Feedrate optimisation/scheduling on sculptured surface machining: a comprehensive review, applications and future directions

Free-form or sculptured surface milling is one of the continually used manufacturing processes for die/mould, aerospace (especially turbine blades), precision machine design, bio-medical devices and automotive industries. Developments of machining technologies for quality enhancement of machining results have become a very important fact in current real industry. Therefore, reducing milling time, tool wear, cutter deflection and improving surface texture quality and machining operations through adaptation and optimisation of tool feedrates based on changing surface geometry in sculptured surface machining is a great step in this direction. Various feedrate optimisation strategies have different feedrate rescheduling control parameters such as chip thickness, material removal rate (MRR), min(mrr,chip,force), max(expo.Acc/dec) and resultant forces. Some commercial CAM softwares come with MRR-based feedrate optimisation algorithms which have a very short calculation time. However, commercial feedrate scheduling systems have some limitations in generating the scheduled feedrates because they use the MRR or the cutting force model which is dependent on milling conditions. However, for the processes in which machining precision/accuracy is very important, it is inevitable that mechanistic force-based feedrate optimisation approaches, for which the calculation time is improved, will be integrated into commercial CAM software packages. Here, developing only the mechanistic cutting force-based algorithm is not enough. In this paper, improvement and optimisation of machining feedrate value, which is one of the cutting parameters which has a tremendous effect on the precise machining of free-form surfaces, was discussed by using the virtual machining framework. For this purpose, the boundary representation solid modelling technique-based free-form milling simulation and feedrate optimisation system integrated with commercial CAD/CAM software is developed for three-axis ball-end milling. This review study includes the information regarding the following topics: The algorithms developed for the feedrate value optimisation, MRR calculation approaches, cutting force computation methods, details of algorithms, the effects on the surface accuracy, the effects on the machining time, the capabilities of the present commercial CAM software packages, the encountered difficulties and overcoming those difficulties, recent developments and future research directions.     

FREE-FORM SURFACE MACHINING AND COMPARING FEEDRATE SCHEDULING STRATEGIES

This article presents mathematical models of cutting forces and surface-form errors for machining of free-form surfaces. Besides the predictive models of cutting forces and surface deflections, a newly developed force based feedrate scheduling (FFS) technique is compared with material removal rate (MRR) based feedrate scheduling method that was used in feedrate optimization packages. With the experimental validations in free-form surfaces, it is shown that the mechanic models predict the forces and surface-form errors quite well. Moreover, by modifying the CNC programs with the new FFS technique, cycle times of the free-form parts can be decreased significantly.     

FREE-FORM SURFACE MACHINING AND COMPARING FEEDRATE SCHEDULING STRATEGIES

This article presents mathematical models of cutting forces and surface-form errors for machining of free-form surfaces. Besides the predictive models of cutting forces and surface deflections, a newly developed force based feedrate scheduling (FFS) technique is compared with material removal rate (MRR) based feedrate scheduling method that was used in feedrate optimization packages. With the experimental validations in free-form surfaces, it is shown that the mechanic models predict the forces and surface-form errors quite well. Moreover, by modifying the CNC programs with the new FFS technique, cycle times of the free-form parts can be decreased significantly.     

Adaptive feedrate scheduling for NC machining along curvilinear paths with improved kinematic and geometric properties

In precision machining of free-form surfaces at high speed, it is very important to ensure part accuracy and machining properties. To achieve this, this paper develops a guide spline-based feedrate scheduling method for machining along curvilinear paths with simultaneous constraints of chord errors and ac/deceleration. Based on two metrics about feedrate scheduling from the view of geometric and kinematic properties, the nonlinear relationships between the arc-length parameter and path parameter are subsequently established with a parameter correction spline. Then a guide spline associated with the modified curvature radius of paths is constructed to the schedule feedrate. It is shown that determining the largest safe feedrate with constant chord error can be reduced to the issue of changing the feedrate proportionally with the square root of path curvature radii and ensuring the safe feed acceleration can be converted into the issue of presetting the largest slope of guide spline. The simulation results prove that the proposed feedrate scheme has potential applications in the field of finish machining.     

