Cutter Contact Points Research Articles

Machine based energy-saving tool path generation for five-axis end milling of freeform surfaces

Energy consumption in five-axis machining can be extremely large, especially for processing large-sized parts such as blades and dies, which often take hundreds of hours to machine. Once the specific machine tool configuration is given, one important objective in planning a five-axis machining operation is to reduce the total amount of energy consumption, which is not only particularly pertinent for mass production type operations but also plausible in today's energy-conscientious environment. While past research in this subject has been mainly focusing on finding better machining or processing parameters such as the cutting depth, feed rate, spindle speed, etc., in this paper, we study the fundamental problem of how to plan a five-axis tool path for machining an arbitrary free-form part surface on a given type of machine tool so that the total amount of energy consumption can be reduced, as compared to a traditional tool path, with everything else – e.g., the cutting depth, feed rate, spindle speed, maximum scallop-height, etc. – being equal. Towards this goal, an algebraic model called machine dependent energy potential field is formulated on the part surface, which encapsulates the specific power demand at any cutter contact point and along any feed direction. With this potential field, a simple tool path generation method is proposed that strives to find a good balance between the best fitting to the potential field (to minimize the total energy consumption) and the desired streamline patterns of the tool path. Experiments of the proposed method are carried out in both computer simulation and physical cutting, and the results are compared with that of some popular tool path generation methods such as the iso-scallop height method. The remarkable more than 25% savings in total consumed energy by the proposed method confirm the original motivation – designing better tool paths adaptive to the given specific machine tool is a powerful approach to reducing the total consumed energy, perhaps in general more effective than the passive selection of machining parameters which often have little room to adjust due to many constraints (e.g., the feed rate is highly regulated by the machine's controller during the cutting).

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.

5-axis tool path smoothing to improve machine tool motion

An optimization model of tool path smoothing in 5-axis CNC machining is built to improve the machine tool acceleration condition in the tool path corner transition motion in linear interpolation. Considering the difference of the five axis acceleration abilities,the ratio of one axis' maximal acceleration in corner transition motion and its allowed maximal acceleration is used to evaluate its acceleration condition,and the rootmean-square value of the five axis acceleration ratios is used to evaluate the machine tool acceleration condition,decreasing which can increase the stability of machine tool motion. The shortest lines method is used to build an admissible domain for tool axis tilt and yaw angles at each cutter contact point in the initial tool path in order to make the tool path respect the cusp height and no gouging constraints after smoothing. An example is given to demonstrate the feasibility of this method in improving the machine tool acceleration condition and increasing the stability of machine tool motion by smoothing the tool path.

Direct 5-axis tool posture local collision-free area generation for point clouds

This paper presents a method of tool posture local collision-free area generation for 5-axis machining point clouds. Considering it is time-consuming and complicated to calculate the entire precise area, in this paper, discrete inclination angles are obtained in its available range, and the precise collision-free rotation angle ranges of each inclination angle are calculated to construct the collision-free area in 2-dimensional configuration space (C-space). In local gouging avoidance, an algorithm is presented to calculate the maximum equivalent tool radius with the local contour line of the point cloud near the cutter contact (CC) point, which defines the local gouging-free ranges of rotation angles and discrete inclination angles. In rear gouging avoidance, if the tool rotates by some specific angles, a rear gouging point will be outside the tool and the gouging is avoided. Based on the way, an algorithm is presented to calculate the gouging-free ranges for discrete inclination angles. Finally, the intersections of local and rear gouging-free rotation angle ranges define the collision-free area. This presented method applies to flat-end milling cutter and torus milling cutter, and two examples are given to illustrate the feasibility.

Simultaneous optimization of the feed direction and tool orientation in five-axis flat-end milling

The two additional rotational motions of five-axis machining make the determination of the optimal feed direction and tool orientation a challenging task. A new model to find the optimal feed direction and tool orientation maximising the machining width and avoiding local gouging at a cutter contact (CC) point with a flat-end cutter considering the tool path smoothness requirement is developed in this paper. The machining error is characterised by a signed distance function defined from a point on the bottom tool circle of the cutter to the design surface. With the help of the differential evolution approach, the optimisation model can be resolved to determine the optimal tool orientation and feed direction at a given CC point, and generate the smooth tool paths following the optimal feed direction. Simulation examples demonstrate the developed techniques can improve the tool orientation and feed direction at a CC point to increase the machining width, improving the efficiency of freeform surface machining.

