A freeform surface manufacturing approach by integration of inspection and tool path generation

Freeform surfaces have been widely used in various engineering applications. Increasing requirements for the accuracy of freeform surfaces have led to significant challenges for the manufacturing of these surfaces. A method for manufacturing of freeform surfaces is introduced in this paper by integrating inspection and tool path generation to improve manufacturing quality while reducing manufacturing efforts. Inspection is conducted by comparing the digitised manufactured surface with the design surface to identify the error regions. In this new inspection technique, the areas on the manufactured surface that are beyond the design tolerance boundaries are used as the objective function during the localisation process, in order to minimise post-inspection machining efforts. The tool path generation methods are then selected based on the geometric characteristics of the identified error regions, for creating tool paths to remove the errors. Computational efficiency, machining efficiency, and quality are considered in this integrated method.     

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.     

Isophote-based ruled surface approximation of free-form surfaces and its application in NC machining

This paper presents a method to approximate free-form surfaces using piecewise ruled surface and its application in five-axis NC machining. New concepts of isophote, iso-inclination curve and iso-inclination angle are introduced to facilitate the generation of the piecewise ruled surfaces. The resulting ruled surfaces are adaptive to the surface features, such as peaks and valleys. Adjusting the isoinclination angle controls the error of this approximation. The application of the isophote-based ruled surface approximation in five-axis NC machining is also studied. The tapered tools are suggested to cut the ruled surfaces. Methods for selecting appropriate tools and generating tool paths are presented. The present case studies show that the new approach may lead to the integration of rough, semi-finish and finish machining of free-form surfaces.     

An interpolation scheme for tool-radius compensated parabolic paths for CNC

In general, NC systems provide only linear and circular interpolations. Complex shapes to be machined are first approximated with linear and circular segments to some predetermined tolerance. Parabolic curves are more suitable for piecewise approximation of higher-order curves because less segments than lines or circular arcs are required. In machining operations, the tool motion controlled by the interpolator does not move along the profile of the job. The tool path is offset from the profile by the tool radius. Tool-radius compensations for linear and circular tool paths involve simple offsets of the initial and final points. The tool paths remain linear or circular. For parabolic profiles, the offset tool paths are not parabolic; hence, parabolic interpolations cannot be used to generate the offset paths. This paper presents an algorithm to perform interpolations for the tool to follow parabolic curves as well as the offset paths passing through two user-defined end points. The parabolic interpolation is based on the principle of operation of the Digital Differential Analyzer (DDA) integrator and is capable of constant tangential velocity.     

Approximation of planar offset curves with globally bounded error for B-spline NC tool paths

The topic of representing the offset of a 2D B-spline curve in the same form has been a topic of research for a long time, and it has many industrial applications, especially in NC tool path generation for pocketing. For B-spline tool paths, it is often required that the tool paths have fewer control points, lower base function degree, and the approximation error is guaranteed within a given tolerance over the entire curve. However, the existing methods utilising global error control approximate the offsets of 2D free-form curves with high function degree and many control points. Although these offsets are useful in computer-aided design, they are inappropriate for the use of CNC machining. To address the problems in order to generate high quality B-spline tool paths, this original work formulates an error function of the offset approximation and then constructs a NURBS curve to globally bound the errors. By checking the maximum coefficient of the bounding curve, the upper bound of all the approximated offset errors is found and the errors can be reduced by segmenting the curve at appropriate knot values. The proposed new approach is more efficient, and the resulting offset approximations are more accurate, with fewer control points and lower function degree. It is useful to generate B-spline tool paths for CNC pocketing, which have the potential for other applications in industry.     