Process modeling and toolpath optimization for five-axis ball-end milling based on tool motion analysis

In free-form surface machining, the prediction of five-axis ball-end milling forces is quite a challenge due to difficulties of determining the underformed chip thickness and engaged cutting edge. Part and tool deflections under high cutting forces may result in poor part quality. To solve these concerns, this paper presents process modeling and optimization method for five-axis milling based on tool motion analysis. The method selected for geometric stock modeling is the dexel approach, and the extracted cutter workpiece engagements are used as input to a force prediction. The cutter entry?Cexit angles and depth of cuts are found and used to calculate the instantaneous cutting forces. The process is optimized by varying the feed as the tool?Cworkpiece engagements vary along the toolpath, and the unified model provides a powerful tool for analyzing five-axis milling. The new feedrate profiles are shown to considerably reduce the machining time while avoiding process faults.     

An adaptive feedrate scheduling method of dual NURBS curve interpolator for precision five-axis CNC machining

Non-uniform rational b-spline (NURBS) tool path is becoming more and more important due to the increasing requirement for machining geometrically complex parts. However, NURBS interpolators, particularly related to five-axis machining, are quite limited and still keep challenging. In this paper, an adaptive feedrate scheduling method of dual NURBS curve interpolator with geometric and kinematic constraints is proposed for precision five-axis machining. A surface expressed by dual NURBS curves, which can continuously and accurately describe cutter tip position and cutter axis orientation, is first used to define five-axis tool path. For the given machine configuration, the calculation formulas of angular feedrate and geometric error aroused by interpolation are given, and then, the adaptive feedrate along the tool path is scheduled with confined nonlinear geometric error and angular feedrate. Combined with the analytical relations of feed acceleration with respect to the arc length parameter and feedrate, the feed profiles of linear and angular feed acceleration sensitive regions are readjusted with corresponding formulas and bi-directional scan algorithm, respectively. Simulations are performed to validate the feasibility of the proposed feed scheduling method of dual NURBS curve interpolator. It shows that the proposed method is able to ensure the geometric accuracy and good machining performances in five-axis machining especially in flank machining.     

An improved feedrate scheduling method for NURBS interpolation in five-axis machining

Five-axis machining plays an important role in manufacturing by dint of its high efficiency and accuracy. While two rotation axes benefit the flexibility of machining, it also brings limitations and challenges. In order to further balance machining precision and efficiency, an improved feedrate scheduling method is presented considering geometric error and kinematic constraints for the Non Uniform Rational B-Spline (NURBS) interpolation in five-axis machining. A simplification method is proposed to calculate the geometric error which describes the deviation between the ideal tool path and the real tool path induced by the non-linear movement. A linear relation between geometric error and feedrate is built to limit the feedrate. The constraints determined by single axis kinematic performance and tangential kinematic performance are also considered. Under these constraints, a constrained feedrate profile is determined. Aiming to get more constant feedrate in the difficult-to-machine areas, this work proposes a scheduling method which combines morphological filtering and S-shape acceleration/deceleration (acc/dec) mode. Simulations and experiments are performed to compare the proposed feedrate scheduling method with two previous feedrate scheduling method and the results prove that the proposed feedrate scheduling method is reliable and effective.     

A strain energy minimization method for generating continuous NURBS-based motion curves in free-form surface machining

In spline-based free-form surface machining, segmented toolpaths are inevitable, and the discontinuities between segments cause large feedrate errors in the generated motion commands. Methods of the geometric design to create smooth composite curves may introduce new error sources in the original curve, and thus they are not suitable for motion planning in high precision free-form surface machining. In this paper, a strain energy minimization model (SEMM) and a non-uniform rational B-spline (NURBS)-based motion planning algorithm is proposed for free-form surface machining. The proposed SEMM and motion planning algorithm are capable of creating composite NURBS-based motion curves with up to C2 integral continuity without oscillations. Results from simulation show that with the proposed energy minimization model and motion curve generation algorithm, the feedrate errors caused by discontinuities in toolpaths can be effectively removed.     

