Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining

We propose a new algorithm to detect patches of free-form surfaces that can be well approximated by envelopes of a rotational cone under a rigid body motion. These conical envelopes are a preferable choice from the manufacturing point of view as they are, by-definition, manufacturable by computer numerically controlled (CNC) machining using the efficient flank (peripheral) method with standard conical tools. Our geometric approach exploits multi-valued vector fields that consist of vectors in which the point-surface distance changes linearly. Integrating such vector fields gives rise to a family of integral curves, and, among them, linear segments that further serve as conical axes are quickly extracted. The lines that additionally admit tangential motion of the associated cone along the reference geometry form a set of candidate lines that are sequentially clustered and ordered to initialize motions of a rigid truncated cone. We validate our method by applying it on synthetic examples with exact envelopes, recovering correctly the exact solutions, and by testing it on several benchmark industrial datasets, detecting manufacturable conical envelope patches within fine tolerances.     

Tool path generation for free form surfaces using Bézier curves/surfaces

Presented in this paper is a tool path generation method for multi-axis machining of free-form surfaces using Bézier curves and surfaces. The tool path generation includes two core steps. First is the forward-step function that determines the maximum distance, called forward step, between two cutter contact (CC) points with a given tolerance. The second component is the side step function which determines the maximum distance, called side step, between two adjacent tool paths with a given scallop height. Using the Bézier curves and surfaces, we generate cutter contact (CC) points for free-form surfaces and cutter location (CL) data files for post processing. Several parts are machined using a multi-axis milling machine. As part of the validation process, the tool paths generated from Bézier curves and surfaces are analyzed to compare the machined part and the desired part.     

Automated tool sequence selection for 3-axis machining of free-form pockets

This paper describes an efficient method to find the lowest cost tool sequence for rough machining free-form pockets on a 3-axis milling machine. The free-form pocket is approximated to within a predefined tolerance of the desired surface using series of 2.5-D layers of varying thicknesses that can be efficiently removed with flat-end milling cutters. A graph-based method finds an optimal sequence of tools for rough machining the approximated pocket. The algorithm used here can be tuned to suit any available tool set and preferred cost models. The tool sequence that is obtained is near optimal, and may take into account tool wear, as well as various overhead costs of the machine shop.     

Correlation between machining direction,cutter geometry and step-over distance in 3-axis milling: Application to milling by zones

Computer-Aided Manufacturing (CAM) occupies an increasingly important role in engineering with all it has to offer in terms of new possibilities and improving designer/manufacturer productivity. The present study addresses machining of free-form surfaces on a 3-axis NC machine tool. There have recently been a large number of studies devoted to planning tool paths on free-form surfaces with various strategies being adopted. These strategies are intended to increase efficiency by reducing the overall length of machining. Often, the choice of the cutter is arbitrary and the work focuses on planning. In order to boost productivity, the present work offers assistance in choosing the cutting tool, the machining direction and cutting by surface zones, adopting a milling strategy by parallel planes. To do so, a comparison is made between milling using a spherical end milling cutter and a torus end milling cutter with the same outer radius. This comparison relates to the radius of curvature of the trace left by the cutter at the point of contact between the tool and the workpiece in relation to the direction of feed motion.     

Tool path planning for 5-axis flank milling of ruled surfaces considering CNC linear interpolation

This paper investigates tool path planning for 5-axis flank milling of ruled surfaces in consideration of CNC linear interpolation. Simulation analyses for machining error show insights into the tool motion that generates a precision machined surface. Contradicting to previous thoughts, the resultant tool path does not necessarily produce minimal machining error when the cutter contacts the rulings of a developable surface. This effect becomes more significant as the distance between two cutter locations is increased. An optimizing approach that adjusts the tool position locally may not produce minimal error as far as the entire surface is concerned. The optimal tool path computed by a global search scheme based on dynamic programming supports this argument. A flank milling experiment and CMM measurement further validate the findings of this work.     