光学微结构的超精密加工技术

微结构光学元件在光电产品及光通讯产品中的应用日益广泛，采用多轴超精密机床加工光学微结构，可达到亚微米级形状精度和纳米级表面光洁度的高精度水平，详细介绍了光学自由曲面及光学微结构的超精密加工技术，并开发了适合超精加工微型槽和微透镜列阵的刀具轨迹自动生成软件。     

Improved time-optimal B-spline feedrate scheduling for NURBS tool paths in CNC machining

Feedrate scheduling in computer numerical control (CNC) machining is of great importance to fully develop the capabilities of machine tools while maintaining the motion stability of each actuator. Smooth and time-optimal feedrate scheduling plays a critical role in improving the machining efficiency and precision of complex surfaces considering the irregular curvature characteristics of tool paths and the limited drive capacities of machine tools. This study develops a general feedrate scheduling method for non-uniform rational B-splines (NURBS) tool paths in CNC machining aiming at minimizing the total machining time without sacrificing the smoothness of feed motion. The feedrate profile is represented by a B-spline curve to flexibly adapt to the frequent acceleration and deceleration requirements of machining along complex tool paths. The time-optimal B-spline feedrate is produced by continuously increasing the control points sequentially from zero positions in the bidirectional scanning and sampling processes. The required number of knots for the time-optimal B-spline feedrate can be determined using a progressive knot insertion method. To improve the computational efficiency, the B-spline feedrate profile is divided into a series of independent segments and the computation in each segment can be performed concurrently. The proposed feedrate scheduling method is capable of dealing with not only the geometry constraints but also high-order drive constraints for any complex tool path with little computational overhead. Simulations and machining experiments are conducted to verify the effectiveness and superiorities of the proposed method. The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-022-00413-1     

Tool path generation via the multi-criteria optimisation for flat-end milling of sculptured surfaces

A method of generating optimal tool paths for sculptured surface machining with flat-end cutters is presented in this paper. The inclination and tilt angles, as well as the feed directions of the cutter at each cutter contact point on a machining path are optimised as a whole so that the machining width of the tool path can be as large as possible, and concerns such as smooth cutter motion, gouging avoidance, scallop height and machining widths overlap are also considered when calculating a path. A multi-criteria tool path optimisation model is introduced, and it is converted into a single objective optimisation with the weighted sum method. The Differential Evolution (DE) algorithm is suitable for solving this highly non-linear problem. However, the searching process of the DE algorithm may be trapped in local minima due to large number of design variables. Therefore, an algorithm combining the DE algorithm and the sequence linear programming algorithm is developed to solve this optimisation model. The proposed method is applied to two freeform surfaces to illustrate its effectiveness.     

Efficient five-axis machining of free-form surfaces with constant scallop height tool paths

Generation of efficient tool paths is essential for the cost-effective machining of parts with complex free-form surfaces. A new method to generate constant scallop height tool paths for the efficient five-axis machining of free-form surfaces using flat-end mills is presented. The tool orientations along the tool paths are optimized to maximize material removal and avoid local gouging. The distances between adjacent tool paths are further optimized according to the specified scallop height constraint to maximize machining efficiency. The constant scallop height tool paths are generated successively across the design surface from the immediate previous tool path and its corresponding scallop curve. The scallop surface, an offset surface of the three-dimensional design surface based on the specified scallop height, is used to establish accurately the scallop curve with the constant scallop height. The present method was implemented and validated through the five-axis machining of a typical free-form surface. The results showed that the conventional isoparametric tool paths were over 36% longer in the total tool path length and less efficient than the constant scallop height tool paths generated by the present method.     

基于曲率的曲面加工刀位轨迹生成算法

提出了一种自由曲面五轴数控加工无干涉刀位轨迹的生成算法。该方法利用曲面的曲率来确定环形刀的刀具姿态,使得刀具随被加工曲面的形状变化而倾斜,从而生成无干涉的刀位轨迹。     

Globally optimal tool paths for sculptured surfaces with emphasis to machining error and cutting posture smoothness