Adaptive feedrate interpolation with multiconstraints for five-axis parametric toolpath

A good adaptive feedrate will be helpful for improving machining accuracy and efficiency, as well as avoiding the excess of the machine’s physical capabilities and feed fluctuations during machining. Therefore, it is highly desirable to consider the constraints of geometric error, cutting performance, and drive constraints in the feedrate scheduling of the parametric curve interpolator for five-axis computer numerical control machining. In this paper, a novel multiconstraints feedrate scheduling method is proposed for the parametric curve interpolator in five-axis machining. In the method, the feed optimization model is first built with the constraints of geometric error, the maximum feedrate and acceleration of cutter tip, and the maximum feedrate and acceleration of five-drive axes. Then, the relations between each constraint and the cutter tip feedrate are derived by means of near arc length parameterization. After that, a linear programming algorithm is applied to obtain the optimal feed profile on the sampling positions of the given tool path. Finally, illustrated examples are given to validate the feasibility and applicability of the proposed feedrate scheduling method. The comparison results show that the proposed method has an ability of the simultaneous guarantees of geometric accuracy, cutting performance, and drive characters of machine tools.     

An intelligent feedrate scheduling based on virtual machining

Off-line feedrate scheduling is an advanced methodology to automatically determine optimum feedrates for NC code modification. However, most existing feedrate scheduling systems have limitations in generating the optimised feedrates because they use the material removal rate or the cutting force model which is dependent on cutting conditions. This paper proposes a feedrate scheduling system based on an improved cutting force model that can predict cutting forces accurately in general end milling situations. Original blocks of NC code were divided into smaller ones with the optimised feedrates to adjust the peak value of cutting forces to a constant value. The acceleration and deceleration characteristics for a given machine tool were considered for realistic feedrate scheduling. Moreover, a modified type of Z-map model was developed to reduce the entry/exit angle calculation error in the cutting force prediction and named the moving edge node Z-map (ME Z-map). Pocket machining experiments show that the proposed method is accurate and efficient in maintaining the cutting force at a desired level.     

Cutting deflection control of the blade based on real-time feedrate scheduling in open modular architecture CNC system

Machining accuracy of thin-walled parts which have low-rigidity is greatly influenced by cutting deflection in flank milling. In this paper, cutting deflection of aero-engine blade during processing is controlled within a required dimensional accuracy based on the strategy of real-time feedrate scheduling which is integrated into an open modular architecture CNC system (OMACS) of five-axis milling machine. The maximum deflection position of blade is determined through combining analytical cutting force model in flank milling and finite element analysis (FEA)-based transient dynamic analysis. Then, the numerical model of blade deflection is established to obtain the numerical relationship among feedrate, cutting force, and blade deflection, which is usually used to get optimized cutting force and feedrate by setting allowable value of blade deflection. To implement blade deflection control during machining, a real-time control strategy of feedrate scheduling based on nonlinear root-finding algorithm of Brent-Dekker and principle of feedrate smooth transition is developed and integrated into OMACS which has functions of real-time cutting force signal processing and real-time feedrate adjustment. Experimental results show that blade deflection is effectively controlled by proposed strategies, machining accuracy, and efficiency are improved.     