Tool path generation for multi-axis freeform surface finishing with the LKH TSP solver

In freeform surface finishing, there are three major types of tool path topologies: the direction-parallel type, the contour–parallel type and the space-filling curve (SFC) type. The SFC topology is capable of covering the whole surface with only one path. In this paper, we present a new way of planning the SFC type tool path by formulating the planning task as a traveling salesman problem (TSP). The optimal path is generated in two steps. Firstly, a set of regular cutter contact (CC) points is generated on the input surface. A cutting simulation method is developed to evaluate the scallop error and determine the position of the next CC point in cross-feed direction. This method is free of local surface curvature assumptions and is therefore accurate for big cutters. Secondly, the obtained CC points are input into an efficient TSP solver LHK for the optimal CC point linking sequences. To stop the CC points from diagonal linking or penetrating linking, the Euclidean distance evaluation function for two CC points is redefined in LHK. The proposed tool path generation method is verified with several freeform surface examples; the results show that the method can automatically find the optimal feed direction and it can generate shorter tool path than the traditional SFC method. The feasibility of the proposed method is also verified by a cutting experiment.

Space cutter compensation method for five-axis nonuniform rational basis spline machining

In view of the good machining performance of traditional three-axis nonuniform rational basis spline interpolation and the space cutter compensation issue in multi-axis machining, this article presents a triple nonuniform rational basis spline five-axis interpolation method, which uses three nonuniform rational basis spline curves to describe cutter center location, cutter axis vector, and cutter contact point trajectory, respectively. The relative position of the cutter and workpiece is calculated under the workpiece coordinate system, and the cutter machining trajectory can be described precisely and smoothly using this method. The three nonuniform rational basis spline curves are transformed into a 12-dimentional Bézier curve to carry out discretization during the discrete process. With the cutter contact point trajectory as the precision control condition, the discretization is fast. As for different cutters and corners, the complete description method of space cutter compensation vector is presented in this article. Finally, the five-axis nonuniform rational basis spline machining method is further verified in a two-turntable five-axis machine.

Preferred feed direction field: A new tool path generation method for efficient sculptured surface machining

This paper presents a new method to generate efficient ball-end milling tool paths for three-axis sculptured surface machining. The fundamental principle of the presented method is to generate the tool paths according to a preferred feed direction (PFD) field derived from the surface to be machined. The PFD at any point on the surface is the feed direction that maximizes the machining strip width. Theoretically, tool paths that always follow the direction of maximum machining strip width at every cutter contact point on the surface would result in shorter overall tool path length. Unfortunately, overlaps of adjacent machining strips commonly exist for tool paths that follow the preferred directions exactly. Such redundant machining can be reduced by iso-scallop tool paths. Nonetheless, iso-scallop tool paths do not in general follow the preferred feed directions. To improve machining efficiency via generating short overall tool path length, the presented method analyzes the PFD field of the surface and segments the surface into distinct regions by identifying the degenerate points and forming their separatrices. The resulting segmented regions are characterized by similar PFD’s and iso-scallop tool paths are then generated for each region to mitigate redundant machining. The developed method has been validated with numerous case studies. The results have shown that the generated tool paths consistently have shorter overall length than those generated by the existing methods.

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.

