A radius compensation method of barrel tool based on macro variables in five-axis flank machining of sculptured surfaces

Barrel tool radius compensation is very important to improve the five-axis CNC machining precision and efficiency of sculptured surfaces. By combining macro variables and math function of CNC controller, a radius compensation method of barrel tool based on macro variables in five-axis flank machining of sculptured surfaces was presented. The basic principle of barrel tool radius compensation in five-axis flank machining was firstly investigated. For a specific five-axis CNC machine tool with dual rotary tables, a relationship equation between compensated cutter location (CL) data and machine control (MC) data could be derived. A post-processor with the function of five-axis barrel tool radius compensation was then developed by using the C++ language, which could generate the NC programme with macro variables of barrel tool radius compensation. Finally, the NC programme was obtained automatically by the developed post-processor for the aero-engine blade surface machining. The machining process was simulated on the software VERICUT, and machining experiments were also conducted on the five-axis machine tool. Both the simulation and experimental results showed that the proposed method could perform the function of barrel tool radius compensation in the NC programme for five-axis flank machining.     

New algorithm to minimise kinematic tool path errors around 5-axis machining singular points

The singular points of a given 5-axis CNC machine could be found in the domain of the joint variables of the machine. In the neighbourhood of a singular point, even for a small change of the tooltip position, an enormous change of axis displacements of the machine is often required. This causes a large deviation between the real cutting path and the desired tool path, and the machining surface could be destroyed. This paper provides with an analytical scheme for identifying singular configuration of 5-axis CNC machines. In particular, an efficient and robust algorithm is proposed to compute the cutter path across the neighbourhood of the singular points identified such that the computed cutter path tracks the desired tool path within a controllable error. Numerical examples and real cutting parts are carried out and discussed to show the effectiveness and the efficiency of the presented method.     

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.     

基于UG NX6.0的整体叶轮的多轴加工技术

叶轮加工是当今多轴联动数控加工最常见的实例,也是数控加工的难点之一.本文从实际出发,使用UG/CAM五坐标编程系统对整体式叶轮进行数控编程,采用插值方式对刀轴矢量进行匀化处理,采用SWARF方法对叶片进行精加工,同时合理控制进退刀,实现了整体叶轮叶片高质量无干涉的五坐标螺旋铣削加工刀位点轨迹生成.为复杂产品的造型和数控加工提供了设计思路和方法,也给其他类型叶轮的设计与加工提供了参考方案.     

Tool path optimisation for flank milling ruled surface based on the distance function

This paper deals with optimised tool path generation for five-axis flank milling using signed point-to-surface distance function. The main idea is that the geometrical deviations between the design surface and the machined surface are minimised by fine tuning the cutter locations. Based on the tangency conditions in envelope theory, the analytic representation of the envelope surface of a cutter undergoing five-axis motion is first obtained. Then the geometrical deviations between the envelope surface (i.e. machined surface) and the design surface are calculated. Optimisation of the five-axis tool path is modeled as the fine tuning of the initial cutter locations under the minimum zone criterion recommended by ANSI and ISO, which requires minimisation of the maximum geometrical deviation between the design surface and the envelope surface. Using the signed point-to-surface distance function, tool path optimisation for finish milling is formulated as a constrained optimisation problem. Based on the first-order Taylor approximation of the signed distance function, two sequential approximation algorithms for the Minimax and Least Square optimisations are developed. Numerical examples, in which a conical tool is chosen as a special case of flank machining ruled surface, verify the proposed strategy.     

A control algorithm for improving the accuracy of five-axis machine tools

An algorithm for reducing the influence of geometrical, thermal, kinematic and stiffness errors in five-axis machine tool components on the desired tool position and orientation is given. This new algorithm is based on the calculation of the cutting tool error matrix for orthogonal machine tools. In the new model of this matrix, all angular errors of the machine links are considered as infinitesimal rotations. The error matrix is a function of the commanded machine component positions and the errors in these positions. To correct errors in the three translational and two angular tool positions, a matrix of commanded tool position and orientation is multiplied by the inverse error matrix in every period of the tool trajectory interpolation. This corrected matrix of the tool position and orientation provides the inverse kinematics used for calculation of the successive links positions required for achieving the given tool trajectory. The control algorithm for five-axis machine tools with the error compensation is implemented both in the CNC system and in the postprocessor. The proposed algorithm is applied on a vertical five-axis turning centre with two translational and three rotational axes. Twenty-four errors that could cause inaccurate machining are recognised on this machine. The machine links and their coordinate frames are denoted using the Denavit–Hartenberg parameters.     

