Graphics-assisted Rolling Ball Method for 5-axis surface machining

In this paper, a graphics hardware-assisted approach to 5-axis surface machining is presented that builds upon a tool positioning strategy named the Rolling Ball Method presented in an earlier paper by the present authors [Comput. Aided Des. 35 (2003) 347]. The depth buffer of the computer's graphics card is used to compute the data needed for the Rolling Ball Method, which generates gouge-free 5-axis curvature-matched tool positions. With this approach, the tool path for a workpiece can be computed with triangulated data instead of parametric surface equations. It also permits the generation of tool paths for multiple surface patch workpieces that have only positional continuity. The method is easy to implement and it is robust since every tool position is computed with the same algorithm regardless of the type of surface. For illustration, tool paths were generated for a workpiece with two bi-cubic surface patches, connected with only position continuity. Simulations for gouge-checking and machining tests were performed. Workpiece cusp heights were measured using a coordinate measuring machine. The maximum undercutting measured in the machining examples was 0.07 and 0.05 mm, which is within the expected NC machine accuracy and measuring capabilities for surfaces.     

Creation of 3-D tiny statue by 5-axis control ultraprecision machining

The study deals with the creation of a 3-dimensional (3-D) complicated tiny statue by means of a 5-axis control ultraprecision machining center and a pseudo ball end mill of single crystal diamond. In recent years, 3-D microstructures are required to provide components for micromechanism as well as metal molds and dies. Thus, as an example of complicated 3-D microstructures, a Buddha head of 3 mm in size was created, based on the scanned data of an actual statue. A control program developed in the study enables a diamond tool to feed around the head and to move from the top of the head to the neck not only by 4-axis control but also by 5-axis control to prevent the tool and its holder from colliding with a workpiece. As a result, a tiny Buddha head could be created with high surface quality.     

Arc-intersect method for 5-axis tool positioning

A new method for 5-axis CNC tool positioning is presented in this paper that improves upon a previous tool positioning strategy named the rolling ball method (RBM), which was developed by the present authors [Gray P, Bedi F, Ismail S. Rolling ball method for 5-axis surface machining. Comput Aided Des 2003;35(4):347-57]. The special property of the RBM is that it computes tool positions by considering the area beneath the tool that the tool will be positioned to cut instead of using surface curvatures computed at a single point on the surface. This enables the RBM to generate gouge-free tool positions without secondary iterative gouge-check and correction algorithms. However, the RBM generates conservative tilt angles in order to guarantee gouge-free tool positions. The new arc-intersect method (AIM) presented in this paper improves upon the RBM by directly positioning the tool to contact the surface and thereby eliminates the conservative nature of the RBM to give optimal tool positions. Like the RBM, the AIM is an area-based method that generates gouge-free tool positions without the use of iterative gouge-check and correction algorithms. The implementation described in this paper uses triangulated surfaces and the computer's graphics hardware to assist in the tool position calculations. However, the method can be applied to any surface representation since it only uses surface coordinates and surface normals for computation. A section of a stamping die was machined to demonstrate the AIM and to show the improvement over the RBM and for comparison with 3-axis ballnose machining. The results showed that the AIM was 1.33 times faster than the RBM and that the AIM, with single direction parallel tool passes, was 1.62 times faster than a zig-zag pattern 3-axis ballnose tool path for the same feed rate, cusp height and tool diameter. The workpieces were measured with a CMM and the data were compared to the CAD model to show no gouging occurred and to check the cusp heights.     

NC tool path generation for 5-axis machining of free formed surfaces

This paper presents a tool axis vector approach for machining sculptured surfaces. Such an approach is well suited for highly twisted, rolled, or bent surfaces. The tool paths are generated for a 5-axis milling machine. The proposed approach is based on tilt angle, cutting direction, and a vector normal to the cutting surface. Gouging is avoided by checking the interference between the cutting tool and the part surface. The algorithm also finds maximum path intervals that generate maximum admissible cusp height within the specified tolerance limits. Such an approach minimizes the tool path and machining time. The paper presents an example to illustrate the details of the algorithm.This research was accomplished by funding provided by the Korean Research Foundation under the Faculty Research Abroad Program and by the advice and support of the second author.     

Performance evaluation of CUDA programming for 5-axis machining multi-scale simulation

5-Axis milling simulations in CAM software are mainly used to detect collisions between the tool and the part. They are very limited in terms of surface topography investigations to validate machining strategies as well as machining parameters such as chordal deviation, scallop height and tool feed. Z-buffer or N-buffer machining simulations provide more precise simulations but require long computation time, especially when using realistic cutting tools models including cutting edges geometry. Thus, the aim of this paper is to evaluate Nvidia CUDA architecture to speed-up Z-buffer or N-buffer machining simulations. Several strategies for parallel computing are investigated and compared to single-threaded and multi-threaded CPU, relatively to the complexity of the simulation. Simulations are conducted with two different configurations including Nvidia Quadro 4000 and Geforce GTX 560 graphic cards.     