Tool path generation for slow tool servo turning of complex optical surfaces

Slow tool servo (STS) turning is a superior process for machining precision and complicated surfaces that has already gained a wide application especially in optics industry. However, it is lack of systematically study of tool path generation for STS turning of complex surfaces, especially of interpolation among discrete cutting location points. This paper presents a comprehensive tool path generation strategy for STS turning of complex surfaces, including cutting location point optimized planning, trajectory interpolation, and machining simulation. First, cutting contact point discretization and tool geometry compensation were analyzed during cutting location point planning procedure. Second, Hermite segment interpolation used by trajectory interpolation was analyzed, and three position-velocity-time (PVT) entrance parameters algorithms were put forward, i.e., the constant speed method, area method, and the three points method. Third, the machining simulation was carried out to evaluate the performance of the generated tool path. The analysis of Z-axis motion characteristics indicated that both the area method (c = 2/3) and three points method can meet the requirements of smooth velocity of Z-axis when the Z-axis reciprocating frequency is similar to the C-axis rotating frequency. From the viewpoint of acceleration, the three points method is much better than the area method when the Z-axis reciprocating frequency is significantly greater than the C-axis rotary frequency. Finally, a progressive addition lens surface was fabricated to prove the feasibility of the proposed tool path generation method.

Optimisation of five-axis machining G-codes in the angular space

Reducing the kinematic errors is an important problem in five-axis machining. Errors of this type substantially affect the quality of the five-axis manufacturing. In this paper, we propose and analyse a new numerical algorithm to reduce the kinematic errors of a five-axis tool path using minimisation of the variation of the rotation angles. Our algorithm finds the locations of the cutter contact points (CC points) in the angular space and the orientation/location of the target surface relative to the mounting table that minimise the angle variation. We show through the numerical experiments and cutting simulations that the proposed method is efficient and accurate.

Five-axis tool path and feed rate optimization based on the cutting force–area quotient potential field

Feed rate assignment in five-axis surface machining is constrained by many factors, among which a particularly critical one is the deflection cutting force on the tool: while a larger feed rate increases the machining productivity by shortening the total machining time, it nevertheless inevitably enlarges the deflection cutting force as well, which will cause the tool to be more prone to bending and the machine more prone to vibration, thus adversely degrading the surface finish quality. In this paper, we present a new five-axis tool path generation algorithm that strives to globally maximize feed rate for an arbitrary free-form surface while respecting a given deflection cutting force threshold. The crux of the algorithm is a new concept of the (cutting) force–area quotient function—at any cutter contact point on the surface, the maximal effective material removal rate (with respect to the deflection cutting force threshold) is a continuous function of the feed direction. This function induces a potential field on the surface and based on which an efficient tool path generation algorithm is designed. Preliminary experiments show that substantial reduction in total machining time can often be achieved by the proposed algorithm.

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.

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.

Optimal CNC plunge cutter selection and tool path generation for multi-axis roughing free-form surface impeller channel

Plunge milling is the most effective way for rough machining of impeller parts, but previous research had not considered the optimization of plunge cutter selection and tool path. In this paper, a new method for optimizing the plunge cutter selection and tool path generation in multi-axis plunge milling of free-form surface impeller channel is proposed in order to improve the efficiency in rough machining. Firstly, in the case of fixing a rotation axis at a certain angle in five-axis machine, a mathematical representation is formulated for the geometric model of the cutter interfering the impeller, and an optimization model of the cutter size is established at a cutter contact point on the impeller channel surface, so the largest tool could be determined. Secondly, by analyzing the machine tool movement characteristics, the geometric constraint model of the plunge tool path which relative to the largest tool, step distance, and row space is established, and a tool orientation calculation method of impeller channel machining is given, and then, the plunge tool path and tool orientation could be obtained. Finally, the generated tool path and tool orientation are simulated and verified in practical processing. Simulation and experimental result shows that the rough machining efficiency of the impeller part is improved up to 40 % with this method.

