Free-form Surface Machining Research Articles

Local toolpath smoothing for five-axis machine tools

When five axis CNC machine tools follow series linear toolpath segments, the drives experience velocity, acceleration and jerk discontinuities at the block transition points. The discontinuities result in fluctuations on machine tool motions which lead to poor surface quality. This paper proposes to insert quintic and septic micro-splines for the tool tip and tool-orientation, respectively, at the adjacent linear toolpath segments. Optimal control points are calculated for position and orientation splines to achieve C3 continuity at the junctions while respecting user-defined tolerance limits. The geometrically smoothed corners are traveled at a smoothly varying feed with cubic acceleration trajectory profile. The proposed method is experimentally demonstrated to show improvements in motion smoothness and tracking accuracy in five-axis machining of free-form surfaces found in dies, molds and aerospace parts.

Augmented Taylor's expansion method for B-spline curve interpolation for CNC machine tools

In computer numerical control (CNC) systems, parametric curves can be used instead of a large amount of linear blocks to describe tool paths for freeform surface or curve machining. However, existing parametric curve interpolation methods may cause large feed fluctuations or even a failure of the machining process near the sharp corners of a parametric curve. Therefore, a parametric curve interpolation method with an error correction and failure prevention scheme is required. In this paper, the augmented Taylor's expansion (ATE) method for computing B-spline curve parameters is proposed. A group of calibrators consisting of the knots and the arc lengths between adjacent knots are pre-computed before the interpolation starts. The parameter is computed based on Heun's method in a prediction–correction manner, and the accumulated errors caused by the cut-off errors of Taylor's expansion are eliminated by the calibrators at the knots. To cope with the extreme cases that usually occur near the sharp corners of a curve, a linear parametric interpolation between the previous parameter and its next calibrator is carried out when Heun's method fails to obtain a parameter in the domain. Simulation and experimental results show that, when the arc length increments are kept small enough near the sharp corners, the ATE method attains high accuracy and robust computation. The proposed method is also applicable to the NURBS curves.

A hybrid analytical- and discrete-based methodology for determining cutter-workpiece engagement in five-axis milling

This paper presents a new method to determine the cutter-workpiece engagement (CWE) for a toroidal cutter during free-form surface machining in five-axis milling. A hybrid method, which is a combination of a discrete model and an analytical approach, was developed. Although the workpiece surface was discretized by a number of normal vectors, there was no calculation to determine the intersection between the normal vector and the cutting tool. The normal vectors were used to define the workpiece surface mathematically; next, the engagement point was calculated using a combination of the workpiece surface equation, the parametric equation of the cutting tool, and the tool orientation data. Three model parts with different surface profiles were tested to verify the validity of the proposed method; the results indicated that the method was accurate. The method also eliminated the need for a large number of discrete vectors to define the workpiece surface. A comparison showed that the proposed method was computationally more efficient. The CWE model was subsequently applied to support the cutting force prediction model. A validation test demonstrated that in terms of trends and amplitudes, the predicted cutting forces exhibit good agreement with the cutting force generated experimentally.

Using the global optimisation methods to minimise the machining path length of the free-form surfaces in three-axis milling

During the machining of free-form surfaces using three-axis numerically controlled machine (NC), several parameters are chosen arbitrary and one of the most important is the feed motion direction. The main objective of this study is to minimise the machining time of complex surfaces while respecting a scallop height criteria. The analytical expression of the machining time is not known and by hypothesis, it is assumed to be proportional to the path length crossed by the cutting tool. This path length depends on the feed direction. To have an optimal feed direction at any point, the surface is divided into zones with low variation of the steepest slope direction. The optimization problem was formulated aiming at minimizing the global path length. Furthermore, a penalty reflecting the time loss due to the movement of the tool from one zone to another one is taken into account. Several heuristics are used to resolve this problem: Clarke and Wrights, Greedy randomized adaptive search procedure, Tabu search and Nearest neighbour search. An example illustrates our work by applying the different heuristics on a test surface. After simulations, the results obtained present a significant saving of paths length of 24% compared to the machining in one zone.