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.     

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.     

Optimizing tool orientations for 5-axis machining by configuration-space search method

This paper presents a methodology and algorithms of optimizing and smoothing the tool orientation control for 5-axis sculptured surface machining. A searching method in the machining configuration space (C-space) is proposed to find the optimal tool orientation by considering the local gouging, rear gouging and global tool collision in machining. Based on the machined surface error analysis, a boundary search method is developed first to find a set of feasible tool orientations in the C-space to eliminate gouging and collision. By using the minimum cusp height as the objective function, we first determine the locally optimal tool orientation in the C-space to minimize the machined surface error. Considering the adjacent part geometry and the alternative feasible tool orientations in the C-space, tool orientations are then globally optimized and smoothed to minimize the dramatic change of tool orientation during machining. The developed method can be used to automate the planning and programming of tool path generation for high performance 5-axis sculptured surface machining. Computer implementation and examples are also provided in the paper.     

Mechanistic modelling of 5-axis milling using an adaptive and local depth buffer

A mechanistic model for 5-axis surface machining with a toroidal-end mill is presented in this work. A graphical representation of the tool movements is used to determine the in-process chip geometry and tool edge contact length using an adaptive and local depth buffer. The graphical representation of the tool movements is generated using either tooth swept sectors that model the tool’s cutting teeth as they rotate or the swept surface of the tool as it moves along the tool path. The mechanistic model was verified with two cutting experiments: The first cutting test showed that the data agrees with the simulation results within 7% of the peak-to-peak forces. The second cutting test modelled a more complex stock surface and tool path. The simulation results were within 10% of the measured peak-to-peak cutting torque.     

Arc–surface intersection method to calculate cutter–workpiece engagements for generic cutter in five-axis milling

Calculating cutter–workpiece engagements (CWEs) is essential to the physical simulation of milling process that starts with the prediction of cutting forces. As for five-axis milling of free form surfaces, the calculation of CWEs remains a challenge due to the complicated and varying engagement geometries that occur between the cutter and the in-process workpiece. In this paper, a new arc–surface intersection method (ASIM) is proposed to obtain CWEs for generic cutter in five-axis milling. The cutter rotary surface is first represented by the family of section circles which are generated by slicing the cutter with planes perpendicular to the tool axis. Based on the envelope condition, two grazing points on each section circle are analytically derived, which divide the circle into two arcs. The feasible contact arc (FCA) is then extracted to intersect with workpiece surfaces. Using arc/surface intersection and distance fields based approach, the boundary of the closed CWEs is accurately and efficiently calculated. Compared with the solid modeler based method and the discrete method, the ASIM has higher computational efficiency and accuracy. Moreover, an analytical solution for calculating CWEs can be obtained with this method in five-axis milling of the workpiece merely comprising of flat and quadric surfaces. Finally, two case tests are implemented to confirm the validity of the ASIM and comparisons have been made with a Vericut based system which utilizes the Z-buffer method. The results indicate that the ASIM is computationally efficient, accurate and robust.     

A multipoint method for 5-axis machining of triangulated surface models

In this paper, we present a multipoint machining method for the 5-axis machining of triangulated surfaces with radiused end mills. The main idea is to drop the tool onto the surface to find an initial point of contact, and then rotate the tool while maintaining tangency with this initial point of contact until a second point of contact is found. The proposed procedure ensures a gouge-free position with two points of contact, allowing for a larger side step than a single point of contact method. This proof of concept paper presents the mathematical equations that must be solved to position the tool with two points of contacts on an STL surface. The paper further verifies the concept with simulations and presents experimental results to confirm the simulations.     

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.     

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.     

Second order approximation of tool envelope surface for 5-axis machining with single point contact

For 5-axis machining with single point contact, this paper proposes a method to calculate second order approximation of the tool envelope surface by using only one tool position. As we known, the true machining errors are deviations between designed surface and tool envelope surface. But it is impossible to determine the whole shape of the tool envelope surface before all tool positions are obtained. Hence, it is difficult to position the tool individually and consider true errors at the same time. Basic Curvature Equations of Locally Tool Positioning (BCELTP) are presented to solve this problem in some degree. By using them under some special conditions, given one tool position, the local shape (second order approximation) of the tool envelope surface can be calculated precisely at the corresponding cutter contact point. These equations make it convenient to adjust the tool position individually until true errors are reduced in some degree. So, they are useful for optimizing tool positions locally. Finally, some examples are given to verify the correctness and practicability of theory.     