复杂自由曲面曲率分布特征对数控铣削性能的影响

针对复杂自由曲面的数控铣削性能难预测的问题,提出曲面曲率分布特征值,用于评价数控加工效率和加工精度。在构建的刀位面上策划等间距行走的刀位轨迹,建立刀位轨迹长度和刀具间的最大残余高度作为加工效率和加工精度的评价指标,分析曲面曲率分布特征值对加工效率和加工精度的影响。试验结果证明该自由曲面数控加工模式的有效性。分析发现,随着曲面曲率分布特征值增大,刀位轨迹长度和最大残余高度同时增加,导致加工效率和加工精度同时下降。此外,在曲面曲率分布特征值小于0.5 mm–1时,加工效率降低幅度不超过7 %,但加工精度却下降6～7倍。因此,曲面曲率分布特征值可用于评价和预测复杂自由曲面的数控铣削性能。     

Force modelling in shallow cuts with large negative rake angle and large nose radius tools—application to hard turning

In finish turning, the applied feedrate and depth of cut are generally very small. In some particular cases, such as the finishing of hardened steels, the feedrate and depth of cut are much smaller than tool nose radius. If a tool with a large tool nose radius and large negative rake angle is used in finish turning, the ploughing effect is pronounced and needs to be carefully addressed. Unfortunately, the ploughing effect has not yet been systematically considered in force modelling in shallow cuts with large negative rake angle and large nose radius tools in 3-D oblique cutting. In this study, in order to model the forces in such shallow cuts, first the chip formation forces are predicted by transforming the 3-D cutting geometry into an equivalent 2-D cutting geometry, then the ploughing effect mechanistic model is proposed to calculate the total 2-D cutting forces. Finally, the 3-D cutting forces are estimated by a geometric transformation. The proposed approach is verified in the turning of hardened 52100 steel, in which cutting conditions are typified as shallow cuts with negative rake angle and large nose radius tools. The workpiece material property of hardened 52100 steel is represented by the Johnson-Cook equation, which is determined from machining tests. The comparison between the experimental results and the model predictions is presented.     

基于临界约束的四轴数控加工刀轴优化方法

针对自由曲面四轴加工中复杂刀具运动导致的干涉和刀具运动不连续等现象,提出一种基于临界约束的刀轴优化方法。基于刀具与工件约束曲面之间的相对位置关系,利用曲线上的点搜索算法确定切触点处的临界刀轴矢量,并计算当前切触点刀轴摆动的可行域;以切削行内所有切触点的刀轴可行域为基础,建立当前切削行内无干涉且相邻刀轴变化最小的刀轴矢量优化模型,实现了自由曲面四轴加工无干涉刀轴矢量的光顺控制。整体叶盘四轴加工试验表明,利用此方法获得的刀轴矢量可以显著改善机床运动的连续性,并避免刀具干涉的产生,提高了加工质量。     

隐曲线的线性和旋转插补

基于数控五轴刀具运动分析,提出了旋转插补的概念,给出了旋转插补的相关定义,在此基础上提出了隐曲线的线性和旋转插补原理和方法,并进一步提出了改进的插补方法。     

ROTARY ULTRASONIC MACHINING OF CARBON FIBER-REINFORCED POLYMER: FEASIBILITY STUDY

Carbon fiber-reinforced polymer (CFRP) has been widely used in aircraft components, automotive parts, and sporting goods. Hole machining is the most frequently employed operation of secondary machining for fiber-reinforced composites. However, challenges (delamination, splintering, burr, short tool life, low machining precision, and low surface quality) still remain for their widespread applications. Rotary ultrasonic machining (RUM) is a non-conventional machining process that has been used to drill holes in composite materials. However, it has not been used to drill this type of CFRP. In this article, RUM is introduced into drilling holes in this type of CFRP for the first time. The feasibility to machine carbon fiber-reinforced epoxy using RUM is investigated experimentally. Chips, edge chipping, surface roughness, tool wear, and thrust force were measured. Effects of RUM process variables (rotation speed, vibration amplitude, and feedrate) on thrust force and surface roughness were studied. Results showed that RUM could be used to drill holes in CFRP with high productivity and low tool wear. A better surface was produced by higher rotation speed and lower feed rate.     