Global optimisation for manufacturing problems is mandatory for obtaining versatile benefits to facilitate modern industry. This paper deals with an original approach of globally optimising tool paths to CNC-machine sculptured surfaces. The approach entails the development of a fully automated manufacturing software interface integrated by a non-conventional genetic/evolutionary algorithm to enable intelligent machining. These attributes have been built using already existing practical machining modelling tools such as CAM systems so as to deliver a truly viable computer-aided manufacturing solution. Since global optimisation is heavily based on the formulation of the problem, emphasis has been given to the definition of optimisation criteria as crucial elements for representing performance. The criteria involve the machining error as a combined effect of chord error and scallop height, the tool path smoothness and productivity. Experiments have been designed considering several benchmark sculptured surfaces as well as tool path parameters to validate the aforementioned criteria. The new approach was implemented to another sculptured surface which has been extensively tested by previous research works. Results were compared to those available in the literature and it was found that the proposed approach can indeed constitute a promising and trustworthy technique for the global optimisation of sculptured surface CNC tool paths.     

Combining physical shell mapping and reverse-compensation optimisation for spiral machining of free-form surfaces

Machining of free-form surfaces has an important role in industrial manufacturing, but conventional tool-path generation strategies for free-form surfaces machining have the drawbacks of serious flattening distortion and poor tool-path continuity. Therefore, a novel method is developed to generate a spiral tool path for the machining of free-form surfaces by improving surface-flattening distortion and tool-path continuity. First, physical shell mapping is presented to flatten a free-form surface into a plane, which takes stretching energy, bending energy, and global energy into account. Then, the spatial spiral polyline is rounded to generate a spiral path by proposing reverse-compensation optimisation. Therefore, the free-form surfaces can be quickly flattened with less distortion, remaining free of overlap, and can in addition be machined at high speed along a C² continuous spiral tool path. Further, the flattening error, tool-path length, mean curvature, mean scallop-height error of the spiral path, machining time and surface roughness are obviously reduced. Finally, simulation results are given to show the effectiveness and feasibility of the presented strategy.     

Fast tool path generation by the iso-scallop height method for ball-end milling of sculptured surfaces

This article reports on tool path generation by the iso-scallop height method for the three-axis ball-end milling of sculptured surfaces. In order to achieve the specified machining accuracy, constant scallop height machining requires an understanding of the three-dimensional machining geometry and the use of iterative approaches. Feng and Li have accomplished such work using the bisection method to search the scallop curves and the tool centre curves. This paper presents an analytic and geometric study of the machining aspects. Analysing the local properties of the distance functions, which indicate where the scallop point and the tool are centred, the bisection method can be replaced by the Newton iterative algorithm which converges faster. The derivatives of the functions are formulated by their Taylor approximations with a small error. The initial guesses are obtained by considering the local machining geometry. The proposed method significantly reduces the total computing time necessary to generate tool paths.     

Unified rough cutting tool path generation for sculptured surface machining

Based on zigzag and contour-offset methods for cutting layers described in pixel maps, three unified tool path generation modules for NC rough cutting of sculptured surfaces are presented. The zigzag-stack-without-island module generates the tool path for a to-be-machined area without any inside island. The zigzagstack-with-islands module is for a to-be-machined area with single or multiple inside islands. For small corners or to-be-machined areas left by the first cutter in a cutting sequence, the boundary-offset-for-corners module is used. An obstacle avoidance module that generates rapid traversal tool paths between adjacent cutting layers or different cutting tool path segments in the same cutting layer is also developed. These modules are easy to implement and robust. When combined with the divide-and-conquer machining method, unnecessary lifts can be avoided and the generated tool paths will be more effective in terms of total machining time for the best cutting sequence (Tao 1999).     

Adaptive nonlinear tool path optimization for five-axis machining

Current tool path computation in the CAM algorithms approximates the surface by piecewise linear interpolation. In the case of three-axis machining on a CNC machine the tool will exactly reproduce this computed tool path. However in the case of five-axis simultaneous machining the real tool path on the CNC machine will not follow the linear approximation computed by the conventional CAM algorithm. A new CAM algorithm is proposed which approximates the surface to be machined by a piecewise curved approximation. This curve represents the real tool path followed on the five-axis machine. This piecewise curved approximation is further optimized by formulating the tool path computation as the generation of a grid based on a variational smoothness penalty function. This new algorithm considerably improves the accuracy and reduces the number of blocks and machining time.     