A tool path generation method for freeform surface machining by introducing the tensor property of machining strip width

Due to the complexity of geometry, the feed direction with maximal machining strip width usually varies among different regions over a freeform surface or a shell of surfaces. However, in most traditional tool path generation methods, the surface is treated as one machining region thus only local optimisation might be achieved. This paper presents a new region-based tool path generation method. To achieve the full effect of the optimal feed direction, a surface is divided into several sub-surface regions before tool path computation. Different from the scalar field representation of the machining strip width, a rank-two tensor field is derived to evaluate the machining strip width using ball end mill. The continuous tensor field is able to represent the machining strip widths in all feed directions at each cutter contact point, except at the boundaries between sub-regions. Critical points where the tensor field is discontinuous are defined and classified. By applying critical points in the freeform surface as the start for constructing inside boundaries, the surface could be accurately divided to such that each region contain continuous distribution of feed directions with maximal machining strip width. As a result, tool paths are generated in each sub-surface separately to achieve better machining efficiency. The proposed method was tested using two freeform surfaces and the comparison to several leading existing tool path generation methods is also provided.

A physically-based model for global collision avoidance in 5-axis point milling

Although 5-axis free form surface machining is commonly proposed in CAD/CAM software, several issues still need to be addressed and especially collision avoidance between the tool and the part. Indeed, advanced user skills are often required to define smooth tool axis orientations along the tool path in high speed machining. In the literature, the problem of collision avoidance is mainly treated as an iterative process based on local and global collision tests with a geometrical method. In this paper, an innovative method based on physical modeling is used to generate 5-axis collision-free smooth tool paths. In the proposed approach, the ball-end tool is considered as a rigid body moving in the 3D space on which repulsive forces, deriving from a scalar potential field attached to the check surfaces, and attractive forces are acting. A study of the check surface tessellation is carried out to ensure smooth variations of the tool axis orientation. The proposed algorithm is applied to open pocket parts such as an impeller to emphasize the effectiveness of this method to avoid collision.

Prediction of toolpath redundancy for NC machining of free-form surfaces based on automatic recognition of steep-wall features

The degree of toolpath redundancy is a critical concern when looking for an appropriate toolpath strategy for free-form surface machining. Hence, quantitative analysis of toolpath redundancy is important to CAM applications. In this work, a novel approach for prediction of toolpath redundancy for free-form surface machining is proposed. Firstly, a general mathematical model to represent toolpath redundancy rate is proposed based on the analysis of local toolpath intervals and their difference from the optimal values. And then, taking the most widely used iso-planar machining as case study, the steep-wall features that bring in the variation of surface slope rates alone machining strips are identified as the main cause of the generation of toolpath redundancy, so a method to automatic recognising steep-wall features from free-form surface is developed. At last, based on the steep-wall feature segmentation, an algorithm is presented to quantitatively predict the toolpath redundancy rate for free-form surface machining. A comparison study is made between the predicted redundancy rates and the experimental results by a number of case studies. The results have validated that the proposed approach can effectively predict the redundancy rate for a surface machining case before the real toolpaths to be generated.

A novel algorithm for the extraction of machining areas based on morphological image processing

In machining of free-form or compound surfaces, machining areas are sometimes required to be expressed in a boundary representation. To extract the boundary easily, Z-map models are commonly employed. Using traditional approaches, boundaries cannot be extracted precisely from a Z-map model. A boundary extraction algorithm for the machining area detection is proposed based on morphological image processing in this paper. Firstly, the Z-map model is transformed into a binary image with a slicing plane. The binary image is then dilated and the boundary pixels of the dilated image are extracted and coded. Finally, preferable accurate boundaries are generated. Experimental results show that the machining area boundaries extracted by this algorithm are more precise and smoother than those using traditional Z-map methods.

Post Processing for Five-Axis Machine Tools with Pose Error Compensation

This paper describes the enhancement of the machining precision of 5-axis machine tools. Most post-processors did not consider the pose errors so that the processing error was increased invisibly. A post processing method with pose error compensation was proposed for table/spindle-tilting type machine tools.12 position errors and 12 rotation errors were compensated by the proposed method. Mathematical model contained pose errors which converted cutter location data into machine motion coordinates was established based on inverse kinematics and the analytical solutions of NC code were derived. The tool paths of the freeform surface machining were posted with the presented method. And the simulation experiment was carried out which verified the feasibility of the post processing method with pose error compensation. Comparison of processing error shows that the post processing with pose error compensation can effectively improve the machining accuracy by approximately 50%.