Efficient tool path planning for five-axis surface machining with a drum-taper cutter

This paper presents a new efficient approach to NC tool path generation for five-axis surface machining. First, an efficient cutter, named a drum-taper cutter, is proposed; its key dimension is determined to avoid gouging in surface machining according to the maximum curvature of the surface calculated with a genetic algorithm. Then, based on the drum-taper cutter, the tool paths are generated so that the scallop height formed by adjacent tool paths in machining is kept constant, and an improved algorithm for calculating the interval between tool paths is presented. Finally, an example of tool path generation with the above method for arbitrary surface impeller machining is conducted, and the results show that the presented method leads to a significant reduction in the total tool path length and is accompanied by a reduction in machining time.     

假肢接受腔阳模数控加工刀具的运动轨迹规划

应用表面建模方法，建立了假肢接受腔的三维数学模型。针对假肢接受腔的独特外形特征，研制了加工假肢接受腔阳模的三轴联动数控机床，该机床控制系统采用开环系统，可以运行CAD／CAM软件。对加工假肢接受腔阳模的刀具进行了运动轨迹规划，推导出了切削点的计算公式。根据三维刀具半径补偿原理，确定了刀具的刀位点运动轨迹。经过临床实例加工表明：该数控机床和刀具运动轨迹规划算法完全满足实际应用要求。     

Compensation of systematic errors in five-axis high-speed machining

A method is described for the compensation of errors associated with tool path generation, particularly during five-axis high-speed machining (HSM). Information on machine tool performance and its dynamic features is used to calculate possible errors and convenient modifications of the NC program, thereby avoiding errors when parts are actually being machined. This 'preprocess method' by means of postprocessing with NC software is presented. The errors dealt with are mainly servo lag errors, but the explored approach can support most systematic errors associated with machine tool performance. These are briefly summarized. Research so far has largely been aimed at the implementation of compensation routines in the CNC controller and at corrections in real time. The problem is that most applications are only available for three-axis milling. The presented approach (compensation before machining by using software routines in a specially designed postprocessor) is based on a fuzzy logic expert system. The benefits can be summarized as data reduction, data improvement, precontrol of feed, and improved component accuracy. The applied procedure is also convenient for implementation in an industrial environment by retrofitting existing equipment. The suggested method provides improved control over machine dynamics, permitting high-speed machining centres to maintain a maximum or near-maximum feed rate despite axis reversals and tool path changes, even at corners. Two categories of results are presented, namely the management of NC data related to expected performance of the machine tool and improvements of the machine tool performance in terms of productivity and accuracy of the machined test components.     

用三坐标数控铣床加工空间曲面时的圆弧插值算法

论述了在三坐标数控铣床上采用球头铣刀铣削空间复杂形面时圆弧插值的计算方法.把刀具中心等距曲线轨迹的计算归结为计算零件轮廓上点的坐标,确定了加工空间等距曲线时插值点的计算流程图.利用圆弧插值算法推导出了坐标增量计算公式,此公式可应用到数控装置修正刀具的半径,从而提高零件廓形的加工精度.此算法也可应用到端铣刀加工时圆弧插值的计算.     

Machining error compensation using radial basis function network based on CAD/CAM/CAI integration concept

This paper presents a machining error compensation methodology using an Artificial Neural Network (ANN) model trained by an inspection database of the On-Machine-Measurement (OMM) system. This is an application of the CAD/CAM/CAI integration concept. First, to improve machining and inspection accuracies, the geometric errors of a three-axis CNC machining centre and the probing errors are compensated using a closed-loop configuration. Then, a workpiece is machined using the machining centre, and the error distributions of the machined surface are inspected using OMM. In order to analyse efficiently the machining errors, two characteristic error parameters, W err and D err , are defined. Subsequently, these parameters are modelled using a Radial Basis Function (RBF) network approach as an ANN model. Based on the RBF network model, the tool path is corrected to effectively reduce the errors using an iterative algorithm. In the iterative algorithm, the changes of the cutting conditions can be identified according to the corrected tool path. In order to validate the approaches proposed in this paper, an experimental machining process is performed, and the results are evaluated. As a result, about 90% of machining error reduction can be achieved through the proposed approaches.     

基于机床体误差模型的加工面形误差预测

零件面形精度满足要求是超精密装备实现其关键功能的重要保证.影响工件加工面形精度的因素很多,机床体误差是其中最关键的因素.通过构建机床误差元与加工面形误差之间的直接关系来进行面形误差预测研究.提出了一种基于机床体误差模型的频域多尺度面形误差预测方法,该方法可结合机床体误差模型、工艺参数、加工轨迹等进行频域多尺度面形误差预测,可为加工路径规划、机床设计等提供理论参考,从而提高加工精度.进行了低频PV面形误差预测的实例研究,采用的机床为一台五轴联动超精密机床,加工表面为凹形截圆锥台锥面.通过实验与理论分别获得PV面形误差,其相对误差为17.3%,证明基于机床体误差模型的低频PV面形误差预测是可行的.     

