Iso-parametric tool path generation from triangular meshes for free-form surface machining

The polyhedral model is widely used in the manufacturing industry. However, apart from the iso-planar method, the tool path generation methods for polyhedral machining are very limited. In such a case, the given tool paths are no longer boundary-conformed or efficient. This paper presents a new approach to iso-parametric tool path generation for triangular meshes. The strategy proposed herein first parameterizes the triangular faces via a harmonic map. The cutter-contact (CC) points and the path interval are then calculated based on the machining tolerance requirements and the iso-parametric tool paths are finally generated. The method is implemented on a computer and some illustrative examples are provided to show the effectiveness of the developed algorithm. The main advantage of the proposed method is that the tool paths can be generated naturally along the boundary of a polyhedral model, thus eliminating internal tight-radius corners in conventional paths. This leads to substantial reductions of tool wear and machining time. In addition, the proposed method can also be used in other non-iso-parametric tool path planning methods for triangular meshes and compound surfaces machining.     

A new STL model-based approach for tool path generation in CNC incremental forming

A new tool path generation method for sheet metal computer numerically controlled incremental forming was proposed based on the stereolithography model, considering the factors of sheet thickness variation, surface smoothness, and extruding direction. The new cutter contact surface modeling algorithm based on the non-equidistant offset was presented, which can be adapted to the sheet thickness variation so as to guarantee a reasonable gap between the forming tool and support. Moreover, a spiral tool path generation algorithm was introduced by considering the scallop height in both z-axis direction and circumferential rotation direction, so that a smoother surface can be obtained. In addition, the algorithm for keeping the tool direction perpendicular to the wall surface was also presented. Finally, the case study shows that the proposed method can automatically generate smooth and continuous spiral tool path with constant scallop height. The developed software system runs steadily and reliably.     

NURBS output based tool path generation for freeform pockets

A robust method is proposed to generate tool paths for NURBS-based machining of arbitrarily shaped freeform pockets with islands. Although the input and output are all of higher-degree NURBS curves, only one simple category of geometric entities, i.e., line segments, is required for initial offsetting and for detecting and removing self-intersecting loops. Furthermore, using those linear non-self-intersecting offsets as the legs of NURBS control polygons, NURBS-format tool paths can be smoothly reconstructed with G¹-continuity, no overcutting, no cusps, and global error control. Since all operations involved in computing tool path curves are linear geometric calculations, the method is robust and simple. Examples with integrated rough and finish cutting tool paths of pockets demonstrate the usefulness and effectiveness of this method.     

基于多学科设计优化的数控机床综合误差补偿

将多学科设计优化理论应用于数控机床综合误差补偿技术中,通过对数控机床进行系统划分,建立各个系统的误差分析模型,并运用多学科设计优化的方法对数控机床综合误差补偿过程进行优化,最终得到精密的数控加工指令.该方法能够避免用几何误差和热误差简单相加来代替综合误差的近似计算,从而提高数控机床的综合误差补偿精度.     

Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming

In this paper, the time-optimal velocity planning problem for five-axis computer numerical control machining along a given parametric tool path under chord error, acceleration, and jerk constraints is studied. The velocity planning problem under confined chord error, feedrate, and acceleration is reduced to an equivalent linear programming problem by discretizing the tool path and other quantities. As a consequence, a polynomial time algorithm with computational complexity O(N ^3.5) is given to find the optimal solution, where N is the number of discretized segments of the tool path. The velocity planning problem under confined chord error, feedrate, acceleration, and jerk is reduced to a linear programming program by using a linear function to approximate the nonlinear jerk constraint. As a consequence, a polynomial time algorithm is given to find the approximate time-optimal solution. Simulation results are used to show the efficiency and effectiveness of the algorithms.     

Incomplete two-manifold mesh-based tool path generation

This paper presents a new paradigm for three-axis tool path generation based on an incomplete two-manifold mesh model; namely, an inexact polyhedron. When geometric data is transferred from one system to another system and tessellated for tool path generation, the model does not have any topological data between meshes and facets. In contrast to the existing polyhedral machining approach, the proposed method generates tool paths from an incomplete two-manifold mesh model. In order to generate gouge-free tool paths, cutter-location meshes (CL-meshes) are generated by offsetting boundary edges, boundary vertices, and facets. The CL-meshes are sliced by machining planes and the calculated intersections are sorted, trimmed, and linked. The grid method is used to reduce the computing time when range searching problems arise. The method is fully implemented and verified by machining an incomplete two-manifold mesh model.     