Determining gouge-free ball-end mills for 3D surface machining from point cloud data

This paper presents an algorithm to automatically determine the optimal size of the ball-end milling tool used for the three-axis finish machining of free-form surfaces directly from discrete coordinate data points. The tool is considered optimal if it is of the largest possible diameter that can access every data point without causing an overcut situation or gouging the other data points. Two well-developed techniques in computational geometry, Voronoi diagram and Delaunay triangulation, are used to establish the geometric relationship among data points from which the information required to determine the optimal tool size is extracted. The result of Delaunay triangulation is a set of tetrahedrons, with the data points as vertices, which define a corresponding set of empty circum-spheres. Each data point is a vertex of several tetrahedrons and the largest of the corresponding circum-spheres represents a valid estimation of the optimal tool size at the point. Since the data points are only a sample of the original 3D surface, accuracy of the estimated tool size can be improved by using the approximated normal vector at the data point. The estimated tool size is evaluated by comparing it to its theoretical value. Extensive simulation tests show that a robust and accurate method of determining the optimal ball-end mill size has been developed.     

Empirical mode decomposition on surfaces

Empirical Mode Decomposition (EMD) is a powerful tool for analysing non-linear and non-stationary signals, and has drawn a great deal of attentions in various areas. In this paper, we generalize the classical EMD from Euclidean space to the setting of surfaces represented as triangular meshes. Inspired by the EMD, we also propose a feature-preserving smoothing method based on extremal envelopes. The core of our generalized EMD on surfaces is an envelope computation method that solves a bi-harmonic field with Dirichlet boundary conditions. Experimental results show that the proposed generalization of EMD on surfaces works well. We also demonstrate that the generalized EMD can be effectively utilized in filtering scalar functions defined over surfaces and surfaces themselves.     

New approach to 5-axis flank milling of free-form surfaces: Computation of adapted tool shape

This paper develops a new approach to solve the problem of interferences during the flank milling of a non-developable ruled surface. Many articles propose to modify the tool path to reduce this problem. A novel approach is proposed here, Computation of Adapted Tool Shape (CATS), which computes and optimizes the tool shape to reduce these interferences. The aim of this CATS method is to maintain a standard CAM system thanks to the tool shape modification. This method is presented for the machining of an industrial part and for a numerical experimental design of nine surfaces.     

Five-axis NC cylindrical milling of sculptured surfaces

In theory, the five-axis numerical control (NC) machining of sculptured surfaces can be classified into facing milling and cylindrical milling (or side milling). In general, the first one, using flat-end cutter, is suitable for the machining of large sculptured surfaces, e.g. the blade of hydraulic turbine, whose binding relations with drive surface (DS) and check surface (CS) are simple, and the second one, using cylindrical cutter, has wide applications for the milling of small and middle dimensional surfaces whose binding relations with DS and CS are more complex, such as the milling of integral turbine wheels. In practice, the second one suffers more difficulties than the first one, which are mostly related to gouge avoidance, interference avoidance and tool strength. This paper, on the basis of the theories of differential geometry and analytical geometry, describes research on algorithms for the toolpath generation of five-axis cylindrical milling of sculptured surfaces with cylindrical cutter. The approach includes (a) single point offset (SPO) algorithm, and (b) double point offset (DPO) algorithm for the cutter location data (CLDATA) calculation of five-axis cylindrical milling.     

High accuracy NC milling simulation using composite adaptively sampled distance fields

We describe a new approach to shape representation called a composite adaptively sampled distance field (composite ADF) and describe its application to NC milling simulation. In a composite ADF each shape is represented by an analytic or procedural signed Euclidean distance field and the milled workpiece is given as the Boolean difference between distance fields representing the original workpiece volume and distance fields representing the volumes of the milling tool swept along the prescribed milling path. The computation of distance field of the swept volume of a milling tool is handled by an inverted trajectory approach where the problem is solved in tool coordinate frame instead of a world coordinate frame. An octree bounding volume hierarchy is used to sample the distance functions and provides spatial localization of geometric operations thereby dramatically increasing the speed of the system. The new method enables very fast simulation, especially of free-form surfaces, with accuracy better than 1 micron, and low memory requirements. We describe an implementation of 3 and 5-axis milling simulation.     