Development of Cutting Strategy in Ultra-Precision Raster Milling of Freeform Surface

This paper studies the development of cutting strategy in the fabrication of freeform surface in ultra-precision raster milling (UPRM). The tasks of developing cutting strategy in freeform machining involve in the selection of cutting parameters and the planning of tool paths. An integrated system is built in this study to develop the cutting strategy, automatically generate NC program, simulate the tool paths and machining process, as well as make predictions for the machining time and the surface quality of the raster milled freeform surface. Experiment is conducted to verify the developed system and the experimental results show that the system is applicable for the machining of freeform surface in UPRM. This study therefore contributes to avoiding the need to conduct expensive and time consuming trial cutting tests to ensure the product quality in the freeform machining.

Research on 3D Model Processing Technologies in the Application of Freeform Surface Machining

Currently CAD/CAM systems have become more and more common in automated manufacturing to enhance the accuracy and efficiency of machining process. On the other hand, 3D model processing technologies has long been researched in computer graphics (CG) fields. However, few algorithms were designed for the application of machining and manufacturing. In this paper, the current researches about the 3D model processing technologies in the application of freeform surface machining were introduced. These researches take the advantage of 3D model processing technology, and focus on the application of machining and manufacturing. They provide a new methodology to enhance the intelligence of the CAM, and improve the integration of CAD and CAM.

Achieving quasi constant machining strip width in five-axis frontal grinding with toroidal tools

Five-axis frontal grinding has an advantage in finish machining of freeform surface due to high surface accuracy and material removal rate. This article focuses on achieving nearly constant machining strip width with toroidal cutter. To begin with, the initial tool path is generated to realize the maximum machining strip width with fixed yaw angle at each cut contact point and then the verges of machined area convergent to the effective machined area after modifying tool posture. The experimental test shows that the proposed method can obtain quasi constant machining strip width.

Precise gouging-free tool orientations for 5-axis CNC machining

We present a precise approach to the generation of optimized collision-free and gouging-free tool paths for 5-axis CNC machining of freeform NURBS surfaces using flat-end and rounded-end (bull nose) tools having cylindrical shank. To achieve high approximation quality, we employ analysis of hyper-osculating circles (HOCs) (Wang et al., 1993a,b), that have third order contact with the target surface, and lead to a locally collision-free configuration between the tool and the target surface. At locations where an HOC is not possible, we aim at a double tangential contact among the tool and the target surface, and use it as a bridge between the feasible HOC tool paths. We formulate all such possible two-contact configurations as systems of algebraic constraints and solve them. For all feasible HOCs and two-contact configurations, we perform a global optimization to find the tool path that maximizes the approximation quality of the machining, while being gouge-free and possibly satisfying constraints on the tool tilt and the tool acceleration. We demonstrate the effectiveness of our approach via several experimental results.

A generic uniform scallop tool path generation method for five-axis machining of freeform surface

In this paper, a generic uniform scallop tool path generation method for five-axis machining is presented. Unlike the conventional methods which are based on the local surface geometry assumptions, this method is inspired by cutting simulation. Initially, the designed surface is planted with dense grasses. If a cutter is put onto the surface, the affected grasses will be cut short. All the affected grasses form a grass ring on the surface. When the cutter moves along the previous tool path, the envelope of the grass rings will form a machining band. Based on the machining band, cutter contact points can be found on the surface to ensure that the cutting edge touches exactly on the side of the band. These cutter contact points are fitted to construct the next tool path. In this way, all the tool paths can be generated recursively. An optimization is also developed to improve the computing efficiency of the path generation process. The proposed uniform scallop tool path generation method is generic. It can be popularized to (1) any kind of end mill with various sizes, (2) any kind of parametric surface and (3) directional- or contour-parallel tool path topologies. Another salient feature of this method is that it is free of local surface geometry assumptions, so the obtained tool paths are more precise. The proposed method is implemented and evaluated with several freeform surface examples. The feasibility of the method is also verified by actual cutting experiment.

