can significantly reduce the path deviation. These show that the proposed algorithm is potentially useful for tool path interpolation for the machining of parametric surfaces.     

Curve fitting and optimal interpolation for CNC machining under confined error using quadratic B-splines

In CNC machining, fitting the polyline machining tool path with parametric curves can be used for smooth tool path generation and data compression. In this paper, an optimization problem is solved to find a quadratic B-spline curve whose Hausdorff distance to the given polyline tool path is within a given precision. Furthermore, adopting time parameter for the fitting curve, we combine the usual two stages of tool path generation and optimal velocity planning to derive a one-step solution for the CNC optimal interpolation problem of polyline tool paths. Compared with the traditional decoupled model of curve fitting and velocity planning, experimental results show that our method generates a smoother path with minimal machining time.     

Machining efficiency comparison direction-parallel tool path with contour-parallel tool path

In molds and dies manufacturing, estimation of the machining time of tool paths is a pre-requisite for planning the machining processes and balancing them. The machining time is computed by dividing the distance of the tool path by its feed-rate. This theoretical machining time always underestimates the actual time, because it does not take into account the effects of the acceleration and deceleration of the CNC machines. This paper proposes a machining time model that considers the acceleration and deceleration of the CNC machines. Using the proposed model, we compare the machining efficiency of the tool paths currently employed in molds and dies manufacturing—three types of direction-parallel tool paths (one-way path, pure-zig-zag path, and smooth-zig-zag path) and contour-parallel tool path. The results of the comparison simulation reveal that the smooth-zig-zag path is the most efficient regardless of feed-rates and path intervals and that the effects of acceleration and deceleration are notably revealed at higher feed-rates.     

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.     

Generation of collision-free 5-axis tool paths using a haptic surface

An intuitive man-machine interface for generating 5-axis tool paths is described in the paper. The system is based on a 5 degree-of-freedom force feedback haptic system, which is used to interface a human with an impenetrable 3D part. In the process of feeling the object, the user ‘teaches’ a milling machine to machine a virtual 3D object. The tool path generation has two phases: recording of access directions at the surface of the object and the post-processing phase. During the recording phase, three functions are carried out simultaneously: first, a fast collision detection algorithm, using hierarchical object representation, to drive the haptic system; second, visual feedback to show the regions that have been accessed by the tool; and third, a system to capture the access directions of the tool as the user touches the object. The post-processing phase involves the use of information generated in the recording phase to generate 5-axis tool paths. First, the access directions at the surface of the part are interpolated; and second, any residual collisions are detected and eliminated. We show the results of the tool path generation for two parts. The system can help an expert user generate, correct and tweak tool paths.