The implementation of adaptive isoplanar tool path generation for the machining of free-form surfaces

Machining of steep regions is an important research topic in the machining of free-form surfaces. A new tool path generation algorithm to adaptively machine free-form surfaces has been recently developed. However, similarly to many newly emerged methods, so far it has not been used in industry because no commercial platform is currently available and the user-developed system is not robust enough for industrial applications. To solve this problem, this paper presents a new implementation method by integrating it in a commercial CAD/CAM system (Pro/Engineer). With this strategy, other than conducts detailed computations for parameters, such as scallop heights and forward steps, or designing the non-cutting functions such as engaging and retracting methods, which are routines in every tool path generation process, the implementation utilizes existing tool path generation templates in Pro/E to generate the required tool paths. This makes the tool path generation process easier and the tool paths generated more practicable because the integration is relieved of the time-consuming routine calculation and the entire cutting and non-cutting functions in the commercial system are transparent to users. Based on the API of Pro/E, the new tool path generation method was successfully implemented and cutting tests were conducted. Not losing generality, the implementation could also be conducted in other commercial systems as similar templates are available in these systems as well.     

Gouging elimination through tool lifting in tool path generation for five-axis milling based on faceted models

Five-axis milling may be performed with a constant tool-orientation or varying optimal tool-orientation. When applying a constant tool orientation, the inclination angle, the angle between the tool axis and the normal vector of a contact point (cc-point), is kept constant along the tool path. On the other hand, when applying a varying optimal tool orientation, the tool inclination angle is dynamically optimized along the tool path in order to maintain the tool to be as close as possible to the surface without gouging. In both tool orientation methods, tool lifting is one of the crucial components and involved in tool path generation, especially when it is used for gouging elimination. For the constant tool orientation, the tool is lifted immediately when the specified inclination angle causes gouging with the part surface. In the case of varying optimal tool orientation, the minimum rotation angle (inclination angle) has to be found first to avoid gouging. If the gouging still occurs (e.g. due to limited rotational axes of the milling machine), then the tool is lifted. In this paper, gouging elimination through tool lifting for five-axis milling based on a faceted model is presented. The tool is lifted based on the types of gouging. These types of gouging are described and the tool lifting procedure has been developed and implemented for gouging elimination in both tool orientation methods.     

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.     

Sheet metal dieless forming and its tool path generation based on STL files

This paper introduces a new sheet metal dieless forming technology. This technology adopts the principle of “layered manufacture” in rapid prototyping technology; it can form sheet metal parts without dies. A new method of tool-path generation based on STL file for sheet metal dieless forming is proposed.     

基于白适应蚁群算法的无人飞行器航迹规划

为求解无人飞行器航迹规划问题,提出自适应蚁群算法,区别于标准蚁群算法的全部搜索模式,该算法采用局部搜索模式。首先根据起始节点与目标节点的相对位置关系选择相应的搜索模式,然后计算各个待选节点的转移概率,最后按照轮盘赌规则选择下一个节点。仿真结果表明,自适应蚁群算法具有搜寻节点数少、速度快等优点,在降低了航迹代价的同时,减小了计算时间。此外,自适应蚁群算法可以避免奇异航迹段的出现,从而保证所获的航迹实际可飞,表明所提算法整体性能明显较标准蚁群算法优异。     

An integrated optimization of cutting parameters and tool path generation in ultraprecision raster milling

This paper provides a new methodology for the integrated optimization of cutting parameters and tool path generation (TPG) based on the development of prediction models for surface roughness and machining time in ultraprecision raster milling (UPRM). The proposed methodology simultaneously optimizes the cutting feed rate, the path interval, and the entry distance in the feed direction to achieve the best surface quality in a given machining time. Cutting tests are designed to verify the integrated optimization methodology. The experimental results show that, in the fabrication of plane surface, the changing of entry distance improves surface finish about 40 nm (R _a ) and 200 nm (R _t ) in vertical cutting and decreases about 8 nm (R _a ) and 35 nm (R _t ) in horizontal cutting with less than 2 s spending extra machining time. The optimal shift ratio decreases surface roughness about 7 nm (R _a ) and 26 nm (R _t ) in the fabrication of cylinder surfaces, while the total machining time only increases 2.5 s. This infers that the integrated optimization methodology contributes to improve surface quality without decreasing the machining efficiency in ultraprecision milling process.     