Tool path generation for five-axis machining of blisks with barrel cutters

A barrel cutter has a cutting segment with a large radius on its profile, and this arc segment allows the cutter to tilt away from the part surface, avoiding the collisions of the tool with the part. Therefore, barrel cutters are suitable for five-axis blisk machining. However, the barrel cutters are more challenging for CAM software to generate paths. A method of generating collision-free and large-machining width flank milling paths with smooth axes movements for blisk machining with barrel cutters is proposed. Local gouge between the tool flute surface and the blade to be machined is considered, and the collisions of the blisk with the non-cutting parts of the tool, i.e. tool shank and holder, are also detected. The machined part geometry is the complement of the cutter’s swept envelope from the stock. Accordingly, the swept profile of the cutter at each cutter contact point is employed to evaluate the machining width naturally. Thereafter, a multi-criteria tool path generation model is established, and it is converted into a single-objective optimization with the weighted sum method. An algorithm based on the Differential Evolution algorithm is developed to solve this model. The numerical example illustrates the effectiveness of the proposed method.     

The optimal feedrate planning on five-axis parametric tool path with geometric and kinematic constraints for CNC machine tools

The optimal feedrate planning on five-axis parametric tool path with multi-constraints remains challenging due to the variable curvature of tool path curves and the nonlinear relationships between the Cartesian space and joint space. The methods for solving this problem are very limited at present. The optimal feedrate associated with a programmed tool path is crucial for high speed and high accuracy machining. This paper presents a novel feedrate optimisation method for feedrate planning on five-axis parametric tool paths with preset multi-constraints including chord error constraint, tangential kinematic constraints and axis kinematic constraints. The proposed method first derives a linear objective function for feedrate optimisation by using a discrete format of primitive continuous objective function. Then, the preset multi-constraints are converted to nonlinear constraint conditions on the decision variables in the linear objective function and are then linearised with an approximation strategy. A linear model for feedrate optimisation with preset multiple constraints is then constructed, which can be solved by well-developed linear programming algorithms. Finally, the optimal feedrate can be obtained from the optimal solution and fitted to the smooth spline curve as the ultimate feedrate profile. Experiments are conducted on two parametric tool paths to verify the feasibility and applicability of the proposed method that show both the planning results and computing efficiency are satisfactory when the number of sampling positions is appropriately determined.     

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.     

Segmented coupled-wave analysis of a curved wire-grid polarizer

The performance of a wire-grid polarizer (WGP) on a curved surface was investigated with a simple numerical model. The computation model combines rigorous coupled-wave analysis with piecewise linear segmentation that approximates a curved surface for two bending configurations. A curvature-induced Rayleigh anomaly is found to be the main performance degradation mechanism that reduces transmittance and polarization contrast. A WGP on a curved surface is more likely to incur the Rayleigh anomaly with smaller surface curvature. For a given curvature, a larger WGP is more vulnerable. Effects of polar and azimuthal incidence angles were also analyzed. Suggestions were made in regard to a WGP design that minimizes the performance degradation.     

Models for tool-path plan optimization in patch-by-patch machining

In this paper, we address the problem of optimizing the tool path plan for patchby-patch machining of parts having multiple surface patches. The tool path plan defines the sequence in which the patches are to be machined and the entry and exit points for the cutting-tool within each patch. Curent CAD/CAM systems require the user to select the tool path plan. When the number of surface patches increases and alternative machining strategies need to be evaluated, it is often difficult for the user to select the optimal tool path plan that minimizes the total time to machine the part. In this paper, we address three cases of this optimization problem, and present models that can be used to incorporate tool path plan evaluation and optimization capabilities in CAD/CAM systems.     

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.     

Interference-free tool path generation in five-axis machining of a marine propeller

The manufacture of a marine propeller typically requires long lead-time to generate five-axis tool paths. It usually takes several days to generate satisfactory tool paths with a general purpose CAD/CAM system. This paper proposes a novel methodology that generates effective five-axis tool paths for marine propellers. The machining of a propeller is accomplished in three steps: rough cut, semi-finish cut, and finish cut. For generating accurate finish cut tool paths, the proposed system computes check vectors that determine a maximum range of valid tool motion based upon tool size and passage width for each CL (Cutter Location) point along the tool path. Interference-free tool paths can be acquired by positioning the tool inside the two check vectors. The modelling capability for propellers is also of importance because it determines the eventual success or failure of the whole process. An iterative B-spline surface modelling technique is employed to improve the accuracy of the models and to increase the productivity. The proposed system generates interference-free tool paths with superior surface finish and reduces lead-time to manufacture a propeller. The system validation and sample results are given and discussed.     

非圆回转曲面CNC 磨削加工轨迹直接插补技术研究

针对非圆回转曲面数控磨削加工轨迹插补特点,动用曲面直接插补（ＳＤＩ）思想,提出一种适合于非圆回转曲面类零件轨迹处理的集成式ＣＮＣ轨迹插补模式,并系统研究了实时插补中加工工艺余量智能决策方法和轨迹自生成原理等,成功地解决了非圆回转曲面磨削加工的轨迹实时插补控制问题。