Prediction of machining accuracy based on a geometric error model in five-axis peripheral milling process

Machining accuracy is the most critical indicator to evaluate the machining quality of parts in metal cutting industry. However, it is difficult to be identified before real cutting, because of a variety of error sources presented in a machining process system, such as assembly inaccuracy of machine tool, deformation caused by temperature variation and dynamic cutting force, tool wear, servo lag and so on. Consequently, it is difficult to determine whether a new machining process can satisfy accuracy requirements beforehand. Traditionally, a machining process is validated through the “trial and error” approach, which is time consuming and costly. If machining accuracy can be predicted to a large extent, a rational process can be planned to ensure the precision of parts and even to maximize resource utilization without trial cuts. For this purpose, this work focuses on machining accuracy prediction for five-axis peripheral milling based on the geometric errors. An error synthesis modeling method is proposed to integrate the geometric errors of the process system, including machine tool geometric error, workpiece locating error, cutting tool dimension error and setup error. From a multi-body system point of view, all these errors are synthesized to generate position error of the cutting contact point in the workpiece coordinate system. Then the machining error is obtained by projecting the position error to the workpiece normal vector, which can be measured by a coordinate measuring machine. The prediction model has been evaluated by a cutting test with our in-house-developed prototype software. The result shows that the proposed method is feasible and effective.

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.

Multi-Axis Spiral Tool Path Generation for Aviation Blade Numerical Control Machining

Aiming at the low machining accuracy, low efficiency, cumbersome programming process, strong empirism and great programming difficulty of special shape blades, a new NC spiral milling method of high-quality and high-efficiency is put forward to process aviation blades. Three methods of constructing spiral tool path are studied, i.e., constructing the spiral using interpolation in parametric domain, constructing the spiral based on a driving surface and projection technology, and segmentally constructing the spiral by plane intersection. By comparison and analysis, their advantages and disadvantages are presented. According to the characteristics of spiral milling, the principles and algorithms of interference-free cutter location calculation for space free-form curved surface are introduced and the focus is put on cutter contact point calculation algorithms.

Face-milling spiral bevel gear tooth surfaces by application of 5-axis CNC machine tool

In order to solve some common problems of CNC-machined spiral bevel gears such as small cutting strip width and poor surface quality, while milled by the ball-end, a machining method of face milling using a disk cutter with a concave end is presented. The research theories are based on the foundation of spiral bevel gears’ geometry structure. Firstly, a bigger diameter disk cutter with a concave end is selected. Then, change the setting order of cutter orientation angles. The functions of cutter tilt and yaw angle are separated, and tooth surfaces machined with big cutting strip width and no bottom land gouge can be expected. Since the cutter yaw angle, determined firstly by cutting contact point, positions in the tooth surface machine, the bottom land gouge interference can be avoided effectively. Then, the tilt angles of the gear pair, both side tooth surfaces, are determined by the theory of sculptured surfaces machined by the flat-end cutter, respectively. As a result, the improved cutting strip width and machining efficiency can be realized. Finally, feasibility of this method is verified through machining experiment and measurement of a spiral bevel gear pair.

A new approach to generating arc length parameterized NURBS tool paths for efficient three-axis machining of smooth, accurate sculptured surfaces

With the development of a new function of computer numerical control controllers, nonuniform rational B-spline (NURBS) interpolation, NURBS tool path generation for sculptured surface machining is under extensive research. The common procedures of the current NURBS tool path planning methods are as follows: first, to find a group of cutter contact points on a sculptured surface; second, to calculate their corresponding cutter locations (CLs); then, to fit a NURBS tool path to the CLs within a prescribed tolerance; and finally, to inspect the tool path for possible gouge by the tool and delete the invalid path segments, if any. However, the NURBS tool path has the following problems: (a) although it passes through the discrete CLs of the theoretical CL path, the deviation along the two paths could be larger than the tolerance; (b) its parameter is not the arc length of the path; and (c) it is difficult to detect gouge along the NURBS path and to remove the invalid segments from it. Consequently, NURBS tool paths generated with the current methods of commercial computer-aided design/computer-aided manufacturing (CAD/CAM) software cannot be used to make smooth and accurate surfaces. To address these problems, this work proposes a new approach to generating arc length parameterized NURBS tool paths with high accuracy in terms of the theoretical CL paths and without gouge and interference. Two practical examples in this work clearly demonstrate the feasibility of this approach and the advantages of the generated NURBS tool paths. Therefore, this approach can be implemented into the CAD/CAM software to promote NURBS machining in industry.