Modelling of dimensional and geometric error prediction in turning of thin-walled components

In die-mold manufacturing and aircraft industry, many components that have thin-walled features are produced by turning operation. The major problem encountered during internal or external turning is cutting force induced deflection of workpiece along the periphery as well as axial length of a component. The present research work aims to develop a mathematical model for estimating dimensional and geometric errors during turning of thin-walled hollow cylinder qualitatively and quantitatively. In the proposed model, a mechanistic approach which is semi-analytical in nature is followed to achieve accuracy of the predicting results. First of all, process geometry model for thin-wall turning is developed based on process geometry variables such as uncut chip thickness, actual feed per revolution, actual depth of cut, peripheral cutting speed, effective cutting area etc. Using these process geometry variables and mechanistic cutting constants, a force model of turning is developed to estimate the tangential and radial force components. Later on, based on the predicted forces, tool-workpiece combined deflection model is developed to estimate radial, diametric and various geometric errors of the turned surface. The developed models are able to predict radial, diametric and various geometric errors such as straightness, circularly and cylindricity errors without conducting expensive actual machining operation. Hence, the present study will be helpful to take care of precautionary measures for controlling of dimensional and geometric errors more efficiently and reliably. Therefore, an attempt has been made to provide a basic platform to machining practitioners and process planners for in-depth comprehension and characterization of dimensional and geometric errors of the entire turned surface for varying machining conditions.     

A postprocessor for table-tilting type five-axis machine tool based on generalized kinematics with variable feedrate implementation

Improvements in the machine tool and the machining process technologies increased the need for generic postprocessors in order to exploit the capabilities of the machine tools. Contrary to conventional machining approach, next-generation machining technologies such as force-based feedrate scheduling and toolpath optimization requires the implementation of the variable feedrate during toolpath which constitutes the aim of this article. Therefore, this paper introduces a postprocessor for table-tilting type five-axis machine tool based on generalized kinematics with variable feedrate implementation. Furthermore, a practical yet effective method for avoiding kinematic singularities by spherical interpolation and NC data correction is presented as well. Proposed approach is validated for various five-axis machine tools with different kinematic configurations via virtual machine simulation module. Results of the verification tests show that presented postprocessing approach can accurately convert the cutter location information into NC codes and it is demonstrated that integrated virtual simulation module can simulate toolpaths with large number of blocks.     

NC machining of free-form Kriging surfaces

An algorithm for three-axis NC tool path generation on sculptured surfaces is introduced when the free-form surface is modeled parametrically by free-form surface Kriging. The flexibility of dual Kriging that easily defines the intersection of the surfaces with a set of parallel planes and Cartesian method are combined to generate the tool-paths automatically. The presented algorithm can simultaneously generate the tool path with a predefined machining accuracy and remove gougings along the tool path. The algorithms are validated by three experiments in rough and finish machining and the results prove its reliability. Since Kriging is based on the interpolation of data points, the proposed algorithm can be used for reverse engineering applications. The system was executed on a standard micro-computer and the software was structured to offer a library of machining functions for endusers.     

基于有限元数值模型和进给速度优化的薄壁件侧铣变形在线控制

为实现在加工过程中对薄壁件侧铣产生的较大切削变形进行在线控制,提出基于有限元数值模型和进给速度优化的在线控制策略。根据薄壁件切削过程的有限元仿真结果,建立数控机床进给速度、切削力、工件切削变形间的数值模型,进而确定用于控制变形的最优目标切削力。在具有开放式模块化的数控系统平台上开发了切削力信号实时采集、滤波功能和基于Brent-Dekker算法的进给速度在线优化策略,并根据滤波后的切削力及相应算法在加工过程中实时调整机床进给速度,保证切削力逐渐接近最优控制目标而实现切削变形的在线控制。试验结果表明,经过进给速度在线优化后的切削过程可将薄壁件侧铣变形控制在规定范围内,同时提高了切削效率。