Five-axis pencil-cut planning and virtual prototyping with 5-DOF haptic interface

In this paper, techniques of 5-axis pencil-cut machining planning with a 5-DOF (degree of freedom) output haptic interface are presented. Detailed techniques of haptic rendering and tool interference avoidance are discussed for haptic-aided 5-axis pencil-cut tool path generation. Five-axis tool path planning has attracted great attention in CAD/CAM and NC machining. For efficient machining of complex surfaces, pencil-cut uses relatively smaller tools to remove the remaining material at corners or highly curved regions that are inaccessible with larger tools. As a critical problem for 5-axis pencil-cut tool path planning, the tasks of tool orientation determination and tool collision avoidance are achieved with a developed 5-DOF haptic interface. A Two-phase rendering approach is proposed for haptic rendering and force-torque feedback calculation with haptic interface. A Dexel-based volume modeling method is developed for global tool interference avoidance with surrounding components in a 5-axis machining environment. Hardware and software implementation of the haptic pencil-cut system with practical examples are also presented in this paper. The presented technique can be used for CAD/CAM, 5-axis machining planning and virtual prototyping.     

Mechanistic modelling of the milling process using an adaptive depth buffer

A mechanistic model of the milling process based on an adaptive and local depth buffer is presented. This mechanistic model is needed for speedy computations of the cutting forces when machining surfaces on multi-axis milling machines. By adaptively orienting the depth buffer to match the current tool axis, the need for an extended Z-buffer is eliminated. This allows the mechanistic model to be implemented using standard graphics libraries, and gains the substantial benefit of hardware acceleration. Secondly, this method allows the depth buffer to be sized to the tool as opposed to the workpiece, and thus improves the depth buffer size to accuracy ratio drastically. The method calculates tangential and radial milling forces dependent on the in-process volume of material removed as determined by the rendering engine depth buffer. The method incorporates the effects of both cutting and edge forces and accounts for cutter runout. The simulated forces were verified with experimental data and found to agree closely. The error bounds of this process are also determined.     

Smooth tool path generation for 5-axis machining of triangular mesh surface with nonzero genus

NC machining of a nonzero genus triangular mesh surface is being more widely confronted than before in the manufacturing field. At present, due to the complexity of geometry computation related to tool path generation, only one path pattern of iso-planar type is adopted in real machining of such surface. To improve significantly 5-axis machining of the nonzero genus mesh surface, it is necessary to develop a more efficient and robust tool path generation method. In this paper, a new method of generating spiral or contour-parallel tool path is proposed, which is inspired by the cylindrical helix or circle which are a set of parallel lines on the rectangular region obtained by unwrapping the cylinder. According to this idea, the effective data structure and algorithm are first designed to transform a nonzero genus surface into a genus-0 surface such that the conformal map method can be used to build the bidirectional mapping between the genus-0 surface and the rectangular region. In this rectangular region, the issues of spiral or contour-parallel tool path generation fall into the category of simple straight path planning. Accordingly, the formula for calculating the parameter increment for the guide line is derived by the difference scheme on the mesh surface and an accuracy improvement method is proposed based on the edge curve interpolation for determining the cutter contact (CC) point. These guarantee that the generated tool path can meet nicely the machining requirement. To improve further the kinematic and dynamic performance of 5-axis machine tool, a method for optimizing tool orientation is also preliminarily investigated. Finally, the experiments are performed to demonstrate the proposed method and show that it can generate nicely the spiral tool path or contour-parallel tool path on the nonzero genus mesh surface and also can guarantee the smooth change of tool orientation.     

Direct 5-axis tool-path generation from point cloud input using 3D biarc fitting

In reverse engineering, geometrical information of a product is obtained directly from a physical shape by a digitizing device. To fabricate the product, manufacturing information (usually tool-path) must be generated from a CAD model. The data digitized must be processed and in most cases, a surface model is constructed from them using some of the surface fitting technologies. However, these technologies are usually complicated and the process for constructing a surface patch from a massive digitizing data is time-consuming. To simplify the process for getting tool-path information, a simple algorithm is proposed in this paper. The algorithm is used to generate a 5-axis machining tool-path. Instead of implementing any complicated surface fitting techniques, a direct method is proposed for constructing three-dimensional (3D) triangular mesh from the digitizing data with the mesh points considered as the tool contact locations. Depending on the locations of the points digitized, a decimation procedure is applied such that some of the digitizing data will be filtered out. Then, the tool axis orientations which must be determined in 5-axis tool-path are calculated and the tool center locations are determined accordingly. A 3D biarc fitting technique is applied for all the tool center locations so that a complete 5-axis tool-path is obtained.     

An accuracy algorithm for chip thickness modeling in 5-axis ball-end finish milling

Chip thickness in milling is one of the most fundamental parameters, which can significantly affect cutting force, cutting heat, cutting stability and machined surface topography for computer-aided process planning. In this paper, a combination of a three-dimensional trochoidal tooth trajectory model (3D3T) and engagement-boundary chip model is developed to determine instantaneous chip thickness in 5-axis ball-end finish milling. In comparison with the chip volume measured in a commercial software package (Unigraphics) the accuracy of the proposed model has been numerically validated with various process parameters including cutting depth, tool–workpiece inclination and cutter runout. The differences in time-varying delay and dynamic chip thickness as well as stability are compared with different models to show the impact of using 3D3T mechanism for chip thickness modeling in 5-axis ball-end finish.