复杂曲面投影法精加工刀轨生成

针对复杂曲面投影法精加工问题,提出一种简捷而有效的计算投影轨迹的方法。该算法以减少计算量,提高干涉调整效率为目的。为了避免传统方法中的复杂的曲面偏置问题,提出了一种新的思路,该方法摒弃了先求偏置面再计算投影轨迹并使用对分法处理干涉问题的思路。首先规划导动轨迹,然后将刀触点轨迹沿曲面法向偏置,再利用刀位点到曲面的最短距离进行干涉检测与调整,最后生成了无干涉的投影法轨迹。仿真实验证明,该方法计算量小,可以消除干涉,加工效果好。     

Non-constant parameter NC tool path generation on sculptured surfaces

An algorithm for three-axis NC tool path generation on sculptured surfaces is presented. Non-constant parameter tool contact curves are defined on the part by intersecting parallel planes with the part model surface. Four essential elements of this algorithm are introduced: initial chordal approximation, true machining error calculation, direct gouge elimination, and non-constant parameter tool pass interval adjustment. A software implementation of this algorithm produces graphical output depicting the tool path superimposed over the part surface, and it outputs cutter location (CL) data for further post-processing. Several applications examples are presented to demonstrate the capabilities of the algorithm. The results of this technique are compared to those generated from a commercially available computer-aided manufacturing program, and indicate that equivalent accuracy is obtained with many fewer CL points.Notation C cutting curve - C ¹ cutting curve tangent - CC ₀,CC ₁, ... cutter contact points - d chordal deviation - /_ABC triangle - w incremental step in parameterw - ABC angle - a small quantity - l chord length - n _s ,n _p , ... normal vectors - P, P _r ,P _c ,P ₁ ,P ₂ , ... space point - Q parametric equation of a surface - R radius of a ball-end milling tool - TC ₀,TC ₁, ... tool center points - u, v, u _s ,u _c ,w, t parameters - angle - curvature - h cusp height - T machining tolerance     

Restraint of tool path ripple based on the optimization of tool step size for sub-aperture deterministic polishing

Tool path ripple error (TPR_error) is one of the main reasons due to the medium-high spatial frequency error on the surface of aspheric optics. The purpose of this paper is to analyze the effect of the tool step size to the TPR_error in sub-aperture deterministic polishing (SDP) and study a method which can optimize the tool step size to restrain this error. Three groups of simulation experiments were conducted using three different tool influence functions to simulate the uniform removal of the material. As the TPR_error is influenced by three factors, which are full width at half maximum (FWHM) of tool influence function (TIF), tool step size, and depth of material removed, each group of the experiments was conducted under the fixed TIF and depth of material removed. It turns out that both peak-to-valley (PV) and root-mean-square (RMS) values of the TPR_error become larger with the increase of the tool step size, and the variation tendency likes a reversed “L” shape curve. And, the method adopted in the simulation was further validated by the experiment. Therefore, the tool step size at the inflection point would be optimal to restrain the TPR_error together with saving the polishing time to a certain extent. This method could be used to determine the best-suited tool step size in SDP whose typical TIF is a Gaussian or Gaussian-like shape.     

Optimal five-axis tool path generation algorithm based on double scalar fields for freeform surfaces

In order to generate efficient tool path with given precision requirements, scallop height should be kept under a given limit, while the tool path should be as short as possible to reduce machining time. Traditional methods generate CC curves one by one, which makes the final tool path far from being globally optimal. This paper presents an optimal tool path generation model for a ball-end tool which strives to globally optimize a tool path with various objectives and constraints. Two scalar functions are constructed over the part surface to represent the path intervals and the feedrate (with directions). Using the finite element method (FEM), the tool path length minimization model and the machining time minimization model are solved numerically. The proposed method is also suitable for tool path generation on mesh surfaces. Simulation results show that the generated tool path can be direction parallel or contour parallel with different boundary conditions. Compared to most of the conventional tool path generation methods, the proposed method is able to generate more effective tool paths due to the global optimization strategy.     

核电封头五轴数控加工刀具路径规划研究

核电封头机械加工余量大,并且球面上非对称的分布这若干管嘴端面,这给高效刀具路径规划造成了极大的难度。在NURBS方法基础上,针对核电水室封头等形状复杂大型工件,从加工效率和稳定性的角度,建立环形铣刀加工曲面的运动几何学模型并应用加工域规划法进行刀具路径规划。合理的刀具路径规划可以有效的避免刀具干涉,缩短刀具路径,提高加工精度。     

Iso-scallop tool path generation in 5-axis milling

This paper presents a new method of computing constant scallop height tool paths in 5-axis milling on sculptured surfaces. Usually, iso-scallop tool path computation methods are based on approximations. The attempted scallop height is modelled in a given plane to ensure a fast computation of the tool path. We propose a different approach, based on the concept of the machining surface, which ensures a more accurate computation. The machining surface defines the tool path as a surface, which applies in 3- or 5-axis milling with the cutting tools usually used. The machining surface defines a bi-parametric modelling of the locus of a particular point of the tool, and the iso-scallop surface allows to easily find iso-scallop tool centre locations. An implementation of the algorithms is done on a free-form surface with a filleted end mill in 5-axis milling.