Generalization of the imprint method to general surfaces of revolution for NC machining

This paper presents a method of determining the shape of the surface swept by a generalized milling tool that follows a 5-axis tool path for machining curved surfaces. The method is a generalization of an earlier technique for toroidal tools that is based on identifying grazing points on the tool surface. We present a new proof that the points constructed by this earlier method are in fact grazing points, and we show that this previous method can be used to construct grazing points on (and only on) the sphere, the cone, and the torus. We then present a more general method that can compute grazing points on a general surface of revolution. The advantage of both methods is that they use simple, geometric formulas to compute grazing points.     

Optimize tool paths of flank milling with generic cutters based on approximation using the tool envelope surface

This paper presents a global optimization method to generate a tool path for flank milling free-form surfaces with a generic cutter based on approximation using the tool envelope surface. It is an extension of our previous work [Gong Hu, Cao Li-Xin, Liu Jian. Improved positioning of cylindrical cutter for flank milling ruled surfaces. Computer Aided Design 2005; 37:1205–13]. First, given initial tool path or tool axis trajectory surface, the grazing points of the tool envelope surface can be calculated. Second, the errors between the tool envelope surface and the designed surface along the normal direction of the tool envelope surface are calculated. Based on this new definition of error, an optimization model is established to get the global optimized tool axis trajectory surface. In order to simplify the calculation, two variants of this method based on the least square criterion are proposed to solve this model. Since this method is really based on the tool envelope surface, it can reduce the initial machining errors effectively. The proposed method can be used not only for cylindrical cutters and conical cutters, but also for generic cutters with a surface of revolution. In addition to ruled surfaces, it also can be used for machining non-ruled surfaces. Finally, several examples are given to prove its effectiveness and accuracy. The generated tool paths and calculated grazing points for test are available in supplementary files for the readers’ convenience in verifying this work in different CAD/CAM systems.     

Oriented bounding box and octree based global interference detection in 5-axis machining of free-form surfaces

Global interference detection is a critical problem in 5-axis NC machining of free-form surfaces. Based on the hierarchical oriented bounding box (OBB) which is used in virtual reality to detect spatial collisions between 3D objects, a new global interference detection method is developed in this paper. In this method, in order to simplify the computation process of updating tool positions and orientations in 5-axis machining, the cutter and cutter holder are modeled by a hierarchical OBB structure, whereas the workpiece surfaces are approximated by an octree. Interference detection is conducted between the tool OBBs and the gray octants of the surface octree with the separating axis theorem. With the hierarchical structure of octree, if interference is found in one octant, its sub-octants are further processed to locate the exact colliding leaf nodes and the discretized surface points contained in these leaf nodes are tested with a conventional vector calculation method for exact interference detection; if no interference is detected, all the sub-octants are then considered as interference free and are not processed further. Meanwhile, with the hierarchical structure of the tool OBBs, should interference occur between octants and the OBBs in the first level of the hierarchical structure, the sub-OBBs in the second level would be further tested. Otherwise it could be determined with certainty that there is no interference between the tool and the octant.     

Automated path planning for face milling of N-sided convex polygonal surfaces using staircasing strategy

In a manufacturing environment, many times, it is difficult to have NC physical effort with actual machining. This effort can be considerably minimized by analytical modeling of tool path. The path selected for face milling of flat convex polygonal surfaces can significantly affect the cutter travelling distance. Past studies have identified that efforts were made to minimize the path selected for maching these surfaces. However, not much information is available on machining convex polygonal parts for N-sides. An object oriented software package was developed in Turbo C++ to graphically simulate the tool path while face milling different N-sided polygonal surfaces following staircasing path. The staircasing strategy was adopted since the shortest length of cut generated is better than that generated by window frame milling. Pop Up menus were created so that the software developed is interactive, user friendly and completed with error handling.     

Improving optimization of tool path planning in 5-axis flank milling using advanced PSO algorithms

This paper studies optimization of tool path planning in 5-axis flank milling of ruled surfaces using advanced Particle Swarm Optimization (PSO) methods with machining error as an objective. We enlarge the solution space in the optimization by relaxing the constraint imposed by previous studies that the cutter must make contact with the boundary curves. Advanced Particle Swarm Optimization (APSO) and Fully Informed Particle Swarm Optimization (FIPS) algorithms are applied to improve the quality of optimal solutions and search efficiency. Test surfaces are constructed by systematic variations of three surface properties, cutter radius, and the number of cutter locations comprising a tool path. Test results show that FIPS is most effective in reducing the error in all the trials, while PSO performs best when the number of cutter locations is very low. This research improves tool path planning in 5-axis flank milling by producing smaller machining errors compared to past works. It also provides insightful findings in PSO based optimization of the tool path planning.     