Problems During Milling and Roughness Registration of Free-form Surfaces

Finishing machining of free-form surfaces is usually performed using ball mills. Constant rotational speed n and feed rate per wedge in axis of the mill fz are applied most often for the whole surface. It causes long machining time and theoretical machined surface roughness Rzt heterogeneity. In the paper we propose a milling method with variable parameters n and fz which gives greater productivity and more homogenous roughness of free-form surfaces. Based on roughness parameter measurement of the samples, many problems have been enumerated: necessity of the surface curvature pre-filtering from primary profile, necessity of 2D roughness assessment in two perpendicular directions, requirement for a high vertical measurement range and special long tips in contact profilometers most often, roughness variability and necessity of milling technology knowledge, to find a region with maximal roughness.

Tool path re-planning in free-form surface machining for compensation of process-related errors

Free-form surfaces are widely used in many applications in today’s industry. This paper presents a new approach to identify and compensate process-related errors in machining of free-form surfaces. The process-related errors are identified online by a newly developed in-process inspection technique. In this technique, the surface is first machined through an intermediate semi-finishing process that is specifically designed to machine different geometric shapes on the surface with different process parameters. An inspection method is developed to identify the process-related errors in the selected regions on the semi-finished surface. The relationship between the machining/surface parameters and process-related error is then achieved using a neural network. This relationship is used to predict the process-related errors in the finishing process. The process-related errors, together with the machine tool geometric errors identified using a method developed in our previous work, are compensated in the finishing tool paths through tool path re-planning. Experiment has been conducted to machine a part with a free-form surface to show the improvements in the machining accuracy.

Non-singular tool path planning by translating tool orientations in C-space

This paper discusses the singular problem in five-axis machining of freeform surfaces. At first, the generating mechanism of the singularities is studied on the unit sphere in the P-system. Then a new method is developed to avoid the singularities by translating the tool orientations in the configuration-space (C-space) at the time just after the initial cutter locations have been generated for a cutter contact (CC) trajectory on the surface. The tool orientation vectors of the initial cutter locations are projected onto the C-space, forming the orientation polyline. In the C-space, a taper circle is defined. The singularities are detected by contact checking between the orientation polyline and the taper circle. Once they contact, the orientation polyline is translated by a minimum translating vector to avoid the contact. The minimum translating vector is picked on the offset polyline of the original orientation polyline. After that, the translated orientation polyline is inversed to calculate the optimized cutter locations in the P-system. The benefit of avoiding singularities at the tool path planning stage is that the original CC points on the CC trajectory are respected. The developed method is programed and tested through contrastive experiments. Results show that the optimized cutter locations can effectively avoid the singularities.

An accurate surface error optimization for five-axis machining of freeform surfaces

This paper presents an accurate surface error interpolation algorithm for five-axis machining of freeform surfaces. One of the most important steps in the interpolation process is to calculate the next cutter contact (CC) point according to the present one. In this paper, the next CC point is calculated by an accurate chord evaluation method. This method is developed based on the cutting simulation process, which can be vividly described as firstly planting dense grasses on the tool path curve and then cutting them when the tool moves by. The left lengths of the grasses either positive or negative are considered to be the machining error. The method is accurate also because the tool geometry and the tool orientation changes during five-axis machining are taken into consideration. With this method, the chord errors between CC points are controlled uniform along the tool path. The proposed interpolation algorithm is compared with the commercial CAM systems like PowerMILL and UG. The results show that the proposed algorithm can significantly reduce the number of cutter locations meanwhile confine the chord error. A real cutting experiment is implemented, and the result indicates its promising value in industrial applications.

High speed non-contact on-machine profile measurement for ultrahigh precision machining of large free-form optical surface

High speed non-contact on-machine profile measurement for ultrahigh precision machining of large free-form optical surface

Multi-axis tool path generation for surface finish machining of a rapid manufacturing process

This paper proposes a completely automated, integrated tool path planning for the finish machining of freeform surfaces as a part of the hybrid metal additive manufacturing and CNC machining. This planning capability spans from a generation of b-spline freeform surfaces, to surface finish optimisation, to collision detection, to tool path generation. Two scallop height methods have been used to compare the optimal tool path strategy. Both collision detection of a tool with neighbouring surfaces and collision correction for a tool are solved using a novel extension of the bounding box, which uses body diagonal points for computation. This paper proposes a multiple screening technique to improve the computational efficiency of tool path generation calculations.