基于AutoCAD的圆柱面上非规则曲线三维建模方法

分析了轧制各种形状花纹板材刀具轨迹的共同特征,研究了各种形状花纹板材的平面设计图与刀具轨迹的对应关系,提出了对平面设计曲线进行二维数据处理的一般方法,对二维数据处理结果向圆柱面上非规则曲线进行变换的三维建模和数据处理方法。在AutoCAD 环境下,利用 Autolisp 语言的编程功能,针对生产实际中切削刀具平面设计图,实现了圆柱面上非规则曲线的三维建模。该模型为刀具的数控加工提供了走刀轨迹仿真依据和走刀加工三维数据。     

NURBS curve interpolation algorithm based on tool radius compensation method

This paper focuses on developing an algorithm that can generate toolpaths in NURBS form for smooth, high speed and accurate machining. The initial toolpaths are obtained by tool radius compensation method which is based on the workpiece boundary offsetting. According to different lengths and the continuous short block (CSB) criterion, these offset linear segments can be regarded as CSBs or long straight segments. Junctions are located where the curvature value is greater than the preset curvature threshold value or where it changes abruptly, or at the two end points of any long straight segment. During machining, the NURBS fitting module first looks ahead several CSBs and converts them into parametric curves in real time. During the conversion, continuities of the position, slope or even curvature at the transition of the parametric curves and unfitted line segments can be guaranteed. Then the acceleration/deceleration feedrate-planning scheme is proposed to determine the transition feedrate at the junction between the fitted curves and unfitted long straight segments, and the corner feedrate within the fitted curve. Simulations and experiments show that the proposed algorithm can significantly improve machining accuracy and reduce cutting time to satisfy today’s high-speed and high-accurate machining requirements.     

用NURBS光顺原理提高曲面铣削加工质量

分析了参数连续性和几何连续性对光顺性的影响。阐述了B样条方法和NURBS方法各自的特点和相互间的不同点,分析了与传统曲线构造方法相比的优点,介绍了NURBS曲面在3D设计中的应用等。建立曲面后,通过高斯云图和反射方法图的分析,检验NURBS曲面的精度和光顺性,针对不光顺的原因,采取相应的解决方法,以生成高精度的曲面。加工时采用NURBS输出,优化刀具轨迹,简化程序,提高生产效益。     

一种基于STL模型的5轴高速加工刀轨优化策略

针对线性插补刀轨不连续且插补点多的缺点,提出了一种基于STL模型的口腔修复体5轴高速铣削数控加工刀轨优化策略。以去除不必要的插补点,简化加工刀轨的数量,优化刀轴矢量包络的曲面为平滑变化的规则面,实现了一种支持HEIDENHAIN数控系统的样条插补新方法。运用该策略线性插补的G代码成功地被转换成样条代码,基于Vericut仿真器,仿真加工出了磨牙冠修复体。结果表明,该优化策略不仅能缩短切削时间、提高加工质量,而且可避免切削颤振。     

Tool path generation for five-axis NC machining using adaptive space-filling curves

We present the concept of an adaptive space-filling curve for tool path planning for five-axis NC machining of sculptured surfaces. Generation of the adaptive space-filling curves requires three steps: grid construction, generation of the space-filling curve, and tool path correction. The space-filling curves, adapted to the local optimal cutting direction, produce shorter tool paths. Besides, the tool path correction stage makes it possible to eliminate the effect of sharp angular turns which characterize standard space-filling curve patterns. Our space-filling curve method is endowed with a new modification of techniques for computing the machining strip width along with a modified formula for the minimum tool inclination angle to avoid gouging. Finally, we show that the adaptive space-filling curves are more efficient compared with the traditional iso-parametric scheme. The numerical experiments are complemented by real machining as well as by test simulations on Unigraphics 18.