Analysis of improved positioning in five-axis ruled surface milling using envelope surface

This article covers side milling of ruled surfaces using a milling cutter. Flank milling is useful for machining objects such as impellers, turbine blades, fan vanes and all workpieces defined by non-developable, ruled surfaces. In the present article, we first introduce two types of positioning on ruled surfaces developed within the Toulouse Mechanical Engineering Laboratory. The positioning studied is taken from the geometric situation not taking the instantaneous speed of rotation of the milling cutter into account. The swept profile of the tool is then determined based on the tool motion. Having defined the envelope surface, we seek to analyse improved and standard positioning errors comparing envelope surfaces with the ruled surface. We then introduce an example to illustrate positioning developed through a first theoretical study before experimentation including machining and measurement of the test piece. Finally, we give our conclusions as to the validity of improved positioning without taking the instantaneous speed of rotation of the milling cutter into account.     

ADAPTIVE STRATEGIES FORNC MACHINING COMPOUND FREE-FORM SURFACES

ＡＤＡＰＴＩＶＥＳＴＲＡＴＥＧＩＥＳＦＯＲＮＣＭＡＣＨＩＮＩＮＧＣＯＭＰＯＵＮＤＦＲＥＥ－ＦＯＲＭＳＵＲＦＡＣＥＳＧａｏＳａｎｄｅ；ＺｈｏｕＹｕｎｆｅｉ；ＺｈａｎｇＸｉｎｆａｎｇ；ＺｈｏｕＪｉＡＤＡＰＴＩＶＥＳＴＲＡＴＥＧＩＥＳＦＯＲＮＣＭＡＣＨＩＮ...     

An approach of designing and controlling free-form surfaces by using NURBS boundary Gregory patches

Designers require a means of designing complex free-form surfaces easily and intuitively. One general approach to designing such surfaces is to first define a curve mesh consisting of characteristic lines, such as cross sections and boundary curves, then to interpolate the curve mesh using free-form surfaces. NURBS surfaces are widely used but make the interpolation of an irregular curve mesh difficult. This has been a major limiting constraint on designers. In this paper, we propose a new surface representation that enables the smooth interpolation of an irregular curve mesh with NURBS curves and surfaces.     

A variable-depth multi-layer five-axis trochoidal milling method for machining deep freeform 3D slots

Trochoidal milling is a popular machining method for slotting operation, as it avoids a full tool-workpiece engagement and hence helps, often significantly, slow down the tool wear, which is particularly a concern in the machining of hard-to-cut materials like titanium alloy. However, as the traditional trochoidal milling method assumes a fixed tool orientation, it can only apply to 2D shaped slots, while for many industrial parts the slot to cut is typically a genuine 3D freeform slot such as grooves on a blisk. In this paper, we present a multi-layer five-axis trochoidal milling method for machining an arbitrary 3D deep slot that is defined by two freeform side boundary surfaces. Aiming at minimizing the total cutting time, instead of conservatively dividing the slot into equi-depth layers, we strive to minimize the number of layers with variable layer depths while at the same time satisfying the two most critical physical constraints on the tool – the tool deformation and the tool stress. Both computer simulation and physical cutting experiments of the proposed method have been carried out, and the experimental results confirm the feasibility and advantages of the proposed method.     

Triple tangent flank milling of ruled surfaces

This paper presents a positioning strategy for flank milling ruled surfaces. It is a modification of a positioning method developed by Bedi et al. [Comput Aided Des 35 (2003) 293]. A cylindrical cutting tool is initially positioned tangential to the two boundary curves on a ruled surface. Optimization is used to move these tangential points to different curves on the ruled surface to reduce the error. A second optimization step is used to additionally make the tool tangent to a rule line, further reducing the error and resulting in a tool position, where the tool is positioned tangential to two guiding rails and one rule line. The resulting surface has 88% less under cutting than the method of Bedi et al.